CN119688091B - Transverse shearing interference wavefront reconstruction method and device - Google Patents
Transverse shearing interference wavefront reconstruction method and deviceInfo
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Abstract
The invention discloses a transverse shearing interference wavefront reconstruction method and device, relates to the technical field of optical measurement, adopts inaccurate shearing quantity to reconstruct wavefront, realizes high-precision wavefront reconstruction, and solves the problem that the wavefront reconstruction in the prior art depends on the shearing quantity calculation precision. The method comprises the steps of performing phase unwrapping on an initial transverse shearing interference image obtained based on a transverse shearing interference device to obtain an initial phase, fitting the initial phase and the initial shearing quantity through a difference Zernike polynomial to obtain an initial wavefront to be measured after fitting, determining initial error values corresponding to the initial shearing quantity through an error function based on the initial phase and the simulation phase, determining a plurality of field error values corresponding to the initial error values based on a neighborhood optimization method, selecting the initial shearing quantity corresponding to the minimum value or the field shearing quantity to update the initial shearing quantity, and determining the iterative wavefront to be measured determined by the updated shearing quantity corresponding to the updated error value as an accurate reconstruction wavefront when the updated error value corresponding to the updated shearing quantity is smaller than a threshold value.
Description
Technical Field
The invention relates to the technical field of optical measurement, in particular to a transverse shearing interference wavefront reconstruction method and device.
Background
The transverse shearing interference is a wave-front interference measurement technology without a reference mirror, and is used for surface shape and wave-front detection of an optical element by superposing a wave-front to be detected and a shearing wave-front which is transversely staggered by the wave-front to be detected. Because of the characteristics of the transverse shearing interference, the phase information extracted through the interference pattern is not the wavefront to be detected, but the differential wavefront of the wavefront to be detected along the shearing direction, so that the wavefront to be detected needs to be reconstructed from the differential wavefront. The wavefront reconstruction method can be mainly divided into a mode method and a region method, but the accuracy of the wavefront reconstruction is affected by the shearing quantity whether the mode method or the region method is adopted, so that whether the calculation of the shearing quantity is accurate or not is very critical.
The method for calculating the shearing quantity can be roughly divided into two types, namely, the shearing quantity is directly calculated through a geometric formula according to structural parameters (such as sensor spacing, optical path geometric dimension and the like) of the wavefront sensor, and the method is easily influenced by system assembly errors, so that the shearing quantity is calculated inaccurately. A calibration method for extracting shearing interference wave front features based on a phase plate extracts shearing quantity information from shearing wave front by utilizing an image processing technology by introducing a rectangular groove with sharp edges on the phase plate, however, the edges of the extracted feature patterns are in a slope shape instead of ideal steep steps due to the limitation of an optical diffraction limit and the limitation of a spatial filter, and the shearing quantity is calculated by the relation between the transverse distance of staggered point light sources and diffraction order distribution of a grating based on a point source microscope.
The other is calculated directly from the interferogram by image processing. A method for obtaining integral curve mutation point by using Radon transformation principle to calculate shear quantity includes such steps as obtaining clear fringe of interference pattern, making fringe not be dark fringe, otherwise finding mutation point and influencing accuracy of calculation of shear quantity.
In summary, the existing methods all realize high-precision wavefront reconstruction by improving the accuracy of the shearing quantity calculation, and have the problems of high optical path requirement and correlation with optical system parameters.
Disclosure of Invention
The embodiment of the invention provides a transverse shearing interference wavefront reconstruction method and device, which adopt inaccurate shearing quantity to reconstruct wavefront, realize high-precision wavefront reconstruction and solve the problem that the wavefront reconstruction in the prior art depends on the shearing quantity calculation precision.
The embodiment of the invention provides a transverse shearing interference wavefront reconstruction method, which comprises the following steps:
Performing phase unwrapping on an initial transverse shearing interference pattern acquired based on a transverse shearing interference device to obtain an initial phase, and fitting the initial phase and the initial shearing quantity through a differential Zernike polynomial to obtain an initial wavefront to be measured after fitting;
generating a simulated transverse shearing interference image by the initial wavefront to be detected and the initial shearing quantity based on transverse shearing interference, and performing phase unwrapping on the simulated transverse shearing interference image to obtain a simulated phase;
And determining a plurality of neighborhood error values corresponding to the initial error value based on a neighborhood optimization method, selecting the initial shearing quantity corresponding to the minimum value or the neighborhood shearing quantity to update the initial shearing quantity, and determining the iteration wavefront to be measured determined by the updating shearing quantity corresponding to the updating error value as an accurate reconstruction wavefront when the updating error value corresponding to the updating shearing quantity is smaller than a threshold value.
