The stochastic parallel gradient descent (SPGD) algorithm is one of the most commonly used control algorithms for wavefront sensorless adaptive optics (AO) systems. This method usually uses the driving voltages of deformable mirrors as control parameters, and the number of actuators is equal to the number of dimensions of the control parameters. It is simple and suitable for AO systems that have a small number of actuators and do not have any requirement for the convergence speed. With the increasing applications of AO, the number of actuators required has gradually increased.

In wavefront sensorless AO systems, when taking the driving voltages of the deformable mirrors as control parameters, an increase in the number of actuators leads to a greater number of dimensions of the control parameters and a larger optimization space of the algorithm, which will lead to slower convergence of the algorithm. Various modal coefficients are often used as control parameters to reduce the dimensions of control parameters. When the modal coefficients are modeled as control parameters, the optimization space of the algorithm can be reduced, and the convergence speed can be improved.

The Zernike polynomial, which was introduced by Zernike to represent the diffraction effects on concave mirrors, is often used to describe optical wavefront aberrations. When using the Zernike mode to calculate the covariance matrix of the amplitude in Kolmogorov turbulence, namely, the Noll matrix, there are nonzero elements outside the diagonal. This inherent modal crosstalk indicates the statistical dependence between modes, which limits the correction ability of AO systems based on these modes. In this study, the Karhunen–Loève (K-L) modal coefficients derived from the Zernike mode are used as the control parameter of a wavefront sensorless AO system. First, the rationality of the K-L mode is analyzed. The aberration-fitting ability of the deformable mirror (DM) to the K-L and Zernike modes is then discussed. Finally, the convergence speed and correction effect of the AO system are compared when the driving voltages of the actuators, K-L modes, and Zernike modes are used as control parameters.

Generally, the order of the mode needs to be determined based on the fitting ability of the deformable mirror, so that the dimension of control parameters can be relatively small while ensuring the correction ability of the deformable mirror. The Zernike modes and K-L modes are fitted with several deformable mirrors with 32, 61, 97, and 127 actuators, respectively. The results show that the fitting ability is relatively stable for K-L modes while fluctuations appear for Zernike modes (Fig.3). We use the error rate (η) as the evaluation standard. The fitting is effective if η<1. The lower the error rate, the better the fitting ability. Notably, 32-element, 61-element, 97-element, and 127-element deformable mirrors can fit the first 22-order, 55-order, 79-order, and 91-order K-L modes, respectively, while they can fit the first 20-order, 36-order, 54-order, and 68-order Zernike modes (Fig.4), respectively. It can be seen from the above data that the ability to fit K-L modes for the deformable mirror is greater than that to fit Zernike modes. A greater number of modes indicates better correction ability, which implies that the correction capability and convergence speed of AO systems can be improved when K-L modal coefficients are used as the control parameters.

The two modal methods only need 20 modes as control parameters when the atmospheric turbulence strength (D/r₀) is 5, and the convergence of the conventional SPGD is used as the reference index. When the Strehl ratio (SR) is up to 0.8, the K-L modal method, Zernike modal method, and conventional SPGD require 122, 139, and 180 iterations, respectively. The convergence speed of the K-L modal method and Zernike modal method is 47.5% and 29.4% greater than that of the conventional SPGD control algorithm, respectively (Fig.5). The correction results also show that when the D/r₀ is 10 (Fig. 6), 15 (Fig.7), and 20 (Fig.8), the correction performance and convergence speed obtained using K-L modal coefficients are better than those obtained using Zernike modal coefficients as control parameters (Table 1).

The SPGD control algorithm, based on optimizing the actuator voltages, is widely used as a control algorithm for wavefront sensorless AO systems. The number of actuators in the deformable mirror determines the dimensions of the control parameters. Generally, the greater the number of actuators, the better the correction effect. Moreover, the more actuators tend to reduce the convergence speed of the AO system. The SPGD algorithm, which is based on optimizing the modal coefficients, can effectively resolve this contradiction. When the control parameters are modal coefficients, the optimization space of the algorithm can be reduced, and the convergence speed can be improved.

The fitting capability of the DM to the aberrations of K-L modes and Zernike modes is compared and analyzed. The convergence speed and correction performance of the AO system are investigated when the voltages of the actuators, K-L modes, and Zernike modes are used as control parameters under various turbulence strengths. The convergence speed of the K-L modal method and Zernike modal method is 47.5% and 29.4% greater than that of the conventional SPGD control algorithm, respectively. The results under several turbulence strengths also show that the correction performance and convergence speed of the K-L modal method are better than those of the Zernike modal method. The results of the study can provide a reference for the practical application of the SPGD control algorithm based on K-L modes.

In diode laser array (DLA) grating-external cavity spectral beam combining (SBC) systems, the combining efficiency and beam quality are very important indicators. However, the beam crosstalk caused by imperfect factors including the divergence angle and deflection angle of DLA emitters results in the degradation of the output beam quality and combining efficiency. Therefore, to understand the physical mechanism of crosstalk in the round-trip propagation of the beams in a DLA grating-external cavity SBC system and further analyze its influence on the performance of the SBC system, the relationship between the crosstalk and the combining efficiency or beam quality is established. In addition, the influences of key factors, including the DLA spacing, focal length of the lens, and line density of the grating, on the performance of the SBC system are analyzed.

To study the behavior of beam crosstalk and its influence on the performance of an SBC system, a round-trip propagation model of a DLA is established. On this basis, by taking the semiconductor laser rate equation involving beam crosstalk injection into consideration, a physical model of combining efficiency of the SBC system is also developed. Furthermore, the influence of the divergence angle and deflection angle on the beam combining performance is studied using numerical calculations and statistical analysis.

With only the divergence angle considered, there is no obvious crosstalk (Fig. 4). This is because the beam emitted by each emitter can be fed back to itself after being reflected by the external cavity. Even when the divergence angle increases to 12 mrad, the beam quality factor M², beam combining efficiency η, and feedback intensity κ are not strongly affected by the divergence angle. With only the deflection angle considered, the feedback beam from the external cavity exhibits different degrees of deviation (Fig. 5). With an increase in the deflection angle, the feedback beam reflected to its own emitter decreases in intensity, whereas the feedback intensity from the other emitters increases, resulting in crosstalk. When the effects of the divergence and deflection angles are considered comprehensively, the feedback beam to the emitters deviates significantly, resulting in an obvious degradation of the output beam quality and combining efficiency (Fig. 6). For a given maximum divergence angle, the combining efficiency remains almost unchanged as the maximum deflection angle increases and then decreases sharply beyond a certain angle. The output beam quality exhibits the same trend. For a given maximum deflection angle, the beam combining efficiency remains almost unchanged up to a divergence angle of 12 mrad, whereas the beam quality decreases significantly. In addition, the DLA spacing, focal length of the lens, and line density of the grating have almost no influence on the combining efficiency with an increase in the maximum deflection angle up to a certain angle, after which the efficiency decreases dramatically (Fig. 7).

We established a round-trip propagation model of a DLA that can reveal the behavior of beam crosstalk and its influence on the performance of the SBC system. By taking the semiconductor laser rate equation involving beam crosstalk injection into consideration, we established a physical model for the combining efficiency of an SBC system. Based on numerical calculations and statistical analysis, we found that the influence of the deflection angle on the beam combining performance is greater than that of the divergence angle. In addition, we found that the focal length of the lens and the DLA spacing have obvious effects on the critical maximum deflection angle, whereas the line density of the grating has little effect on the critical maximum deflection angle. In conclusion, it is necessary to appropriately reduce the focal length of the lens and increase the DLA spacing in practical applications.

Laser technology has gained widespread applications in various fields, such as communication, guidance, and precision machining. However, the accuracy of these applications is often compromised by beam pointing instability caused by uneven internal laser temperature and external environmental changes. Traditional methods of improving beam pointing stability, including using materials with low thermal expansion coefficients, adopting cooling systems and deformation mirrors, and reducing vibration, have proven to be limited in their effectiveness. More advanced lasers have internal beam pointing correction systems, but their performance is limited by their size, and they cannot correct pointing deviations caused by external factors. In view of these limitations, the use of an external beam pointing deviation correction system has emerged as a promising solution. The beam pointing deviation correction system based on fast steering mirrors (FSMs) is considered to be the most mature and effective approach. However, the Z-shaped beam path commonly used in these systems changes the propagation direction of the original beam, resulting in poor expansion performance. In this paper, we present a U-shaped beam pointing deviation correction system based on FSMs that does not change the original beam propagation direction. The system is modeled using geometric optics, including the mapping model from FSMs to four-term beam pointing deviations and the FSMs control model. To further enhance the system's performance, we propose a predictive control model, simplifying the model operation and improving the system responsiveness. Our results demonstrate that the constructed system exhibits excellent beam pointing deviation correction performance.

The beam pointing deviation correction system consists of three main components: detector, controller, and actuator. The detector consists of a uniform beam splitter and two vertically distributed high-accuracy position-sensitive detectors (PSDs). The non-uniform beam splitter diverts a small portion of the beam from the main beam into the detector, where deviations in the beam's position from the center of the PSDs can be detected and used to determine beam pointing deviations. The controller is a computer that implements four distinct models: a beam pointing deviation detection model, a FSM attitude control model, a beam pointing deviation prediction model, and a simplified FSM attitude control model. The beam pointing deviation detection model calculates the four beam pointing deviations from the position deviations of PSDs. The FSM attitude control model determines the control angles of the FSMs from the four beam pointing deviations to realize the correction of beam pointing deviations. The latter two models, i.e., the beam pointing deviation prediction model and the simplified FSM attitude control model, are constructed to achieve predictive correction of the beam pointing deviation. The beam pointing deviation prediction model is based on the mean deviation correction method and predicts future beam pointing deviations, while the simplified FSM attitude control model has a simpler operation and can rapidly obtain the control angle of the FSMs. The FSMs act as actuators, adjusting their attitude based on control signals to correct the beam pointing deviations and improve the beam pointing stability.

The constructed beam pointing deviation prediction model has a slight lag in the prediction of beam pointing deviations, but it still has a high accuracy and can filter the high-frequency signals in the pointing deviations (Fig. 4). Therefore, the attitude of the corrected FSMs can be calculated based on the predicted pointing deviations. The simplified FSM attitude control model has a reliable accuracy (Fig. 5). The error between the FSMs' control angles obtained from the simplified model and the results calculated based on geometrical optics is within 1 μrad. Therefore, the simplified model can be used to correct the beam pointing deviations. The experiments show that the constructed beam pointing deviation detection model and FSM attitude control model also have high accuracy. The beam pointing deviation correction system can effectively reduce the beam pointing deviations. Although the beam pointing deviations are not completely corrected due to the open-loop control without additional feedback, the errors of the beam pointing deviations in X and Y directions are reduced by 78.08% and 70.28%, respectively.

A U-shaped beam pointing deviation correction system is designed, and a beam pointing deviation model and a FSM attitude control model are constructed based on geometric optics. Two PSDs are used to detect the beam pointing deviations, and two FSMs are used to correct the beam pointing deviations. A predictive beam pointing deviation correction model is proposed. A beam pointing deviation prediction model based on the average deviation correction method is constructed to correct the attitudes of FSMs based on the predicted beam pointing deviations rather than the real-time detections. The calculation of the control angles of the FSMs is simplified. A mapping model is constructed to calculate the control angle, which avoids solving the control angle in the original FSM attitude control model and effectively improves the response performance of the system. At last, experiments demonstrate that the developed system and model can effectively reduce the beam pointing deviations. The pointing deviations of the beam are reduced by 78.08% and 70.28% in the X and Y directions, respectively.

In recent years, vernier effect has attracted much attention in the field of optical fiber sensing due to its sensitivity amplification effect, which has been used to measure gas pressure, temperature, strain, refractive index, etc. The configurations used to introduce optical vernier effects fall into two broad categories. The first type consists of configurations containing a single type of interferometer. The second type consists of a hybrid configuration in which two different types of interferometers are combined. The optical vernier effect can be applied to different types of interference structures, such as Mach-Zehnder interferometers (MZIs), Fabry-Perot interferometers (FPIs) and Sagnac interferometers (SIs), etc. Since the double-helix micro-nano fiber coupler (DHMC) is highly birefringent, the superposition of two orthogonal polarization interference spectra in x direction and y direction with slightly different interference periods can form the vernier envelope. However, how to get the DHMC that can produce the vernier envelope spectrum? What’s more, when the optical vernier effect of the DHMC is applied to temperature, strain and refractive index sensing, whether the sensing characteristics are consistent or not is a problem that needs to be considered. In the present study, the internal mechanism and spectral characteristics of the vernier effect of the DHMC are studied theoretically. DHMCs with different diameters are fabricated, and experiments of the strain, temperature and refractive index sensing are carried out. We hope that the above results have a good guiding significance for the preparation of DHMC and the applications of refractive index, temperature and strain sensing.

