CN106482664A - A kind of synthetic wavelength phase extraction method theoretical based on circle carrier frequency Moire fringe - Google Patents

Abstract

The invention discloses a kind of synthetic wavelength phase extraction method theoretical based on circle carrier frequency Moire fringe, when detecting aspherical based on Moire fringe is theoretical using dual wavelength interference testing device, the round carrier frequency moiré topography after two kinds of wavelength-interferometric stripe stack can be obtained, it is proposed that a kind of method from circle carrier frequency moiré topography extracting directly synthetic wavelength phase place.By carrying out phase shift with the pi/2 of synthetic wavelength as phase shift stepping-in amount, to after circle carrier frequency Moire fringe phase-shift interference removal DC component square, and adopt secondary polar coordinate transform, obtain line carrier frequency moiré topography, re-construction theory is overlapped in conjunction with carrier frequency, the extraction of the synthetic wavelength component to low frequency being realized in spectrum domain, finally extracting synthetic wavelength phase place, when solving the problems, such as that Single wavelength is detected, striped is overstocked cannot recover phase place.

Description

A kind of synthetic wavelength phase extraction method theoretical based on circle carrier frequency Moire fringe

Technical field

The invention belongs to field of optical measuring technologies, particularly a kind of synthesis theoretical based on circle carrier frequency Moire fringe Wavelength phases extracting method.

Background technology

Phase shift interferes detection high have the advantages that high accuracy, contactless and automatic degree, thus in optical element face The aspects such as the test of shape, Performance of Optical System and optical material characteristic have a wide range of applications.Traditional phase shift Interfere detection using the LASER Light Source of single wavelength, its test scope is limited to its operation wavelength, thus in detection During the big graded face shape of aspherical grade its interference fringe can be overstocked and lead to not demodulation phase.

In order to solve the above problems, following methods are generally adopted：First, the resolution ratio for improving detector can make The more intensive interference fringe of resolution, so as to reach the purpose of extension measurement range, but high-resolution detection Device price general charged is expensive, meanwhile, the raising of detector resolution also results in the decline of test speed.Second, Big gradient sphere or aspherical can be measured using zero compensation e measurement technology, but due to tested optical surface and most Deviation between good fitting face is typically unknown, even if being tested using zero compensation, interference pattern is likely to It is difficult to analyze.3rd, survey can also be extended to a certain extent using the interferometer of longer wavelengths of infrared band Amount scope, but the interferometer of infrared band needs optical material and the Infrared Detectors using infrared band, processing Big, the high cost with resetting difficulty.4th, can using sub- Nyquist (Sub-Nyquist) Sample acquisition method To solve the problems, such as to detect that aspherical striped is overstocked using traditional PS I, but as SNI deviates zero-bit interference condition, Can there is larger hysterisis error and special alignment technique is needed, and require to visit using thinned array in SNI Device is surveyed, its design and processing want more conventional detector complicated.5th, using shear interference technology, by measurement Difference corrugated in two vertical direction is recovering original wave-front, it is also possible to realize the measurement of large deviation face shape, though So the measurement apparatus of this method are simple, but follow-up data handling procedure and its numerous and diverse, and precision is relatively low.The Six are detected using sub-aperture stitching, and optical element is divided into some sub-aperture, by mobile interferometer measuration system or Measured piece completes the interferometry to each sub-aperture, obtains a series of corrugated data, then these corrugated data are entered Row fitting splicing, obtains the surface form deviation of whole surface.But tiring out due to stitching error when sub-aperture stitching is detected The kinematic error of product and sub-aperture causes precision low, and detection process needs to carry out each sub-aperture in order Measurement, wastes time and energy, and measurement efficiency is very low.