Preferably, the initial phase is as follows:
Wherein I 1(x,y),I2(x,y),I3(x,y),I4 (x, y) represents the light intensity of the four interference images, Represents the extraction phase of the point (x, y), phi (i,j) represents the corresponding unwrapped phase of the point (x, y), and k represents the fringe order of the interference fringe.
Preferably, the initial wavefront to be measured is expressed by the following formula:
ΔW=ΔZa
ΔWx＝ΔZxa
ΔWy＝ΔZya
Wherein W (x, y) represents an initial wavefront to be measured, a j represents coefficients of a Zernike polynomial, J represents the number of terms of the employed Zernike polynomial, and Z j (x, y) represents normalizing the Zernike polynomial in a Cartesian coordinate system; Representing the generalized inverse of ΔZ, ΔW x and ΔW y representing the column vectors of N 2 ×1, respectively, ΔZ x and ΔZ y representing the matrix of N 2 × (J-1), s x representing the initial shearing amount of x, s y representing the initial shearing amount of y, W (x+s x, y) representing the shearing wavefront with an initial to-be-measured wavefront W (x, y) of s x in the x-direction, Z j(x+sx, y) representing the Zernike polynomial with an x-direction lateral displacement of s x, W (x, y+s y) representing the shearing wavefront with an initial to-be-measured wavefront W (x, y) of s y in the y-direction, Z j(x,y+sy representing the Zernike polynomial with a y-direction lateral displacement of s y, Is an x-direction differential Zernike polynomial,Representing the y-direction differential Zernike polynomials.
Preferably, the determining, by an error function, an initial error value corresponding to the initial shearing amount based on the initial phase and the simulated phase specifically includes:
And respectively obtaining an x-direction error function, a y-direction error function and a total error function based on the initial phase and the simulation phase through the following formulas, and determining an initial error value corresponding to the initial shearing quantity according to the total error function, wherein the x-direction error function, the y-direction error function and the total error function are shown as follows:
Where E x denotes the x-direction error function, E y denotes the y-direction error function, E denotes the total error function, Δw x (x, y) is the x-direction initial unwrapped phase, Δw 'x (x, y) is the x-direction simulated unwrapped phase, Δw y (x, y) is the y-direction initial unwrapped phase, and Δw' y (x, y) is the y-direction simulated unwrapped phase.
Preferably, the determining, based on a neighborhood optimization method, a plurality of neighborhood error values corresponding to the initial error values, and selecting the initial clipping amount or the neighborhood clipping amount corresponding to the minimum value to update the initial clipping amount specifically includes:
Sequentially obtaining a first wavefront to be measured, a first transverse shearing interference pattern, a first simulation phase and a neighborhood error value according to the initial phase and the neighborhood shearing quantity of the initial shearing quantity;
And selecting a neighborhood error value or an initial error value with the minimum value according to the magnitudes of the neighborhood error values and the initial error value, and updating the initial clipping amount by using the neighborhood clipping amount or the initial clipping amount with the minimum value.
Preferably, when the minimum value is smaller than a threshold value, determining the iterative wavefront to be measured determined based on the initial shearing amount or the neighborhood shearing amount corresponding to the minimum value as an accurate reconstructed wavefront, including:
if the neighborhood error value or the initial error value with the minimum value is smaller than the set threshold value, determining a neighborhood shearing quantity or an initial shearing quantity according to the minimum value, and determining the iteration wavefront to be measured determined based on the neighborhood shearing quantity or the initial shearing quantity as an accurate reconstruction wavefront.
The embodiment of the invention provides a transverse shearing interference wavefront reconstruction device, which comprises:
The obtaining unit is used for performing phase unwrapping on the initial transverse shearing interference image obtained based on the transverse shearing interference device to obtain an initial phase, and fitting the initial phase and the initial shearing quantity through a differential Zernike polynomial to obtain an initial wavefront to be measured after fitting;
The first determining unit is used for generating a simulated transverse shearing interference image based on transverse shearing interference of the initial wavefront to be detected and the initial shearing quantity, and performing phase unwrapping on the simulated transverse shearing interference image to obtain a simulated phase;
And the second determining unit is used for determining a plurality of neighborhood error values corresponding to the initial error values based on a neighborhood optimization method, selecting the initial shearing quantity corresponding to the minimum value or the neighborhood shearing quantity to update the initial shearing quantity, and determining the iteration wavefront to be detected determined by the updating shearing quantity corresponding to the updating error value as the accurate reconstruction wavefront when the updating error value corresponding to the updating shearing quantity is smaller than a threshold value. An embodiment of the present invention provides a computer device, where the computer device includes a memory and a processor, where the memory stores a computer program, and when the computer program is executed by the processor, the processor is caused to execute any one of the above methods for reconstructing a transverse shearing interference wavefront.
