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COHERENCE OPTICS AND STATISTICAL OPTICS|8 Article(s)
Phase Unwrapping Based on Large Dynamic Range Synthetic Wavelength for Phase-Sensitive SD-OCT
Zeguo Song, Yi Wang, Yijie Wang, and Zhenhe Ma
ObjectiveIn conventional spectral domain optical coherence tomography (SD-OCT), depth information is calculated by fast Fourier transform (FFT) to bring an axial resolution typically within the range of 10 μm. Sub-micrometer resolution is achieved by employing broadband light sources. Phase-sensitive SD-OCT (PSSD-OCT) provides nanometer-level precision and can be employed for film thickness measurement, displacement sensing, optical fiber Fabry-Perot sensors, quantitative phase microscopy, and surface profile imaging. Phase wrapping is an inherent issue in optical interference techniques, and various phase unwrapping algorithms have been proposed to enhance the dynamic range. The current approaches are typically to first calculate a low-precision solution by frequency estimation methods, followed by determining the phase cycle number. However, the frequency estimation methods are highly susceptible to noise, which makes them suitable only for interference spectra with high signal-to-noise ratio (SNR). Synthetic wavelength methods are widely adopted for expanding the phase dynamic range. Since the synthetic wavelength is much larger than the wavelength of the light source, it can increase the dynamic range to the synthetic wavelength size. However, when the measurement range exceeds the synthetic wavelength, phase wrapping still occurs. To improve the dynamic range of existing synthetic wavelength methods, we propose a high dynamic range synthetic wavelength (HDR-SW) phase unwrapping method. This method eliminates the phase wrapping limitation and achieves a dynamic range of millimeters. Finally, a method is provided for displacement measurements with a large dynamic range, high sensitivity, and high speed.MethodsThe experimental system mainly consists of a fiber Michelson interferometer, a SLD light source, and a spectrometer. Light from the SLD is directed into a fiber circulator. Then, it is split into reference and sample beams by a beam splitter. The beams reflected from the sample and reference arms enter a spectrometer. The spectrometer has a spectral width of 30 nm and a spectral resolution of 0.0146 nm. Both the reference and sample arms are in free space, and achromatic lenses are utilized to eliminate the dispersion mismatch between the two arms.Firstly, the synthetic phase is calculated by splitting the interference spectrum into two sub-spectra. Then, the correct integer number of phase cycles is computed from the full-length spectrum and the half-length spectrum located in the middle of the spectrometer. The method combines the demodulation results of the interference spectra with full-length and half-length to eliminate the ±1 phase cycle jump that is easily affected by noise.Results and DiscussionsThe experimental results demonstrate that the HDR-SW method enables high-sensitivity phase demodulation for a large dynamic range. Compared with the linear regression method, the HDR-SW method has higher anti-noise ability and higher precision [Fig. 2(f)-(i)]. The linear regression method conducts phase unwrapping by comparing the phase differences between adjacent points. For the case of low SNR, phase unwrapping may result in a 2π error and consequently a larger linear fitting error. In contrast, the proposed method directly calculates the unknown phase cycles. By combining the results of the spectra with full-length and half-length, the phase cycle jump can be corrected. However, when the error in the low-precision solution exceeds λc/2 with λc of the central wavelength, Eq. (7) introduces an error of λc in the high-precision solution.Conventional SD-OCT is frequently employed for conducting imaging on multi-layer samples using FFT for optical path demodulation. Due to the inherent frequency resolution limitations of FFT, the results of the FFT method show lower precision [Fig. 4(b) and (c)]. When the proposed method is applied to multi-layer samples, it also suffers from frequency resolution limitations. The interlayer spacing must be greater than π/Δk, and the interference spectra must be separated by filtering. The theoretical sensitivity of PSSD-OCT primarily depends on the phase sensitivity. In the case of a common-path configuration, the sensitivity of this experimental system reaches the nanometer level. In the non-common-path configuration, due to the influence of environmental vibrations, the sensitivity