Theoretical and experimental analysis methods are employed in this paper. Firstly, COMSOL software was used to establish the DHMC simulation model (Fig.1). Then, by setting parameters such as wavelength range, diameter and refractive index, the effective refractive indices of odd and even modes in x- and y-polarization states were obtained, and then the simulated vernier spectra were obtained through Eqs. (5) and (6). Secondly, two standard single-mode fibers (SMF-28) were used to fabricate DHMC, for which the optical fibers with the coating layer stripped off were twisted in parallel direction to obtain helical structures with different turns. The optical fiber pulling machine (OB-612) was used to pull the DHMC, and the broadband light source (1250-1650 nm) and optical spectrum analyzer (OSA) were connected at both ends of the optical fiber. The spectrum of DHMC was observed in real time during the pulling process, so as to estimate the diameter and waist length of the prepared DHMC online. Thirdly, we used the fabricated DHMC to conduct the strain, temperature and refractive index sensing experiments. The spectrum evolutions of the DHMC under different strain, temperature and surrounding refractive index were recorded, respectively. Fast Fourier transform (FFT) and bandpass filtering method were used to extract the characteristic interference spectra, thus obtaining the spectra in x- and y-polarization states, and then the vernier spectrum was obtained by the superposition of the interference of the extracted x- and y-polarization spectra. At last, the sensitivities of the strain, temperature and refractive index of DHMC for x polarization, y polarization and vernier spectrum were analyzed.

The free spectral range (FSR) of the vernier spectrum of the DHMC is related to the waist length, wavelength and the difference of effective refractive index between x- and y-polarization states. The waist length L plays a major role in FSR, and the increase of L leads to the decrease of FSR (Fig.3). It can be concluded that when L is fixed and the surrounding refractive index (SRI) is 1, with the increase of wavelength, the absolute value of the effective refractive index difference increases faster than the increase of wavelength square, and the envelope FSR also decreases [Fig.3(a)]. When the SRI is larger than 1.3310, the results are the opposite, and the envelope FSR increases accordingly [Fig.3(b)]. Under the same SRI of 1.3328, the odd-even refractive index difference between x- and y-polarization states decreases and FSR increases with the increase in the diameter of DHMC. In the liquid environment (SRI is 1.3328), when the diameter is 6 μm, only a complete vernier envelope can be observed in the wavelength range of 1250-1650 nm (Fig. 4).

In general, the axial strain sensitivity of vernier spectrum of the DHMC is lower than those of x- and y-polarization spectra (Fig.6). Similarly, the temperature sensitivities of DHMC in x- and y-polarization spectra are higher than that of vernier spectrum of DHMC (Fig.7). Conversely, the refractive index sensitivity of vernier spectrum of the DHMC is larger than those of x- and y-polarization spectra (Fig.9). According to Eq.(10), in temperature and axial strain sensing, because the absolute difference between the sensitivity of x- and y-polarization states is very small, the calculated differences between M_xS_x and M_yS_y cancel out each other, thus showing a weakened optical vernier effect. However, in refractive index sensing, the absolute difference of the refractive index sensitivity of x- and y-polarization states is much larger than that of temperature and axial strain sensitivity. It can be concluded that the subtraction of M_xS_x and M_yS_y is larger than the refractive index sensitivity of a single polarization state, thus showing the enhanced optical vernier effect.

DHMC has the advantages of high sensitivity, compact structure, easy preparation and low cost. In this work, the internal mechanism and spectral characteristics of the vernier effect of DHMC are studied in detail, and its sensing characteristics of refractive index, temperature and strain are analyzed. The simulation results show that the waist length of DHMC plays a major role in the FSR of its vernier envelope, and the FSR decreases with the increase of the waist length. In the process of DHMC preparation, the waist length and diameter of DHMC can be estimated by monitoring the number of envelopes in the wavelength range of 1250-1650 nm with the OSA online. The vernier spectrum formed by the superposition of the interference spectra of x- and y-polarization states of DHMC is compared with the interference spectra of single x- and y-polarization states. The vernier spectrum shows a weakened optical vernier effect for strain and temperature sensing, while it shows an enhanced optical vernier effect for refractive index sensing. The conclusion of this paper has a good guiding significance for the preparation of DHMC sensor and its application in the sensing field.

Ultra-narrow-band optical filters are key components for signal processing in the fields of microwave photonics, coherent communication and dense wavelength-division multiplexing. The ideal ultra-narrow-band optical filter has a rectangular frequency response composed of an ultra-flat passband and a very steep edge. The flat passband has high signal fidelity and can prevent the signal from being distorted, whereas the steep edge can suppress the crosstalk between adjacent bands. Fiber Bragg gratings (FBGs) that achieve various frequency responses are commonly used in bandpass optical filters owing to their small size, low insertion loss and compatibility with other optical fiber devices and systems. However, for the application of ultra-narrow-band optical filters, the spectral and performance parameters of FBG are extremely demanded to obtain the rectangular spectral response with flat passband and high side-mode suppression ratio (SMSR). In the process of FBG fabrication, the stability of the writing optical path, the uniformity of the ultraviolet (UV) spot and the accuracy of apodization process are highly required whether the UV irradiation method of the phase mask or the point-by-point scanning method is adopted. The writing error will lead to the reduction of the spectral performance of the grating, which directly affects the quality of the signal. Therefore, the influence of UV irradiation inhomogeneity on the spectral properties of FBG is analyzed in this paper.

Solid-state laser point-by-point writing method is used for the fabrication of uniform narrow?band optical FBG. The uniformity of UV spot and the accuracy and stability of the optical path will affect the optical fiber grating refractive index modulation distribution, thus affecting the performance of FBG spectrum. By theoretical simulation, the influence of different UV irradiation inhomogeneity on the spectrum of FBG is analyzed. The apodization function is modified based on the analysis results to compensate for the effect of irradiation inhomogeneity, so as to achieve the improvements of the grating spectral performance. Using the proposed method, FBG is prepared after correcting the apodization function, which can compensate the writing errors caused by UV spot and optical path adjustment, and the SMSR of FBG is increased to 30 dB, greatly improving the performance of optical filter.

When the UV irradiation inhomogeneity function F(z) is introduced, it will not only affect the photo-induced refractive index background, but also affect the modulation depth of the photo-induced refractive index. Through the transmission matrix method, the influence of F(z) function distribution on the spectral performance of the FBG under different conditions is theoretically analyzed by MATLAB simulation software according to Eq.(2). As can be seen from Fig.1, when the length of the grating remains unchanged and the reflectance of the FBG remains the same (about－20 dB), the error of the refractive index modulation depth nˉ₁ increases with the increase of the inhomogeneity, that is, the increase of the linear slope k of the F(z) function. The 3 dB bandwidth and 25 dB bandwidth of the FBG also increase, the side band steepness N of the grating decreases, and the rectangularity of the reflection of the grating becomes worse. In experiments, by specifically adjusting the height of the fiber fixture on both ends (Fig.4), UV irradiation error is introduced. Thus the FBG reflection spectra and the change trend of grating parameters are obtained for FBGs written at different fiber tilt angles. The experimental results show that with the increase of the fiber tilt angle, the 3 dB bandwidth and 25 dB bandwidth gradually increase, and the side band steepness decreases, that is, the rectangularity of the grating reflection spectrum deteriorates. This is not conducive to the writing of gratings with ultra-narrow bandwidth and high rectangularity requirements which are important performances for optical filter applications. In further experiments, the UV spot irradiation inhomogeneity function F(z) is calculated according to the energy meter measurement results. By modifying the apodization function based on F(z), the 3 dB bandwidth of the obtained FBG is 96.22 pm, the 25 dB bandwidth is 150.92 pm, the SMSR is greater than 30 dB, and the side band steepness N is increased to 0.8044 dB/pm. As can be seen from the comparison in Fig.7, the SMSR and rectangularity of the grating spectrum written after the correction of spot irradiation inhomogeneity function are much improved, which also verifies the theoretical and experimental results.

According to the requirements of ultra-narrow-band FBG used in optical filters, the inhomogeneity of refractive index modulation caused by UV spot or optical path adjustment in grating fabrication by point-by-point scanning method is analyzed theoretically and experimentally. We propose to modify the apodization function based on the UV spot irradiation inhomogeneity function F(z) to compensate for the effect of irradiation inhomogeneity. The FBG fabricated by the above method has a high rectangularity and the SMSR is greater than 30 dB. To further obtain an ultra-narrow-band FBG, only the length of the grating region needs to be increased. The method of fabricating ultra-narrow-band FBG is simple, which can solve the difficulty of high-precision adjustment of the writing optical path and reduce the influence of non-uniform spot distribution of the laser itself, and greatly improve the application ability of ultra-narrow-band FBG for optical filters.

Among the many photonic devices, the Bragg grating of chalcogenide glass fibers is important. As a linear device, it can be applied to infrared sensors. In nonlinear optical applications, it can achieve all-optical signal processing. In addition, it is necessary to apply Bragg grating with high reflectivity to obtain efficient integrated chalcogenide glass fiber lasers, such as the distributed feedback Brillouin lasers. For chalcogenide glass fibers, it is complex to write Bragg gratings, mainly because the cladding and core components of chalcogenide glass fibers are similar; thus, both show photosensitivity, resulting in the weak photosensitivity of the fiber core. In our previous study, near-bandgap light close to the absorption edge of the material was selected to irradiate the chalcogenide glass fiber. The fiber core showed high photosensitivity, which solved the weak photosensitivity caused by sub-bandgap light far from the absorption edge of the material. However, when the fiber is used to write a Bragg grating, the depth of the grating transmission peak is not extended and cannot satisfy the actual usage requirements. This requires methods to further improve the photosensitivity of chalcogenide fibers. Therefore, this study extensively investigated the photosensitivity of chalcogenide optical fibers in tension applied in the axial direction to improve the photosensitivity of chalcogenide fibers and provide a new approach to writing gratings with high reflectivity. The findings provide new ideas and approaches for preparing chalcogenide grating photonic devices and will promote the development of chalcogenide photonics.

The photosensitivity of chalcogenide optical fibers was determined by measuring the change in the refractive index of the fiber core based on the Fabry-Perot (FP) etalon principle. In this experimental device, an optical fiber clamp with a slider was designed to apply tension, and a continuous dual-frequency Nd∶YAG laser with a working wavelength of 532 nm was used as the illumination source. After the laser beam was expanded using the beam-expansion system, it was focused onto the sample surface through a cylindrical lens to form a light spot with a height of approximately 1.1 mm and width of approximately 5 mm. The As₂S₃ optical fiber was cut using an ultrasonic cutter to produce an FP etalon of approximately 15 mm in length.

An improved Sagnac interference system, constructed using the same Nd∶YAG laser and a phase mask with a +1/-1 diffraction order, was used to form interference fringe patterns for writing the fiber Bragg gratings. In this system, the optical path of the Sagnac interference system was optimized to ensure that the two Gaussian light spots have improved coincidence and obtain interference fringes with increased contrast.

The experimental results show a significant difference in photosensitivity between the presence and absence of tension (Figs. 2 and 3). By applying tension, the photorefractive index change in the first fast process presents a decrease in the amplitude of the negative change of the refractive index, and the duration of the first fast process shortens. During the second slow process under tension, the recovery time of the photorefractive index change in the positive direction also shortens, and the change in the photorefractive index slowly recovers with the extension of the illumination time and can reach 10^-3 orders of magnitude. Under the same tension, during the first fast process of photorefractive index change, its duration is significantly shortened with an increase in light power [Figs. 2(b) and 3(b)], which can be shortened to tens of seconds. During the second slow process, the recovery of the photorefractive index change is also accelerated, and the change in the photorefractive index shows a positive increase under a specific tension, which can reach 5.41×10^-3. Under the same light power, the duration of the first fast process is significantly shortened with an increasing axial tension, whereas the negative change amplitude of the photorefractive index change decreases. In the second slow process, the change in the photorefractive index recovers faster under larger tension (Fig. 4).

The dynamic characteristics of Bragg grating written on a small-diameter fiber sample under a tension of 0.196 N were investigated. Without applying axial tension, the maximum depth of the transmission peak of the engraved Bragg grating was approximately 6.65 dB, and the reflectivity is approximately 78% (Fig. 6). However, when a tension of 0.196 N is applied, the transmission peak of the Bragg grating can reach 9.85 dB, the reflectivity increases to 89.7%, and the grating bandwidth is approximately 0.48 nm (Fig. 7). During the exposure time of 70-110 s under tension, the average depth of the transmission peak of the grating reaches 9.46 dB, the average reflectivity reaches 88.6%, and a good-quality grating spectrum can be obtained (Fig. 7).

In this study, the characteristics of the photorefractive index change of an As₂S₃ chalcogenide optical fiber under axial tension were experimentally investigated. The experimental results show that there is a significant difference in the photosensitivity with and without tension. By applying tension, the negative change amplitude of the photorefractive index change in the first fast process can reduce, and the duration of the first fast process shortens significantly, which can be shortened to tens of seconds under a particular tension. In the second slow process, under tension, the recovery time of the photorefractive index change in the positive direction also shortens, and the photorefractive index change shows a positive increase under a certain tension, which can reach 5.41×10^-3. On this basis, the As₂S₃ chalcogenide fiber Bragg grating was written based on the remarkable photosensitivity caused by the application of tension. The grating spectrum shows that within 70-110 s short exposure time, the average depth of transmission peak of the grating reaches 9.46 dB, the maximum depth of peak is 9.85 dB, the maximum reflectivity reaches 89.7%, and the grating spectrum quality is good. These experimental results are crucial in applying chalcogenide glass fibers in the near-middle infrared field as force sensors, achieving all-optical signal processing, and improving photosensitivity for preparing fiber gratings with high reflectivity.