An embodiment of the present invention provides a computer readable storage medium storing a computer program, where the computer program when executed by a processor causes the processor to execute any one of the above methods for reconstructing a transverse shearing interference wavefront.
The embodiment of the invention provides a method and a device for reconstructing a transverse shearing interference wave front, wherein the method comprises the steps of performing phase unwrapping on an initial transverse shearing interference image obtained based on a transverse shearing interference device to obtain an initial phase, fitting the initial phase and the initial shearing quantity through a differential Zernike polynomial to obtain an initial wave front to be detected after fitting, generating a simulated transverse shearing interference image based on transverse shearing interference by the initial wave front to be detected and the initial shearing quantity, performing phase unwrapping on the simulated transverse shearing interference image to obtain a simulated phase, determining an initial error value corresponding to the initial shearing quantity through an error function based on the initial phase and the simulated phase, determining a plurality of neighborhood error values corresponding to the initial error value based on a neighborhood optimization method, selecting the initial shearing quantity or the neighborhood shearing quantity corresponding to the minimum value to update the initial shearing quantity, and determining the iterative wave front to be detected determined by the updated shearing quantity corresponding to the updated shearing quantity to be accurately reconstructed when the updated error value corresponding to the updated shearing quantity is smaller than a threshold value. The method comprises the steps of carrying out four-step phase shift on an obtained shearing interference pattern to extract wrapping phase information, unwrapping a wrapping phase by utilizing a least squares phase unwrapping algorithm based on DCT, carrying out wave front fitting according to a differential Zernike principle by adopting inaccurate shearing quantity, then regenerating a simulated transverse shearing interference pattern by utilizing a transverse shearing interference principle on the initial wave front to be measured after fitting, and carrying out preprocessing and unwrapping on the simulated transverse shearing interference pattern to obtain a simulated phase. Determining an error function and an initial error value corresponding to the initial shearing quantity for the initial phase and the simulated phase, and finally obtaining an accurate reconstruction wave front through iteration, wherein the method uses the phase information extracted from the actual interferogram as an optimization target by adjusting the initial inaccurate initial shearing quantity, carries out iterative optimization based on the error function, and finally obtains the accurate shearing quantity and the accurate reconstruction wave front after the iterative optimization, thereby realizing high-precision wave front reconstruction; the method can obtain accurate reconstructed wave front under the condition of inaccurate calculation of the initial shearing quantity, greatly improves the practical applicability of the method, and is particularly very useful when the shearing quantity is difficult to accurately determine under engineering conditions. Further, the reconstruction result of the method provided by the embodiment of the invention is consistent with the result obtained by the differential Zernike fitting, and the accuracy and precision of the reconstructed wavefront are ensured.
Drawings
In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic flow chart of a method for reconstructing a transverse shearing interference wavefront according to an embodiment of the present invention;
FIG. 2A is a schematic diagram of an x-direction 4-amplitude phase-shift shearing interference according to an embodiment of the present invention;
FIG. 2B is a schematic diagram of a shearing interference with 4 phase shifts in the y-direction according to an embodiment of the present invention;
fig. 3A is a schematic diagram of unwrapping phases in the x direction corresponding to fig. 2A according to an embodiment of the present invention;
fig. 3B is a schematic diagram of unwrapping phases in the y direction corresponding to fig. 2B according to an embodiment of the present invention;
Fig. 4A is a schematic diagram of a reconstructed wavefront obtained by using differential Zernike fitting between an initial shearing amount provided by an embodiment of the present invention and unwrapped phases shown in fig. 3A and 3B;
FIG. 4B is a schematic diagram of a wavefront to be measured according to an embodiment of the present invention;
Fig. 4C is a schematic diagram of a reconstructed wavefront shown in fig. 4A and a residual error schematic diagram of the wavefront to be measured shown in fig. 4B after being reconstructed according to an embodiment of the present invention;
FIG. 5A is a schematic diagram of an x-direction 4-magnitude simulated phase-shift shearing interference based on transverse shearing interference according to an embodiment of the present invention;
FIG. 5B is a schematic diagram of a simulated phase-shifting shearing interference in the y-direction of 4 pieces obtained based on transverse shearing interference according to an embodiment of the present invention;
fig. 6A is a schematic diagram of unwrapping phases based on the x direction of fig. 5A according to an embodiment of the present invention;
Fig. 6B is a schematic diagram of unwrapping phases based on the y direction of fig. 5B according to an embodiment of the present invention;
FIG. 7A is a schematic diagram of a wavefront reconstruction obtained by a method according to an embodiment of the present invention;
FIG. 7B is a schematic diagram of a wavefront to be measured according to an embodiment of the present invention;
Fig. 7C is a schematic diagram of residual errors after reconstructing the reconstructed wavefront map shown in fig. 7A and the wavefront to be measured shown in fig. 7B according to an embodiment of the present invention;
Fig. 8 is a schematic structural diagram of a transverse shearing interference wavefront reconstruction device according to an embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Terms related in the embodiments of the present invention:
1. Neighborhood optimization (Neighborhood Optimization Method) is a widely used technique in optimization problems. The basic idea is to gradually refine the optimization objective by searching for better solutions within the "neighborhood" of the current solution. By neighborhood, we mean a set of solutions that are relatively close to the current solution in solution space under some distance metric. For example, in a simple two-dimensional function optimization problem, assuming that the solution is a point (x, y) on a plane, then the neighborhood of this point can be defined as all points within a circle centered on (x, y) with a radius r. This radius r determines the size of the range of the neighborhood.