From 1971 by James. White (J.C.Wyant) exists《Testing aspherics using two-wavelength holography》(APPLIED OPTICS,10(9):Propose in 2113-2118,1971) Since double-wavelength holographic interference measuring technology, on this basis, dual wavelength interference testing technology is developed. Dual wavelength Moire fringe theory refers to that the interference fringe lower to different wave length test is multiplied or linear superposition generation Moiré topography is processed, so as to extract synthetic wavelength phase information.Little open country temple (Onodera) in 1988 Et al.《Two-Wavelength Interferometry That Uses a Fourier-Transform Method》 (APPLIED OPTICS,37(34):7988～7994,1988) propose dry in the phase shift of wavelength tuning dual wavelength The spectrogram of dual wavelength Moire fringe on the basis of interferometer, is obtained using Fourier transformation, is processed and is obtained composite wave Long phase place, but which is confined to the process of 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) on the basis of analysis dual wavelength Moire fringe light distribution On, it is proposed that time domain dual wavelength Moire fringe light distribution is fitted using curve point by point, its curve representation formula is respectively joined By a series of, number can assume that calculating, iteration are tried to achieve, finally solve and obtain synthetic wavelength phase distribution.Although The algorithm can directly process dual wavelength moire map and obtain synthetic wavelength phase place, but its complex and Process is loaded down with trivial details.2014, peeping for South China Normal University flat (Wangping Zhang) et al. existed 《Simultaneous phase-shifting dual-wavelength interferometry based on two-step demodulation algorithm》(Optics Letters,39(18):5375～5378,2014) in dual wavelength not You are analyzed in striped light distribution, it is proposed that a kind of Moire fringe in figure from online two-wavelength-interferometer is extracted The algorithm of synthetic wavelength phase place, the juche idea of algorithm are to realize the interference to different wave length by setting amount of phase shift The extraction of striped, so as to solve Single wavelength phase place respectively, finally solves and obtains synthetic wavelength phase place, but the algorithm The overstocked situation of Single wavelength striped is not considered.

Content of the invention

It is an object of the invention to provide a kind of synthetic wavelength phase extraction theoretical based on circle carrier frequency Moire fringe Method, while solve Single wavelength to detect that aspherical striped is overstocked and direct each point when processing circle carrier frequency Moire fringe Amount is difficult to detached problem.

The technical solution for realizing the object of the invention is：A kind of composite wave theoretical based on circle carrier frequency Moire fringe Long phase extraction method, method and step are as follows：

The first step：λ is respectively using operation wavelength₁And λ₂Dual wavelength interference testing device detect aspherical face Shape, wherein λ₁≠λ₂, two kinds of wavelength are while work, the axial location for adjusting test mirrors introduces round load by out of focus Frequently, the round carrier frequency moiré topography after two kinds of wavelength-interferometric stripe stack is obtained.

Second step：The output voltage of control Phase shifting adapter, realizes with synthetic wavelengthPi/2 Phase shift is carried out for phase shift stepping-in amount, CCD collects the oval load of double wave of one group of 4 frame phase shift stepping-in amount for pi/2 Frequency moire map, its light distribution is：

Wherein, I_kFor the oval carrier frequency moire map light distribution of kth frame double wave, A is i.e. DC component,For wavelength X₁Modulation degree,For wavelength X₁Phase place to be measured, D for circle carrier frequency coefficient, S²For horizontal Pixel coordinate square and longitudinal direction pixel coordinate square sum (i.e. S²=x²+y², x is horizontal pixel coordinate, y For longitudinal pixel coordinate), δ_1,kFor kth frame interference pattern medium wavelength λ₁Amount of phase shift,For wavelength X₂Modulation Degree,For wavelength X₂Phase place to be measured, δ_2,kFor kth frame interference pattern medium wavelength λ₂Amount of phase shift.

3rd step：The oval carrier frequency moire map of double wave to collecting removes direct current using the method for average and divides After amount, carry out square, the oval carrier frequency moire map light intensity I ' of the double wave after obtaining square_nIt is distributed as：

Wherein, A ' for square after DC component, B₁For wavelength X₁The coefficient of two harmonics, i.e.,With wavelength X₁Downward systemRelevant, B₂For wavelength X₂The coefficient of two harmonics, i.e.,With wavelength X₂Downward systemRelevant, B₃For wavelength X₁Downward systemWith wavelength X₂Under Modulation degreeProduct,For synthetic wavelength phase place, δ_eq,kDry for kth frame Relate in figure wavelength X_eqAmount of phase shift.

4th step：Determine the fringe center for justifying carrier frequency moire map in second step per frame, to above-mentioned More Striped phase-shift interference carries out secondary polar coordinate transform respectively, obtains the load of the dual wavelength line after corresponding Coordinate Conversion Frequency Moire fringe phase-shift interference, its coordinate transform formula is：

Wherein, (ρ, θ) is the point coordinates under polar coordinate system, and (x, y) is cartesian coordinate system corresponding to point (ρ, θ) Under point coordinates, (x₀,y₀) for the fringe center point coordinates under cartesian coordinate system.

5th step：According to overlapping re-construction theory, the dual wavelength line carrier frequency Moire fringe phase shift after Coordinate Conversion is done Relating to figure carries out interlocking to be spaced obtaining its space-time bar graph.

