Contents
2008
Volume: 28 Issue 7
40 Article(s)
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Diffraction and Gratings
Optimized Design of Transmission Grating Used for 13.4 nm Soft X-Ray Interference Lithography
Zhu Weizhong, Wu Yanqing, Chen Min, Wang Naxiu, Tai Renzhong, and Xu Hongjie
Based on the rigorous coupled-wave analysis, considering the actual fabrication processes for nanometer level gratings, the first-order diffraction efficiency was simulated for a normally-incident transmission grating at wavelength of 13.4 nm. The influence on the first-order diffraction efficiency by parameters, such Based on the rigorous coupled-wave analysis, considering the actual fabrication processes for nanometer level gratings, the first-order diffraction efficiency was simulated for a normally-incident transmission grating at wavelength of 13.4 nm. The influence on the first-order diffraction efficiency by parameters, such as grating materials, relief thickness, gap/period ratio, and trapezoidal angle on the relief are analyzed quantitatively. The results show at the wavelength, the phase of the relief (Si3N4, Cr, Au) effects grating diffraction greatly. The phase shift of the nonmetallic relief (Si3N4) is found to precede the metallic materials (Cr, Au). After optimization, Si3N4, Cr and Au gratings with Si (Si3N4) substrate are proposed , which have the higher first-order diffraction efficiency than the Cr/Si3N4 compound gratings currently used for soft X-ray interference lithography..
Acta Optica Sinica
- Publication Date: Jan. 01, 1900
- Vol. 28, Issue 7, 1225 (2008)
Characteristics Analysis of Binary Optic Liquid Crystal Blazed Grating
Zhang Cuiyu, and Huang Ziqiang
Based on binary optics, a new binary optic liquid crystal blazed grating was proposed by combining wave optics and liquid crystal orientation vector theories. Step-shaped phase was obtained by applying a step-shaped voltage on liquid crystal grating electrode and its diffraction efficiency is derived. By changing the nBased on binary optics, a new binary optic liquid crystal blazed grating was proposed by combining wave optics and liquid crystal orientation vector theories. Step-shaped phase was obtained by applying a step-shaped voltage on liquid crystal grating electrode and its diffraction efficiency is derived. By changing the number of steps in one unit, the diffraction angle is changed. The maximum diffraction efficiency can exceed 90% and form blazed grating at this order. The range of the first order of diffraction angle is 0°～10°..
Acta Optica Sinica
- Publication Date: Jan. 01, 1900
- Vol. 28, Issue 7, 1231 (2008)
Fiber Optics and Optical Communications
Clock Division of High-Repetition Rate Optical Pulses from Fabry-Pérot Laser Diode
Zhao Yuepeng, Zhang Mingjiang, An Yi, and Wang Yuncai
The high-repetition rate optical pulses clock division is investigated based on the nonlinear dynamics of optically injected Fabry-Pérot semiconductor laser. A train of 6.32 GHz injected optical pulses divided into 3.16 GHz is obtained. Effects of the bias current of laser diode, the injected optical power, and inThe high-repetition rate optical pulses clock division is investigated based on the nonlinear dynamics of optically injected Fabry-Pérot semiconductor laser. A train of 6.32 GHz injected optical pulses divided into 3.16 GHz is obtained. Effects of the bias current of laser diode, the injected optical power, and injected optical spectrum etc. on the clock division, has been analyzed. The high-repetition rate optical pulses clock division is realized with the periodically oscillated nonlinear dynamics in optically injected F-P laser diode. The clock division will occur when the injected pulse spectral width is narrow, a certain longitudinal mode of the F-P laser diode is locked, and the conditions of low bias current and appropriate injected optical power are met. In addition, the effect of the laser bias currents, linewidth enhancement factor, and injected optical power on clock division is numerically investigated. Numerical simulations are consistent well with the experimental results..
Acta Optica Sinica
- Publication Date: Jan. 01, 1900
- Vol. 28, Issue 7, 1236 (2008)
Application of FFT Algorithm Associated with CZT in Demodulation of Fabry-Pérot Pressure Sensors
Dai Xiajuan, Wang Ming, and Ben Yuhong
The fast Fourier transform (FFT) demodulation method conbined with chirp Z-translation (CZT) is adopted for Fabry-Pérot pressure sensors and its principle and error are analyzed theoretically. In the simulation, cavity lengths from 397 to 403 μm with the space of 0.5 μm are simulated. The result shows that the relThe fast Fourier transform (FFT) demodulation method conbined with chirp Z-translation (CZT) is adopted for Fabry-Pérot pressure sensors and its principle and error are analyzed theoretically. In the simulation, cavity lengths from 397 to 403 μm with the space of 0.5 μm are simulated. The result shows that the relative error by this new method is less than 0.01% and the maximum absolute error is less than 0.05 μm. In the experiment of the demodulation of the MEMS Fabry-Pérot pressure sensor, whose metrical range is from 0 to 3 MPa, its resolution reaches 0.01 MPa, its linearity between the length of the cavity and pressure achieves 0.99316 and the standard deviation between measured pressures and real pressures is less than 0.005 MPa. Experiments show that this new method adapts to the practical demand with higher resolution and less calculation consumption..
Acta Optica Sinica
- Publication Date: Jan. 01, 1900
- Vol. 28, Issue 7, 1241 (2008)
A Novel Reconfigurable Optical Add-Drop Multiplexer Based on Thin-Film Filter
Yu Kan, Liu Wen, Huang Dexiu, and Chang Jin
A novel reconfigurable optical add-drop multiplexer (ROADM) based on narrowband thin-film filter is proposed. The ROADM consists of three single-fiber collimators, a pair of three-port optical circulators, a pair of mirrors and one particularly designed angle-tuned narrowband multiple cavities filter. By control a stepA novel reconfigurable optical add-drop multiplexer (ROADM) based on narrowband thin-film filter is proposed. The ROADM consists of three single-fiber collimators, a pair of three-port optical circulators, a pair of mirrors and one particularly designed angle-tuned narrowband multiple cavities filter. By control a stepping motor to change the incident angle of the thin-film filter, the ROADM can add or drop a selective wavelength. The characteristics of the ROADM are studied experimentally, and especially the crosstalk is analyzed and calculated in detail. In the experiment, the channel isolation is more than 34 dB and its tunable range is over 26 nm, which coincide with the results of theoretical calculation. The RAODM has many advantages such as simple structure, wide tunable range, high isolation, low polarization-dependent loss, low cost and so on. It can be widely used in practical DWDM system..