reduces to tens of nanometers.ConclusionsPhase wrapping is an inherent issue in optical interference techniques to cause a limited dynamic range in PSSD-OCT. A large dynamic range synthetic wavelength-based phase unwrapping method is proposed to improve the dynamic range in the traditional synthetic wavelength methods. By selecting the full-length interference spectrum and the half-length interference spectrum located in the middle of the spectrometer, the correct integer number of phase cycles is computed. The method combines the demodulation results of the interference spectra with full-length and half-length to eliminate the phase cycle jump that is easily affected by noise. Imaging experiments using a step calibration block, a coin, and a circuit board demonstrate that this method enables high-sensitivity displacement demodulation with a large dynamic range (millimeter-scale). ObjectiveIn conventional spectral domain optical coherence tomography (SD-OCT), depth information is calculated by fast Fourier transform (FFT) to bring an axial resolution typically within the range of 10 μm. Sub-micrometer resolution is achieved by employing broadband light sources. Phase-sensitive SD-OCT (PSSD-OCT) provides nanometer-level precision and can be employed for film thickness measurement, displacement sensing, optical fiber Fabry-Perot sensors, quantitative phase microscopy, and surface profile imaging. Phase wrapping is an inherent issue in optical interference techniques, and various phase unwrapping algorithms have been proposed to enhance the dynamic range. The current approaches are typically to first calculate a low-precision solution by frequency estimation methods, followed by determining the phase cycle number. However, the frequency estimation methods are highly susceptible to noise, which makes them suitable only for interference spectra with high signal-to-noise ratio (SNR). Synthetic wavelength methods are widely adopted for expanding the phase dynamic range. Since the synthetic wavelength is much larger than the wavelength of the light source, it can increase the dynamic range to the synthetic wavelength size. However, when the measurement range exceeds the synthetic wavelength, phase wrapping still occurs. To improve the dynamic range of existing synthetic wavelength methods, we propose a high dynamic range synthetic wavelength (HDR-SW) phase unwrapping method. This method eliminates the phase wrapping limitation and achieves a dynamic range of millimeters. Finally, a method is provided for displacement measurements with a large dynamic range, high sensitivity, and high speed.MethodsThe experimental system mainly consists of a fiber Michelson interferometer, a SLD light source, and a spectrometer. Light from the SLD is directed into a fiber circulator. Then, it is split into reference and sample beams by a beam splitter. The beams reflected from the sample and reference arms enter a spectrometer. The spectrometer has a spectral width of 30 nm and a spectral resolution of 0.0146 nm. Both the reference and sample arms are in free space, and achromatic lenses are utilized to eliminate the dispersion mismatch between the two arms.Firstly, the synthetic phase is calculated by splitting the interference spectrum into two sub-spectra. Then, the correct integer number of phase cycles is computed from the full-length spectrum and the half-length spectrum located in the middle of the spectrometer. The method combines the demodulation results of the interference spectra with full-length and half-length to eliminate the ±1 phase cycle jump that is easily affected by noise.Results and DiscussionsThe experimental results demonstrate that the HDR-SW method enables high-sensitivity phase demodulation for a large dynamic range. Compared with the linear regression method, the HDR-SW method has higher anti-noise ability and higher precision [Fig. 2(f)-(i)]. The linear regression method conducts phase unwrapping by comparing the phase differences between adjacent points. For the case of low SNR, phase unwrapping may result in a 2π error and consequently a larger linear fitting error. In contrast, the proposed method directly calculates the unknown phase cycles. By combining the results of the spectra with full-length and half-length, the phase cycle jump can be corrected. However, when the error in the low-precision solution exceeds λc/2 with λc of the central wavelength, Eq. (7) introduces an error of λc in the high-precision solution.Conventional SD-OCT is frequently employed for conducting imaging on multi-layer samples using FFT for optical path demodulation. Due to the inherent