CN106840418B - A kind of anti-vibration method of phase-shifting interferometer - Google Patents
A kind of anti-vibration method of phase-shifting interferometer Download PDFInfo
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- G—PHYSICS
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- G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
- G01J9/00—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength
- G01J9/02—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength by interferometric methods
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
- G01J9/00—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength
- G01J9/02—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength by interferometric methods
- G01J2009/0234—Measurement of the fringe pattern
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Abstract
The invention discloses a kind of anti-vibration method of phase-shifting interferometer, the phase-shifting interferometer camera in this method acquires second group of phase-shift interference in the case where opening and closing combination of pixels function with first group of phase-shift interference of high speed acquisition and with low speed.Second group of phase-shift interference obtains third group phase-shift interference identical with first group of phase-shift interference resolution ratio after uniform sampling.Extracts low resolution phase mehtod from first group of phase-shift interference using three step iterative algorithms of amendment, and is fallen into a trap evaluation time associated arguments from third group phase-shift interference using it as initial value using correcting three step iterative algorithms.After bi-directional scaling time correlation parameter, least squares equation is constructed in conjunction with second group of phase-shift interference, calculates high-resolution phase mehtod, it is final to reconstruct measured surface height.The method of the present invention takes full advantage of the characteristics of three step iterative algorithm of combination of pixels function and amendment of phase-shifting interferometer camera, has admirably achieved phase-shifting interferometer to the purpose of anti-vibration using lower hardware cost.
Description
Technical field
The invention belongs to phase-shifting interference measuring fields, and in particular to a kind of anti-vibration method of phase-shifting interferometer.
Background technique
Phase-shifting interferometer is the important instrument for measuring Optical Surface, has the spy of high-precision and high spatial resolution
Point.But traditional phase-shifting interferometer is very sensitive to extraneous vibration, and atomic small vibration can all lead to apparent measurement error.
In order to meet the needs of measuring under in-site measurement, on-position measure and other vibration environments, researchers have developed iterative algorithm, can
To extract phase mehtod from the phase-shift interference of vibrated interference.It is wherein representative for correcting three step iterative algorithms (MTIA)
One kind, can with caused by compensation vibration inclination Phase-shifting Errors and contrast fluctuation, can be refering to the document " Q. published
Liu, Y. Wang, J. He, et al. Modified three-step iterative algorithm for
phase-shifting interferometry in the presence of vibration. Applied Optics.
2015, 54: 5833-5841.".Correcting three step iterative algorithms is to input initial value, warp using phase-shift interference as data basis
After iterative cycles several times, convergence obtains correct phase mehtod.Correcting an important factor for three step iterative algorithms can restrain is
The selection of initial value, initial value can be the amount of phase shift or phase distribution of estimation.Initial value is closer with exact value, iterative calculation
Convergence rate is faster, and otherwise convergence rate is slow or will not restrain.If the speed of phase-shifting interferometer phase shifter and the frame frequency of camera
It is all very high, the acquisition of phase-shift interference is completed within a very short time, and the influence vibrated in this way will be weakened, and be conducive to amendment three
Step iterative algorithm converges to correct result (at this point, the shock resistance of three step iterative algorithms of amendment is good).However, in the prior art
Under level, camera is obtained and the speed of transmission image data is limited, and high spatial resolution can not be realized under high frame frequency
Image Acquisition.But camera generally all has combination of pixels (binning) function, opens combination of pixels function, and camera is obtained and passed
The frame frequency of defeated image is high, then the resolution ratio of image will be very low；Combination of pixels function is closed, camera works in full resolution shape
State obtains the high resolution of image, then camera obtains and the frame frequency of transmission image will be very low.For phase-shifting interferometer,
The high-resolution of camera means finer measurement result, can see surface details clearly.Three step iterative algorithms of amendment are come
It says, the high frame frequency of the camera of phase-shifting interferometer and the implacable contradiction of high-resolution have led to three step iterative algorithm antivibratioves of amendment
Contradiction between dynamic performance and fine measurement result needs to develop for phase-shifting interferometer a kind of both with well to anti-vibration
The method that ability can reconstruct high-resolution surface again.
Summary of the invention
Technical problem to be solved by the invention is to provide a kind of anti-vibration methods of phase-shifting interferometer.