Glass fiber reinforced polymer (GFRP) with excellent wave-transparent properties are the preferred choice for optoelectronic devices and microwave dielectric materials owing to their high strength, light weight, and excellent electrical properties. Traditional cutting techniques for processing GFRP have problems such as severe tool wear, low efficiency, and low accuracy. The application of laser processing can solve these problems and has broader application prospects. However, some problems remain in the processing of reduced materials by a single laser beam, such as the shielding of the subsequent laser by the pyrolysis gas, transformation of the target absorption mode due to incomplete pyrolysis of the residual carbon, and irregularity of the ablation morphology. The laser processing assisted by tangential air flow can solve these problems and improve the efficiency of material processing. In this study, a detailed investigation on the target perforation time, ablation morphology, and temperature distribution on the ablation surface under different power densities and tangential air flow was carried out. These results are helpful for improving the processing efficiency and profile of GFRP.

A fiber laser (wavelength of 1070 nm) with a maximum output power of 20 kW was used to interact with the GFRP in a relatively confined metal target chamber. Tangential air flow was provided by an air compressor and flowed out through a nozzle, and the air flow rate was measured using the Pitot tube method. A manometer was used to measure the pressure of the tangential air flow output from the nozzle; therefore, the stability of the air flow was monitored. The range of air flow rate used in the experiment was 0-1.0 Ma. The temperature evolution from the front and rear surfaces of the target was recorded using an infrared thermometer imager. The temperature data of the perforation point was extracted to draw a temperature change curve with time, and the perforation time was obtained from the falling edge of the temperature curve.

The perforation effects of GFRP are investigated at different laser power densities (848-1556 W/cm²) and tangential air flow velocities (0-1.0 Ma). It is found that the effect of increasing the laser power density on the ablation rate of GFRP is more significant than that of varying the tangential air flow rate (Figs.4 and 8). With an increase in the tangential air flow rate, the perforation time shows a decreasing trend and then a slow increase (Fig.8). This behavior is related to three effects caused by the tangential air flow: reducing the surface residual carbon content to promote the bulk absorption of the target (Fig.5), enhancing the heat convection on the target surface to accelerate the cooling (Fig.7), and providing tangential shear force to produce a mechanical erosion effect.

The perforation effect of GFRP at different laser power densities (848-1556 W/cm²) and tangential air flow rates (0-1.0 Ma) is investigated using a continuous laser with a wavelength of 1070 nm. The experimental results show that the perforation time decreases with increasing power density. A large amount of pyrolysis gas is generated in a shorter time period at higher power densities, which further results in a higher pore pressure and promotes the exfoliation process of the target. The effects of tangential air flow on the GFRP perforation process include reducing the surface residual carbon content to promote the bulk absorption process of the target, enhancing the cooling effect on the target surface, and providing a tangential shear force to produce a mechanical erosion effect. The three effects caused by tangential air flow have an obvious competitive relationship in the perforation process of the target. For the laser power density of 848 W/cm², when the tangential air flow rate is ≤ 0.4 Ma, the effect of tangential air flow is mainly used to promote resin pyrolysis, reduce the residual carbon content, and change the target absorption mode. Hence, the target perforation time decreases with an increase in the air flow rate. When the tangential air flow rate is in the range of 0.8-1.0 Ma, the cooling effect is more obvious. Therefore, the perforation time of the target material increases slowly with an increase in the air flow rate. In addition, compared with the tangential air flow rate, the effect of the power density on the perforation time of the GFRP is more significant.

A 1.5 μm pulse fiber amplifier in the eye-safe band is one of the prominent areas of research in pulse fiber laser technology. Depending on the pulse width, fiber amplifiers are used on different occasions; nanosecond fiber amplifiers are used in lidar, and microsecond fiber amplifiers are used in special material processing, biomedicine, and other fields. However, compared with nanosecond fiber amplifiers, the study of high-power microsecond pulsed fiber amplifiers is more challenging because of the steepening of the pulse waveform during amplification and the significantly increase in amplified spontaneous emission (ASE) at low repetition frequencies. In this study, a two-stage master oscillator power amplifier (MOPA) all-fiber structure was used to design and realize a 1550 nm microsecond rectangular pulse fiber amplifier with an adjustable repetition frequency of 10 Hz to 10 kHz. Compared with the fiber amplifier mentioned by M. Yu. Koptev and Svitlana Pavlova, the present one reduced the system complexity and cost and realized a wider range of adjustable repetition frequencies.

The entire fiber amplifier consists of four parts: signal optical pulse modulation, preamplifier, power amplifier, and pulse signal driving and control (Fig. 1). The optical signal pulse is modulated by a continuous seed source using an acousto-optic modulator (AOM). The preamplifier consisted of a double-clad erbium-ytterbium co-doped fiber (Nufern, PM-EYDF-12/130, length of 2.4 m), pump laser diode (pump wavelength is 940 nm, maximum optical power of 10 W), multimode pump beam combiner (MPC), and cladding pump stripper (CPS). The power amplifier included a double-clad erbium ytterbium co-doped fiber (Nufern, PM-EYDF-12/130, length 3.8 m), pump laser diode (940 nm, 80 W), MPC, and CPS. Both the preamplifier and power amplifier use the pulse-pump mode. The RF driver of the AOM, preamplifier pump driver, and power amplifier pump driver can be accurately synchronized and controlled, and the pulse width can be adjusted. The AOM operation is used to solve the waveform distortion caused by the narrowing of the pulse width in two different modes. By controlling the timing of the pulse signal and pre-shaping the waveform, the challenges of rapid ASE growth and transient effect of the pulse fiber amplifier are addressed.

By setting the pulse timing and pulse width of the AOM RF driver, the preamplifier pump driver, and power amplifier pump driver of the pulse fiber amplifier (Table 2), and optimizing the parameter settings of the AOM to pre-shape the pulse waveform of the input signal light, the output signal optical pulse waveform of the fiber amplifier is made rectangular (Fig. 4). The peak power reached 30 W at different pulse repetition frequencies and widths (Table 3). When the AOM was operated in mode 1, the optical-to-optical conversion efficiency was approximately 34%. Because the timing of the signal light pulse and pump pulse has been optimized to suppress the growth of the ASE, the spectral side-mode suppression ratio is close to 55 dB (Fig. 5), and there is no ASE generation. When the AOM operates in mode 2, the optical-to-optical conversion efficiency gradually increases from 19.50% to 24.19%. As the pulse repetition frequency continues to increase, the interval between two adjacent pulses becomes shorter, and the ASE accumulation time decreases, which is conducive to an increase in the signal optical power. However, keeping the pulse width constant and increasing the pulse repetition frequency leads to a continuous increase in the pulse duty cycle and number of pulses per unit time, resulting in an increase in the absorbed pump optical energy per unit time. The spectral side-mode suppression ratio is 25 dB. This is because when the pulse width is narrow, and the excess energy of a single pump pulse continues to convert energy between ions. The rapid accumulation of the ASE leads to a decrease in the spectral side-mode suppression ratio.

A 1550 nm microsecond pulse fiber amplifier with an adjustable repetition frequency of 10 Hz-10 kHz was designed and realized. The fiber amplifier adopts a pulse-pumped all-fiber dual-stage MOPA structure. By setting two working modes of the acousto-optic modulator (AOM), it realizes a working wavelength of 1550 nm, peak output power of 30 W, pulse width of 10 μs to 1 ms, and wide range adjustable rectangular pulse repetition frequency of 10 Hz to 10 kHz. In this system, the rapid growth of the ASE is suppressed by optimizing the timing and pulse width of the signal and pump beams. The waveform distortion problem caused by the transient gain effect in microsecond pulse fiber amplification is overcome by pre-shaping the signal optical pulse waveform, and a better rectangular pulse laser output is obtained. A microsecond pulse fiber amplifier has high peak power. The pulse width and repetition frequency of the amplifier can theoretically be adjusted to a wider range. The microsecond pulse fiber amplifier has broad application prospects in laser drilling, laser coloring, and biomedicine.

High-energy and high-peak-power 2 μm solid-state laser plays an important role in many fields. Currently, two types of pumping source can be used to pump an Ho∶YLF laser. One is the Tm doped solid-state laser, and the other is the Tm doped-fiber laser. It is known that Ho∶YLF crystal has different polarized absorption characteristics in the π and σ directions. Therefore, quantitative research on the optical-optical conversion efficiencies affected by the polarization of the pump light will be remarkably significant. Electro- and acousto-optic Q-switching are two methods for realizing pulsed output of Ho∶YLF laser. The former method has advantages in terms narrower-pulse-width laser output. Therefore, we demonstrate an electro-optic Q-switched Ho∶YLF laser pumped by Tm∶YAP laser, and a laser output with high-peak-power and narrow-pulse-width is obtained. A peak power of megawatt level is achieved at a lower pump power by adopting the technical scheme. Moreover, the laser has a compact configuration. It will potentially provide a high-quality laser source for the application of mid- and long-infrared optical parametric oscillators, laser radar, and other fields.

This study develops layouts of the Ho-laser based on an end-pumped structure with L-shape resonator. The experimental device is depicted in Fig. 2. A home-made Tm∶YAP solid-state laser at wavelength 1.94 μm is used as a pumping source. The dimensions of the Tm∶YAP crystal are 3 mm×3 mm×12 mm, and the doping concentration (atomic fraction) is 3.0%. The Tm∶YAP crystal is b-cut. The dimensions of the Ho∶YLF crystal are 6 mm×6 mm×40 mm. The Ho∶YLF crystal is a-cut, and the doping concentration (atomic fraction) is 0.5%. The M₄ mirror is a half-wave plate and is used to examine the effect of polarization on the output characteristics of the Ho∶YLF laser. To achieve good mode matching, the size of the pump light spot is adjusted to be approximately 1.2 times the size of the Ho∶YLF laser spot. We select an RbTiOPO₄ (RTP) crystal as the electro-optic Q-switch for achieving high-peak-power laser output. Further, we adopt a long-pulse Tm∶YAP laser to pump the Ho∶YLF crystal to obtain high beam quality while the output energy is adjusted. To study the effect of different pump pulse energy on the characteristics of the laser output, the laser beam quality factors are measured using the knife-edge method.

The Ho∶YLF crystal is pumped by a linear-polarized Tm∶YAP solid state laser with a power of 30.2 W. Under continuous-wave operation, the central wavelength of Ho∶YLF laser is 2.06 μm, and the beam quality factors are 1.3 and 1.2 in the horizontal and vertical directions, respectively. The spot sizes at different positions and beam shape are shown in Fig.6. A half-wave plate is placed after the Tm∶YAP laser, which is used to change the polarized direction of the pump light. As the proportion of the pump laser in the direction of π polarization changes from 100% to 0, the optical-to-optical conversion efficiency changes from 28.9% to 7.1%. This indicates that the efficiency can be significantly improved by adopting linearly-polarized pumping light. The experimental results are shown in Fig. 7. Based on electro-optical Q-switching technology, a pulse laser output is obtained when the Tm∶YAP laser power is 15.4 W and repetition frequency is 100 Hz. The maximal output energy is 9.5 mJ, with a pulse width of 13.0 ns, and peak power is 0.73 MW. The pulse waveform and change of pulse energy with the pump energy are shown in Fig. 8.

In this study, an Ho∶YLF solid-state laser and the corresponding Tm∶YAP pump laser are built, and a pulsed laser with peak megawatt power at 100 Hz is realized. The effect of the polarized characteristics of the pump source on the output characteristics of the Ho∶YLF laser is studied; the results indicate that linear-polarized light pumping is an effective manner to improve the optical-to-optical efficiency of an Ho∶YLF laser. The laser has the advantages of compact configuration and high-peak power and therefore has broad application prospects in the field of optical parametric oscillator pumping. Furthermore, the results of electro-optical Q-switching under long pulse pumping also provide solid foundations for Ho-doped lasers with higher energy and higher peak power.

The first international aerosol carbon detection LiDAR (ACDL), which was developed by Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, was successfully launched and has been continuously operated in orbit since April 2022. This Lidar uses a high-energy single beam pulsed laser with frequency stabilization at three wavelengths (532 nm/1064 nm/1572 nm). High-power space lasers typically produce a large amount of heat during operation; however, heat concentration in the laser causes the temperature of the laser diode (LD), which is a key device in the laser, to rise, resulting in a drift in the LD output wavelength that causes the overall efficiency of the laser to decrease or fail. Simultaneously, large amounts of heat also increases the temperature of the internal optical structure, resulting in a large temperature gradient, which causes the main laser structure to deform and stress accumulation inside the core optical components, thereby resulting in extremely serious effects on the laser output power, beam pointing, divergence angle, and polarization characteristics. An efficient and stable thermal control technology is one of the core technologies in the development of space laser loads. To meet the requirements of on-orbit applications, it is necessary to design, simulate, and test the thermal control system of the space high-energy pulsed solid-state laser used in the system.

Generally, the LiDAR is operated on a sun-synchronous orbit with an orbital altitude of 705 km and an orbital inclination of 98.1°. The laser is preferably installed inside the main body of the LiDAR and insulated from its main structure, and the connection is done in series through a heat pipe to transfer heat to a radiant cooling plate (Fig. 4). The thermal control states of the main and standby lasers are consistent when operated separately. Simultaneously, a single laser can transfer the heat to the second laser through a heat pipe to ensure an effective storage temperature. The temperature fluctuation and temperature gradient of the laser are controlled using the temperature-control form of multichannel active compensation heating, and the heating temperature control circuit is arranged on the top surface, lateral face, and external heat pipe of the laser shell to independently control the local temperature. The radiant cooling plate is installed on the nonilluminated surface, which is less influenced by the external heat flow when dissipating the high-power heat generated by the laser.

