CN106482664B - A kind of synthetic wavelength phase extraction method based on circle carrier frequency Moire fringe theory - Google Patents
A kind of synthetic wavelength phase extraction method based on circle carrier frequency Moire fringe theory Download PDFInfo
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Abstract
The invention discloses a kind of synthetic wavelength phase extraction methods based on circle carrier frequency Moire fringe theory, when detecting aspherical using dual wavelength interference testing device based on Moire fringe theory, circle carrier frequency moiré topography after available two kinds of wavelength-interferometric stripe stacks proposes a kind of method for directly extracting synthetic wavelength phase from circle carrier frequency moiré topography.By carrying out phase shift by phase shift stepping-in amount of the pi/2 of synthetic wavelength, to after circle carrier frequency Moire fringe phase-shift interference removal DC component squares, and use secondary polar coordinate transform, obtain line carrier frequency moiré topography, re-construction theory is overlapped in conjunction with carrier frequency, the extraction to the synthetic wavelength component of low frequency is realized in spectrum domain, finally extracts synthetic wavelength phase, and phase can not be restored by solving the problems, such as when Single wavelength detection that striped is overstocked.
Description
Technical field
The invention belongs to field of optical measuring technologies, especially a kind of synthetic wavelength based on circle carrier frequency Moire fringe theory
Phase extraction method.
Background technique
Phase shift interference detection has many advantages, such as that high-precision, contactless and automatic degree are high, thus in optical component surface shape, light
System performance and the test of optical material characteristic etc. is learned to have a wide range of applications.Traditional phase shift interference detection is using single
The laser light source of one wavelength, test scope is limited to its operation wavelength, thus is detecting the big change of gradient face shape such as aspherical
When its interference fringe can be overstocked and lead to not demodulation phase.
To solve the above-mentioned problems, following methods are generallyd use: first, the resolution ratio for improving detector can be allowed to differentiate
More intensive interference fringe, thus achieve the purpose that extend measurement range, but high-resolution detector price general charged is expensive,
Meanwhile the raising of detector resolution also results in the decline of test speed.Second, it can be surveyed using zero compensation measuring technique
Measure big gradient spherical surface or aspherical, but due to the deviation being tested between optical surface and best fit face be usually it is unknown, i.e.,
Make to be tested using zero compensation, interference pattern may also be difficult to analyze.Third, using the interference of longer wavelengths of infrared band
Instrument can also extend measurement range to a certain extent, but the interferometer of infrared band needs the optical material using infrared band
With infrared detector, processing is big with resetting difficulty, at high cost.4th, utilize sub- Nyquist (Sub-Nyquist) Sample acquisition
Method, which can solve, detects the overstocked problem of aspherical striped using traditional PS I, but since SNI deviates zero-bit interference condition, meeting
Need special alignment technique there are biggish hysterisis error, and in SNI require use thinned array detector, design and
Processing will be compared with conventional probes complexity.5th, using shear interference technology, pass through the difference corrugated in two vertical direction of measurement
Restore original wave-front, the measurement of large deviation face shape also may be implemented, it is although the measuring device of this method is simple, subsequent
Data handling procedure and its many and diverse, and precision is lower.6th is detected using sub-aperture stitching, and optical element is divided into several sons
Hole completes the interferometry to each sub-aperture by mobile interferometer measuration system or measured piece, obtains a series of corrugated data, then
By these corrugateds, data are fitted splicing, obtain the surface form deviation of whole surface.But due to splicing when sub-aperture stitching detects
The accumulation of error and the kinematic error of sub-aperture make precision relatively low, and detection process needs in sequence to carry out each sub-aperture
Measurement, time-consuming and laborious, measurement efficiency is very low.