The anti-vibration method of phase-shifting interferometer of the invention, its main feature is that, the method the following steps are included:
A. start phase-shifting interferometer, make phase-shifting interferometer work in phase shift mode, when acquiring adjacent two width phase-shift interference
The optical path difference variation that phase shifting equipment generates is Δ, and calculating default amount of phase shift is 2 π Δs/λ, and λ is optical source wavelength；
B. the combination of pixels function of phase-shifting interferometer camera is opened, phase shifting equipment cooperates camera frame frequency to generate optical path difference change
Change, phase-shifting interferometer acquires first group of phase-shift interference, and the resolution ratio of total L1 width, every width phase-shift interference is R1 × C1；
C. the combination of pixels function of phase-shifting interferometer camera is closed, phase shifting equipment cooperates camera frame frequency to generate optical path difference change
Change, the camera of phase-shifting interferometer acquires second group of phase-shift interference, total L2 width, the resolution ratio of every width phase-shift interference be R2 ×
C2, R2/R1=M, C2/C1=N, M, N are the integer greater than 1；
D. it using default amount of phase shift as initial value, is calculated from first group of phase-shift interference using three step iterative algorithms of amendment
Phase mehtod I；
E. in second group of phase-shift interference each width phase-shift interference carry out uniform sampling, obtain resolution ratio be R1 ×
The third group phase-shift interference of C1；
F. it using phase mehtod I as initial value, is calculated from third group phase-shift interference using three step iterative algorithms of amendment
Time correlation parameter, the time correlation parameter includes: lateral phase shift obliquity factor kx1、kx2、…、kxL2, longitudinal phase shift inclines
Oblique factor ky1、ky2、…、kyL2, phase shift translational movement d1、d2、…、dL2, background fluctuations factor a1、a2、…、aL2, modulation degree fluctuation
Factor b1、b2、…、bL2；
G. by the lateral phase shift obliquity factor kx in step f1、kx2、…、kxL2Modified laterally shifting is obtained divided by N respectively
Tilt factor K x1、Kx2、…、KxL2, by longitudinal phase shift obliquity factor ky1、ky2、…、kyL2It is obtained respectively divided by M modified vertical
To phase shift obliquity factor Ky1、Ky2、…、KyL2；
H. the amount of phase shift D of (x, y) a pixel on second group of phase-shift interference is calculated1(x,y)= Kx1×x+ Ky1×y
+d1、D2(x,y)= Kx2×x+ Ky2×y+d2、…、DL2(x,y)= KxL2×x+ KyL2×y+dL2, by corresponding pixel
Gray value of image I1(x,y)、I2(x,y)、…、IL2(x, y) takes out, with D1(x,y)、D2(x,y)、…、DL2(x,y)、a1、
a2、…、aL2、b1、b2、…、bL2Least squares equation is constructed, least squares equation is solved and obtains the position of (x, y) a pixel
Phase φ (x, y)；
I. step h is repeated, until the position phase of all pixels point on second group of phase-shift interference is obtained, by position mutually according to pixel
Sequence deposit two-dimensional matrix o'clock on second group of phase-shift interference obtains phase mehtod II, to II unpacking of phase mehtod, root
According to the reconstruct measured surface height distribution of optics corresponding relationship.
Uniform sampling described in step e are as follows: take out and own (a+mM, b+nN) a pixel on R2 × C2 image in different resolution
Gray value, and it is stored in by original sequence the matrix of R1 × C1 size, 1≤a < M, 1≤b < N, m=0,1 ..., R1-1, n=0,
1,…, C1-1。
L1 and L2 are all larger than equal to 4.
The anti-vibration method of phase-shifting interferometer of the invention provides a kind of inexpensive, function admirable for phase-shifting interferometer
To the method for anti-vibration, while can guarantee to obtain high-resolution measurement result.This method takes full advantage of phase-shifting interferometer
The combination of pixels function and measured surface feature of camera immovable feature in a short time, first with three step iterative algorithms of amendment from acquisition
High frame frequency phase-shift interference in calculate low resolution phase mehtod, then using the phase mehtod of low resolution as initially
Value is fallen into a trap evaluation time associated arguments from the high-resolution phase-shift interference of uniform sampling with three step iterative algorithms of amendment, then solved
The least squares equation of time correlation parameter and high-resolution phase-shift interference construction, the final standard for realizing high-resolution phase mehtod
Really extract.