Acta Optica Sinica
- Publication Date: Jan. 01, 1900
- Vol. 28, Issue 7, 1247 (2008)
Geometric Optics
Propagation of Partially Coherent Flat-Topped Beams in Gradient-Index Media
Pan Pingping, Dan Youquan, and Zhang Bin
By using the method of generalized Huygens-Fresnel diffraction integral, the analytical expression for the cross-spectral density of partially coherent flat-topped beams propagating in the gradient-index media has been derived. Consequently, the propagation properties of partially coherent flat-topped beams propagatingBy using the method of generalized Huygens-Fresnel diffraction integral, the analytical expression for the cross-spectral density of partially coherent flat-topped beams propagating in the gradient-index media has been derived. Consequently, the propagation properties of partially coherent flat-topped beams propagating in the gradient-index media have been studied. Moreover, the influence of the gradient-index parameter of media, the beam order and the beam coherence on the propagation properties has been discussed. The results show that the on-axis intensity distribution of partially coherent flat-topped beams propagating in the gradient-index media varies periodically. The period depends on the gradient-index parameter, but has no relation with the beam coherence. The on-axis peak intensity in media increases with the beam order, the beam coherence parameter, and the gradient-index parameter of media. Furthermore, the intensity distribution near the plane of peak intensity varies rapidly with the propagation distance..
Acta Optica Sinica
- Publication Date: Jan. 01, 1900
- Vol. 28, Issue 7, 1252 (2008)
Study on Propagation of Light Inside Liquid Drop
Sun Weimin, Wang Xiaoli, Zhang Zhilin, Wan Zhong, Liu Qiang, and Guo Minglei
To guarantee the consistency and reliability of the fiber drop analysis technique, it is important to understand the propagation of light inside the liquid drop in detail. Three experimental systems in different directions were designed and fabricated. Pure water was chosen as the experimental sample. The light fields To guarantee the consistency and reliability of the fiber drop analysis technique, it is important to understand the propagation of light inside the liquid drop in detail. Three experimental systems in different directions were designed and fabricated. Pure water was chosen as the experimental sample. The light fields of refracted light in three directions from the liquid drops were monitored. Through analyzing the distribution of the refracted light and the experimental law of output light-field from fibers, the transmission traces and the propagation law of the light inside the liquid drops were proposed. The forming process of peaks of fiber fingerprint drop traces (FFDT) was explained. The experimental results show that different peaks of FFDT correspond with different transmission modes of light inside the liquid drop..
Acta Optica Sinica
- Publication Date: Jan. 01, 1900
- Vol. 28, Issue 7, 1257 (2008)
Image Processing
Image Reconstruction in Fluorescence Molecular Tomography Based on Full Time-Resolved Scheme
Zhang Limin, He Huiyuan, Gao Feng, and Zhao Huijuan
In fluorescence molecular tomography (FMT), the time-resolved (TR) measurement can provide the richest information on photon migration. A full time-resolved scheme is extended to time-domain fluorescence molecular tomography, based on the finite element-finite time difference diffusion equation in forward model and theIn fluorescence molecular tomography (FMT), the time-resolved (TR) measurement can provide the richest information on photon migration. A full time-resolved scheme is extended to time-domain fluorescence molecular tomography, based on the finite element-finite time difference diffusion equation in forward model and the Newtown-Raphson inversion method. The abilities of spatial resolution, quantitativenesss, discerning the differences in target size, grayscale resolution and noise robustness are validated by using simulated data. The proposed method is demonstrated with the capability of simultaneously recovering the fluorescent yield and lifetime. Compared with the generalized pulse spectrum technique for reconstructing images, it shows its superiority in almost every aspect..
Acta Optica Sinica
- Publication Date: Jan. 01, 1900
- Vol. 28, Issue 7, 1262 (2008)
A New Algorithm for Phase Reconstruction from a Single Carrier-Frequency Interferogram
Wang Chao, and Feng Guoying
A new algorithm for phase reconstruction from a single carrier-frequency interferogram without phase unwrapping is proposed. The algorithm directly derives two real-valued partial derivatives of the desired phase from the interferogram. Through direct integration of the two derivatives, the desired phase with high resoA new algorithm for phase reconstruction from a single carrier-frequency interferogram without phase unwrapping is proposed. The algorithm directly derives two real-valued partial derivatives of the desired phase from the interferogram. Through direct integration of the two derivatives, the desired phase with high resolution is retrieved. The algorithm needs no phase unwrapping process, so the phase error or distortion brought by unwrapping operation is avoided. The algorithmn is efficient and insensitive to the nonuniformity of the intensity distribution of the interferogram and the shape of the domain boundaries. The feasibility of the algorithm is demonstrated by both numerical simulation and experiment. The method is effective for real-time measurements of dynamical processes..
Acta Optica Sinica
- Publication Date: Jan. 01, 1900
- Vol. 28, Issue 7, 1269 (2008)
Imaging Systems
Microchannel Plate Gated X-Ray Nanosecond Framing Camera
Niu Lihong, Liu Jinyuan, Peng Wenda, Niu Hanben, Yang Qinlao, Liao Hua, Zhou Junlan, and Zhan Jinsong
A novel microchannel plate (MCP) gated X-ray nanosecond framing camera is developed. The camera system consists of a proximity-focused framing image-converted tube with traveling-wave gated micro-stripe optoelectric cathode, an electronic control unit, a mechanical system for pinholes mounting, adjusting and a high vacA novel microchannel plate (MCP) gated X-ray nanosecond framing camera is developed. The camera system consists of a proximity-focused framing image-converted tube with traveling-wave gated micro-stripe optoelectric cathode, an electronic control unit, a mechanical system for pinholes mounting, adjusting and a high vacuum system. The electronic control unit provides all the power supply of the camera system including voltage to phosphor screen, gating pulses to MCP, bias and static checking voltage of MCP. The images are recorded with a scientific CCD camera coupled to the fiber optic phosphor screen. The photocathode of image-converted tube consists of Au of 50 nm thickness. Eight framing images can be abtained. The energy spectrum response of the camera ranges from 0.1 keV to 10 keV. The exposure time of the camera can be changed is 1 ns, 2 ns and 5 ns in three scales and time interval between frames from 2 ns, 5 ns and 10 ns in three scales. The dynamic spatial resolution is better than 18 lp/mm. The triggering jitter is down to 100 ps with exposure time shifting less than 5%. The fiber remote transmission and control are incorporated in the nanosecond framing camera system. The achieval experimental results on the static, dynamic characteristics and Z-pinch application show that the camera can run in a strong electromagnetic environment. In this case, the camera has little geometric distortion and wide dynamic range and provides good control and high capturing rate. Such a camera system can be utilized in the investigation of Z-pinch for recording X-ray..