The space vacuum environment and space radiation cold background are simulated using a space environment simulator, and an infrared light array is used to simulate the external heat flow environment of the LiDAR in different directions (Fig. 8). High-temperature and low-temperature tests are conducted under thermal vacuum equilibrium conditions, where the temperature of the laser internal amplifier is maintained between 18.9 ℃ and 26.8 ℃, the temperature of the laser shell is maintained between 19.2 ℃ and 21.5 ℃, and the maximum temperature fluctuation is ±0.67 ℃ (Fig. 11). After the LiDAR is launched into orbit, an on-orbit test is conducted and the laser and laser thermal control system operate normally. By analyzing the correlation between the laser energy fluctuation and temperature measurement value, the laser energy fluctuation cycle is found to be consistent with the external heat flow fluctuation cycle. Additionally, the laser telemetry energy fluctuation is 4.9%, and the temperature control parameters of the laser external heater are adjusted using the on-orbit injection number to improve the temperature control accuracy of the laser during the on-orbit test. For the on-orbit thermal control parameter optimization process, the duty cycle of the heat pipe heater is reduced by reducing the temperature threshold of the heat pipe heater and opening the laser shell temperature compensation backup heater to increase the temperature control threshold of the heat pipe mounting surface heater. After on-orbit adjustment, the temperature fluctuation of the laser in orbit is ±0.033 ℃ (Fig. 12), and the fluctuation of laser energy telemetry is 1.2%.

Using simulation calculations and space environment thermal experiments, the design verification index is completed to ensure the usage requirements are met. After the LiDAR is launched into orbit, the laser thermal control system operates normally and meets the long-term stable working requirements of lasers in orbit. Therefore, the laser thermal control technology used in this study is reasonable, feasible, and has high reliability and design margin, making it an important reference for the thermal design of high-power space laser loads.

High-power femtosecond lasers are widely utilized in various research fields such as terahertz (THz) generation, frequency comb, and high harmonic generation because of their short pulsed width, high peak frequency, and good beam quality. However, owing to strong thermal lens effect, the output power of lasers based on traditional bulk-shaped gain medium is limited to the 20 W level. Further, fiber lasers are restricted by nonlinear effects such as stimulated Brillouin scattering at high output power. The emergence of thin disk lasers (TDL) has facilitated the simultaneous solving of these two problems. A thickness of only a few hundreds of micrometers combined with effective back-side cooling technique can significantly reduce the influence of thermal lens effect and nonlinear effects. In addition, multiple pass pump module guarantees high absorption efficiency under the condition that the gain medium is extremely thin. Currently, femtosecond lasers based on thin disk medium are mainly achieved using the semiconductor saturable absorber mirror (SESAM) mode-locking and Kerr Lens mode-locking (KLM). The highest output power obtained using the former (350 W) is higher than that of KLM (270 W); however, KLM lasers exhibit better performance in the aspect of pulse width, peak power, cost, and stability of key components. Thus, KLM TDL is a promising candidate for light sources in high field science and nonlinear optical researches.

We investigate KLM thin disk lasers by using our home-made 72-pass pump module. First, we analyze the principles of Kerr lens mode-locking in thin disk lasers to ensure that the mode radius at the pinhole decreases at a proper ration following the insertion of the Kerr medium, or the virtual Kerr Lens at the beam waist. Subsequently, we demonstrate the cavity design method based on ABCD matrix and soliton mode-locking theory. On the basis of this method, we design the KLM TDL cavity by employing a focusing mirror pair with the radius of curvature (RoC) of 150 mm. In addition, we simulate the mode radius in the cavity under continuous wave (CW) and KLM operation with an iteration algorithm. Finally, a KLM TDL experiment is conducted based on a 72-pass pump module. Moreover, the cavity is optimized based on the former experiment, and the higher output power is achieved.

The experiment conducted with the first cavity structure yields a femtosecond output of 11.78 W at fundamental transverse mode when pumped at 72 W. The pulse train with a frequency of 81.45 MHz measured via an oscilloscope shows good stability in the time scale of 2 μs (Fig. 8). The pulse width measured using an autocorrelator to be 243 fs, assuming sech² pulse shape, is shown in Fig. 9. Further, the spectral width is measured to be 4.6 mm (Fig. 10). The multiple peaks in the spectrum may be caused by the uneven group delay dispersion (GDD) curve of the home-made dispersive mirrors in the wavelength range of 1025-1035 nm. The corresponding time-bandwidth product is 0.317, which is slightly larger than the theoretic minimum value. On further increasing the pump power to 81 W, stable double pulse output can be observed (Fig. 11). This phenomenon is attributed to the strong spectral broadening effect under high power single pulse operation. If the output mode transforms into double pulse operation, the narrowed spectrum fits better into the emission spectrum of Yb∶YAG.

Following the optimization of the cavity structure by increasing the RoC of the focusing lens pair to 200 mm, the output power is increased to 22.33 W at the pump power of 94 W with an optical-to-optical efficiency of 24%. However, the repetition frequency remains almost unchanged at 79.36 MHz and the pulse energy is 0.28 μJ. The corresponding pulse width is measured to be 393 fs (Fig. 13).

We analyze the principles of Kerr lens mode-locked thin disk lasers based on a 72-pass pump module and the design of the KLM cavity. The design principles are examined according to the ABCD matrix method and soliton mode-locking theory. Finally, the KLM laser oscillator based on thin disk medium is constructed. The stable femtosecond pulse output at 11.78 W with the pulse width of 245 fs and repetition rate of 81.45 MHz is obtained when pumped at 72 W. The output result is nearly identical to the designed target. After changing the RoC of the focusing mirror pair to 200 mm, the output power is increased to 22.33 W at the pump power of 94 W with the corresponding pulse width of 393 fs. In future studies, to increase the output power to a higher level, the RoC of focusing mirrors will be increased, and the optimized dispersion compensation will be provided. In addition, the cavity will be placed in a vacuum environment to reduce the influence of air disturbance and air dispersion.

InGaAs materials as absorption layers and Si materials as multiplication layers are potential alternatives for achieving high-performance avalanche photodiodes (APDs). However, simple and well-performing InGaAs/Si APDs are difficult to fabricate owing to the 7.7% lattice mismatch between InGaAs and Si. Investigators have recently reported that a-Si was introduced at the InGaAs/Si APD bonding interface to inhibit the nucleation of mismatch dislocations and realize an ultra-low dark current. However, owing to the large bandgap of a-Si, the bonding interface has a large conduction band and valence band offset. This causes the gain of the device to decrease. Ge and Si are both indirect band gap semiconductors, and Ge materials have the advantages of a small gap width and a long absorption cutoff wavelength in the infrared region. Hence, in this study, a method to mitigate the effect of the InGaAs/Si lattice mismatch on APD performance from the source side is theoretically proposed. Here, a-Ge or poly-Ge bond layers are introduced into the InGaAs/Si bond interface, and the variation in the InGaAs/Si APD performance with the bond layer thickness is simulated and compared. In this work, theoretical guidance for the development of ultralow-noise and high-gain InGaAs/Si APDs will emerge.

An a-Ge or poly-Ge bond layer is introduced into the InGaAs/Si bond interface, and variations in APD performance with bond layer thickness are simulated and compared. Initially, the optical and dark currents of the APD are simulated and compared considering the thickness of the bonding layer. Subsequently, the recombination rate and carrier concentration of the APD under light conditions are simulated to understand the cause of the change in the APD optical current. To further understand the cause of the change in the electron concentration of the APD, the changes in the APD energy band under light conditions are simulated. Then, the changes in charge concentration, impact ionization rate, electric field, and other parameters with the bond layer thickness are simulated and compared. Finally, the gain and gain bandwidth products of the APD are simulated and compared to further explore the performance improvement of the device.

After introducing a-Ge or poly-Ge bond layers, the dark current of the APD before avalanche can be as low as 10^-11 A (Fig. 2). Moreover, potential barriers or wells appear in the energy band of the bonding interface (Figs. 8 and 9). Owing to the barrier effect and hole trapping effect, optical and dark current gaps appear in both (Fig. 2), and this phenomenon is more obvious in the APD with the poly-Ge bond layer. These results indicate that both the a-Ge and poly-Ge bonding layers can reduce device noise. The gain and gain-bandwidth products of the APD are simulated and compared. The results show that when a-Ge is used as the bonding layer and the thickness of the bonding layer is 0.5 nm, the gain and gain bandwidth product can reach its maximum. The maximum gain of the APD can reach 451.3 (Fig. 15), and the maximum gain bandwidth product can reach 13.7 GHz (Fig. 20). Theoretically, an InGaAs/Si APD with high gain and ultralow noise is obtained.

In this study, the effects of a-Ge and poly-Ge bonding layer thicknesses introduced at the InGaAs/Si bonding interface on the performance of InGaAs/Si APD are theoretically studied. The results show that the dark current before the avalanche can be as low as 10^-11 A when the a-Ge and poly-Ge bond layers are introduced. Furthermore, the APD with a-Ge or poly-Ge bond layers introduced after the avalanche exhibits optical and dark current bandgaps. This will help the APD achieve ultralow noise. Similarly, the gain and gain bandwidth products of the APD with an a-Ge bonding layer are much larger than those with a poly-Ge binding layer. The gain and gain bandwidth products of the APD decrease with an increase in the bond layer thickness. The APD performance is optimum when a-Ge is used as the bonding layer and the bond layer thickness is 0.5 nm. At this time, the maximum gain can reach 451.3 and the maximum gain bandwidth product can reach 13.7 GHz. However, when poly-Ge is used as the bonding layer, the maximum gain of the APD is only 7.9 and the maximum gain bandwidth product is only 598 MHz. Therefore, the use of a-Ge as the bonding layer material and the selection of a thin bonding layer are considered ideal schemes for preparing InGaAs/Si APD with improved device performances.

The space-ground laser time transfer experiment using the laser ranging and laser timing payload equipped on the lunar orbiter scheduled to be launched in 2023 by the Chinese Academy of Sciences aims to evaluate the performance of the on-board atomic clock and study the high-accuracy time comparison technology and autonomous navigation technology in Earth-Moon space to support China’s manned lunar exploration project and other interstellar missions in the future. Compared with dedicated time transfer experiments such as Time Transfer by Laser Link (T2L2) and Atomic Clock Ensemble in Space (ACES), whose model is studied in the local geocentric frame of reference, the model for laser time transfer in Earth-Moon space needs to be represented in the solar-system barycentric space-time frame of reference using the Barycentric Coordinate Time (TCB) or Barycentric Dynamical Time (TDB) as the reference time scale. To ensure the smooth progress of the high-accuracy time comparison mission, a measurement model for laser time transfer in Earth-Moon space with an uncertainty of order 1 ns is developed.

The proposed model is represented in the Barycentric Celestial Reference System (BCRS) using TCB as the reference time scale. The numerical time ephemeris of the earth, TE405, which is calculated using NASA’s Jet Propulsion Laboratory (JPL) development ephemerides, was employed to achieve a transformation with a 0.1 ns level accuracy between the Geocentric Coordinate Time (TCG) and TCB. Based on the IAU resolution B1.5 (2000), the nominal trajectory of the lunar spacecraft was used to calculate the influence of the gravitational fields of celestial bodies in the solar system on the rate of the on-board atomic clock. The round-trip light time model of laser pulses with an accuracy of 10 ps level was deduced. We built the model of Shapiro time delay with an accuracy of better than 10 ps, and established center of mass correction model, geometric position correction model, system delay model. Finally, based on the engineering background of the lunar orbiter scheduled to be launched in 2023, factors such as the stochastic and deterministic clock errors, satellite visibility, echo rate setting, and discontinuity of observations were all considered when performing the data simulation using the proposed measurement model for laser time transfer.

The data generated by the proposed measurement model are paired to identify the triplets, analyzed and processed to estimate the time offset and frequency offset of the on-board clock. Random white noise is then superimposed onto the nominal trajectory of the satellite to generate the position of the satellite, which is not constrained by the dynamic model and is used for data processing, resulting in a 1σ error of 3300 ns in the calculation of the one-way light time. This drowns out the deterministic error of the on-board clock by half an hour (0.5 ns/s×1800 s=900 ns). Thus, during data preprocessing, instead of using the traditional observed minus computed (O-C) residuals method to remove the trend caused by the orbit, the effective echoes are directly extracted from the observations (Fig.9, Fig.10). Such a processing method results in a lower accuracy of frequency offset estimation (the estimation error is approximately 15%) and larger root mean square error (approximately 40 ns). The dynamic model will be introduced into the proposed data processing procedure to constrain the variation in the kinematic parameters, which will certainly reduce these errors. Moreover, the standard deviation of the time comparison is at the ns-level (Fig.11, Fig.12), indicating that the precision of our measurement model reaches this level.

In this study, a calculation error for the relativistic shift of approximately 1.1×10^-16 was obtained by neglecting the 1/c⁴ term and influence of the gravitational field of celestial bodies, other than that of the sun, earth, and moon. Consequently, the accuracy of time transformation between the proper time and TCB is better than 3.5 ns within one year, and the calculation error of the Shapiro delay is less than 10 ps when only considering the gravitational fields of the sun and earth. Moreover, the light time model of the round-trip is deduced and the model error caused by neglecting the 1/c⁴ term is less than 20 ps. The clock error time histories are also generated from Allan variance or Hadamard variance profiles using two different methods, the power-law spectral density model and Kalman filter state function. Although the calculation time for the former is equal to approximately 10% of the latter, the noise characteristics generated by the latter are closer to the given index. The feasibility of the ns-level uncertainty of the proposed measurement model for use in the high-accuracy laser time comparison missions in Earth-Moon space is also verified. The proposed time transformations, clock error model, and light time model can also be used in other scenarios such as in the development of a high-precision and accurate measurement model for microwave time transfer in Earth-Moon space, and in laser asynchronous transponders in Earth-Moon space.