Detailed description of the invention
Fig. 1 is the work flow diagram of the anti-vibration method of phase-shifting interferometer of the invention；
Fig. 2 is the three step iterative algorithm schematic illustration of amendment of the anti-vibration method of phase-shifting interferometer of the invention；
Fig. 3 is that first group of phase shift that the camera of the phase-shifting interferometer in the present invention acquires after opening combination of pixels function is dry
Relate to figure；
Fig. 4 is that second group of phase shift that the camera of the phase-shifting interferometer in the present invention acquires after closing combination of pixels function is dry
Relate to figure；
Fig. 5 is the phase mehtod extracted from first group of phase-shift interference using three step iterative algorithms of amendment in the present invention
Ⅰ；
Fig. 6 is that the pixel during the uniform sampling of the embodiment in the present invention divides schematic diagram；
Fig. 7 is four kinds of image schematic diagrames that the uniform sampling of the embodiment in the present invention obtains；
Fig. 8 is the third group phase-shift interference that second group of phase-shift interference in the present invention obtains after uniform sampling；
Fig. 9 is the phase mehtod II calculated from second group of phase-shift interference using least square method in the present invention；
Figure 10 is the measured surface that the phase mehtod II in the present invention reconstructs after unpacking and using optics corresponding relationship
Height distribution map.
Specific embodiment
The invention will now be described in detail with reference to the accompanying drawings.
The anti-vibration method of phase-shifting interferometer of the invention, its main feature is that, the method the following steps are included:
A. start phase-shifting interferometer, make phase-shifting interferometer work in phase shift mode, when acquiring adjacent two width phase-shift interference
The optical path difference variation that phase shifting equipment generates is Δ, and calculating default amount of phase shift is 2 π Δs/λ, and λ is optical source wavelength；
B. the combination of pixels function of phase-shifting interferometer camera is opened, phase shifting equipment cooperates camera frame frequency to generate optical path difference change
Change, phase-shifting interferometer acquires first group of phase-shift interference, and the resolution ratio of total L1 width, every width phase-shift interference is R1 × C1；
C. the combination of pixels function of phase-shifting interferometer camera is closed, phase shifting equipment cooperates camera frame frequency to generate optical path difference change
Change, the camera of phase-shifting interferometer acquires second group of phase-shift interference, total L2 width, the resolution ratio of every width phase-shift interference be R2 ×
C2, R2/R1=M, C2/C1=N, M, N are the integer greater than 1；
D. it using default amount of phase shift as initial value, is calculated from first group of phase-shift interference using three step iterative algorithms of amendment
Phase mehtod I；
E. in second group of phase-shift interference each width phase-shift interference carry out uniform sampling, obtain resolution ratio be R1 ×
The third group phase-shift interference of C1；
F. it using phase mehtod I as initial value, is calculated from third group phase-shift interference using three step iterative algorithms of amendment
Time correlation parameter, the time correlation parameter includes: lateral phase shift obliquity factor kx1、kx2、…、kxL2, longitudinal phase shift inclines
Oblique factor ky1、ky2、…、kyL2, phase shift translational movement d1、d2、…、dL2, background fluctuations factor a1、a2、…、aL2, modulation degree fluctuation
Factor b1、b2、…、bL2；
G. by the lateral phase shift obliquity factor kx in step f1、kx2、…、kxL2Modified laterally shifting is obtained divided by N respectively
Tilt factor K x1、Kx2、…、KxL2, by longitudinal phase shift obliquity factor ky1、ky2、…、kyL2It is obtained respectively divided by M modified vertical
To phase shift obliquity factor Ky1、Ky2、…、KyL2；
H. the amount of phase shift D of (x, y) a pixel on second group of phase-shift interference is calculated1(x,y)= Kx1×x+ Ky1×y
+d1、D2(x,y)= Kx2×x+ Ky2×y+d2、…、DL2(x,y)= KxL2×x+ KyL2×y+dL2, by corresponding pixel
Gray value of image I1(x,y)、I2(x,y)、…、IL2(x, y) takes out, with D1(x,y)、D2(x,y)、…、DL2(x,y)、a1、
a2、…、aL2、b1、b2、…、bL2Least squares equation is constructed, least squares equation is solved and obtains the position of (x, y) a pixel
Phase φ (x, y)；
I. step h is repeated, until the position phase of all pixels point on second group of phase-shift interference is obtained, by position mutually according to pixel
Sequence deposit two-dimensional matrix o'clock on second group of phase-shift interference obtains phase mehtod II, to II unpacking of phase mehtod, root
According to the reconstruct measured surface height distribution of optics corresponding relationship.