Acta Optica Sinica
- Publication Date: Jan. 01, 1900
- Vol. 28, Issue 7, 1274 (2008)
Quantitative Phase Imaging System with Active Phase Stabilization Based on White-Light Interferometry
Li Xinhong, Zhang Haijun, and Zhang Dongxian
A novel self-stable quantitative phase imaging system, based on a white light Michelson interferometer with Kohler illumination is reported. An actively stabilized phase-lock circuit is employed in the system to reduce phase noise. A phase-shifting technique is used to obtain quantitative phase images of the sample. MiA novel self-stable quantitative phase imaging system, based on a white light Michelson interferometer with Kohler illumination is reported. An actively stabilized phase-lock circuit is employed in the system to reduce phase noise. A phase-shifting technique is used to obtain quantitative phase images of the sample. Mirror, standard negative test chart and polystyrene beads are used as samples in experiments. Clear quantitative phase images are obtained and real-time observation is realized. The system uses halogen lamp as the light source and the vertical resolution of 5 nm is obtained. The structure of Kohler illumination in the system ensures high spatial coherence. Experimental results show this system can get rid of the interfering signal from other optical surfaces, such as lens surfaces..
Acta Optica Sinica
- Publication Date: Jan. 01, 1900
- Vol. 28, Issue 7, 1279 (2008)
Suppression of Surface Dark Current Based on Periodic Inverted Mode
Zhang Wenwen, and Chen Qian
In order to suppress surface dark current of electron multiplying CCDs, Shockley-Read-Hall theory is applied to describe the generation progress of surface dark current. The theoretical model of surface dark current is established by curve fitting. Recovery characteristic time of surface dark current is obtained througIn order to suppress surface dark current of electron multiplying CCDs, Shockley-Read-Hall theory is applied to describe the generation progress of surface dark current. The theoretical model of surface dark current is established by curve fitting. Recovery characteristic time of surface dark current is obtained through a quantitative analysis when the device is switched from inverted mode to non-inverted mode. Periodic inverted mode is proposed based on the timing character. Imaging clocks are modulated by periodic inverted pulses during signal integration. The device is switched from inverted mode to non-inverted mode at a period less than surface dark current recovery time. Simulation results show that surface dark current dramatically decreases as periodic inverted frequency increases. When the period equals 0.2 ms, average surface dark current is 0.051 nA/cm2, approaching inverted mode level. The results are in good agreement with theoretical analysis and the feasibility of periodic inverted mode is proved..
Acta Optica Sinica
- Publication Date: Jan. 01, 1900
- Vol. 28, Issue 7, 1283 (2008)
Fourier Transform Profilometry by Original Grating Reconstruction from Deformed Grating Pattern
Yang Chuping, and Weng Jiawen
In Fourier transform profilometry (FTP) for three-dimensional (3-D) shape measurement, in order to obtain the height and phase information of a testing object, two images are needed, i.e. original grating pattern and its deformed grating pattern. Therefore, if the optical system is changed, it is necessary to obtain a In Fourier transform profilometry (FTP) for three-dimensional (3-D) shape measurement, in order to obtain the height and phase information of a testing object, two images are needed, i.e. original grating pattern and its deformed grating pattern. Therefore, if the optical system is changed, it is necessary to obtain a new original grating pattern. Such arrangement does harm to fast measurement. For overcoming the shortage, a new method is proposed for obtaining the information of the original grating pattern from its deformed grating pattern. First the information of the original grating pattern is recorded in its deformed grating image. Then its frequency and phase are obtained from the deformed grating image by means of image analysis. Finally the complete original grating image is reconstructed and 3-D shape measurement is relized. The experimental results show that the above method is available..
Acta Optica Sinica
- Publication Date: Jan. 01, 1900
- Vol. 28, Issue 7, 1287 (2008)
Analysis on Measurement Method of Improved Fourier Transforms Profilometry
Mao Xianfu, Su Xianyu, Chen Wenjing, and Jin Hailong
A flexible optical geometry of Fourier transform profilometry (FTP) is discussed. The fringe acquisition formula was derived, as well as the phase acquisition formula and the phase-height mapping formula, when the exit pupil of the projecting lens and the entrance pupil of the imaging lens do not share the same height A flexible optical geometry of Fourier transform profilometry (FTP) is discussed. The fringe acquisition formula was derived, as well as the phase acquisition formula and the phase-height mapping formula, when the exit pupil of the projecting lens and the entrance pupil of the imaging lens do not share the same height and the axes of the two lenses are not in the same plane. Compared with the traditional Fourier transform profilometry, the experimental setup is simple and it is easier to obtain the full-field fringe through adjusting either the location of the projector or that of imaging device. Compared with the improved Fourier transform profilometry, only three length system parameters need to be measured, so the operation is simple and the measurement is more accurate..
Acta Optica Sinica
- Publication Date: Jan. 01, 1900
- Vol. 28, Issue 7, 1291 (2008)
Instrumentation, Measurement and Metrology
Fabry-Pérot Interferometer Using Tunable Diode Laser
Ma Jichi, Li Yan, Sun Wenke, and Xu Jie
In order to calibrate the nonlinear error of laser interferometers and high-precision displacement sensors with an accuracy of nanometer order, the linearity, stability and measurement range of the beat frequency Fabry-Pérot interferometer developed by National Institute of Metrology and Tsinghua University shouldIn order to calibrate the nonlinear error of laser interferometers and high-precision displacement sensors with an accuracy of nanometer order, the linearity, stability and measurement range of the beat frequency Fabry-Pérot interferometer developed by National Institute of Metrology and Tsinghua University should be improved. Based on analysis of the influences of factors, such as the change of air refractive index and the tunable range of He-Ne laser, a vacuum system that airproofs the interference light path is designed and built, and a diode laser with a large tunable range is used to take place of the He-Ne laser. The experimental results show that the nonlinear error of the system in the range of longer than a quarter of the wavelength is reduced from 8.93 nm to 1.19 nm..