frequency resolution limitations of FFT, the results of the FFT method show lower precision [Fig. 4(b) and (c)]. When the proposed method is applied to multi-layer samples, it also suffers from frequency resolution limitations. The interlayer spacing must be greater than π/Δk, and the interference spectra must be separated by filtering. The theoretical sensitivity of PSSD-OCT primarily depends on the phase sensitivity. In the case of a common-path configuration, the sensitivity of this experimental system reaches the nanometer level. In the non-common-path configuration, due to the influence of environmental vibrations, the sensitivity reduces to tens of nanometers.ConclusionsPhase wrapping is an inherent issue in optical interference techniques to cause a limited dynamic range in PSSD-OCT. A large dynamic range synthetic wavelength-based phase unwrapping method is proposed to improve the dynamic range in the traditional synthetic wavelength methods. By selecting the full-length interference spectrum and the half-length interference spectrum located in the middle of the spectrometer, the correct integer number of phase cycles is computed. The method combines the demodulation results of the interference spectra with full-length and half-length to eliminate the phase cycle jump that is easily affected by noise. Imaging experiments using a step calibration block, a coin, and a circuit board demonstrate that this method enables high-sensitivity displacement demodulation with a large dynamic range (millimeter-scale).
Acta Optica Sinica
- Publication Date: Feb. 10, 2024
- Vol. 44, Issue 3, 0303001 (2024)
Design and Experimental Verification of Coded Synthetic Aperture Lidar System Based on Optical Phase-Locked Loop
Fuping Fang, Heng Hu, Pengpeng Yan, Zhaoyang Li, Yinhuan Lü, Weiming Xu, and Rong Shu
Synthetic aperture lidar has the advantage that the imaging resolution is independent of the detection distance. Compared with microwave, laser has a wavelength at least 3 orders of magnitude smaller. Thus, synthetic aperture lidar can achieve imaging with a higher resolution. However, due to the shorter wavelength, it is also more vulnerable to the phase error introduced by the system itself, which results in imaging blur. To eliminate the influence of this error on imaging, the paper adopts an optical phase-locked loop (OPLL) technology to suppress the random phase noise of the coded synthetic aperture lidar system. At the transmitting end, the laser signal is modulated by an electro-optic modulator driven by the coded signal for detecting the target. At the receiving end, the received echo signal and the local oscillation light are subjected to orthogonal demodulation. The proposed coded synthetic aperture lidar based on OPLL works at the 1550 nm band. Its modulation bandwidth is 1.25 GHz, and the pulse repetition frequency is up to 1.2 MHz/s. The experimental results show that the random phase fluctuation of the system is greater than 100 rad without OPLL. In the presence of OPLL, the phase fluctuation of the internal system is smaller than 0.1 rad. To sum up, the OPLL technology greatly improves the phase stability of the system and the synthetic imaging accuracy in the azimuth direction. Synthetic aperture lidar has the advantage that the imaging resolution is independent of the detection distance. Compared with microwave, laser has a wavelength at least 3 orders of magnitude smaller. Thus, synthetic aperture lidar can achieve imaging with a higher resolution. However, due to the shorter wavelength, it is also more vulnerable to the phase error introduced by the system itself, which results in imaging blur. To eliminate the influence of this error on imaging, the paper adopts an optical phase-locked loop (OPLL) technology to suppress the random phase noise of the coded synthetic aperture lidar system. At the transmitting end, the laser signal is modulated by an electro-optic modulator driven by the coded signal for detecting the target. At the receiving end, the received echo signal and the local oscillation light are subjected to orthogonal demodulation. The proposed coded synthetic aperture lidar based on OPLL works at the 1550 nm band. Its modulation bandwidth is 1.25 GHz, and the pulse repetition frequency is up to 1.2 MHz/s. The experimental results show that the random phase fluctuation of the system is greater than 100 rad without OPLL. In the presence of OPLL, the phase fluctuation of the internal system is smaller than 0.1 rad. To sum up, the OPLL technology greatly improves the phase stability of the system and the synthetic imaging accuracy in the azimuth direction.