From 1971 by James White (J.C.Wyant) in " Testing aspherics using two-
Wavelength holography " propose that double-wavelength holographic is dry in (APPLIED OPTICS, 10 (9): 2113-2118,1971)
Since relating to measuring technology, on this basis, dual wavelength interference testing technology is developed.Dual wavelength Moire fringe theory refers to
It is multiplied to the interference fringe under different wave length test or the moiré topography of linear superposition generation is handled, to extract synthesis
Wavelength phases information.1988 small open country temple (Onodera) et al. " Two-Wavelength Interferometry That
Uses a Fourier-Transform Method " (APPLIED OPTICS, 37 (34): 7988~7994,1988) proposes
On the basis of wavelength tuning dual wavelength phase-shifting interferometer, the spectrogram of dual wavelength Moire fringe is obtained using Fourier transformation,
Processing obtains synthetic wavelength phase, but its processing for being confined to line carrier coded fringes, and carrier frequency amount is not high.2003, Zhe Fu
(Tetsuo)《Phase calculation based on curve fitting with a two-wavelength
Interferometer " (Optics Express, 11 (8): 895~898,2003) in analysis dual wavelength Moire fringe light intensity point
It on the basis of cloth, proposes and the Moire fringe light distribution of time domain dual wavelength is fitted using curve point by point, curve representation formula is respectively joined
Number can be calculated by a series of hypothesis, iteration acquires, and finally solved and obtained synthetic wavelength phase distribution.Although the algorithm can be with
Directly processing dual wavelength moire map obtains synthetic wavelength phase, but its complex and process is cumbersome.2014, China
Peeping for southern normal university flat (Wangping Zhang) et al. is in " Simultaneous phase-shifting dual-
wavelength interferometry based on two-step demodulation algorithm》(Optics
39 (18): Letters analyzes dual wavelength Moire fringe light distribution in 5375~5378,2014), proposes one kind
The algorithm of synthetic wavelength phase is extracted from the moiré topography of online two-wavelength-interferometer, the juche idea of algorithm is by setting
Determine amount of phase shift and realizes that the extraction to the interference fringe of different wave length is finally solved and closed to solve Single wavelength phase respectively
At wavelength phases, but the algorithm does not consider the overstocked situation of Single wavelength striped.
Summary of the invention
The purpose of the present invention is to provide it is a kind of based on circle carrier frequency Moire fringe theory synthetic wavelength phase extraction method,
It solves Single wavelength simultaneously and detects what each component when carrier frequency Moire fringe is justified in the overstocked and direct processing of aspherical striped was difficult to separate
Problem.
The technical solution for realizing the aim of the invention is as follows: a kind of composite wave appearance based on circle carrier frequency Moire fringe theory
Position extracting method, method and step are as follows:
Step 1: being respectively λ using operation wavelength1And λ2Dual wavelength interference testing device detect aspheric surface, wherein
λ1≠λ2, two kinds of wavelength work at the same time, and the axial position for adjusting test mirrors introduces circle carrier frequency by defocus, and it is dry to obtain two kinds of wavelength
Circle carrier frequency moiré topography after relating to stripe stack.
Step 2: the output voltage of control Phase shifting adapter, is realized with synthetic wavelengthPi/2 be phase shift
Stepping-in amount carries out phase shift, and CCD collects the oval carrier frequency moire map of double wave that one group of 4 frame phase shift stepping-in amount is pi/2,
Its light distribution are as follows:
Wherein, IkFor the oval carrier frequency moire map light distribution of kth frame double wave, A is i.e. DC component,For wave
Long λ1Modulation degree,For wavelength X1Phase to be measured, D be circle carrier frequency coefficient, S2For horizontal pixel coordinate square and longitudinal picture
The sum of plain coordinate square (i.e. S2=x2+y2, x is horizontal pixel coordinate, and y is longitudinal pixel coordinate), δ1,kFor in kth frame interference pattern
Wavelength X1Amount of phase shift,For wavelength X2Modulation degree,For wavelength X2Phase to be measured, δ2,kFor kth frame interference pattern medium wavelength
λ2Amount of phase shift.