Acta Optica Sinica
- Publication Date: Jan. 01, 1900
- Vol. 28, Issue 7, 1296 (2008)
Dynamic Compensation for Interpolation Error of Moiré Fringe Signals
Piao Weiying, and Yuan Yibao
Lacking effective error compensation method is one of the important reasons that limit the advance of measurement precision of the grating ruler. A dynamic compensation method for eliminating the interpolation error of moiré fringe signals is put forward. The interpolation error is caused by zero offset, quadraturLacking effective error compensation method is one of the important reasons that limit the advance of measurement precision of the grating ruler. A dynamic compensation method for eliminating the interpolation error of moiré fringe signals is put forward. The interpolation error is caused by zero offset, quadrature phase shift and unequal amplitude of two signals. Eight characteristic points (zero points and absolute amplitude joints of two channels signals) on a grating signal period is traced, and the zero offset of sinusoidal signal is separated from amplitude of characteristic points, and compensated. Then the compensated signal is traced, and the zero offset of cosinusoidal signal can also be separated and compensated. The compensative signal is traced continuely, the unequal amplitude error and the error of quadrature phase shift can be separated and compensated respectively. The above three errors can be totally compensated in no more than three grating signal periods. The influence of harmonics was analyzed and the improvement method was presented. Experiments verify this method's validity..
Acta Optica Sinica
- Publication Date: Jan. 01, 1900
- Vol. 28, Issue 7, 1301 (2008)
Multiple-Surface Interference Fringes Analysis Based on Least-Squares Iteration
Xu Jiancheng, Shi Qikai, Chai Liqun, Deng Yan, and Xu Qiao
To accurately profile transparent elements with parallel surfaces, a method based on least-squares iteration is presented to extract the phase information from multiple-surface interference fringes. According to the principle of wavelength-tuned phase shifting, the least-squares iteration is applied to obtain the actuaTo accurately profile transparent elements with parallel surfaces, a method based on least-squares iteration is presented to extract the phase information from multiple-surface interference fringes. According to the principle of wavelength-tuned phase shifting, the least-squares iteration is applied to obtain the actual phase shifts of the different two-beam interference fringes in each frame. Therefore, it allows extraction of front surface, back surface and thickness variation from multiple-surface interference fringes with high precision. The simulation results show that when the phase-shifting error is less than 0.2 rad, the proposed algorithm needs only 10 iterations and reduces the residual phase errors from 0.512 rad (peak value, PV) and 0.103 rad (root-mean-square, RMS) obtained by Okada's algorithm to 0.005 rad (PV) and 0.002 rad (RMS). Its validation is also demonstrated by the experiment of three-surface fringes analysis..
Acta Optica Sinica
- Publication Date: Jan. 01, 1900
- Vol. 28, Issue 7, 1307 (2008)
Concave Aspherical Surface Testing with Twin Computer-Generated Holograms
Xie Yi, Chen Qiang, Wu Fan, Hou Xi, Zhang Jing, and Wu Gaofeng
In order to test concave aspherical surfaces precisely, a binary phase twin computer-generated hologram (CGH) is proposed and designed. The designed twin CGH consists of two segments, called main CGH and alignment CGH, used for testing aspherical surfaces and aligning main CGH respectively. The principle of testing aspIn order to test concave aspherical surfaces precisely, a binary phase twin computer-generated hologram (CGH) is proposed and designed. The designed twin CGH consists of two segments, called main CGH and alignment CGH, used for testing aspherical surfaces and aligning main CGH respectively. The principle of testing aspherical surfaces is reviewed and the design method is introduced. Then a design example for testing a paraboloidal mirror (Φ140, F/2) is presented, and its root-mean-square (RMS) error is 0.062λ. The pattern distortion error of main CGH is derived from analyzing the errors of alignment CGH, and then the integrative error is 0.06λ. The validity of the test result is demonstrated and compared with that of autocollimation test, which is 0.062λ (RMS). It is demonstrated that the results show a good agreement..
Acta Optica Sinica
- Publication Date: Jan. 01, 1900
- Vol. 28, Issue 7, 1313 (2008)
Uncertainty Evaluation of Centroid Detection
Chen Jiechun, Ding Zhenliang, and Yuan Feng
A new method of uncertainty evaluation of centroid detection is proposed. The uncertainty associated with the intensity of a pixel, belonging to the target to be detected, is firstly evaluated from the pixel intensity and the image gradient at the pixel. Then the uncertainties associated with the centroid detector are A new method of uncertainty evaluation of centroid detection is proposed. The uncertainty associated with the intensity of a pixel, belonging to the target to be detected, is firstly evaluated from the pixel intensity and the image gradient at the pixel. Then the uncertainties associated with the centroid detector are evaluated according to the relation between the evaluation of pixel intensity uncertainty and the pixel. The mathematical model to evaluate the uncertainty of pixel intensity and the analytical expression to evaluate the uncertainty of centroid detection are presented. The experimental results show that the uncertainty of centroid detection can be evaluated accurately with this method..
Acta Optica Sinica
- Publication Date: Jan. 01, 1900
- Vol. 28, Issue 7, 1318 (2008)
Dispersion Measurement for Optical Fiber in Ring Cavity Using Fiber Laser Sideband Spectrum
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Based on the sideband spectrum produced by the interference of dispersion wave and solition wave in the passively mode-locked fiber laser. The wavelength offset from the central wavelength in the sideband spectrum is measured, the total cavity dispersion is obtained with the relation between the sideband offset and theBased on the sideband spectrum produced by the interference of dispersion wave and solition wave in the passively mode-locked fiber laser. The wavelength offset from the central wavelength in the sideband spectrum is measured, the total cavity dispersion is obtained with the relation between the sideband offset and the total cavity dispersion. Ring cavities with different lengths of the same type fibers have different dispersions. The slope of the variation of dispersions corresponding to the fiber length is the dispersion coefficient to be measured. The platform of a passively mode-locked fiber laser is built, and the dispersion coefficient of G.652 fiber has been measured, whose experimental value is 16 ps/(nm·km) that is agrees well with the conventional value of 17 ps/(nm·km)..