The double-headed screw rotor is a common and critical power generating component and the accuracy of its profile has a direct bearing on the mechanical properties and service life of various products. The current profile accuracy measurement methods for double-headed screw rotors are all contact-type, and are divided into two type. One type is to manually measure the profile accuracy with a single-parameter instrument such as a micrometer. Although measurement accuracy and efficiency are both low, this method can be used for on-machine measurement. The second type refers to automatic measurement of the profile accuracy with a coordinate measuring machine (CMM). Despite its high measurement accuracy, this method consumes significant auxiliary time, increases the positioning error in off-machine measurement and cannot guarantee the post-correction accuracy of a nonconforming screw. To measure the profile of double-headed screw rotors with high precision and efficiency, an on-machine measuring (OMM) system based on a laser triangulation displacement sensor (LTDS) is designed and implemented by considering a four-axis whirlwind milling machine as the carrier.

To improve the measurement accuracy of the system, the generalized variable-structural-element morphological method, polynomial interpolation algorithm, and ellipse fitting method are combined to realize micron-level centroid extraction from a noise-containing spot image. Then, the hybrid method is experimentally verified. Subsequently, a smoothing algorithm for point cloud data is devised based on the Lagrange multiplier method to avoid the defects associated with the piecewise curve fitting method, that is, function continuity and differentiability cannot be satisfied at piecewise points. Finally, the profile parameters are calculated in real time according to the data reconstruction results, and the machining quality is assessed.

The measuring results are shown in Fig.9. In comparison with that of the traditional LTDS-based measuring method, the profile measured through the OMM method is closer to the CMM result. This outcome indicates that the LTDS data acquisition accuracy can be improved with the proposed method in Section 3.1, that is, the generalized variable-structural-element morphological edge extraction algorithm is applied first to realize effective edge measurement of the spot image and then the polynomial interpolating subpixel edge positioning algorithm is applied to realize rapid subpixel positioning. Ultimately, centroid extraction is conducted through the ellipse fitting algorithm. As shown in Table 3, all difference values are within the acceptable tolerance zone for all three standard measuring methods compared with their corresponding nominal values, indicating that the screw rotor part is acceptable after machining. However, the proposed spot centroid extraction method can improve the measurement accuracy of traditional LTDS for a free-form surface compared to OMM. The profile accuracy of the screw rotor obtained through the proposed LTDS-based on-machine measuring system is within ±9 μm from the difference values between OMM and CMM results.

Such whirlwind milling machines configured with four-axis screw rotors have been placed in operation. Actual results indicate that the measurement accuracy using the proposed method is ±9 μm, in which the measurement uncertainties of major axis, minor axis, and screw pitch are 0.72, 0.69, and 1.65 μm, respectively, and measuring one screw pitch consumes 39.7 s. Therefore, the results indicate that the proposed on-machine measuring system can satisfy the requirements for accurate control and rapid measurement of large workpieces in actual operation.

Absolute laser ranging is widely used in scientific research and industry. Several types of absolute distance measurement methods can be used, such as the time-of-flight method, phase ranging method, multiwavelength interferometry, and dual-comb ranging. The polarization laser ranging method is a phase-ranging method that establishes the functional relationship among the laser polarization, modulation frequency, and measurement distance. As laser polarization is less susceptible to interference from environmental disturbances, the polarization laser ranging method can achieve higher precision than the phase-ranging method. Laser polarization rangefinders have an irreplaceable role in fields such as assembly and inspection of large structural parts and field baseline construction. However, owing to technological monopoly and blockades, no independently developed laser polarization rangefinders are available in China. Research in universities and research institutes has mainly focused on system implementation and error analysis. The swing method is the only polarization laser ranging algorithm used in these studies. Waveform distortion would reduce the swing method accuracy; therefore, research on polarization laser ranging algorithms is necessary to improve ranging accuracy.

Based on the principle of polarization modulation ranging, the reason for waveform distortion and the influence of the local minimum point frequency accuracy on the ranging accuracy are studied. To obtain the minimum points of the demodulated signal, the swing and least square methods for polarization laser ranging are compared. The swing method is affected by waveform distortion. The least square method is widely used in curve fitting, which can effectively reduce the influence of waveform distortion and increase the accuracy by using higher-order fitting polynomials. The least square method uses all data to fit the curve; however, the polarization laser ranging algorithm focuses solely on the local minimum ranges. In terms of fitting efficiency and accuracy, it is not completely applicable to resolve the local minimum points of the demodulated signal. The moving least square (MLS) method is an optimization algorithm of the least square method that can simultaneously realize interval fitting and high-precision fitting near special points. This is suitable for high-precision curve fitting using the local minimum range data. In this study, a polarization-ranging algorithm based on the improved moving least square (IMLS) algorithm is proposed. The algorithm flow is as follows. First, the algorithm achieves global fit and determines the intervals containing the minimum points. Second, it performs curve fitting using the MLS algorithm along the curve in one of the intervals until it finds the minimum point in this interval. Then, the influence radius is selected automatically according to the mean square deviation, and the frequency corresponding to the local minimum point is calculated. Finally, the distance is calculated using two adjacent frequency values of the local minimum points. A flowchart of the improved MLS algorithm for polarization laser ranging is shown in Fig. 4.

Distance-measurement experiments are conducted to verify the accuracy of the IMLS algorithm. First, the influence of the key IMLS algorithm parameters, such as the weight function and influence radius, is tested. Thus, the influence radius is extremely important. If the value is too small, it can cause matrix singularity and fitting anomaly, as shown in Fig.3. The experimental results listed in Table 3 indicate that the higher the influence radius, the smaller the IMSL residual error with the same weight function. However, to ensure the movement characteristics of the MLS algorithm and decrease the number of calculations, the influence radius should be less than 10% of the sweep interval. The comparison results under comprehensive parameters are listed in Table 4, and indicate that the measurement mean square deviation is subject to the common influence of both the weight functions and the influence radius. The measurement mean square deviations of the normal weighted function, cubic spline function, and Gaussian function are 0.111, 0.237, and 0.177, respectively. The comparative results of the IMLS algorithm, swing method, and least square method are presented in Table 5. When the measured distance is 11.94 m, the minimum errors of the swing method, least square method, and IMLS algorithm are 0.219, 0.317, and 0.111 mm, respectively. The accuracy of the IMLS algorithm is higher than those of the swing and least square methods.

In this study, the IMLS method is applied to implement a polarization laser ranging algorithm. The experimental results show that the IMLS algorithm can reduce the impact of waveform distortion and improve the precision of the polarization ranging system. The IMLS algorithm has a higher precision than the swing and least square methods. The proposed IMLS algorithm is suitable for determining the polarization modulation range and provides a reference for research on polarization laser ranging algorithms.

Spaceborne lidar has a high orbit and wide observation range, which facilitates the accurate and rapid acquisition of large-scale three-dimensional spatial information. It is a key research area, both domestically and internationally. Spaceborne lidar has been increasingly used in marine remote sensing and topographic mapping. With the continuous development of China's space laser altimeter, the measurement accuracy has increased from 5.0 m to 0.3 m. The stability requirements of the optical-mechanical structure continue to increase and the measurement accuracy also increases at the same time. Simultaneously, the laser itself is also a highly sensitive component of the optomechanical instrument. There can be shape and position errors of the onboard interface owing to factors such as production, emission vibration, and changes in satellite temperature. These errors lead to a deviation in the optical axis of the laser altimeter. The traditional installation method considers the rigidity requirements of the instrument rather than the precision requirements. In this study, the core accuracy of the altimeter is considered to be the main optimization goal. The flexibility of the supporting structure is optimized to isolate a part of the deformation caused by the outside surroundings. This ensures that the optical accuracy of the laser altimeter is better than that of the traditional method.

This study designs the support structure of an altimeter based on the kinematic installation method. The rigidity of the optical plate of the laser altimeter is enhanced, and the rigidity of the supporting structure is reduced as much as possible while meeting the requirements of the satellite. Thus, most structural deformations caused by changes in the mechanical and thermal environments are isolated. The flexibility of the support structure is implemented by the arcuate hinge, and the parameters of the arcuate hinge are optimized to set reasonable flexibility. The structural deformation of the deck which is caused by the change in the mechanical and thermal environments is transmitted to the equipment by comparing their stiffness values. The carbon fiber composite honeycomb panel is equivalent to an aluminum panel with a certain thickness using the equivalent method. The relative stiffness of the instrument and deck at the installation point is obtained using finite element analysis. The range of the errors is set according to the temperature and structural deviation ranges provided by the satellite. The optical axis stability performance of the laser altimeter under the support structure designed in this study is obtained by stiffness calculation and statistical analysis of the errors. Mechanical and thermo-optical tests are designed to verify the conclusions of the analysis.

The stiffness ratio between the support structure and the optical plate is 1∶8 (Tables 2 and 3) by structural optimization. The test shows that the first-order frequency of the device reaches 88 Hz (Fig.7). The statistical analysis of the errors shows that the optical axis change of the laser altimeter is only approximately 8.5 μrad (Table 7) under the interference of the external environment. The analysis results above imply that the supporting structure designed in this study can satisfy the requirements of the structural rigidity of the satellite. Additionally, it can protect the optical performance of the laser altimeter from structural deformation of the platform. The change in the optical axis of the laser altimeter is approximately 30 μrad (Table 8) before and after the mechanical vibration. The mechanical stability of the structure satisfies the optical requirements. During the thermo-optical test, the optical axis stability of the device is about 8.5 μrad (Fig.8), indicating that when the environment temperature alternates between high and low boundaries (20 ℃±30 ℃), the support structure can absorb most of the thermal deformation to ensure optical stability.

There are shape and position errors in the onboard interface due to factors such as production, emission vibration, and changes in the satellite temperature. These errors lead to a deviation in the optical axis of the laser altimeter. To reduce the influence of errors in the onboard interface, this study designs the support structure of the altimeter based on the kinematic installation method. The support structure is optimized by stiffness analysis between the deck and the laser altimeter. The error distribution of the onboard interface is analyzed using the Monte Carlo statistical method, and the errors in the installation area are determined as the analysis inputs. The analysis and experimental results show that the first-order fundamental frequency of the designed support structure reaches 88 Hz, the change in the laser emission-receiving optical axis caused by installation is approximately 8.5 μrad, and the change before and after mechanical vibration is 30 μrad. The thermo-optic test shows that the optical axis stability is 8.5 μrad between the high- and low-temperature boundaries. The designed support structure can satisfy the requirements of laser altimeter. The design ideas and test results in this study provide a reference for the design of similar type of laser load on satellites.

It is an effective means to identify and track the target using the airborne electro-optical platform with high-resolution imaging equipment. However, in the actual combat process, it is challenging to meet the optimal observation conditions of nadir looking. Usually, it is necessary to quickly locate the remote target at a certain height, resulting in a large inclination of the photograph and a small angle between two observations. Furthermore, a motion camera's relative pose estimation is the key visual location technology based on an airborne electro-optical platform. Typical pose estimation methods include the vision-based pose estimation method and the vision-based pose estimation method with an inertial measurement unit (IMU). The latter introduces additional angle constraints based on the former. Under typical limited observation conditions such as a large inclination angle and small intersection angle, the camera's pose estimation accuracy is easily affected by the attitude angle error and the image point extraction error, which makes the target location accuracy difficult to meet application requirements. Therefore, it is of great significance to study target tracking and location under limited observation conditions to improve operational efficiency.

The unavoidable problem is that the measurement angle of the IMU drifts with time, and the calibration of the installation relationship between the IMU and the camera is cumbersome. Therefore, this paper proposes a ground target location method under the fixed installation of the IMU and the camera. This method does not require the installation relationship information between the calibration camera and the IMU. Firstly, two adjacent frames of images are extracted and matched through the scale-invariant feature transformation (SIFT) matching algorithm. Secondly, the IMU installed in the fixed link is used to provide the relative rotation angle information for the motion camera. Combined with the robust estimation algorithm random sample consensus (RANSAC) algorithm, the relative rotation and translation of two adjacent frames are estimated according to a relative rotation angle and four corresponding image points. Then, combined with the external parameters of the first frame image, the external parameter matrix of any frame can be obtained. Finally, the projection matrix is used to intersect the spatial location of the target.

Under the RANSAC framework, the smaller the minimum number of points required to solve the model, the same confidence level can be achieved with fewer iterations. Therefore, compared with other traditional algorithms, the algorithm proposed in this paper can significantly improve the computational efficiency under the same ratio of outliers (Fig. 3). In the simulation and flight experiment, the airborne electro-optical platform is 5 km away from the target and observes the target at an angle of 66.42°. Monte Carlo simulation analysis shows that the location accuracy of the proposed method is affected by the accuracy of pixel extraction (Fig. 5), relative rotation angle (Fig. 6), and the platform location (Fig. 7). Under the same pixel extraction error, the method in this paper shows apparently excellent performance. And the larger the intersection angle, the smaller the location error. According to the flight experiment, this method introduces the relative rotation angle constraint, which can more accurately estimate the relative rotation and translation of the camera than the traditional method and improve the location accuracy under limited observation conditions (Table 3).