Fig. 1 is a schematic flow chart of a method for reconstructing a transverse shearing interference wavefront according to an embodiment of the present invention, and the method for reconstructing a transverse shearing interference wavefront according to the embodiment of the present invention is described in detail below with reference to fig. 1 to 7C as an example. As shown in fig. 1, the method mainly comprises the following steps:
step 101, performing phase unwrapping on an initial transverse shearing interference pattern acquired based on a transverse shearing interference device to obtain an initial phase, and fitting the initial phase and the initial shearing quantity through a differential Zernike polynomial to obtain an initial wavefront to be measured after fitting;
102, generating a simulated transverse shearing interference image based on transverse shearing interference by the initial wavefront to be detected and the initial shearing quantity, and performing phase unwrapping on the simulated transverse shearing interference image to obtain a simulated phase;
And 103, determining a plurality of neighborhood error values corresponding to the initial error values based on a neighborhood optimization method, selecting the initial shearing quantity or the neighborhood shearing quantity corresponding to the minimum value to update the initial shearing quantity, and determining the iteration wavefront to be measured determined based on the initial shearing quantity or the neighborhood shearing quantity corresponding to the minimum value as the accurate reconstruction wavefront when the minimum value is smaller than a threshold value.
In step 101, an initial transverse shearing interference pattern needs to be acquired based on a transverse shearing interference device, specifically, when a wavefront with measured surface information passes through a shearing device, a shearing wavefront transversely shifted with an original wavefront is obtained, interference occurs between the shearing wavefront and the original wavefront in an overlapping area, the interference wavefront passes through an imaging lens and enters a focal plane splitting imaging system, so that four synchronous phase shift interference images are simultaneously obtained, specifically, 4 phase shift shearing interference images in the x direction shown in fig. 2A and 4 phase shift shearing interference images in the y direction shown in fig. 2B. For each point (x, y) within the region, the four interferograms can be represented by the following formulas:
with the four different phase shifted interferograms described above, the phase of the point (x, y) can be calculated by the following formula:
wherein I 1(x,y)、I2(x,y)、I3 (x, y) and I 4 (x, y) respectively represent the illumination intensity of the interference field, a (x, y) represents the direct current light intensity component of the interference pattern, b (x, y) represents the alternating current modulation term, Representing the differential wrapped phase of point (x, y).
Further, as can be seen from the formula (2), when the arctangent operation is performed at the time of extracting the phase, the extracted wrapping phase is between (-pi, pi), and discontinuous jumps occur in the extracted phase distribution. Such jumps do not reflect the actual phase information and require that such discontinuous phase information be spliced and spread into a continuous phase to obtain phase information comprising the actual profile of the optical element.
The embodiment of the invention provides a method for realizing unwrapping of the phase by adopting a least square method based on DCT, in particular to the following steps:
If the wrapping phase extracted in this embodiment is within an m×n discrete rectangular region, the wrapping phase can be expressed as Wherein i=0, 1,..m-1;j =0, 1,..n-1. Whereas phi (i,j) is the corresponding unwrapped phase, the relationship between wrapped and unwrapped phases can be expressed by the following formula:
Where k represents the fringe number of the interference fringe, i=0, 1,..m-1;j =0, 1,..n-1.