Step 3: removing DC component using the method for average to the oval carrier frequency moire map of the double wave collected
Afterwards, it carries out square, the oval carrier frequency moire map light intensity I ' of double wave after obtaining squarenDistribution are as follows:
Wherein, A ' be square after DC component, B1For wavelength X1The coefficient of two harmonics, i.e.,With
Wavelength X1Downward systemIt is related, B2For wavelength X2The coefficient of two harmonics, i.e.,With wavelength X2Downward systemIt is related, B3For wavelength X1Downward systemWith wavelength X2Downward systemProduct,
For synthetic wavelength phase, δeq,kFor kth frame interference pattern medium wavelength λeqAmount of phase shift.
Step 4: the fringe center of every frame circle carrier frequency moire map in second step is determined, to above-mentioned Moire fringe
Phase-shift interference carries out secondary polar coordinate transform respectively, and the dual wavelength line carrier frequency Moire fringe after obtaining corresponding coordinate conversion moves
Interference figure, coordinate transform formula are as follows:
Wherein, (ρ, θ) is the point coordinate under polar coordinate system, and (x, y) is the point under cartesian coordinate system corresponding to point (ρ, θ)
Coordinate, (x0,y0) be cartesian coordinate system under fringe center point coordinate.
Step 5: according to overlapping re-construction theory, to the dual wavelength line carrier frequency Moire fringe phase-shift interference after coordinate conversion
Staggeredly it is alternatively arranged to obtain empty bar graph at that time.
Step 6: clock synchronization sky bar graph carries out Fourier transformation, its spectrum distribution is obtained, is selected in clock synchronization sky bar graph frequency spectrum
The forward direction for being located at orientation in the 5th step is selected, and the phase spectrum at origin d/4 carries out bandpass filtering, wherein d is frequency spectrum
Overall length in orientation, obtains phase component.
Step 7: carrying out inverse Fourier transform to phase component, its briquetting extension phase P ' is obtained, briquetting is extended into phase
P ' is inversely extracted according to arrangement mode in the 5th step, is restored to the briquetting phase P of original phase size, is solved to it
Packet, which obtains, unpacks phase UPq。
Step 8: to the unpacking phase UP of acquisitionqAccording to the inverse transformation mode of secondary polar coordinate transform in the 4th step, by pole
Coordinate is transformed to cartesian coordinate system, acquires final phase distribution UP.
Compared with the prior art, the advantages of the present invention are as follows: (1) pass through the circle after two kinds of wavelength-interferometric stripe stacks of processing
High frequency is obtained the synthetic wavelength stripe information that Single wavelength interference fringe information is converted to low frequency, expanded by carrier frequency moiré topography
Detection range；(2) circle carrier coded fringes are transformed to by line carrier coded fringes using secondary polar coordinate transform, reduce processing difficulty, mentions
High precision；(3) combining carrier frequency to overlap re-construction theory realizes its frequency spectrum and each point using synthetic wavelength pi/2 as phase shift stepping-in amount
The separation of amount, is easy to extract the synthetic wavelength phase component of low frequency, and is able to suppress the influence of Phase-shifting Errors simultaneously.
Detailed description of the invention
Fig. 1 is a kind of synthetic wavelength phase extraction method flow chart based on circle carrier frequency Moire fringe theory.
Fig. 2 is in the embodiment of the present invention using the height of 100mm bore dual wavelength fizeau interferometer detection radius of curvature 41.4m
The anti-oval carrier frequency moire map of the collected double wave of spherical surface.
Fig. 3 is that the oval carrier frequency moire map of double wave is double after secondary polar coordinate transform in the embodiment of the present invention
Wavelength line carrier frequency moire map.
Fig. 4 is the space-time that dual wavelength line carrier frequency moire map obtain after folded array in the embodiment of the present invention
Bar graph.
Fig. 5 is the briquetting phase P of original phase size under polar coordinate system in the embodiment of the present invention.
Fig. 6 is to be asked in the embodiment of the present invention using the synthetic wavelength phase extraction method based on circle carrier frequency Moire fringe theory
Solution obtains phase distribution to be measured.