Acta Optica Sinica
- Publication Date: Jan. 01, 1900
- Vol. 28, Issue 7, 1323 (2008)
Integrated Optics
Experimental Study of Wavelength Conversion at Various Modulation Formats Based on Four-Wave Mixing in a Semiconductor Optical Amplifier
Dong Jianji, Zhang Xinliang, and Huang Dexiu
The wavelength conversion based on four-wave mixing (FWM) in semiconductor optical amplifier (SOA) for a variety of modulation formats is demonstrated. As for nonreturn-to-zero (NRZ) format, the single-to-triple channel wavelength conversion is reported. The modulation speed varies from 10 Gb/s to 40 Gb/s. As for returThe wavelength conversion based on four-wave mixing (FWM) in semiconductor optical amplifier (SOA) for a variety of modulation formats is demonstrated. As for nonreturn-to-zero (NRZ) format, the single-to-triple channel wavelength conversion is reported. The modulation speed varies from 10 Gb/s to 40 Gb/s. As for return-to-zero (RZ) format, the wavelength conversion at 20 Gb/s and 40 Gb/s is realized. As for carrier suppressed RZ (CSRZ) format, the 40 Gb/s wavelength conversion is achieved. A notch filter made by fiber Bragg grating is used to separate the conjugated light and the pump light. As for NRZ-differential phase shift keying (DPSK) format, the wavelength conversion at 20 Gb/s and 40 Gb/s is realized. A home-made fiber delayed interferometer (FDI) is employed to demodulate the converted DPSK signal. The output extinction ratio (ER) of the converted signal based on FWM is higher than 7 dB, and the ER degradation is about 3 dB..
Acta Optica Sinica
- Publication Date: Jan. 01, 1900
- Vol. 28, Issue 7, 1327 (2008)
Study on Clad Absorption Spectrum Characteristics and Solution Concentration Sensing using Fermi Refractive Index Waveguides
Wang Haihong, Chen Baoxue, Zou Renling, and Mamoru Iso
Fermi refractive-index distribution gradient waveguides are fabricated on the optical glass B270 using ion exchange process in the composite salt of 0.004AgNO3-0.996NaNO3. Absorption spectrum characteristics of the Fermi graded refractive index waveguide with an absorbent clad is theoretically analyzed. The experimentaFermi refractive-index distribution gradient waveguides are fabricated on the optical glass B270 using ion exchange process in the composite salt of 0.004AgNO3-0.996NaNO3. Absorption spectrum characteristics of the Fermi graded refractive index waveguide with an absorbent clad is theoretically analyzed. The experimental result about propagation loss of the waveguides is coincident with the analytic result. A testing waveguide circuit with a double-sample serial structure for measuring the liquid absorption loss is presented. The measured result shows that there is a remarkable linear relationship between solution concentration and refractive index's imaginary part which represents the feature of solution clad absorption, and the sensitivity is related to the modes and the parameters of waveguide, and particularly to the depth of waveguide. By using this sensing relationship, the concentrations C. I. Pigment Green7 solution samples 13 with kinds of different concentrations have been measured. The standard deviation between the measured values and the actual values is less than 0.07％..
Acta Optica Sinica
- Publication Date: Jan. 01, 1900
- Vol. 28, Issue 7, 1333 (2008)
Materials
A Three-Dimensional Measurement Method by Combining Binocular and Monocular Vision Systems
Lei Yanzhang, Zhao Huijie, and Jiang Hongzhi
Based on the combination of binocular vision measurement and monocular vision measurement, a new three-dimensional (3D) measurement method is proposed with the two systems, the common field of view is reconstructed by a binocular vision system, and the unmatched area is filled up by two monocular vision systems, which Based on the combination of binocular vision measurement and monocular vision measurement, a new three-dimensional (3D) measurement method is proposed with the two systems, the common field of view is reconstructed by a binocular vision system, and the unmatched area is filled up by two monocular vision systems, which is composed of the projector and cameras separately. Their world cooridinate systems can be unified to a common reference with uniform calibration. In the measurement of gesso head portrait, the data missing near the nose can be avoided by this method. While the reconstruction precision of the binocular vision system is maintained, this method improves the measurement results efficiently..
Acta Optica Sinica
- Publication Date: Jan. 01, 1900
- Vol. 28, Issue 7, 1338 (2008)
Polarization State Research of Transmitted Light on Cholesteric Liquid Crystal Based on Matrix Theory
Xie Jianing, Feng Shimeng, and Chen Ting
The cholesteric liquid crystal can be regarded as a multilayer structure consisting of many uniaxial thin films which exhibit optical rotation. A new method is proposed to study the polarization states of the transmitted light through a cholesteric liquid crystal. It is found that the cholesteric liquid crystal can comThe cholesteric liquid crystal can be regarded as a multilayer structure consisting of many uniaxial thin films which exhibit optical rotation. A new method is proposed to study the polarization states of the transmitted light through a cholesteric liquid crystal. It is found that the cholesteric liquid crystal can completely change the polarization state of the transmitted light. The direction of linear polarization can be turned by 90°, and the left circularly polarized light can be translated into right one, when it passes through the cholesteric liquid crystal..
Acta Optica Sinica
- Publication Date: Jan. 01, 1900
- Vol. 28, Issue 7, 1343 (2008)
Study on First Principle of Optical Property of Oxygen Vacancy-Doped Anatase TiO2
Hou Qingyu, Zhang Yue, and Zhang Tao
The effect of oxygen vacancy in anatase TiO2 crystal on the optical property was studied by using the plane waves ultrasoft pseudopotential technique, which was based on density functional theory. The crystal structure of anatase with oxygen vacancies was optimized by using the first principle. Then electronic-state deThe effect of oxygen vacancy in anatase TiO2 crystal on the optical property was studied by using the plane waves ultrasoft pseudopotential technique, which was based on density functional theory. The crystal structure of anatase with oxygen vacancies was optimized by using the first principle. Then electronic-state density , complex refractive index,dielectric functions and absorption spectra in pure and oxygen doped anatase TiO2 crystal were calculated. By comparing the results, we find there are some changes in electronic structure, which lead to a change of the interaction between electrons. The Fermi surface of the total density of states (TDOS) extends into the conducting band, and causes Mott phase transformation, and the Ti 3d state of the anatase crystal of TiO2 at -6.097 eV shows new split peaks. Positions of imaginary part of dielectric functions and real part of the absorption spectrum and complex refractive index are identified, showing there are inner relations between them, which are related to the state density of the electrons. By theoretical analysis and calculation, we find that the imaginary part of dielectric functions and the peak position of absorption spectrum are caused by the relaxation effect, meanwhile the height of the peaks is related to the transition probability of the electrons, and anisotropism of the crystal is determined by its symmetry structure of crystal..