6th step：Fourier transformation is carried out to space-time bar graph, its spectrum distribution is obtained, to space-time bar graph frequency Select to be located at the forward direction of orientation in the 5th step in spectrum, and the phase spectrum at initial point d/4 carries out band logical filter Ripple, wherein d are overall length of the frequency spectrum in orientation, obtain phase component.

7th step：Inverse Fourier transform is carried out to phase component, obtains its briquetting extension phase place P ', by briquetting Extension phase place P ' according to arrangement mode in the 5th step, inversely extracted, return to the pressure of original phase size Bag phase place P, carries out unpacking acquisition unpacking phase place UP to which_q.

8th step：To unpacking phase place UP for obtaining_qInverse transformation side according to secondary polar coordinate transform in the 4th step Formula, is cartesian coordinate system by polar coordinate transform, tries to achieve final phase distribution UP.

Compared with prior art, it is an advantage of the current invention that：(1) by processing two kinds of wavelength-interferometric stripe stack Round carrier frequency moiré topography afterwards, high frequency is obtained the composite wave strip that Single wavelength interference fringe information is converted to low frequency Line information, expands detection range；(2) circle carrier coded fringes are transformed to by line carrier frequency using secondary polar coordinate transform Striped, reduces intractability, improves precision；(3) combine carrier frequency and re-construction theory is overlapped, with synthetic wavelength pi/2 For phase shift stepping-in amount, it is achieved that its frequency spectrum is separated with each component, it is easy to which the synthetic wavelength phase place for extracting low frequency is divided Amount, and while the impact of Phase-shifting Errors can be suppressed.

Description of the drawings

Fig. 1 is a kind of synthetic wavelength phase extraction method flow chart theoretical based on circle carrier frequency Moire fringe.

Fig. 2 is to detect radius of curvature using 100mm bore dual wavelength fizeau interferometer in the embodiment of the present invention 41.4m the oval carrier frequency moire map of the collected double wave of the anti-sphere of height.

Fig. 3 be in the embodiment of the present invention the oval carrier frequency moire map of double wave through secondary polar coordinate transform Dual wavelength line carrier frequency moire map afterwards.

Fig. 4 is that dual wavelength line carrier frequency moire map is obtained after carrying out folded array in the embodiment of the present invention Space-time bar graph.

Fig. 5 is briquetting phase place P of original phase size under polar coordinate system in the embodiment of the present invention.

Fig. 6 be using based on the theoretical synthetic wavelength phase extraction of circle carrier frequency Moire fringe in the embodiment of the present invention Method is solved and obtains phase distribution to be measured.

Specific embodiment

Below in conjunction with the accompanying drawings the present invention is described in further detail.

In conjunction with Fig. 1, a kind of synthetic wavelength phase extraction method theoretical based on circle carrier frequency Moire fringe, step is such as Under：

The first step：It is λ using operation wavelength₁And λ₂Striking rope type (application number：CN201310589143) or Safe graceful type dual wavelength interference testing device (application number：CN201410342492) detection aspheric surface, two Wavelength is planted while working, the axial location for adjusting test mirrors introduces round carrier frequency by out of focus, obtains two kinds of wavelength and does Relate to the round carrier frequency moiré topography after stripe stack.

Second step：The output voltage of control Phase shifting adapter, realizes with synthetic wavelengthPi/2 Phase shift stepping-in amount carries out phase shift, collects the oval carrier frequency More of double wave of one group of 4 frame phase shift stepping-in amount for pi/2 Interference fringe, its light distribution is：

Wherein, I_kFor the oval carrier frequency moire map light distribution of kth frame double wave, A is i.e. DC component, For wavelength X₁Modulation degree,For wavelength X₁Phase place to be measured, D for circle carrier frequency coefficient, S²For horizontal pixel Coordinate square and longitudinal direction pixel coordinate square sum (i.e. S²=x²+y², x is horizontal pixel coordinate, and y is vertical To pixel coordinate), δ_1,kFor kth frame interference pattern medium wavelength λ₁Amount of phase shift,For wavelength X₂Modulation degree,For wavelength X₂Phase place to be measured, δ_2,kFor kth frame interference pattern medium wavelength λ₂Amount of phase shift.

3rd step：DC component is removed using the method for average to collecting double wave oval carrier frequency moire map Afterwards, carry out square, the oval carrier frequency moire map light distribution of the double wave after obtaining square is：

Wherein, A ' for square after DC component, B₁For wavelength X₁The coefficient of two harmonics, i.e., With wavelength X₁Downward systemRelevant, B₂For wavelength X₂The coefficient of two harmonics, i.e.,With Wavelength X₂Downward systemRelevant, B₃For wavelength X₁Downward systemWith wavelength X₂Downward systemTake advantage of Product,For synthetic wavelength phase place, δ_eq,kFor kth frame interference pattern medium wavelength λ_eq Amount of phase shift.