Specific embodiment
Present invention is further described in detail with reference to the accompanying drawing.
In conjunction with Fig. 1, a kind of synthetic wavelength phase extraction method based on circle carrier frequency Moire fringe theory, steps are as follows:
Step 1: being λ using operation wavelength1And λ2Striking rope type (application number: CN201310589143) or safe graceful type double wave
Long interference testing device (application number: CN201410342492) detects aspheric surface, and two kinds of wavelength work at the same time, adjustment test
The axial position of mirror introduces circle carrier frequency by defocus, the circle carrier frequency moiré topography after obtaining two kinds of wavelength-interferometric stripe stacks.
Step 2: the output voltage of control Phase shifting adapter, is realized with synthetic wavelengthPi/2 phase shift step
Input carries out phase shift, collects the oval carrier frequency moire map of double wave that one group of 4 frame phase shift stepping-in amount is pi/2, light
Strong distribution are as follows:
Wherein, IkFor the oval carrier frequency moire map light distribution of kth frame double wave, A is i.e. DC component,For wave
Long λ1Modulation degree,For wavelength X1Phase to be measured, D be circle carrier frequency coefficient, S2For horizontal pixel coordinate square and longitudinal pixel
The sum of coordinate square (i.e. S2=x2+y2, x is horizontal pixel coordinate, and y is longitudinal pixel coordinate), δ1,kFor kth frame interference pattern medium wave
Long λ1Amount of phase shift,For wavelength X2Modulation degree,For wavelength X2Phase to be measured, δ2,kFor kth frame interference pattern medium wavelength
λ2Amount of phase shift.
Step 3: after to the oval carrier frequency moire map of double wave is collected using method of average removal DC component,
It carries out square, the oval carrier frequency moire map light distribution of double wave after obtaining square are as follows:
Wherein, A ' be square after DC component, B1For wavelength X1The coefficient of two harmonics, i.e.,With
Wavelength X1Downward systemIt is related, B2For wavelength X2The coefficient of two harmonics, i.e.,With wavelength X2Downward systemIt is related, B3For wavelength X1Downward systemWith wavelength X2Downward systemProduct,For
Synthetic wavelength phase, δeq,kFor kth frame interference pattern medium wavelength λeqAmount of phase shift.
Step 4: determining the fringe center for collecting round carrier frequency moire map, Moire fringe phase shift is interfered
Figure carries out secondary polar coordinate transform respectively, obtains dual wavelength line carrier frequency Moire fringe phase-shift interference, coordinate transform formula are as follows:
Wherein, (ρ, θ) is the point coordinate under polar coordinate system, and (x, y) is the point under cartesian coordinate system corresponding to point (ρ, θ)
Coordinate, (x0,y0) be cartesian coordinate system under fringe center point coordinate.
Step 5: according to overlapping re-construction theory to coordinate conversion after dual wavelength line carrier frequency Moire fringe phase-shift interference into
Row staggeredly is alternatively arranged to obtain empty bar graph at that time, dual wavelength line under the polar coordinate system before space-time bar graph and conversion after conversion
The relationship of carrier frequency Moire fringe phase-shift interference are as follows:
S'(Nx+n, y)=Sn(x,y)；
Step 6: clock synchronization sky bar graph carries out Fourier transformation, its spectrum distribution is obtained, is selected in clock synchronization sky bar graph frequency spectrum
Select the phase spectrum for being located at positive at origin 1/4d (d is overall length of the frequency spectrum in orientation) of orientation in step 5
Bandpass filtering is carried out, phase component is obtained.
Step 7: carrying out inverse Fourier transform to phase component, its briquetting extension phase P ' is obtained, briquetting is extended into phase
P ' is inversely extracted according to arrangement mode in step 5, is restored to the briquetting phase P of original phase size, is solved to it
Packet, which obtains, unpacks phase UPq。
Step 8: to the unpacking phase UP of acquisition according to the inverse transformation mode of polar coordinate transform secondary in step 4, by pole
Coordinate is transformed to cartesian coordinate system, acquires final phase distribution UP.