Acta Optica Sinica
- Publication Date: Jan. 01, 1900
- Vol. 28, Issue 7, 1347 (2008)
Analysis of Mode Properties of Photonic Crystal Fiber with High Birefringence
Zhang Xiaojuan, Zhao Jianlin, and Cui Li
The mode cutoff, confinement loss, modal radius, and numerical aperture of photonic crystal fiber (PCF) with high birefringence were analyzed by using full-vector finite difference frequency domain (FDFD) method. The numerical simulation results shown that, by choosing suitable structural parameters, the birefringence The mode cutoff, confinement loss, modal radius, and numerical aperture of photonic crystal fiber (PCF) with high birefringence were analyzed by using full-vector finite difference frequency domain (FDFD) method. The numerical simulation results shown that, by choosing suitable structural parameters, the birefringence of the PCF may reach the order of 10-3 with broad single-mode region (600～1800 nm). A low confinement loss less than 10-4 dB/m and high numerical aperture can be obtained in a properly designed geometrical structure of PCF, so the focusing ability is enhanced. Moreover, by fitting the distribution of the fundamental mode using Gaussian curve, the obtained modal radius agrees well with the actual one..
Acta Optica Sinica
- Publication Date: Jan. 01, 1900
- Vol. 28, Issue 7, 1379 (2008)
Analysis of Real Photonic Crystal Fibers by Finite-Difference Frequency-Domain Method Combined with Digital Image Processing
Yao Yuhong, Li Yanfeng, Liu Bowen, Hu Minglie, Chai Lu, Wang Qingyue, Tong Weijun, and Luo Jie
A finite-difference frequency-domain method combined with digital image processing is used to analyze real photonic crystal fibers. To overcome the difficulties imposed by the irregularity of the fiber cross section, the fiber structure is first obtained from the scanning electron microscopy (SEM) image of a real photoA finite-difference frequency-domain method combined with digital image processing is used to analyze real photonic crystal fibers. To overcome the difficulties imposed by the irregularity of the fiber cross section, the fiber structure is first obtained from the scanning electron microscopy (SEM) image of a real photonic crystal fiber by such digital image processing techniques as thresholding segmentation and Wiener filtering. Image interpolation and window filtering method are then employed to realize mesh division and permittivity averaging. Parameters obtained above are used in fiber property analysis by the finite-difference frequency-domain method. It is shown that the proposed method gets accurate fiber dispersion compared with measurement, and also that the calculated mode field distributions correspond well with those recorded in the experiment..
Acta Optica Sinica
- Publication Date: Jan. 01, 1900
- Vol. 28, Issue 7, 1384 (2008)
OPTICAL DATA STORAGE
Simulation Analysis and Experimental Validation of a New Multi-Level Read-Only Optical Recording Method
[in Chinese], [in Chinese], [in Chinese], [in Chinese], and [in Chinese]
A multi-level method using wave-shape modulation is presented. In this method, a short pit or land is added to the original marks, which leads to a recognizable “disturbance” in the readout signal and results in wave-shape modulation of readout signal. Using a simplified mastering model and angular-spectrum decompositiA multi-level method using wave-shape modulation is presented. In this method, a short pit or land is added to the original marks, which leads to a recognizable “disturbance” in the readout signal and results in wave-shape modulation of readout signal. Using a simplified mastering model and angular-spectrum decomposition-based readout model, this method is simulated on the DVD system. Simulation determines how many levels can be realized for each run-length as well as the writing parameters for each level. Experiments on typical run-length of 6T and 11T are carried out. The readout signal agrees with the simulated one. Level error rates less than 1×10-4 and 1×10-5 are achieved. Experiments validate this new multi-level recording method..
Acta Optica Sinica
- Publication Date: Jan. 01, 1900
- Vol. 28, Issue 7, 1353 (2008)
Optical Design and Fabrication
Design and Optimization of Three Cylindrical Reflectors Optical System
Liang Minyong, Liao Ningfang, Feng Jie, Lin Yu, and Cui Deqi
A single cylindrical reflector usually has defects of distortional imaging beam and limited field of view usually less than 1°. A three cylindrical reflectors system is presented to overcome these defects. Based on the ray tracing of cylindrical reflector, a three circularly cylindrical reflectors and a three coniA single cylindrical reflector usually has defects of distortional imaging beam and limited field of view usually less than 1°. A three cylindrical reflectors system is presented to overcome these defects. Based on the ray tracing of cylindrical reflector, a three circularly cylindrical reflectors and a three conic-cylindrical reflectors system have been designed. The full field of view (FOV) has reached 3° in tangential plane; on the edge of FOV, the modulation transfer function (MTF) of the former design at 45 lp/mm is better than 0.2 and the latter is better than 0.6. A new optimization method using parabolic-cylindrical reflector is presented. This method can be used to optimize the MTF in tangential plane, and the final MTF satisfies the requirement of the high spatial resolution in imaging spectrometer field..
Acta Optica Sinica
- Publication Date: Jan. 01, 1900
- Vol. 28, Issue 7, 1359 (2008)
Discussion of Illuminance Formula in Optical Design
Qu Enshi, Zhang Hengjin, Cao Jianzhong, and Yang Zheng
Some improper points of system illuminance formula in the optics textbook and optical software have been found and analyzed, and more practical formula have been deduced. On the assumption that an optical lens is a passive transfer system, after analysis of the original formula the relationship of the off-axial field oSome improper points of system illuminance formula in the optics textbook and optical software have been found and analyzed, and more practical formula have been deduced. On the assumption that an optical lens is a passive transfer system, after analysis of the original formula the relationship of the off-axial field of view with the relative illuminance is cos4ω'. When the field angle in image space becomes smaller, the energy will be enlarged, which is impractical in a passive transfer system. Then, by taking entrance pupil as reference, we recalculate the illuminance formula and obtain a reasonable one. Software simulation validates the new function. And the illuminance of image plane off-axial fields is proportional to the cos4ω of the objective field angle..