Further, defining the wrapping operator as W r, the wrapping operator can be expressed by the following formula:
the difference in the x-direction can be calculated according to the following formula Difference from y direction
Further, the equations (5) and (6) are combined to obtain the equation set V:
Transforming the normal equation of equation (7) can result in a discretized poisson equation in the discrete region as shown below:
φ(i+1,j)-2φ(i,j)+φ(i-1,j)+φ(i,j+1)-2φ(i,j)+φ(i,j-1)=
ρ(i,j)(8)
In the formula (8), the expression "a",
Discrete cosine transform spectrum according to the obtained unwrapped phase phi (i,j) And performing inverse discrete cosine transform to obtain:
Wherein, the p=0,ω1(p)=1,1≤o≤m-1,q=0,ω1(q)=1,1≤q≤n-1。
Further, performing discrete cosine transform on phi (i,j) to obtainThen solving phi (i,j) by inverse discrete cosine transform:
simplifying the formula (9), and accurately solving according to the following formula
The relationship between the x and y direction unwrapped phases and the differential wavefronts ΔW x and ΔW y is as follows:
In the formula, For spatial angular frequency, λ is the wavefront of the light wave to be measured, ΔW x and ΔW y are the differential wavefronts of the wavefront to be measured, and φ x (x, y) and φ y (x, y) are the differential phases of the wavefronts to be measured.
The embodiment of the invention adopts a least square method based on DCT to realize phase unwrapping, wherein unwrapping phases of 4 phase-shift shearing interferometry images in the x direction shown in fig. 2A are shown in fig. 3A, and unwrapping phases of 4 phase-shift shearing interferometry images in the y direction shown in fig. 2B are shown in fig. 3B.
In practical applications, radon transformation is used to calculate the projection of a certain graphic matrix in a specified direction θ, and can also be regarded as the line integral of the graphic matrix in the specified direction θ. The Radon transform of an image in a given direction can be expressed as:
Wherein R θ represents the line integral of the interference pattern in a specified direction theta, x 'and y' are two directions perpendicular to each other along a rectangular coordinate system established along the direction theta, and I represents the illumination intensity of the interference pattern.
And selecting different projection directions (generally selecting 0-180 degrees) for the interferogram, and calculating line integrals of the interferogram in different directions to obtain a projection result of Radon transformation. In the embodiment of the invention, the transverse shearing interference pattern has the largest light spot area in the shearing direction and the smallest light spot area in the direction perpendicular to the transverse shearing interference pattern, and the difference value between the widths of the largest light spot area and the smallest light spot area is the shearing quantity. And analyzing a Radon transformation result, wherein the Radon transformation result is a dark area outside the light spot area, the gray value is smaller, the Radon transformation value in the area is linearly increased and slowly changed, and enters the light spot area, the transformation value is rapidly increased, mutation exists at the edge of the light spot, the width of the light spot area in the appointed projection direction can be calculated by searching the position of the mutation point (taking the x-direction transverse shearing interference pattern as an example, the general 0-degree projection direction corresponds to the largest light spot area, and the 90-degree projection direction corresponds to the smallest light spot area), so that the x-direction initial shearing quantity s x is obtained, and the y-direction initial shearing quantity s y is obtained.
Further, based on the determined initial phase and initial shearing amount, fitting is performed by using a Zernike polynomial, and in practical application, the wavefront W (x, y) to be measured may be represented by a series of stripe Zernike polynomials:
Where J represents the number of terms of the Zernike polynomial, Z j (x, y) represents the normalized Zernike polynomial in the cartesian coordinate system, and a j is the coefficient of the Zernike polynomial.
Further, the differential wavefront in the x and y directions generated by the two wavefronts in the overlap region is expressed as:
Wherein, (s x,sy) is the initial shearing quantity in x and y directions, W (x+s x, y) is the shearing wave front of the wave front W (x, y) to be detected with the transverse displacement quantity s x in the x direction, Z j(x+sx, y) is the Zernike polynomial of the transverse displacement quantity s x in the x direction, W (x, y+s y) is the shearing wave front of the wave front W (x, y) to be detected with the transverse displacement quantity s y in the y direction, Z j(x,y+sy) is the Zernike polynomial of the transverse displacement quantity s y in the y direction, a j represents the coefficient of the Zernike polynomial, Is an x-direction differential Zernike polynomial,Is a y-direction differential Zernike polynomial.