Acta Optica Sinica
- Publication Date: Mar. 07, 2022
- Vol. 42, Issue 6, 0603001 (2022)
Detection Technology of H2S and CO2 Based on Fiber Amplifier Enhanced Photoacoustic Spectroscopy
Fengxiang Ma, Yu Tian, Ke Chen, Bo Zhang, Chenxi Li, Guangyin Zhang, Min Guo, Beilei Yang, and Yue Zhao
High-concentration CO2 has a great impact on the accuracy of H2S detection. Thus, this paper proposed a H2S and CO2 detection system based on fiber amplifier enhanced photoacoustic spectroscopy. A single distributed feedback (DFB) laser in series with a high-power erbium-doped fiber amplifier (EDFA) was taken as the photoacoustic excitation source for the high-precision detection of H2S and CO2 simultaneously. In addition, we analyzed the interference of CO2 on H2S detection at the selected H2S absorption line and corrected the measured H2S concentration with the detected CO2 concentration. The results show that the deviation of the corrected H2S concentration remains within -5% to 5%. Moreover, we used Allan variance analysis to calculate the detection limit of the system. When the integral time is 1 s, the detection limits to H2S and CO2 are 656.3×10 -9 and 25.2×10 -6, respectively; when the time is 100 s, the detection limits can reach 61×10 -9 and 2.6×10 -6, respectively. For trace H2S detection, the normalized noise equivalent absorption (NNEA) coefficient is calculated to be 5.5×10 -9 cm -1·W·Hz -1/2. In conclusion, the proposed system has high detection accuracy and good stability. High-concentration CO2 has a great impact on the accuracy of H2S detection. Thus, this paper proposed a H2S and CO2 detection system based on fiber amplifier enhanced photoacoustic spectroscopy. A single distributed feedback (DFB) laser in series with a high-power erbium-doped fiber amplifier (EDFA) was taken as the photoacoustic excitation source for the high-precision detection of H2S and CO2 simultaneously. In addition, we analyzed the interference of CO2 on H2S detection at the selected H2S absorption line and corrected the measured H2S concentration with the detected CO2 concentration. The results show that the deviation of the corrected H2S concentration remains within -5% to 5%. Moreover, we used Allan variance analysis to calculate the detection limit of the system. When the integral time is 1 s, the detection limits to H2S and CO2 are 656.3×10 -9 and 25.2×10 -6, respectively; when the time is 100 s, the detection limits can reach 61×10 -9 and 2.6×10 -6, respectively. For trace H2S detection, the normalized noise equivalent absorption (NNEA) coefficient is calculated to be 5.5×10 -9 cm -1·W·Hz -1/2. In conclusion, the proposed system has high detection accuracy and good stability.
Acta Optica Sinica
- Publication Date: Apr. 11, 2021
- Vol. 41, Issue 7, 0703002 (2021)
Analysis of Influences of Micro-Rough Surface Parameters on Laser Speckle Field
Weike Gao, Xiaoping Du, Yang Wang, and Buyi Yang
In order to analyze the influences of rough surface parameters on the statistical characteristics of laser speckles, it is necessary to study the mapping relationship between laser speckles and target materials. Random rough surfaces with different combinations of root-mean-square roughness, correlation length, skewness, and kurtosis are simulated by computer, and the laser speckle patterns generated by these random surfaces are analyzed and processed based on the theoretical model of the laser speckle field. The results show that various surface characteristic parameters will affect the statistical characteristics of the laser speckle field, and the laser speckle fields formed under different combinations of surface parameters show great specificity. Therefore, the statistical characteristics of laser speckles studied in this paper may be used as effective information to distinguish the surface of materials in the future. In order to analyze the influences of rough surface parameters on the statistical characteristics of laser speckles, it is necessary to study the mapping relationship between laser speckles and target materials. Random rough surfaces with different combinations of root-mean-square roughness, correlation length, skewness, and kurtosis are simulated by computer, and the laser speckle patterns generated by these random surfaces are analyzed and processed based on the theoretical model of the laser speckle field. The results show that various surface characteristic parameters will affect the statistical characteristics of the laser speckle field, and the laser speckle fields formed under different combinations of surface parameters show great specificity. Therefore, the statistical characteristics of laser speckles studied in this paper may be used as effective information to distinguish the surface of materials in the future.