4th step：Determine the fringe center for collecting round carrier frequency moire map, to Moire fringe phase shift Interference pattern carries out secondary polar coordinate transform respectively, obtains dual wavelength line carrier frequency Moire fringe phase-shift interference, its seat Marking transformation for mula is:

Wherein, (ρ, θ) is the point coordinates under polar coordinate system, and (x, y) is under cartesian coordinate system corresponding to point (ρ, θ) Point coordinates, (x₀,y₀) for the fringe center point coordinates under cartesian coordinate system.

5th step：The dual wavelength line carrier frequency Moire fringe phase shift after Coordinate Conversion is interfered according to overlapping re-construction theory Figure carries out staggered being spaced and obtains its space-time bar graph, the polar coordinates before the space-time bar graph after conversion and conversion Under system, the relation of dual wavelength line carrier frequency Moire fringe phase-shift interference is：

S'(Nx+n, y)=S_n(x,y)；

6th step：Fourier transformation is carried out to space-time bar graph, its spectrum distribution is obtained, to space-time bar graph frequency (d is frequency spectrum in orientation at initial point 1/4d to select the forward direction positioned at orientation in step 5 in spectrum Overall length) phase spectrum carry out bandpass filtering, obtain phase component.

7th step：Inverse Fourier transform is carried out to phase component, obtains its briquetting extension phase place P ', by briquetting Extension phase place P ' according to arrangement mode in step 5, inversely extracted, return to the pressure of original phase size Bag phase place P, carries out unpacking acquisition unpacking phase place UP to which_q.

8th step：To obtain unpacking phase place UP according to secondary polar coordinate transform in step 4 inverse transformation mode, It is cartesian coordinate system by polar coordinate transform, tries to achieve final phase distribution UP.

Embodiment 1

The first step：Aspherical using the test of 100mm bore dual wavelength fizeau interferometer, interferometer work wavelength divides Wei not λ₁=632.8nm and λ₂=532nm, the axial location for adjusting test mirrors obtains two kinds of wavelength-interferometric stripeds Round carrier frequency moiré topography after superposition；

Second step：The output voltage of control Phase shifting adapter, realizes with synthetic wavelength λ_eq=3.339 μm of pi/2 Adopting phase shift stepping-in amount carries out phase shift, integrates the dual wavelength for obtaining one group of 4 frame phase shift stepping-in amount as pi/2 using CCD Circle carrier frequency moire map, the oval carrier frequency moire map of its double wave are specifically as shown in Figure 2；

3rd step：Divided using method of average removal direct current to collecting the oval carrier frequency moire map of double wave After amount, carry out square, the oval carrier frequency moire map light distribution of the double wave after obtaining square；

4th step：Determine the fringe center for collecting round carrier frequency moire map, to Moire fringe phase shift Interference pattern carries out secondary polar coordinate transform respectively, obtains dual wavelength line carrier frequency Moire fringe phase-shift interference, and which two Dual wavelength line carrier frequency moire map after secondary polar coordinate transform is specifically as shown in Figure 3

5th step：The dual wavelength line carrier frequency Moire fringe phase shift after Coordinate Conversion is interfered according to overlapping re-construction theory Figure carries out staggered being spaced and obtains its space-time bar graph, and the space-time bar graph after conversion is as shown in Figure 4；

6th step：Fourier transformation is carried out to space-time bar graph, its spectrum distribution is obtained, to space-time bar graph frequency (d is frequency spectrum in orientation at initial point 1/4d to select the forward direction positioned at orientation in step 5 in spectrum Overall length) phase spectrum carry out bandpass filtering, obtain phase component；

7th step：Inverse Fourier transform is carried out to phase component, obtains its briquetting extension phase place P ', by briquetting Extension phase place P ' according to arrangement mode in step 5, inversely extracted, return to the pressure of original phase size Bag phase place P unpacks phase place UP as shown in figure 5, carrying out unpacking to which obtaining_q；

8th step：To obtain unpacking phase place UP according to secondary polar coordinate transform in step 4 inverse transformation mode, It is cartesian coordinate system by polar coordinate transform, tries to achieve final phase distribution UP as shown in Figure 6.