Uniform sampling described in step e are as follows: take out and own (a+mM, b+nN) a pixel on R2 × C2 image in different resolution
Gray value, and it is stored in by original sequence the matrix of R1 × C1 size, 1≤a < M, 1≤b < N, m=0,1 ..., R1-1, n=0,
1,…, C1-1。
L1 and L2 are all larger than equal to 4.
Embodiment 1
In the present embodiment, using Fizeau type plane phase-shifting interferometer, optical source wavelength 633nm is promoted using piezoelectric ceramics
Dynamic device (PZT) is used as phase shifting equipment.When phase-shifting interferometer is run under phase shifting work mode, in the adjacent double sampling of camera
It engraves PZT and pushes the mobile 79.1nm of reference mirror, consider double light path, then the optical path difference variation of each step is 158.2nm, then can be with
Calculating default amount of phase shift is pi/2.Phase-shifting interferometer acquires 4 width phase-shift interferences (i.e. L1=4) under camera high-speed mode, composition
First group of phase-shift interference；9 width interference patterns (i.e. L2=9) are acquired under camera high resolution mode, form second group of phase shift interference
Figure.The camera of phase-shifting interferometer is the digital CMOS camera of USB3.0 interface in the present embodiment, and the size of the effective target surface of camera is all
It is 1/3 inch.After opening combination of pixels function, the parameter of the camera is: frame frequency 274fps, resolution ratio 240 × 320；Close picture
After plain combination function, the parameter of the camera is: frame frequency 100fps, resolution ratio 480 × 640.
The operation of the present embodiment is carried out according to process shown in FIG. 1, and relevant parameter is R1=240, C1=320, R2=480, C2
=640, M=N=2.
The principle flow chart for correcting three step iterative algorithms is as shown in Figure 2.It corrects three step iterative algorithms and calculates input when starting
Initial value can be phase mehtod, be also possible to time correlation parameter (phase shift obliquity factor, phase shift translational movement, background fluctuations
The factor, modulation degree fluctuate the factor).The numerical value exported after iteration convergence can be time correlation parameter, be also possible to phase mehtod.
The each loop iteration for correcting three step iterative algorithms is divided into three modules: a module is gone using known time correlation parameter
Calculate phase mehtod；One module be go to calculate using the time correlation parameter in known phase mehtod and the direction x the direction y when
Between associated arguments；The last one module is to go to calculate the direction x using the time correlation parameter of known phase mehtod and the direction y
Time correlation parameter.It is gone to calculate unknown quantity with the numerical value that other two module latest computeds obtain in each module, favorably
In the fast convergence of iteration.Each module solves unknown quantity and uses least square method.
Phase-shift interference is acquired under vibration interference using the phase-shifting interferometer of the present embodiment.It is adopted under camera high-speed mode
First group of phase-shift interference (totally 4 width) of collection is as shown in Figure 3.The second group of phase-shift interference acquired under camera high resolution mode
(totally 9 width) is as shown in Figure 4.
When calculating first phase mehtod from first group of phase-shift interference using three step iterative algorithms of amendment, use it is initial
Value is: phase shift translational movement be 0, pi/2, π, 3 pi/2s, all phase shift obliquity factors are zero, the background fluctuations factor and modulation degree fluctuation because
Son is 1,1,1,1.By 5 iterative cycles, first phase mehtod of calculating is as shown in Figure 5.