The above relationship is expressed in a vector form, which can be expressed as:
ΔW=ΔZa (18)
Wherein DeltaW x and DeltaW y are column vectors of N 2 ×1, respectively, deltaZ x and DeltaZ y are matrices of N 2 × (J-1),
Solving a coefficient a of the wavefront expression to be measured according to a least square method, which can be expressed as:
In the formula, Represents the generalized inverse of deltaz,Given by the formula:
Further, an initial measured wave surface W (x, y) can be obtained by fitting Zernike coefficients, which is expressed by formula (14). Fig. 4A is a schematic diagram of a reconstructed wavefront obtained by using differential Zernike fitting between an initial shearing amount provided by an embodiment of the present invention and unwrapped phases shown in fig. 3A and 3B, fig. 4B is a schematic diagram of a wavefront to be measured provided by an embodiment of the present invention, and fig. 4C is a schematic diagram of a residual error after the reconstructed wavefront shown in fig. 4A and the wavefront to be measured shown in fig. 4B are reconstructed, where PV (Peak to Valley) of the residual error is 1.3268 λ, and RMS (Root-Mean-Square) is 0.3254 λ.
PV represents the difference between the maximum value (highest point of surface shape) and the minimum value (lowest point of surface shape) in the surface shape W (x, y) of the optical element, that is:
PV=Wmax-Wmin (21)
Wherein W max and W min represent maximum and minimum values, respectively, in the profile W (x, y), x and y being the sequence numbers of the active elements of the rows and columns of the profile, respectively.
RMS represents the root mean square value of the surface error and its calculation formula is as follows:
wherein W (x, y) is the surface shape of the optical element, x and y are the serial numbers of the effective elements of the rows and columns of the surface shape respectively, and N is the number of the effective elements in the surface shape.
In step 102, after the initial to-be-measured wavefront is determined according to the above steps, the initial to-be-measured wavefront and the initial shearing quantity may generate a simulated transverse shearing interference pattern based on transverse shearing interference, and further, the simulated transverse shearing interference pattern is subjected to phase unwrapping to obtain a placement phase. The step 101 may be referred to for phase unwrapping the simulated transverse shearing interferogram, which is not described herein. In an embodiment of the present invention, fig. 5A provides an x-direction 4-magnitude simulated phase-shift shearing interference schematic diagram obtained based on transverse shearing interference, and fig. 5B provides a y-direction 4-magnitude simulated phase-shift shearing interference schematic diagram obtained based on transverse shearing interference. Fig. 6A provides an unwrapped phase schematic in the x-direction corresponding to fig. 5A, and fig. 6B provides an unwrapped phase schematic in the y-direction corresponding to fig. 5B.
Further, from the initial phase and the simulated phase determined in step 101, an initial error function, in particular, may be constructed by the following formula:
the error functions in the x-direction and y-direction are as follows:
Further, from the above error functions in the x-direction and the y-direction, a total error function can be obtained, which is as follows:
Where E x denotes the x-direction error function, E y denotes the y-direction error function, E denotes the total error function, Δw x (x, y) is the x-direction initial unwrapped phase, Δw 'x (x, y) is the x-direction simulated unwrapped phase, Δw y (x, y) is the y-direction initial unwrapped phase, and Δw' y (x, y) is the y-direction simulated unwrapped phase.
In step 103, an initial error value corresponding to the initial shearing amount may be determined according to the above 102, further, a plurality of neighborhood shearing amounts corresponding to the initial shearing amount may be determined based on a neighborhood optimization method, and a neighborhood error value corresponding to each neighborhood shearing amount may be determined at the same time, a minimum value is selected from the plurality of neighborhood error values and the initial error value, the initial shearing amount is updated by using the neighborhood shearing amount or the initial shearing amount corresponding to the minimum value, and in a plurality of iteration processes, if the determined minimum value is smaller than a threshold value, an iterative wavefront to be measured determined according to the neighborhood shearing amount or the initial shearing amount corresponding to the minimum value may be determined as a final accurate reconstructed wavefront.
For example:
step 103-1, determining an initial error value corresponding to the initial shearing amount according to the initial shearing amount (s x,sy).
Step 103-2, if it is determined that the plurality of neighborhood shearing amounts of the initial shearing amount are (sx-1,sy-1)、(sx,sy-1)、(sx+1,sy-1)、(sx-1,sy)、(sx+1,sy)、(sx-1,sy+1)、(sx,sy+1)、(sx+1,sy+1), each neighborhood shearing amount is brought into the initial shearing amount of step 101, and a neighborhood error value corresponding to each neighborhood shearing amount can be determined based on step 101 and step 102;
Step 103-3, comparing the initial shearing quantity with the initial error value corresponding to the neighborhood shearing quantity and the neighborhood error value, selecting the initial shearing quantity or the neighborhood shearing quantity corresponding to the minimum value to update the initial shearing quantity to obtain the updated shearing quantity, and repeatedly executing step 103-1 to step 103-3 once to obtain an updated shearing quantity.