Acta Optica Sinica
- Publication Date: Jun. 06, 2021
- Vol. 41, Issue 11, 1103001 (2021)
Novel Simulation Method for Non-Diffracting Two-Dimensional Optical Lattices
Zheng Qu, Chunguang Hu, Ridong Zha, Xiaodong Hu, and Xiaotang Hu
The function transfer method is primarily used for the numerical calculation and analysis of non-diffracting optical lattices. But it has complicated mathematical expressions and the programming is challengeable as well. These features make the method difficult for flexibly analyzing the influence of individual optical component as well as its defects and the optical structure on the physical formation of optical lattices. Here, we propose a simulation approach to make the analysis easier. With this simulation method, typical lattices structure, such as fundamental square lattices, maximum symmetric combined fundamental square lattices, and first sparse square lattices, were realized. The non-diffraction performance of the structured beam was verified. These results illustrate the feasibility of the proposed method. Furthermore, the method is useful to find out the correlations among the optical system structure, optical components and the optical lattices. It helps to clarify the formation mechanism and the regulation method of non-diffracting two-dimensional optical lattices and, thus, to develop the potential application. The function transfer method is primarily used for the numerical calculation and analysis of non-diffracting optical lattices. But it has complicated mathematical expressions and the programming is challengeable as well. These features make the method difficult for flexibly analyzing the influence of individual optical component as well as its defects and the optical structure on the physical formation of optical lattices. Here, we propose a simulation approach to make the analysis easier. With this simulation method, typical lattices structure, such as fundamental square lattices, maximum symmetric combined fundamental square lattices, and first sparse square lattices, were realized. The non-diffraction performance of the structured beam was verified. These results illustrate the feasibility of the proposed method. Furthermore, the method is useful to find out the correlations among the optical system structure, optical components and the optical lattices. It helps to clarify the formation mechanism and the regulation method of non-diffracting two-dimensional optical lattices and, thus, to develop the potential application.
Acta Optica Sinica
- Publication Date: May. 04, 2019
- Vol. 39, Issue 5, 0503001 (2019)
Cantilevered Plate Vibration Analysis Based on Electronic Speckle Pattern Interferometry and Digital Shearing Speckle Pattern Interferometry
Yinhang Ma, Hanyang Jiang, Meiling Dai, Xiangjun Dai, and Fujun Yang
Based on the random phase perturbation of light waves in laser optical paths, the formation mechanism of mode fringe patterns is analyzed in the real-time image subtraction using an electronic speckle pattern interferometry (ESPI). An amplitude-fluctuation measurement method is proposed. The systems of ESPI and digital shearing speckle pattern interferometry (DSSPI) are established and used for the out-of-plane vibration analysis. In addition, the vibration properties of the intact and the cracked cantilever aluminum plates are investigated experimentally. The experimental results show that the visibility of mode fringe patterns obtained in the real-time image subtraction mode is obviously superior to those by the other methods. The obtained first 10 orders of modal fringe patterns are well consistent with the calculation results by the finite element method. Compared with ESPI, DSSPI is more sensitive to the local stiffness variation and flaws of specimens. Based on the random phase perturbation of light waves in laser optical paths, the formation mechanism of mode fringe patterns is analyzed in the real-time image subtraction using an electronic speckle pattern interferometry (ESPI). An amplitude-fluctuation measurement method is proposed. The systems of ESPI and digital shearing speckle pattern interferometry (DSSPI) are established and used for the out-of-plane vibration analysis. In addition, the vibration properties of the intact and the cracked cantilever aluminum plates are investigated experimentally. The experimental results show that the visibility of mode fringe patterns obtained in the real-time image subtraction mode is obviously superior to those by the other methods. The obtained first 10 orders of modal fringe patterns are well consistent with the calculation results by the finite element method. Compared with ESPI, DSSPI is more sensitive to the local stiffness variation and flaws of specimens.