Uniform sampling is carried out to second group of phase-shift interference in Fig. 4.For the present embodiment, second group of phase-shift interference
Uniform sampling can have following four kinds of modes.First the pixel of second group of phase-shift interference is divided according to Fig. 6, then
Image to after four kinds of uniform samplings shown in Fig. 7.1st kind: (1+2m, the 1+2n) in piece image is taken, (m=0,1 ...,
239;N=0,1 ..., 319), i.e., the pixel gray values marked as a all in Fig. 6 are taken out, are arranged according to original sequence
Column, obtain piece image in Fig. 7.Similarly, all pixel gray values marked as b, c, d, available Fig. 7 are taken respectively
In second and third, four width images.In the present embodiment, the 1st kind of uniform sampling mode is selected, third group phase-shift interference is obtained, such as schemed
Shown in 8.
Using first phase mehtod as initial value, calculated from third group phase-shift interference using three step iterative algorithms of amendment
Time correlation parameter.By 5 iterative cycles, obtained time correlation parameter is as shown in table 1.The shifting of first width phase-shift interference
It tilts the factor and phase shift translational movement is defaulted as zero, the background fluctuations factor and the modulation degree fluctuation factor are defaulted as 1.
Since N=2 obtain modified lateral phase shift obliquity factor Kx to lateral phase shift tilt quantity divided by 2i, it is respectively
0.651×10-4、-0.338×10-4、-1.019×10-4、-0.765×10-4、-0.630×10-4、-0.308×10-4、
0.366×10-4、0.434×10-4rad/pixel.Since M=2 obtain modified vertical to longitudinal phase shift tilt quantity divided by 2
To phase shift obliquity factor Kyi, it is 0.940 × 10 respectively-4、0.889×10-4、0.023×10-4、0.176×10-4、0.138×
10-4、-0.008×10-4、0.218×10-4、1.606×10-4rad/pixel。
To (x, y) a pixel in second group of phase-shift interference, modified lateral phase shift obliquity factor, amendment are utilized
Longitudinal phase shift obliquity factor, phase shift translational movement di calculates (x, y) a one group of amount of phase shift D of pixel in table 1i(x,y)= Kxi
×x+ Kyi×y+di, (i=1,2 ..9).Take out the ash of (x, y) a pixel on all images in second group of phase-shift interference
Angle value Ii(x, y), background fluctuations factor ai, modulation degree fluctuate factor bi, least squares equation is constructed, such as formula (1) ~ (3).
(1)
(2)
(3)
Obtained X is one 3 × 1 matrix.The position phase φ (x, y) of (x, y) a pixel is calculated from X using formula (4),
X (2), X (3) are second and third element in X respectively.
(4)
Least squares equation established to pixel all on second group of phase-shift interference, available 480 × 640
The position phase data of pixel.According to pixel putting in order in second group of phase-shift interference, the position of pixel is mutually stored in
The matrix of one 480 × 640 size obtains second phase mehtod, as shown in Figure 9.
Unpacking operation is carried out to second phase mehtod, and optics is established according to the specific optical path form of phase-shifting interferometer
Relationship, reconstructing surface elevation information.In the present embodiment, phase-shifting interferometer uses Fizeau type optical interference circuit, and used swashs
Light device wavelength is 632.8nm.In this way, being to the relational expression of φ (x, y) unpacking and gauging surface height h (x, y)
(5)
In formula, unwrap is unpacking operation.The apparent height distribution finally reconstructed is as shown in Figure 10.The result and surface
Exact height distribution it is very close.
Directly using default amount of phase shift 0, pi/2,3 pi/2s ..., 11 pi/2s as initial value, using correcting three step iterative methods to second
Group phase-shift interference is calculated, and by 10 iteration, the surface of obtained phase mehtod and reconstruct deviates considerably from the standard on surface
Really height is distributed, and shows to measure failure at this time.Therefore, the method for the present invention can be quasi- from the phase-shift interference for be vibrated interference
Phase mehtod really is restored, and is able to maintain high spatial resolution.