Step 103-4, comparing the update error value with the minimum value with a threshold value when the update error value corresponding to the update cut amount obtained after updating is the minimum value of the update error values obtained after updating for a plurality of times, if the update error value with the minimum value is smaller than the threshold value, determining the iteration wavelength to be measured determined according to the update error value with the minimum value as the accurate reconstruction wave front, correspondingly, if the update error value with the minimum value is not smaller than the threshold value, jumping out of the neighborhood in order to prevent the local optimal solution, giving the random value of the initial cut amount in the step 101 in a set area, and then re-executing the steps 103-1 to 103-3 to obtain the update cut amount, and if the update error value corresponding to the update cut amount is the minimum value update error value and is smaller than the threshold value at the same time, determining the iteration wavelength to be measured with the minimum value update error value as the accurate reconstruction wave front.
Fig. 7A provides a wavefront reconstruction diagram, fig. 7B provides a wavefront diagram to be measured, and fig. 7C provides a residual schematic diagram of the reconstructed wavefront diagram and the wavefront to be measured after reconstruction, wherein the residual has a PV of 4.9979 × -10 λ and an RMS of 1.0757 × -10 λ.
The embodiment of the invention provides a transverse shearing interference wave front reconstruction method, which comprises the steps of carrying out four-step phase shift on an obtained shearing interference image to extract wrapping phase information, unwrapping a wrapping phase by utilizing a least squares phase unwrapping algorithm based on DCT, carrying out wave front fitting according to a differential Zernike principle by adopting inaccurate shearing quantity, regenerating a simulated transverse shearing interference image by utilizing a transverse shearing interference principle on the initial wave front after fitting, and carrying out preprocessing and unwrapping on the simulated transverse shearing interference image to obtain a simulated phase. Determining an error function and an initial error value corresponding to the initial shearing quantity for the initial phase and the simulated phase, and finally obtaining an accurate reconstruction wave front through iteration, wherein the method uses the phase information extracted from the actual interferogram as an optimization target by adjusting the initial inaccurate initial shearing quantity, carries out iterative optimization based on the error function, and finally obtains the accurate shearing quantity and the accurate reconstruction wave front after the iterative optimization, thereby realizing high-precision wave front reconstruction; the method can obtain accurate reconstructed wave front under the condition of inaccurate calculation of the initial shearing quantity, greatly improves the practical applicability of the method, and is particularly very useful when the shearing quantity is difficult to accurately determine under engineering conditions. Further, the reconstruction result of the method provided by the embodiment of the invention is consistent with the result obtained by the differential Zernike fitting, and the accuracy and precision of the reconstructed wavefront are ensured.
Based on the same inventive concept, the embodiment of the invention provides a transverse shearing interference wavefront reconstruction device, and because the principle and the method of solving the technical problem of the device are similar, the implementation of the device can be referred to the implementation of the method, and the repetition is omitted.
As shown in fig. 8, the apparatus includes an obtaining unit 801, a first determining unit 802, and a second determining unit 803.
The obtaining unit 801 is configured to unwrap the phase of the initial transverse shearing interference pattern obtained based on the transverse shearing interference device, obtain an initial phase, and fit the initial phase and the initial shearing quantity through a differential Zernike polynomial, so as to obtain an initial wavefront to be measured after fitting;
The first determining unit 802 is configured to generate a simulated transverse shearing interference pattern based on the initial wavefront to be measured and the initial shearing quantity based on transverse shearing interference, and perform phase unwrapping on the simulated transverse shearing interference pattern to obtain a simulated phase;
And a second determining unit 803, configured to determine a plurality of neighborhood error values corresponding to the initial error values based on a neighborhood optimization method, select the initial shearing amount corresponding to a minimum value or a neighborhood shearing amount to update the initial shearing amount, and determine an iterative wavefront to be measured determined by the updated shearing amount corresponding to the updated error value as an accurately reconstructed wavefront when the updated error value corresponding to the updated shearing amount is smaller than a threshold value.
It should be understood that the above unit included in the transverse shearing interference wavefront reconstruction device is only a logic division according to the functions implemented by the device, and in practical application, the above unit may be overlapped or split. The functions of the device for reconstructing a transverse shearing interference wavefront provided in this embodiment are in one-to-one correspondence with those of the method for reconstructing a transverse shearing interference wavefront provided in the above embodiment, and the more detailed process flow of the device is described in detail in the above method embodiment one, which is not described in detail herein.