Acta Optica Sinica
- Publication Date: Apr. 07, 2019
- Vol. 39, Issue 4, 0403001 (2019)
Coherence Properties of Cosine-Gaussian-Correlated Schell-Model Pulse After Random Medium Scattering
Xinliang Zhao, Haixia Wang, Yongtao Zhang, and Tonghai Li
We investigate the coherence properties of a cosine-Gaussian-correlated Schell-model (CGSM) pulse scattered from a quasi-homogeneous random medium. Further, we derive an analytic expression to obtain the temporal coherent degree of the scattered field in the far-zone and investigate the influences of the pulse parameters and properties of the medium on the temporal coherent degree of the scattered field. The numerical calculations denote that the cosine order plays an important role in the distribution of temporal coherent degree of the scattered field. Furthermore, we compare the coherent characteristics, similarities, and differences between a CGSM pulse and a Gaussian Schell-model pulse. We investigate the coherence properties of a cosine-Gaussian-correlated Schell-model (CGSM) pulse scattered from a quasi-homogeneous random medium. Further, we derive an analytic expression to obtain the temporal coherent degree of the scattered field in the far-zone and investigate the influences of the pulse parameters and properties of the medium on the temporal coherent degree of the scattered field. The numerical calculations denote that the cosine order plays an important role in the distribution of temporal coherent degree of the scattered field. Furthermore, we compare the coherent characteristics, similarities, and differences between a CGSM pulse and a Gaussian Schell-model pulse.
Acta Optica Sinica
- Publication Date: Nov. 04, 2019
- Vol. 39, Issue 11, 1103001 (2019)
Controlling of Goos-Hänchen Shift in Quantum Coherence Surface Plasmon Resonance System
Yuanyuan Chen, Weizhi Zhang, and Xiaona Yan
When the beam is totally reflected on the interface between two media, the reflected light has a transverse Goos-H nchen (GH) shift. An atomic medium is introduced in the Kretschmann structure, and the surface plasmon wave is excited by the coupling light. The reflective GH shift of probe light under the surface plasmon assisted interference effect is studied. When the free propagating wave and the surface plasmon wave are respectively used as the coupling light, the reflectivity and the reflective GH shift of probe light are compared. It is shown that there is an asymmetric line-shape similar to Fano resonance in the reflectivity curve when the incident angle of the probe light deviates from the resonance angle, and the reflective GH shift can shift linearly between positive and negative values. When the coupling light is the surface plasmon wave, the reflective GH shift is more sensitive to the variation of the detuning of the probe beam. When the beam is totally reflected on the interface between two media, the reflected light has a transverse Goos-H nchen (GH) shift. An atomic medium is introduced in the Kretschmann structure, and the surface plasmon wave is excited by the coupling light. The reflective GH shift of probe light under the surface plasmon assisted interference effect is studied. When the free propagating wave and the surface plasmon wave are respectively used as the coupling light, the reflectivity and the reflective GH shift of probe light are compared. It is shown that there is an asymmetric line-shape similar to Fano resonance in the reflectivity curve when the incident angle of the probe light deviates from the resonance angle, and the reflective GH shift can shift linearly between positive and negative values. When the coupling light is the surface plasmon wave, the reflective GH shift is more sensitive to the variation of the detuning of the probe beam.
Acta Optica Sinica
- Publication Date: Oct. 09, 2017
- Vol. 37, Issue 9, 0903001 (2017)
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