Acta Optica Sinica
- Publication Date: Jan. 01, 1900
- Vol. 28, Issue 7, 1364 (2008)
Optical Devices
Noise Analysis of HgCdTe Photoconductive Detector with Different Response Wavelength
Zhang Yan, and Fang Jiaxiong
The influence of background radiation on noise of medium-wave and extremely-long-wave HgCdTe detectors is studied. It is found that the noise of extremely-long-wave detector decreases with the background radiation increasing, while for the medium-wave detector is shows the different way. Noise spectra show that the maiThe influence of background radiation on noise of medium-wave and extremely-long-wave HgCdTe detectors is studied. It is found that the noise of extremely-long-wave detector decreases with the background radiation increasing, while for the medium-wave detector is shows the different way. Noise spectra show that the main noise sources are generation-recombination (G-R) noise and 1/f noise which have the similar trend while the background is changing. The G-R noise for different wavelength response detectors is calculated using carriers and effective lifetime theory. There exists a maximum value when G-R noise changes with background radiation. While the noise is on the different position for medium-wave and extremely-long-wave detectors, the influence of background radiation on their effective lifetime is different. So noise behaves differently. Based on these, a new concept of “critical-background-radiation-flux-density” is put forward..
Acta Optica Sinica
- Publication Date: Jan. 01, 1900
- Vol. 28, Issue 7, 1369 (2008)
Transient Characteristics in All-Optical Switching Using Electron Spin Relaxation
Jiang Zhen, Wang Tao, Wang Bing, and Li Gang
An all-optical transmission switching model based on electron spin relaxation was designed, and this new configuration of optical switch grants the features of short switching time, simple structure, and high optical nonlinearities. The exciton saturation caused by phase-space filling (PSF) and Coulomb screening(CS) inAn all-optical transmission switching model based on electron spin relaxation was designed, and this new configuration of optical switch grants the features of short switching time, simple structure, and high optical nonlinearities. The exciton saturation caused by phase-space filling (PSF) and Coulomb screening(CS) in GaAs/AlGaAs multiple quantum well was discussed under the right circularly polarized pump beam. The absorption coefficients variations of the circularly polarized probe beam in the same and opposite polarization direction with the pump beam were calculated. The differential transmission change of both polarization as a function of delay time was obtained. The pump-probe experiment was carried out to measure the change curve in transmission of the same circularly polarized states probe beam at room temperature, and obvious saturation phenomenon is observed which agrees with the numerical result..
Acta Optica Sinica
- Publication Date: Jan. 01, 1900
- Vol. 28, Issue 7, 1374 (2008)
Quantum Optics
Raman Atomic Fountain Clock
Qu Qiuzhi, Zhou Zichao, Wan Jinyin, and Liu Liang
An atomic fountain clock based on Raman laser field instead of microwave cavity is proposed. This scheme combines the separate Raman fields technology and the cold atomic fountain technology, cancels the microwave fountain clock in the vacuum cavity and meanwhile keeps a high accuracy.The interaction process of the colAn atomic fountain clock based on Raman laser field instead of microwave cavity is proposed. This scheme combines the separate Raman fields technology and the cold atomic fountain technology, cancels the microwave fountain clock in the vacuum cavity and meanwhile keeps a high accuracy.The interaction process of the cold atomic fountain and the Raman laser field is studied with the semiclassical theory and the Ramsey fringes are acquired. The Raman fountain clock is compared with the atomic beam clock of hot cesium atoms, and it is found that the accuracy of Raman fountain clock higher and its capacity and power consumption are much smaller. Compared with the microwave fountain clock, the Raman fountain clock must consider the influence of photon recoil. With the photon recoil, it is proposed to measure the fine structure constant by using two Raman fountain clocks..
Acta Optica Sinica
- Publication Date: Jan. 01, 1900
- Vol. 28, Issue 7, 1390 (2008)
Quantum Coherence Properties of Atom Laser Induced by Light Field
Kong Fanzhi, Zhou Ming, and Huang Chunjia
The quantum coherence properties of atom laser induced from atomic Bose-Einstein condensation (BEC) interacting with several sorts of important light fields are studied by quantum theory. The results show that the atom lasers induced by light field in Fock state, coherent state, and squeezing coherent state are always The quantum coherence properties of atom laser induced from atomic Bose-Einstein condensation (BEC) interacting with several sorts of important light fields are studied by quantum theory. The results show that the atom lasers induced by light field in Fock state, coherent state, and squeezing coherent state are always anti-bunching, the nth-order coherent, and bunching, respectively. These results indicate that the quantum coherence properties of atom laser are completely identical to that of the initial light field interacting with the atomic BEC..
Acta Optica Sinica
- Publication Date: Jan. 01, 1900
- Vol. 28, Issue 7, 1395 (2008)
Remote Sensing and Sensors
Novel Fabry-Pérot Fiber-Optic Refractive-Index Sensor Based on Laser Micromachining
Liu Weijun, Rao Yunjiang, Ran Zengling, and Liao Xian
A novel Fabry-Pérot (F-P) fiber-optic sensor for refractive index (RI) measurement is proposed. The sensor consists of a single-mode fiber end surface and a short air cavity which is close to this surface and produced by 157 nm laser micromachining. The light reflected from the end surface interferes with the lighA novel Fabry-Pérot (F-P) fiber-optic sensor for refractive index (RI) measurement is proposed. The sensor consists of a single-mode fiber end surface and a short air cavity which is close to this surface and produced by 157 nm laser micromachining. The light reflected from the end surface interferes with the light reflected from the air cavity. The fringe contrast of interference from the reflection spectrum of the sensor is influenced by the refractive index to be measured outside. The maximal contrast exists in the trough of the fringe envelop, and the refractive index outside can be gained through this contrast. The sensor can provide temperature-independent measurement of wide range of RI. In the range of 1.33～1.44,the RI sensitivity is about 27 dB, with resolution about 1.12×10-4; and in the range of 1.45～1.62, the RI sensitivity is about 24 dB, with resolution about 1.26×10-4..
Acta Optica Sinica
- Publication Date: Jan. 01, 1900
- Vol. 28, Issue 7, 1400 (2008)
Synthetic Aperture Ladar (Ⅲ): Circulated Duplex Telescope
Liu Liren
A kind of circulated duplex telescope for synthetic-aperture laser imaging radar is presented, in which a circulator connects among a reception-channel 4-f system with defocusing and phase biasing, a transmitting-channel 4-f system with defocusing and phase biasing and a primary telescope. By controlling the biasing fuA kind of circulated duplex telescope for synthetic-aperture laser imaging radar is presented, in which a circulator connects among a reception-channel 4-f system with defocusing and phase biasing, a transmitting-channel 4-f system with defocusing and phase biasing and a primary telescope. By controlling the biasing functions and the defocusing amounts of both channels it is realized with a single telescope to receive the echo with its aberration eliminated and to transmit a beam with an additional quadratic phase. As a result, a suitable and controllable phase history can be generated to correctly synthesize the image in the azimuth-direction. The designs as well as a full transmission equation are detailed in the paper..