Under limited observation conditions such as a long distance, a large inclination, and a small intersection angle, the accuracy of ground target location is challenging to meet the task requirements. Therefore, this paper proposes a ground target location method with the fixed installation of an IMU and a camera. When the IMU is fixedly installed with the camera, it can directly provide the relative rotation angle for the camera. What's more, it reduces the degrees of freedom of the relative pose estimation problem and the number of solutions. Under the RANSAC framework, the proposed method is more likely to find the appropriate solution from the same number of iterations. This method can significantly improve the calculation efficiency and the target location accuracy under limited observation conditions.

Quartz crystal is an important birefringence material, which is widely used in optical related fields. The two main optical parameters of quartz crystal wave plate are phase retardation and fast axis azimuth. Due to the influence of manufacturing process, these two actual parameters will deviate from the theoretical value, so it is usually necessary to accurately measure the optical parameters before use. Ellipsometry is usually used to measure the parameters of quartz crystal in a wide spectrum, but the existing ellipsometric measuring instruments often assume that the optical axis of the crystal is aligned with the measuring optical path, which introduces measurement error, especially in the ultraviolet band. Therefore, it is necessary to propose a fitting model for accurate measurement of quartz crystal parameters. The model contains rich information and the fitting results are accurate. This model has important reference value for measuring the accurate parameters of anisotropic materials by ellipsometry.

A Mueller matrix model for accurate measurement of quartz crystal parameters by ellipsometry is proposed. Firstly, the crystal coordinate system (a, b, c) is transformed into the measurement coordinate system (x, y, z) by coordinate transformation, which involves three Euler angles ?_E, θ_E, and ψ_E (Fig. 1). After coordinate transformation, the expression of dielectric tensor of quartz crystal in the measurement coordinate system can be obtained. Then, the Berreman 4×4 matrix theory is used to establish the correlation between quartz crystal parameters and Mueller matrix. The Mueller matrix measurement value of the sample is obtained by the Mueller matrix ellipsometer, and then the Mueller matrix model is used for iterative fitting. The Levenberg-Marquardt algorithm is used for fitting, and the evaluation function is defined as root mean square error (RMSE). The fitting parameters are adjusted by nonlinear iterative regression to minimize the evaluation function, that is, when the evaluation function converges to the global minimum, the actual parameters of the sample are obtained. Finally, the thickness of the crystal, Euler angles and the phase retardation can be obtained by fitting calculation.

In order to fully demonstrate the effect of the fitting model, we measured two samples with different thicknesses. Both samples were placed in different directions in turn, and different incident angles were selected for measurement at each placement azimuth (Fig. 2). Firstly, the built-in model of ellipsometer is used to fit the phase retardation. In the ultraviolet band, the fitting results of the phase retardation at different azimuth angles show significant non-zero values, and the maximum value is close to 4° (Fig. 3). Obviously, the built-in model has defects in fitting the phase retardation of quartz crystal. The Mueller matrix model described in this paper is then used for experiments. Taking the thick sample as an example, the actual measured Mueller matrix dispersion curve [Fig. 4(a)], the Mueller matrix dispersion curve fitted by the Mueller matrix model [Fig. 4(b)], and the difference between the two curves [Fig. 4(c)] can be obtained. The average value of the difference is -0.0007, and the maximum value is 0.231. At different sample azimuth angles and incident angles, the maximum and average RMSE of thick samples are 4.182 and 4.127, respectively, and the maximum and average RMSE of thin samples are 3.906 and 3.770, respectively (Fig. 5). The fitting thicknesses of thick and thin samples are 0.832 mm and 0.691 mm, respectively. In comparison, the measured thicknesses using micrometers are 0.834 mm and 0.695 mm, respectively. The relative errors are 0.24% and 0.57%, respectively (Table 1). The Euler angles θ_E of thick and thin samples are 1.902' and 1.932', respectively.

This paper proposes a Mueller matrix model for accurately measuring quartz crystal parameters. Based on the coordinate transformation and Berreman 4×4 matrix theory, the correlation model between the measured values of Mueller matrix and crystal thickness, Euler angle and dielectric tensor is established, and the fitting effect of the model is evaluated by using the RMSE as the evaluation function. The experimental results show that the fitted Mueller matrix dispersion curves are highly consistent with the measured dispersion curves. The RMSE of the model can be stabilized in a small range (<5) under different sample azimuth angles and incident angles. The thickness obtained by fitting is similar to that measured by micrometer (relative error <1%), and the fitted Euler angle is consistent with the measurement results. The experimental results fully show the accuracy of the fitting results of the established Mueller matrix model, and the thickness, Euler angle and phase retardation of the quartz crystal are successfully obtained. Using this model combined with the dual-rotating compensator Mueller matrix ellipsometer, rich information of the sample can be accurately obtained through simple measurement steps and model fitting, which provides an important reference for accurately measuring the parameters of anisotropic materials.

High-precision CMM (coordinate measuring machine) is a key equipment for product quality control in high-end precision manufacturing fields such as aerospace, shipbuilding, and engineering machinery, and so on. At present, the primary CMM geometric error detection means are some physical reference methods based on laser interferometers, ballbars, and step gauges. However, the above measurement methods are complicated, and the operation is cumbersome and time-consuming. The model of synthetic error has a certain approximation, and the test conditions are not entirely consistent with the working conditions of CMM. The measuring range of laser tracers is less than 20 m, the measuring accuracy can reach 0.2 μm+0.3 μm/m, and the measuring efficiency is close to that of laser tracker. Therefore, the laser tracer is more suitable for the measurement and compensation of CMM and high-grade CNC (computerized numerical control) equipment volume error. In order to solve the problem of slow convergence of Levenberg-Markuardt (L-M) algorithm in the application of laser tracer multi-station measurement, the L-M algorithm based on the strategy of adding trust region radius was proposed to effectively achieve calibration of laser tracing multi-station measurement technology for CMM.

The solution of the laser tracer multi-station measurement system model was divided into two parts: one is the self-calibration of the laser tracer station, the other is to solve the actual coordinates of the planned measurement points within the CMM space. The L-M algorithm which adds trust region radius strategy was used to solve the laser tracer multi-station measurement system model. Based on L-M algorithm, the determination of the trust region was conducted by adding the positive parameters of the search direction, and the optimal iteration direction and iteration step size were determined, making the algorithm can quickly converge to the global domain optimal solution. The process of trust region determination was to first define the quadratic function, and then consider the ratio of the increment of the quadratic function value to the target function value based on the current positive parameters to determine whether the selection of positive parameters is reasonable. When the absolute value of the ratio is large, the positive parameters should be obtained the smaller to increase the modulus length of the search direction. When the absolute value of the ratio is small, the value of the positive parameter should be increased to limit the modulus length of the search direction. The iterative result can be less than the tolerance error of the laser tracer multi-station measurement system by continuously adjusting the positive parameters through the selection rules of trust region radius, realizing global domain convergence to self-calibrate the laser tracer station and obtain the actual coordinates of the planned measurement points within the CMM space.

The built laser tracer multi-station system was shown in Fig. 1. The measurement paths were planned based on laser tracer multi-station measurement methods. The L-M algorithm and the L-M algorithm with trust region radius strategy were used to solve this laser tracer multi-station measurement system model. The experimental results show that the average number of iterations in the self-calibration process of laser tracer station based on L-M algorithm is 1553, and the average number of iterations of the L-M algorithm with trust region radius strategy is 9. The latter algorithm greatly improves the convergence speed. The Val parameter is used to represent the accuracy of the algorithm when solving the actual coordinates of the planned measurement points within the CMM space. The average accuracy of the L-M algorithm is 2.30×10^-7 mm with a standard deviation of 2.78×10^-7 mm, and the average accuracy of the L-M algorithm with trust region radius strategy is 8.75×10^-10 mm with a standard deviation of 7.47×10^-10 mm. It could be seen that the latter algorithm improves the measurement accuracy.

The measurement data were obtained by establishing a laser tracer multi-station measurement system, the nonlinear equations were established based on the spatial distance formula, and the objective function was established through the least square idea. The traditional L-M algorithm is optimized by introducing the trust region radius strategy. By adjusting the positive parameters of the search direction, the trust region determination is determined, so the optimal iteration direction and iteration step size for each iteration are determined. Thus, the algorithm can rapidly converge to the optimal solution in the global domain. And the high-efficiency and high-precision of the volume error measurement of CMM planned measurement points based on the laser tracer multi-station measurement technology can be realized.

The rapid development of cavity optomechanical systems has attracted extensive attention, and these systems are widely used in quantum information and precision measurement. In recent years, three-cavity optomechanical systems have attracted considerable attention. Compared with the single-mode optomechanical system, the multiple-mode system provides significantly higher flexible controllability. Furthermore, optomechanically induced transparency and four-wave mixing have been research hotspots in different optomechanical systems. For example, the four-wave mixing in a hybrid optomechanical system is theoretically investigated, which has important implications for the nonlinear optical properties. It is of great significance for theoretically exploring the transmission spectrum and four-wave mixing in a three-cavity optomechanical system.

The hybrid optomechanical system consists of a microwave cavity a with resonance frequency ωa and an optical cavity c₁ with resonance frequency ωc1, which are coupled to a common mechanical resonator b, while an optical cavity c₂ with resonance frequency ωc2 is coupled to the optical cavity c₁. A strong pump laser beam E_e with frequency Ωe is applied to the microwave cavity a. A weak probe laser beam E_p with frequency Ωp and a strong pump laser beam E_o with frequency Ωo are applied to the optical cavity c₁ simultaneously. In the rotating frame of the pump fields with frequency Ωe and Ωo, the whole Hamiltonian of the system is obtained. According to the Heisenberg equation and making the ansatz, we finally obtain the transmission spectrum and the four-wave mixing spectrum intensity. Then, we investigate how the evolutions of the transmission spectrum and the four-wave mixing spectrum are affected by the coupling strength and the frequency of the mechanical resonator.

When the optical cavity c₂ is absent in the hybrid optomechanical system (J=0), the transmission spectrum of the probe field shows a Lorentzian line shape. However, when J≠0, the Lorentzian peak splits into two symmetrical peaks and a transparent window occurs (Fig.2). It is clear that with the increase in the coupling strength from J=0.5κ_o to J=2κ_o, the distance between the peaks increases, and the peak value of the transmission spectrum of the probe field also increases (Fig.3). We depict the variation of the four-wave mixing spectrum with the detuning of the probe field-cavity field Δp for J=0, 0.5κ_o, κ_o, 2κ_o when ω_m=2π×5.6 MHz. In the case of Δc1=Δc2=Δa=0, when J=0, the four-wave mixing spectrum has three peaks. A Lorentzian peak locates at Δp=0 and two splitting peaks locate on both sides of the Lorentzian peak [Fig.4(a)]. With the choice of J≠0, a significant change in the four-wave mixing spectrum can be observed. The Lorentzian peak splits into two peaks. As the coupling strength J increases, the peak value decreases greatly and the distance between the peaks gradually increases [Figs.4(b)-(d)]. Next, we study how the evolution of the four-wave mixing spectrum is affected by the frequency of the mechanical resonator while the optical cavity c₂ is not in the hybrid optomechanical system (J=0). It can be seen that as the frequency of the mechanical resonator increases, the peak value of the four-wave mixing spectrum gradually decreases. Further, the peaks on both sides of the four-wave mixing spectrum located at ±Δp just correspond to the frequency ω_m of the mechanical resonator (Fig.5). Moreover, we investigate the four wave mixing spectrum as a function of the detuning Δp for the frequencies of mechanical resonator of ω_m=2π×4.6 MHz, ω_m=2π×5.6 MHz, and ω_m=2π×6.6 MHz when J=κ_o. As the frequency of the mechanical resonator increases, the peak value and the distance between the two symmetrical splitting peaks in the middle decrease. The positions of the peaks on both sides exactly correspond to the three different frequencies of the mechanical resonator. The results show that the four-wave mixing can be tuned by the frequency of the mechanical resonator (Fig.6).

We investigate the optomechanically induced transparency and four-wave mixing in a hybrid optomechanical system composed of two optical cavities, a microwave cavity, and a mechanical resonator. When the microwave cavity is driven to the red sideband and the two optical cavities are driven to the blue sideband, the optomechanically induced transparency can be changed by changing the coupling strength between the two optical cavities. Furthermore, the four-wave mixing spectrum can be modulated by controlling the coupling strength between the two optical cavities and by changing the frequency of the mechanical resonator during resonant detuning Δp=0. At the same time, a nonlinear optical method for measuring the frequency of a mechanical resonator is provided. The positions of the peaks on both sides of the four-wave mixing spectrum correspond exactly to the frequency of the mechanical resonator. These results have important significance and application prospects in quantum sensing and quantum information processing.

In the space channel continuous variable quantum key distribution (CVQKD), the quantum coherent state modulation system is more versatile with the classical optical communication equipment, and has better compatibility with the fiber channel. It is one of the future space channel CVQKD network construction schemes. Aiming at the effects of beam expansion, absorption, scattering, and drift of optical quantum signals in turbulent channels, as well as the phase difference jitter between local oscillator light and signal light, we construct a simulation model of CVQKD key rate under turbulent channels. The model focuses on analyzing the influence of turbulent channel parameters, phase delay and detection method on the system key rate. The results show that the total excess noise of the system is positively correlated with the transmission distance, the delay time between the local oscillator light and the signal light, and the intensity of atmospheric turbulence. Heterodyne detection has a higher key rate in short-distance transmission, and homodyne detection can achieve longer transmission distance. The simulation results can provide reference for the design and optimization of actual free-space CVQKD systems.