Compared with the conventional method, based on the theoretical synthetic wavelength phase extraction method of circle carrier frequency Moire fringe by place Round carrier frequency moiré topography after two kinds of wavelength-interferometric stripe stack of reason, high frequency is obtained Single wavelength interference fringe information The synthetic wavelength stripe information of low frequency is converted to, expands detection range；And will circle using secondary polar coordinate transform Carrier coded fringes are transformed to line carrier coded fringes, reduce intractability, improve precision；Overlapping in combination with carrier frequency Re-construction theory, with synthetic wavelength pi/2 as phase shift stepping-in amount, it is achieved that its frequency spectrum is separated with each component, it is easy to The synthetic wavelength phase component of low frequency is extracted, and while the impact of Phase-shifting Errors can be suppressed.

Claims (1)

1. a kind of based on the synthetic wavelength phase extraction method for justifying carrier frequency Moire fringe theory, it is characterised in that Method and step is as follows：

The first step：λ is respectively using operation wavelength₁And λ₂Dual wavelength interference testing device detect aspherical face Shape, wherein λ₁≠λ₂, two kinds of wavelength are while work, the axial location for adjusting test mirrors introduces round load by out of focus Frequently, the round carrier frequency moiré topography after two kinds of wavelength-interferometric stripe stack is obtained；

Second step：The output voltage of control Phase shifting adapter, realizes with synthetic wavelengthPi/2 Phase shift is carried out for phase shift stepping-in amount, CCD collects the oval load of double wave of one group of 4 frame phase shift stepping-in amount for pi/2 Frequency moire map, its light distribution is：

Wherein, I_kFor the oval carrier frequency moire map light distribution of kth frame double wave, A is i.e. DC component,For wavelength X₁Modulation degree,For wavelength X₁Phase place to be measured, D for circle carrier frequency coefficient, S²For horizontal Pixel coordinate square and longitudinal pixel coordinate square sum, S²=x²+y², x is horizontal pixel coordinate, and y is Longitudinal pixel coordinate, δ_1,kFor kth frame interference pattern medium wavelength λ₁Amount of phase shift,For wavelength X₂Modulation degree,For wavelength X₂Phase place to be measured, δ_2,kFor kth frame interference pattern medium wavelength λ₂Amount of phase shift；

3rd step：The oval carrier frequency moire map of double wave to collecting removes direct current using the method for average and divides After amount, carry out square, the oval carrier frequency moire map light intensity I ' of the double wave after obtaining square_nIt is distributed as：

Wherein, A ' for square after DC component, B₁For wavelength X₁The coefficient of two harmonics,B₂For wavelength X₂The coefficient of two harmonics,B₃For wavelength X₁Under Modulation degreeWith wavelength X₂Downward systemProduct, For synthetic wavelength Phase place, δ_eq,kFor kth frame interference pattern medium wavelength λ_eqAmount of phase shift；

4th step：Determine the fringe center for justifying carrier frequency moire map in second step per frame, to above-mentioned More Striped phase-shift interference carries out secondary polar coordinate transform respectively, obtains the load of the dual wavelength line after corresponding Coordinate Conversion Frequency Moire fringe phase-shift interference, its coordinate transform formula is：

$\{\begin{array}{c}x=x_0+\sqrt{\mathrm{\ρ}}\cos \mathrm{\θ}\\ y=y_0+\sqrt{\mathrm{\ρ}}\sin \mathrm{\θ}\end{array}---\left(3\right)$

Wherein, (ρ, θ) is the point coordinates under polar coordinate system, and (x, y) is cartesian coordinate system corresponding to point (ρ, θ) Under point coordinates, (x₀,y₀) for the fringe center point coordinates under cartesian coordinate system；

5th step：According to overlapping re-construction theory, the dual wavelength line carrier frequency Moire fringe phase shift after Coordinate Conversion is done Relating to figure carries out interlocking to be spaced obtaining its space-time bar graph；

6th step：Fourier transformation is carried out to space-time bar graph, its spectrum distribution is obtained, to space-time bar graph frequency Select to be located at the forward direction of orientation in the 5th step in spectrum, and the phase spectrum at initial point d/4 carries out band logical filter Ripple, wherein d are overall length of the frequency spectrum in orientation, obtain phase component；

7th step：Inverse Fourier transform is carried out to phase component, obtains its briquetting extension phase place P ', by briquetting Extension phase place P ' according to arrangement mode in the 5th step, inversely extracted, return to the pressure of original phase size Bag phase place P, carries out unpacking acquisition unpacking phase place UP to which_q；

8th step：To unpacking phase place UP for obtaining_qInverse transformation side according to secondary polar coordinate transform in the 4th step Formula, is cartesian coordinate system by polar coordinate transform, tries to achieve final phase distribution UP.