Embodiment 1
Step 1: aspherical using the test of 100mm bore dual wavelength fizeau interferometer, interferometer work wavelength is respectively λ1
=632.8nm and λ2=532nm, the axial position for adjusting test mirrors obtains the circle carrier frequency after two kinds of wavelength-interferometric stripe stacks
Moiré topography；
Step 2: the output voltage of control Phase shifting adapter, is realized with synthetic wavelength λeq=3.339 μm of pi/2 adopts shifting
Phase stepping-in amount carry out phase shift, integrated using CCD obtain one group of 4 frame phase shift stepping-in amount be the oval carrier frequency Moire fringe of the double wave of pi/2 do
Figure is related to, the oval carrier frequency moire map of double wave is specifically as shown in Figure 2；
Step 3: after to the oval carrier frequency moire map of double wave is collected using method of average removal DC component,
It carries out square, the oval carrier frequency moire map light distribution of double wave after obtaining square；
Step 4: determining the fringe center for collecting round carrier frequency moire map, Moire fringe phase shift is interfered
Figure carries out secondary polar coordinate transform respectively, obtains dual wavelength line carrier frequency Moire fringe phase-shift interference, secondary polar coordinate transform
Dual wavelength line carrier frequency moire map afterwards is specifically as shown in Figure 3
Step 5: according to overlapping re-construction theory to coordinate conversion after dual wavelength line carrier frequency Moire fringe phase-shift interference into
It is as shown in Figure 4 that row staggeredly is alternatively arranged to obtain empty bar graph, the space-time bar graph after conversion at that time；
Step 6: clock synchronization sky bar graph carries out Fourier transformation, its spectrum distribution is obtained, is selected in clock synchronization sky bar graph frequency spectrum
Select the phase spectrum for being located at positive at origin 1/4d (d is overall length of the frequency spectrum in orientation) of orientation in step 5
Bandpass filtering is carried out, phase component is obtained；
Step 7: carrying out inverse Fourier transform to phase component, its briquetting extension phase P ' is obtained, briquetting is extended into phase
P ' is inversely extracted according to arrangement mode in step 5, is restored to the briquetting phase P of original phase size as shown in figure 5, right
It, which unpack obtaining, unpacks phase UPq；
Step 8: to the unpacking phase UP of acquisition according to the inverse transformation mode of polar coordinate transform secondary in step 4, by pole
Coordinate is transformed to cartesian coordinate system, and it is as shown in Figure 6 to acquire final phase distribution UP.
Compared with the conventional method, the synthetic wavelength phase extraction method based on circle carrier frequency Moire fringe theory passes through processing two
Circle carrier frequency moiré topography after kind wavelength-interferometric stripe stack, obtains Single wavelength interference fringe information for high frequency and is converted to low frequency
Synthetic wavelength stripe information, expands detection range；And circle carrier coded fringes are transformed to by line carrier frequency using secondary polar coordinate transform
Striped reduces processing difficulty, improves precision；Re-construction theory is overlapped in combination with carrier frequency, is walked by phase shift of synthetic wavelength pi/2
Input realizes the separation of its frequency spectrum Yu each component, is easy to extract the synthetic wavelength phase component of low frequency, and is able to suppress simultaneously
The influence of Phase-shifting Errors.