Claims (3)
1. a kind of anti-vibration method of phase-shifting interferometer, which is characterized in that the method the following steps are included:
A. start phase-shifting interferometer, make phase-shifting interferometer work in phase shift mode, phase shift when acquiring adjacent two width phase-shift interference
The optical path difference variation that device generates is Δ, and calculating default amount of phase shift is 2 π Δs/λ, and λ is optical source wavelength；
B. the combination of pixels function of phase-shifting interferometer camera is opened, phase shifting equipment cooperates camera frame frequency to generate optical path difference variation, moves
Relevant interferometer acquires first group of phase-shift interference, and the resolution ratio of total L1 width, every width phase-shift interference is R1 × C1；
C. the combination of pixels function of phase-shifting interferometer camera is closed, phase shifting equipment cooperates camera frame frequency to generate optical path difference variation, moves
The camera of relevant interferometer acquires second group of phase-shift interference, and total L2 width, the resolution ratio of every width phase-shift interference is R2 × C2, R2/
R1=M, C2/C1=N, M, N are the integer greater than 1；
D. using default amount of phase shift as initial value, position phase is calculated from first group of phase-shift interference using three step iterative algorithms of amendment
Distribution I；
E. uniform sampling is carried out to each width phase-shift interference in second group of phase-shift interference, obtaining resolution ratio is R1 × C1's
Third group phase-shift interference；
F. it using phase mehtod I as initial value, is fallen into a trap evaluation time using three step iterative algorithms of amendment from third group phase-shift interference
Associated arguments, the time correlation parameter includes: lateral phase shift obliquity factor kx1、kx2、…、kxL2, longitudinal phase shift inclination because
Sub- ky1、ky2、…、kyL2, phase shift translational movement d1、d2、…、dL2, background fluctuations factor a1、a2、…、aL2, the modulation degree fluctuation factor
b1、b2、…、bL2；
G. by the lateral phase shift obliquity factor kx in step f1、kx2、…、kxL2Modified lateral phase shift inclination is obtained divided by N respectively
Factor K x1、Kx2、…、KxL2, by longitudinal phase shift obliquity factor ky1、ky2、…、kyL2Modified longitudinal phase shift is obtained divided by M respectively
Obliquity factor Ky1、Ky2、…、KyL2；
H. the amount of phase shift D of (x, y) a pixel on second group of phase-shift interference is calculated1(x,y)= Kx1×x+ Ky1×y+d1、
D2(x,y)= Kx2×x+ Ky2×y+d2、…、DL2(x,y)= KxL2×x+ KyL2×y+dL2, by the image of corresponding pixel
Gray value I1(x,y)、I2(x,y)、…、IL2(x, y) takes out, with D1(x,y)、D2(x,y)、…、DL2(x,y)、a1、a2、…、aL2、
b1、b2、…、bL2Least squares equation is constructed, least squares equation is solved and obtains the position phase φ (x, y) of (x, y) a pixel；
I. step h is repeated, until obtaining the position phase of all pixels point on second group of phase-shift interference, position is mutually existed according to pixel
Sequence deposit two-dimensional matrix on second group of phase-shift interference obtains phase mehtod II, to II unpacking of phase mehtod, according to light
Learn corresponding relationship reconstruct measured surface height distribution.
2. the anti-vibration method of phase-shifting interferometer according to claim 1, which is characterized in that uniformly adopted described in step e
Sample are as follows: take out the gray value for owning (a+mM, b+nN) a pixel on R2 × C2 image in different resolution, and be stored in R1 by original sequence
The matrix of × C1 size, 1≤a < M, 1≤b < N, m=0,1 ..., R1-1, n=0,1 ..., C1-1.
3. the anti-vibration method of phase-shifting interferometer according to claim 1, which is characterized in that L1 and L2 are all larger than equal to 4.
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| CN101968383A (en) * | 2010-09-02 | 2011-02-09 | 北京理工大学 | Anti-disturbance time-frequency domain wave-front detection method |
| CN102175332A (en) * | 2011-01-21 | 2011-09-07 | 南京理工大学 | Method for recovering phases from interferograms containing phase-shift error |
| CN102425988A (en) * | 2011-11-20 | 2012-04-25 | 中国科学院光电技术研究所 | Phase extraction method for phase-shifting interference fringe pattern |
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| CN101968383A (en) * | 2010-09-02 | 2011-02-09 | 北京理工大学 | Anti-disturbance time-frequency domain wave-front detection method |
| CN102175332A (en) * | 2011-01-21 | 2011-09-07 | 南京理工大学 | Method for recovering phases from interferograms containing phase-shift error |
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