Acta Optica Sinica
- Publication Date: Jan. 01, 1900
- Vol. 28, Issue 7, 1405 (2008)
Thin Films
Influence of Annealing on ZnO Films and ZnO/p-Si Heterojunctions
Chen Chuanxiang, and Qi Hongxia
ZnO films were deposited on p-Si (100) substrate by pulsed laser deposition (PLD). Then the samples were annealed at 500 ℃, 600 ℃ and 700 ℃ respectively. X-ray diffraction (XRD) was employed to analyze the effects of annealing on the crystalline structure of the ZnO films. The sheet resistance of the ZnO films and the ZnO films were deposited on p-Si (100) substrate by pulsed laser deposition (PLD). Then the samples were annealed at 500 ℃, 600 ℃ and 700 ℃ respectively. X-ray diffraction (XRD) was employed to analyze the effects of annealing on the crystalline structure of the ZnO films. The sheet resistance of the ZnO films and the I-V characteristics of the heterojunctions were also studied. The results show that higher annealing temperature enhances the films' crystal quality. The intensity of the (002) diffraction peak increases and the full width at half maximum (FWHM) decreases with the rise of annealing temperature, mean while, the internal stress in film decreases and the ZnO crystal grain size increases. Without light illumination, the dark leakage current of the heterojunctions increases with the rise of annealing temperature. With illumination of 650 nm light, the best photoelectric effect is obtained from the sample annealed at 600 ℃. It is revealed that the interface of the heterojunctions might be degraded at higher annealing temperature. Therefore, proper annealing temperature is necessary for high quality photoelectric devices..
Acta Optica Sinica
- Publication Date: Jan. 01, 1900
- Vol. 28, Issue 7, 1411 (2008)
Diffraction Property of Multi-Layer Dielectric Grating with Trapezium Groove
Kong Weijin, Yun Maojin, Cui Chunling, Jin Yunxia, Shao Jianda, and Fan Zhengxiu
The rigorous coupled-wave analysis is used to describe the diffraction of multi-layer diffraction grating (MDG) with trapezium groove. The diffraction performance of multi-layer dielectric grating with the trapezium groove of 70° is discussed. Trapezium MDG used for wavelength of 1053 nm and incident angle of 51.2The rigorous coupled-wave analysis is used to describe the diffraction of multi-layer diffraction grating (MDG) with trapezium groove. The diffraction performance of multi-layer dielectric grating with the trapezium groove of 70° is discussed. Trapezium MDG used for wavelength of 1053 nm and incident angle of 51.2° is designed by optimizing the duty cycle, depth and residual thickness of the top layer. For gratings etched into the top HfO2 layer, diffraction efficiency of 99.5% can be attained when the duty cycle is 0.35, groove depth is 200 nm and the residual thickness of HfO2 is 50nm. Whereas for SiO2 as the top corrugated layer, the groove depth is 800 nm and the top SiO2 residual layer is 320 nm in order to obtain the same diffraction efficiency as 99.5%. Furthermore, the trapezium MDG with HfO2 on the top has wider wavebandth compared with the design of SiO2 on the top of MDG to obtain the same diffraction efficiency. Numerical calculation indicates that the coupled-wave analysis model has excellent convergence and stable performance to analyze the diffraction of trapezium MDG..
Acta Optica Sinica
- Publication Date: Jan. 01, 1900
- Vol. 28, Issue 7, 1415 (2008)
Structural and Optical Characteristics of ZnO Films on LiGaO2 Substrate
Huang Taohua, Zhou Shengming, Teng Hao, Lin Hui, and Wang Jun
ZnO films were fabricated on LiGaO2 (001), (100) and (010) planes by magnetron sputtering. The structural, morphological and optical properties of as-grown ZnO films were investigated by X-ray diffraction (XRD), atomic force microscopy (AFM), transmission spectra and photoluminescence (PL) spectra. The results show thaZnO films were fabricated on LiGaO2 (001), (100) and (010) planes by magnetron sputtering. The structural, morphological and optical properties of as-grown ZnO films were investigated by X-ray diffraction (XRD), atomic force microscopy (AFM), transmission spectra and photoluminescence (PL) spectra. The results show that ZnO films on various planes of LiGaO2 have different preferred orientations. ［0001］, ［1100］ and ［1120］ oriented ZnO films are obtained on LiGaO2 (001), (100) and (010) planes, respectively. The ZnO films show different surface morphologies and high transmittance in visible spectrum range. Only UV emission peaks located at 378 nm are observed in PL spectra of ZnO films. The (1100) ZnO film shows the highest UV emission intensity with the smallest full width at half maximum (FWHM) value. The difference in PL properties of the ZnO films is mainly due to different grain sizes..
Acta Optica Sinica
- Publication Date: Jan. 01, 1900
- Vol. 28, Issue 7, 1420 (2008)
Reflection Spectra Properties of Guided-Mode Resonance Filters with Buffer Layer
Wang Zhenhua, Wu Yonggang, Sang Tian, Wang Zhanshan, Peng Donggong, Jiao Hongfei, Chen Naibo, and Cao Hong
Guided-mode resonance reflection filters are presented by adding a buffer layer in designing homogeneous thin-film reflection filters for studying the influence of buffer layer on reflection spectra of the guided-mode resonance filters. With the thickness increase of buffer layer, the reflection spectra of guided-mode Guided-mode resonance reflection filters are presented by adding a buffer layer in designing homogeneous thin-film reflection filters for studying the influence of buffer layer on reflection spectra of the guided-mode resonance filters. With the thickness increase of buffer layer, the reflection spectra of guided-mode resonance filters with one, two, three and four channels are calculated with the rigorous coupled-wave theory, two, three and four narrowband reflection peaks are found. When the buffer layer is chosen as 796.35 nm, the filling factor from 0.2 to 0.9, and the depth of grating between 100 nm and 200 nm, the resonant wavelength location and reflection ratio are nearly invariable, showing good characteristic of the filters..
Acta Optica Sinica
- Publication Date: Jan. 01, 1900
- Vol. 28, Issue 7, 1425 (2008)
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