Claims (1)
1. a kind of synthetic wavelength phase extraction method based on circle carrier frequency Moire fringe theory, which is characterized in that method and step is such as
Under:
Step 1: being respectively λ using operation wavelength1And λ2Dual wavelength interference testing device detect aspheric surface, wherein λ1≠
λ2, two kinds of wavelength work at the same time, and the axial position for adjusting test mirrors introduces circle carrier frequency by defocus, obtain two kinds of wavelength-interferometric items
The superimposed round carrier frequency moiré topography of line；
Step 2: the output voltage of control Phase shifting adapter, is realized with synthetic wavelengthPi/2 be phase shift stepping-in amount
Phase shift is carried out, CCD collects the oval carrier frequency moire map of double wave that one group of 4 frame phase shift stepping-in amount is pi/2, light intensity
Distribution are as follows:
Wherein, IkFor the oval carrier frequency moire map light distribution of kth frame double wave, A is DC component,For wavelength X1's
Modulation degree,For wavelength X1Phase to be measured, D be circle carrier frequency coefficient, S2It is flat for horizontal pixel coordinate square and longitudinal pixel coordinate
The sum of side, S2=x2+y2, x is horizontal pixel coordinate, and y is longitudinal pixel coordinate, δ1,kFor kth frame interference pattern medium wavelength λ1Shifting
Phasor,For wavelength X2Modulation degree,For wavelength X2Phase to be measured, δ2,kFor kth frame interference pattern medium wavelength λ2Phase shift
Amount；
Step 3: after removing DC component using the method for average to the oval carrier frequency moire map of the double wave collected, into
Row square, the oval carrier frequency moire map light intensity I of double wave after obtaining squaren' distribution are as follows:
Wherein, A ' be square after DC component, B1For wavelength X1The coefficient of two harmonics,B2For wavelength
λ2The coefficient of two harmonics,B3For wavelength X1Downward systemWith wavelength X2Downward systemProduct, For synthetic wavelength phase, δeq,kFor kth frame interference pattern medium wavelength λeqAmount of phase shift；
Step 4: the fringe center of every frame circle carrier frequency moire map in second step is determined, to above-mentioned round carrier frequency More item
Line interference pattern carries out secondary polar coordinate transform respectively, the dual wavelength line carrier frequency Moire fringe phase shift after obtaining corresponding coordinate conversion
Interference pattern, coordinate transform formula are as follows:
Wherein, (ρ, θ) is the point coordinate under polar coordinate system, and (x, y) is that the point under cartesian coordinate system corresponding to point (ρ, θ) is sat
Mark, (x0,y0) be cartesian coordinate system under fringe center point coordinate；
Step 5: being carried out according to overlapping re-construction theory to the dual wavelength line carrier frequency Moire fringe phase-shift interference after coordinate conversion
Staggeredly it is alternatively arranged to obtain empty bar graph at that time；
Step 6: clock synchronization sky bar graph carries out Fourier transformation, its spectrum distribution is obtained, selects position in clock synchronization sky bar graph frequency spectrum
The forward direction of orientation in the 5th step, and the phase spectrum at origin d/4 carries out bandpass filtering, wherein d is that frequency spectrum is being arranged
Overall length on column direction, obtains phase component；
Step 7: carrying out inverse Fourier transform to phase component, its briquetting extension phase P ' is obtained, briquetting extension phase P ' is pressed
It according to arrangement mode in the 5th step, is inversely extracted, is restored to the briquetting phase P of original phase size, it is carried out to unpack and is obtained
Phase UP must be unpackedq；
Step 8: to the unpacking phase UP of acquisitionqAccording to the inverse transformation mode of secondary polar coordinate transform in the 4th step, by polar coordinates
It is transformed to cartesian coordinate system, acquires final phase distribution UP.
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| CN106931905B (en) * | 2017-03-09 | 2019-02-05 | 北京理工大学 | A kind of digital Moiré patterns phase extraction method based on nonlinear optimization |
| CN110375641B (en) * | 2019-07-19 | 2021-04-09 | 黑龙江大学 | Circular carrier frequency digital holographic detection device and method based on improved Michelson structure |
| CN114485473B (en) * | 2022-02-21 | 2024-01-30 | 上海电机学院 | Laser interference phase demodulation method based on component synthesis and gradient projection |
| CN114608472A (en) * | 2022-02-22 | 2022-06-10 | 珠海迈时光电科技有限公司 | Wide spectrum interference microscopic measuring method, device, electronic equipment and medium |
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