In the common time division multiplexing CVQKD system, the phase difference jitter between the local oscillator light and the signal light will increase the channel excess noise and reduce the system key rate. In this paper, the effects of turbulent channel parameters, phase delay and detection methods on system noise and key rate are studied by establishing a simulation model of CVQKD under turbulent channels. The principle of the simulation model in this paper includes key rate theory, turbulent channel transmission efficiency theory, interruption probability theory, local light and signal light phase difference jitter theory. Then, the corresponding simulation work is carried out, and the channel excess noise caused by the phase difference jitter between the local oscillator light and the signal light is discussed.

According to the theoretical model and under specific simulation parameters, the following simulations are carried out: the probability distribution of the system transmittance (Fig. 3), the influence of different time delays on the total system noise (Fig. 4), the influence of different turbulence intensities on the total system noise (Fig. 5), and the influence of different turbulence intensities on the system key rate (Fig. 6). It can be seen from Fig. 3 that under the condition of a fixed transmission distance, there is a peak in the transmittance distribution, and the probability density first decreases and then increases with the increase of distance. It can be seen from Figs. 4 and 5 that with the increase of time delay and atmospheric turbulence intensity, the system key rate decreases. It can be seen from Fig. 6 that heterodyne detection has a higher key rate in short-distance transmission, and homodyne detection can achieve longer transmission distance.

Turbulent channel CVQKD has important applications in wide-area quantum communication networks. It is necessary to study the influence of turbulent channel structure parameters on free-space CVQKD system. In order to meet this demand, the CVQKD model of turbulent channel is established in this paper, and the effects of turbulent channel parameters, local oscillation light and signal light delay time and different detection methods on CVQKD system noise and key rate are studied. According to the simulation results, the total excess noise of the system increases slowly and then rapidly with the increase of distance. Increasing the delay time will increase the total noise of the system. The actual CVQKD system needs to select the delay time according to the specific situation. The increase of atmospheric turbulence intensity will increase the total noise of the system, and the phase noise spectral density is positively correlated with the product of signal transmission distance and atmospheric turbulence intensity. The enhancement of atmospheric turbulence will reduce the channel transmittance, increase the system interruption probability and excess noise, and make the system key rate drop rapidly. Heterodyne detection has a high key rate in short-distance transmission, and homodyne detection can achieve longer transmission distance. In the actual system, the receiving antenna size can be appropriately expanded, the delay time between the local oscillation light and the signal light can be optimized, or the adaptive optical system can be used for phase compensation, and the appropriate optical carrier wavelength and detection mode can be selected, so as to improve the key rate or the safe transmission distance of the system. This paper can provide reference for the design and optimization of high performance and practical CVQKD system under turbulent channels.

Accurate measurement of temperature and relative humidity plays an important role in many fields, such as health care, environmental testing, and safety monitoring. Various sensor devices have been developed to meet various needs, but traditional mechanical hygrometers and thermometers, as well as temperature and humidity sensors based on capacitance and resistance, have disadvantages, such as large space occupation and deterioration from aging. Fiber sensors have become a popular research topic because of their small size, light weight, resistance to electromagnetic interference, corrosion resistance, and many other advantages. Researchers have designed optical fiber temperature and humidity sensors that use grating structures, interference structures, and surface plasmon resonance (SPR) effects by combining optical fibers with temperature- and humidity-sensitive materials. The SPR effect has attracted considerable attention because it improves the sensitivity of optical fibers in sensing the change in the refractive index of the surrounding medium. We propose an SPR-based single-mode fiber (SMF) temperature- and humidity-sensing structure. It is made of a single-mode fiber coated with a silver film that partially removes cladding and senses the changes in temperature and relative humidity via a sensitive material, which is on the outer side of the silver.

The coating layer with a length of ~10 mm was first removed from the middle of a single-mode fiber, after which an HF acid solution with a volume fraction of 37.6% was applied dropwise to the surface of the fiber. The cladding was submerged in HF, and corrosion was observed several times with a microscope. The diameter of the cladding was corroded to ~15 μm after 1 h and 20 min. The treated fiber was then fixed on a glass slide and placed in a magnetron sputter coater to plate a silver film with a thickness of 40 nm. At the end of the first silver plating, the fiber-optic sensing structure was flipped to the back side, and silver plating was repeated to ensure uniform coating of the entire fiber-optic sensing structure. In the next step, an appropriate amount of liquid PDMS was applied dropwise to one side of the fiber-sensing structure, and a small amount of PVA solution was applied to the other side of the fiber-sensing structure. Finally, the structure was placed on a drying table at 60 ℃ until it completely solidified and was left to cool to room temperature. The sample drop-coated PVA solution with mass fraction of 1%, 2%, and 3% was recorded as s-1, s-2, s-3, respectively.

The proposed sensing structure has advantages in temperature and humidity sensing. With an increase in temperature and relative humidity, the double-resonance absorption peaks are significantly shifted. The SPR peak has good stability with the change in time, the resonance peak gradually shifts to the short wavelength direction when the temperature increases, and the central wavelength shift is basically linear with the temperature change within 20-70 ℃ (Fig.6). Owing to the hydrophobicity of PDMS, its refractive index is barely affected by relative humidity; therefore, the material has a weak cross-sensitivity (Fig.7). In the humidity test, samples s-1, s-2, and s-3 produce resonance peaks at different central wavelengths (Fig.9). The resonance peak of sample s-2 at a certain relative humidity was selected as the measurement sample, and the shift in the resonance peak was recorded under a change in temperature from 20 to 90 ℃ (Fig.10). It can be observed from the figure that the wavelength of the center of the resonance peak shifts to the left as the temperature increases.

In this study, a temperature and humidity sensor based on SPR is designed. The outer side of the fiber, with part of the cladding removed, was coated with a nano-silver film. This method excites the cladding modes of the fiber core light with silver to produce an SPR effect. Then, temperature- and humidity-sensitive materials were coated on silver film to achieve a highly sensitive measurement of temperature and relative humidity. The experimental results show that the central wavelength of the humidity resonance peak is blue-shifted as the thickness of PVA decreases. When the relative humidity varies in the range of 30%-78%, the average sensitivity of the sensing structure with 2% (mass fraction) PVA solution drop-coated reaches -4.36 nm/%. When the temperature varies in the range of 20-70 ℃, the average sensitivity of the sensor reaches -2.01 nm/℃, and the linearity reaches 99.5%. The temperature and humidity cross-sensitivity tests demonstrate that PDMS is barely affected by changes in relative humidity, whereas PVA undergoes smaller refractive index changes under temperature changes. The temperature and humidity sensor proposed in this study has the characteristics of high sensitivity, wide range, good stability, and low cross-sensitivity and can be applied to the field of temperature and humidity sensing.

Atmospheric lidar has been widely used in horizontal scanning measurements for air pollution monitoring in recent years. The determination of the boundary value of the aerosol extinction coefficient (AEC) and the retrieval of the AEC profile are the key issues for quantitative atmospheric applications. In this work, a new method based on an improved Douglas-Peucker (DP) algorithm is proposed to find the linear region in the logarithmic lidar curve, from which the boundary value of the AEC is estimated. Combined with the classical Klett method, the AEC profile can be obtained in horizontal scanning measurements. The feasibility and performance of the improved DP algorithm has been validated through comparison studies of the AEC scanning map.

The experimental data evaluated in this work were obtained by a scanning Scheimpflug lidar (SLidar) system installed in Xianyang City, Shaanxi Province (Fig. 1), employing high power laser diodes as light sources and area image sensors as detectors. The elevation angle of the SLidar system during horizontal scanning measurements is about 3°. The scanning period is about 20 min with a rotation step of 2°. The DP algorithm has been proposed to automatically search linear regions in the logarithmic lidar signal. The DP algorithm decimates the original logarithmic lidar curve to a similar curve with fewer points through an iterative end-point fit algorithm. Besides, the variance of the distance between the logarithmic lidar signal and the corresponding line segment is used as the threshold to replace the farthest/maximum distance threshold in the classical DP algorithm, which can be used to obtain the linear region of the logarithmic lidar curve more accurately. The slope method is then employed for the determination of the AEC boundary value in the linear region, where the atmosphere is considered to be homogeneous. With the boundary value of the AEC as the input, the AEC profile can be obtained in horizontal scanning measurements according to the Klett method. Long enough linear regions (>3500 m) with an R² correlation coefficient beyond 0.9999 are selected as reference signals, from which the AEC profile can be reliably obtained. By comparing with the AEC profile retrieved from the reference signal, the performances of the classical DP algorithm and the improved DP algorithm are evaluated.

It has been found out that the maximum distance threshold used in classical DP algorithm cannot be well adapted to different atmospheric conditions. On the other hand, the variance of the distance between the logarithmic lidar signal and the corresponding line segment, considering the deviations of all data points in the potential linear region, is more reliable for evaluating the linearity of the logarithmic lidar signal segment. According to comprehensive comparison studies, the variance threshold can be set to 1×10^-4 to obtain the optimum result under various atmospheric conditions. The improved DP algorithm based on the variance threshold is then utilized to retrieve the boundary value of AEC from lidar signals. Finally, the AEC map can be obtained according to the Klett method (Fig. 14). It can be seen that the AEC retrieved by the classical DP algorithm (Fig. 7) is prone to sudden changes due to the influence of signal fluctuations. The improved DP algorithm can effectively avoid the influence of signal fluctuations, and the retrieved AEC result is more robust. To further verify the feasibility and accuracy of this method, statistical analysis on a one-week measurement is carried out. It can be seen from Fig. 15 that the AEC retrieved by the SLidar system and the proposed algorithm is in good agreement with the PM₁₀ concentration reported by a nearby monitoring station with a correlation coefficient of 0.88. Figure 16 shows the relationship between PM₁₀ concentration and aerosol extinction coefficient under different humidity conditions, implying that relative humidity also has a large impact on the relationship between AEC and the mass concentration of dry particles.

In this work, an improved DP algorithm based on a variance threshold is proposed for automatically searching linear region in the logarithmic lidar signal. The slope method is employed for the determination of the boundary value in a subinterval linear region, where the atmosphere is homogeneous. The AEC profile is then retrieved by the Klett method. The feasibility and performance of the classical and the improved DP algorithms are validated through detailed AEC comparison studies. It has been found that the retrieved AEC based on the improved DP algorithm is in good agreement with the PM₁₀ concentration reported by a nearby air pollution monitoring station for a continuous measurement campaign. The promising results demonstrate that the improved DP algorithm can provide an effective approach for determining the boundary value in horizontal scanning lidar measurements.

Infrared remote sensing is widely used for Earth and Ocean observations. With the development of optical technology, infrared detection systems are developing toward higher resolution, hyperspectrum, and higher sensitivity. With the increasing scale of the detector array, the working wavelength also covers long waves. To ensure working performance, an infrared Dewar module must be more strictly designed to suppress stray radiation. On the one hand, to suppress stray radiation, the Dewar window adopts low-temperature optical technology. On the other hand, the Dewar window weight increases with array size, suggesting higher requirements for the supporting strength and heat insulation of the shell. In addition, the Dewar module goes through three working states, from assembly to application, and the window deformations in these three working states are different, affecting the design of the infrared optical system.

The temperature field of the large-aperture infrared and long-wave Dewar window was analyzed by finite element analysis and verified by experiments. The influence of the temperature of the Dewar window on the stray light and heat radiation of the cold screen was clarified. To reduce heat leakage between the low-temperature window and the flange surface, the strength and heat insulation performance of the three types of shell support materials were compared. The effects of force, heat, and force-heat coupling on the design parameters of the Dewar window, such as the thickness and aperture margin, were analyzed. The deformation of the Dewar window was fitted using a Zernike polynomial, and the modulation transfer function (MTF) and wave aberration were used as evaluation indices to control window deformation of the large-aperture long-wave infrared Dewar module. Subsequently, the influence of Dewar window deformation on the imaging quality of the infrared camera system under three conditions was analyzed.

When the window temperature decreases to 200 K, the window stray light and cold screen radiation are well suppressed (Fig. 3). When the target temperature is 220 K, the window radiation spurious ratio is less than 10%, satisfying the design requirements (Fig. 2). To reduce the heat leakage caused by the low-temperature window and ensure reliable use, a titanium alloy shell with higher strength and lower heat conductivity is adopted. Under the same temperature difference (300-250 K), the heat conduction of the titanium alloy shell is 278 mW; this is 49% and 43% lower than those of Kovar alloy (4J29) and stainless steel (304L), respectively (Fig. 4, Table 2). In mechanical-heat coupling, the window deformation caused by the heat load is dominant (Figs. 5 and 7), and increasing the window aperture is helpful to improve the window surface shape under mechanical-heat coupling (Fig. 8). When the thickness and aperture of the window are 4 mm and 8 mm, respectively, the influence of window deformation on the imaging quality can be neglected under the three conditions (Tables 4 and 5).

The application of a large-aperture long-wave Dewar window is studied, and the operating temperature of the window is determined according to the design requirements for stray light in engineering projects. Combined with the working temperature of the window, the deformation under the coupling of force and heat is analyzed, and the window design is optimized. Combined with the optical imaging design, the MTF and wave aberration are analyzed, and the influence of Dewar window deformation on the detector imaging quality under the three conditions is confirmed. This study provides a reference for optical system optimization and heat control-related designs.

The filamentation process of ultra-intense femtosecond lasers in the atmosphere is accompanied by significant nonlinear optical effects such as self-focusing, self-steepening, and plasma defocusing. This is essential for studying lidar, new light sources, artificial rainfall, air pollution detection, and laser remote sensing. When the femtosecond laser pulse is propagated into the atmosphere, a random multifilament phenomenon occurs owing to air refractive index perturbation caused by atmospheric turbulence and the initial inhomogeneous energy distribution of the femtosecond laser. This affects the energy distribution of the filament, shortens the propagation distance of the filament, and reduces the spot quality of the beam, therefore limits the practical application of the filament. This review summarizes local and international research progress on multifilaments in the past two decades. A series of multifilament control methods are reviewed, including the introduction of the elliptical rate of the incident beam, variation of the laser field gradient, modulation of the laser phase, and introduction of image dispersion to establish a reference for the study of multifilament regulation in femtosecond lasers.

With continuous advancements in laser technology, the peak intensity of femtosecond laser pulse obtained in laboratory tests has far exceeded the relativistic threshold (10¹⁸ W/cm²) and even reaches 10²³ W/cm², which significantly reduces the difficulty of femtosecond laser atmospheric filamentation. This serves as a foundation for experimental research and the practical application of the filament. Researchers have found that the multifilament phenomenon is mainly caused by the perturbation of the refractive index of air and the initial uneven energy distribution of the femtosecond laser. Further studies have also shown that during the formation of femtosecond laser filaments, only a small portion of the laser energy is concentrated in the filament, and most of the laser energy is stored around the filaments as background energy, which is often called the background energy reservoir. In this regard, Mlejnek et al. proposed the theory of dynamic energy compensation for optical filament propagation. It is believed that an energy reservoir with a low light intensity concentrated around the optical filament provides energy for the propagation of the laser filament, and the interaction between background energy reservoirs can sustain the filament. This theory was experimentally confirmed in 2005. Liu et al. interrupted the transmission of background energy by shielding the filament's outer ring, immediately stopping the filament's propagation. In subsequent simulation studies, they found that the required background energy must be at least 50% higher than the total energy required to sustain the self-guided propagation of the filament. The main reasons for the multifilament phenomenon are atmospheric turbulence caused disturbance of air refractive index and the uneven distribution of the initial energy of the femtosecond laser. To effectively control the generation of a stable multifilament structure, researchers have proposed several methods; these methods include introducing ellipticity in the incident beam, changing the laser field intensity gradient (Fig. 1, Fig. 2), introducing astigmatism (Fig. 3), modulating the wavefront phase (Fig. 4), introducing axicon, introducing optical anisotropy of the introduced species (Fig. 5), and using polarization axis symmetry breaking (Fig. 6). These methods reduce and even eliminate the effect of random perturbations on femtosecond filament transmission by modulating the initial energy distribution of the femtosecond laser or the perturbation of the air refractive index cause by atmospheric turbulence, thereby achieving experimentally reproducible femtosecond laser transmission processes. In addition, by increasing the distance between the background energy reservoirs of the filaments and reducing the mutual interference between the energy pools, a multifilament structure with stable transmission can also be produced. Another method to control the orderly spatial distribution of femtosecond multifilaments involves inhibiting the generation of multifilaments, that is, turning the multifilaments into single filaments during laser transmission. Similar to regulating multifilaments, inhibiting multifilament production can also produce controllable filaments. One of the main ways of suppressing the generation of multifilaments is by making the initial light intensity distribution of the laser pulse as smooth as possible, thus reducing the influence of the initial uneven distribution of light intensity and preventing the generation of multiple"hot spots". Another method is to reduce the distance between "hot spots", causing the energy pools of each "hot spot" to overlap with each other so that the multifilaments are fused into a single filament. Based on these two techniques, researchers have proposed the use of telescopic systems for beam reduction (Fig. 7), the introduction of astigmatism, the use of spatial light modulators or phase templates (Fig. 8), and the use of iris diaphragms and axicons to control multifilaments.

The formation process of femtosecond laser filaments is accompanied by rich optical effects such as fluorescence radiation, pulse self-compression, and supercontinuum generation. It has important application prospects in atmospheric pollution detection, new light sources, laser triggering, and terahertz radiation sources. Moreover, the study of femtosecond laser filamentation processes also benefits the development of the optics theory. Random multifilaments limit the practical applications of laser filamentation; hence, the significance of regulating multifilaments is to expand the practical applications of femtosecond lasers. Existing regulation methods for the multifilament phenomenon focus on generating controllable and stable structures and inhibiting multifilament production. Various research methods can be used to eliminate the randomness of multifilaments when the femtosecond laser is propagated to a certain extent in the atmosphere. However, there are still certain problems in multifilament control such as a low distribution control accuracy and shortened laser transmission distance due to laser energy loss. Therefore, the regulation of multifilaments needs to be studied further before it can be widely applied to various fields.

Laser heterodyne spectrum measurement technology has the characteristics of high spectral resolution, high detection sensitivity and short sampling time. This technology can not only obtain the high-resolution spectral information of the whole layer of atmospheric molecules, but also facilitate the observation of gas concentration in different scenarios due to its small size and easy integration. Therefore, it has been widely concerned by researchers. At present, domestic research on laser heterodyne spectrum measurement system mainly focuses on solar tracking, spectral resolution and inversion algorithm. Due to the low power of the detection signal received by the heterodyne system, the signal-to-noise ratio (SNR) of the heterodyne system is low in actual operation. Therefore, based on the principle of Kepler telescope, a set of sunlight beam shaping structure is designed to improve the sunlight power, and the system SNR is improved by matching the size of the two beams.

In this paper, a 3.93 μm distributed feedback interband cascade laser (DFB-ICL) is used as the local oscillator light source to build a laser heterodyne spectrum measurement system, and sunlight is used as the signal light. The coupling of sunlight and laser is designed and simulated by Zemax optical simulation software. In the experiment, considering the distance between the shaping lens and the photosensitive surface of the detector, the coupling efficiency and the performance of the detector, the incident sunlight diameter is set to 4.5 mm, the plane-convex lens 1 with a focal length of 750 mm and the plane-convex lens 2 with a focal length of 500 mm are selected to form the Kepler telescope structure for shaping the sunlight. The absorption spectrum of N₂O in the range of 2542.9-2545.0 cm^-1 is measured by studying the beam reduction rule of the sunlight and the SNR of the system. The optimal estimation method is used to inverse the measured spectra, and the N₂O column concentration is obtained. Finally, the inversion results of the laser heterodyne spectrum measurement system and the commercial Fourier transform spectrometer are compared and analyzed.

After the laser is emitted from the collimator, the spot diameter is 3.0 mm. Zemax simulation software is used to simulate the structure for sunlight beam reduction. After the simulation and optimization of Kepler telescope structure, the input parameters are as follows: the distance between the two lenses is 1320.155 mm, and the radius of sunlight after 1.5 times beam reduction is 1499.76 μm (Fig. 7). These meet the required spot size requirements. The diameter of the sunlight spot before beam shaping is 4.5 mm, and the SNR of the system is 80.6 when compared with the laser beat frequency result of 3.0 mm diameter sunlight spot. In this case, the size of the two spots can be matched while improving the sunlight power. The optical power of the two beams at the beat frequency is fully utilized, and the heterodyne coupling efficiency is the best. Therefore, the SNR of the system can reach the highest, which is 162.1 [Fig. 9(a)]. According to the best SNRs of the system with the diameter of 2.2, 2.5, 3.0, 3.4 and 4.1 mm after the sunlight beam is reduced through the lenses, the more matched the diameters of the two facula, the higher the SNR of the system (Fig. 8). The N₂O absorption spectrum in the range of 2542.9-2545.0 cm^-1 was measured before and after the beam shaping structure was added. There are two N₂O absorption spectral lines in this band [Fig. 9(b)]. The measurement results show that the amplitude of the spectral signal after beam shaping is significantly improved when only the size of the sunlight spot is changed, which can provide more accurate spectral data for the subsequent inversion of N₂O concentration profile and column concentration.

Comparing the measured spectrum with the inversion fitting spectrum, the residual error of the two curves is within ±0.08 V (Fig. 10). The N₂O column concentration results obtained by the laser heterodyne spectrum measurement system are compared with the measured results of commercial Fourier transform spectrometer EM27/SUN. The variation trend of N₂O concentration measured by the two methods is relatively consistent, and the measurement results obtained using the two methods show a correlation coefficient of 0.856 (Fig. 12).

In this paper, a set of high-resolution laser heterodyne system is built with a 3.93 μm laser as the local oscillator light source, the sunlight is taken as the signal light, and the Kepler telescope structure and Zemax optical simulation software are used to shape the sunlight, so that the size and focus angle of the light spot incident on the photosensitive surface of the detector are smaller than the effective receiving area and field of view of the detector, respectively. The beam reduction of the sunlight in the free space and the size matching of the two spots on the photosensitive surface are realized. The experimental results show that the single-pass SNR of the system is up to 162.1 after the sunlight is shaped and matched with the laser beam, which is twice as high as that of the system without beam shaping. At the same time, the absorption spectrum of N₂O was measured, the optimal estimation method was used to realize the inversion of N₂O column concentration, and the inversion results were compared with those measured by the Fourier transform spectrometer EM27/SUN. The variation trend of N₂O column concentration obtained by the two methods is relatively consistent, and the measurement results obtained using the two methods show a correlation coefficient of 0.856. Through the research on the 3.93 μm laser heterodyne spectrum measurement system, the main factors affecting the SNR of the heterodyne optical path are grasped. The follow-up research will be carried out on the system signal processing and instrument linear function optimization to further improve the SNR and provide favorable conditions for the subsequent high-sensitivity detection of greenhouse gases in the atmosphere.

There are significant differences in the actual optical characteristics of specific targets in different spectral bands. Thus, the two imaging systems shared an aperture for detection and identification. The internal light was separately imaged after passing through an optical device that separated the visible near-infrared and infrared light. In this way, the light from the two bands could be used to synchronously detect and image the target, allowing it to track the target more effectively. Thus, it could meet the all-day, wide-range, and high-resolution detection requirements. There have been few research reports on visible near-infrared and mid-infrared dual-band large-angle spectroscopy. Therefore, this research has an important reference value for dual-band infrared detection and imaging technology.

The width and reflectance of the cut-off band at large angles were studied using the evaporation coating method. After practical calculation, it was concluded that at least four groups of film stacks should be used as the initial film system. A spectral curve that met the requirements could be obtained based on this optimization of the initial film system. The stress of ZnS film is generally compressive, while the stress of YbF₃ film is generally tensile. The control variable method was used to optimize the deposition process and adjust the corresponding thickness to change the stress of the ZnS and YbF₃ single-layer films. Because the film system was formed by depositing alternate layers of high and low refractive index materials, the tensile stress and compressive stress could offset each other. Therefore, the deformation of the substrate was smaller when the single-layer stresses of the high and low refractive index materials with corresponding thicknesses were closer. The film system structure was analyzed based on the measured stress results, which showed that the two sides of the film could offset each other and tended to be smaller in the design.

Based on a study of the characteristics of the high and low refractive index materials, the deposition process parameters of the film material (Table 2) were selected as the auxiliary parameters of the ion source (Table 3). Before coating, a constant temperature was 1 h. Thereafter, the ion source was used to clean the substrate for 15 min. A constant temperature of 200 ℃ was maintained for 2 h after coating, then the temperature was naturally cool to 90 ℃ for venting. The stress changes before and after coating are listed in Table 4. It can be seen from the analysis of the parameters before and after the process adjustment that the stress of the single-layer ZnS did not match that of the single-layer YbF₃. The ZnS and YbF₃ deposition rates and auxiliary process parameters of the ion source were adjusted. The ZnS deposition rate was adjusted from 2 nm/s to 1.5 nm/s, and the deposition parameters of the YbF₃ ion source was adjusted from 200 V and 5 A to 220 V and 5 A. After adjusting the process parameters, the stress of the single-layer ZnS was close to that of the single-layer YbF₃ (Table 4). The antireflective film coated on the reverse side presented a tensile stress state, which could compensate for the stress on the spectral surface. The antireflective film coated on the reverse side met the requirements (Fig. 6). The spectrum of the deposited film was obtained and analyzed (Fig. 7), and the spectral data were imported into the film system design software for fitting. It was found that the actual thickness of the ZnS was 1.08 times the design thickness, and the actual thickness of the YbF₃ was 0.95 times the design thickness. After adjusting the film thickness ratio, the transmission spectrum curve of the spectral surface after deposition (Fig. 8) showed that the overall spectrum was well fitted with the design without obvious deviation (transmittance of 3.7-4.8 μm under the condition of the single-sided coating). The theoretical average transmittance in the band of 3.7-4.8 nm was 79.5%, and the average measured transmittance was 77%. The measured spectrum was fitted, and the fitting results showed that the spectral performance was not caused by the mismatch of the film thickness. After analysis, it was found that the addition of ion source-assisted deposition in the adjustment of the stress matching resulted in an increase in the absorption of the ZnS and YbF₃ films but still met the technical specifications.

In this study, the temperature, deposition method, and ion source parameters were adjusted using the control variable method. The film stress was calculated using the Stoney formula. Then, the stresses of specific-thickness single-layer ZnS and YbF₃ were adjusted to make these stresses match. When the stress of the antiantireflection surface was used to compensate for the stress of the spectral surface, the surface accuracy (PV value) of the spectral surface decreased from 0.63λ to 0.182λ. Then, the problem of the poor surface shape of the spectroscope could be solved. Based on a reverse analysis of the film deposition results, the film thickness was adjusted to improve the reflectivity and transmittance at an incidence of 55°. In the 0.6-0.9 μm wave band, the average reflectivity was 90.77%. In the 3.7-4.8 μm wave band, the average transmittance was 91.15%. The prepared film basically met the use requirements of the system components.