The invention further provides computer equipment, which comprises a processor and a memory, wherein the memory is used for storing computer program codes, the computer program codes comprise computer instructions, and when the processor executes the computer instructions, the electronic equipment executes the steps of the transverse shearing interference wavefront reconstruction method in the method flow shown in the method embodiment.
In another embodiment, the present invention further provides a computer readable storage medium, where computer instructions are stored, where the computer instructions, when executed on a computer device, cause the computer device to execute the steps of the method for reconstructing a transverse shearing interference wavefront in the method flow shown in the above method embodiment.
While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. It is therefore intended that the following claims be interpreted as including the preferred embodiments and all such alterations and modifications as fall within the scope of the invention.
It will be apparent to those skilled in the art that various modifications and variations can be made to the present invention without departing from the spirit or scope of the invention. Thus, it is intended that the present invention also include such modifications and alterations insofar as they come within the scope of the appended claims or the equivalents thereof.
Claims (8)
1. A method of reconstructing a transverse shear interference wavefront, comprising:
Performing phase unwrapping on an initial transverse shearing interference pattern acquired based on a transverse shearing interference device to obtain an initial phase, and fitting the initial phase and the initial shearing quantity through a differential Zernike polynomial to obtain an initial wavefront to be measured after fitting;
generating a simulated transverse shearing interference image by the initial wavefront to be detected and the initial shearing quantity based on transverse shearing interference, and performing phase unwrapping on the simulated transverse shearing interference image to obtain a simulated phase;
determining a plurality of neighborhood error values corresponding to the initial error values based on a neighborhood optimization method, and selecting the initial shearing quantity corresponding to the minimum value or the neighborhood shearing quantity to update the initial shearing quantity;
The determining an initial error value corresponding to the initial shearing quantity through an error function based on the initial phase and the simulation phase specifically comprises the following steps:
And respectively obtaining an x-direction error function, a y-direction error function and a total error function based on the initial phase and the simulation phase through the following formulas, and determining an initial error value corresponding to the initial shearing quantity according to the total error function, wherein the x-direction error function, the y-direction error function and the total error function are shown as follows:
Wherein E x denotes an x-direction error function, E y denotes a y-direction error function, E denotes a total error function, Δw x (x, y) is an x-direction initial unwrapping phase, Δw 'x (x, y) is an x-direction simulated unwrapping phase, Δw y (x, y) is a y-direction initial unwrapping phase, Δw' y (x, y) is a y-direction simulated unwrapping phase, n x denotes the number of points involved in calculation in the x-direction, and n y denotes the number of points involved in calculation in the y-direction.
2. The method of claim 1, wherein the initial phase is as follows:
Wherein I 1(x,y),I2(x,y),I3(x,y),I4 (x, y) represents the light intensity of the four interference images, Represents the extraction phase of the point (x, y), phi (i,j) represents the corresponding unwrapped phase of the point (x, y), k represents the fringe number of the interference fringe, arctan represents the arctangent function.
3. The method of claim 1, wherein the initial test wavefront is represented by the following formula:
ΔW=ΔZa
ΔWx＝ΔZxa
ΔWy＝ΔZya
Wherein W (x, y) represents an initial wavefront to be measured, a j represents coefficients of a Zernike polynomial, J represents the number of terms of the employed Zernike polynomial, and Z j (x, y) represents normalizing the Zernike polynomial in a Cartesian coordinate system; Representing the generalized inverse of ΔZ, ΔW x and ΔW y representing the column vectors of N 2 ×1, respectively, ΔZ x and ΔZ y representing the matrix of N 2 × (J-1), s x representing the initial shearing amount of x, s y representing the initial shearing amount of y, W (x+s x, y) representing the shearing wavefront with an initial to-be-measured wavefront W (x, y) of s x in the x-direction, Z j(x+sx, y) representing the Zernike polynomial with an x-direction lateral displacement of s x, W (x, y+s y) representing the shearing wavefront with an initial to-be-measured wavefront W (x, y) of s y in the y-direction, Z j(x,y+sy representing the Zernike polynomial with a y-direction lateral displacement of s y, Is an x-direction differential Zernike polynomial,The vector is represented by a y-direction differential Zernike polynomial, deltaW represents a vector formed by combining differential wavefront data in two orthogonal directions, deltaZ represents a matrix formed by combining components of the differential Zernike polynomial in the x and y directions, the matrix is a basis function matrix of wavefront reconstruction, and a represents a weighting coefficient vector when an original wavefront is unfolded into the Zernike polynomial.
4. The method of claim 1, wherein the determining a plurality of neighborhood error values corresponding to initial error values based on a neighborhood optimization method, selecting the initial clipping amount or neighborhood clipping amount corresponding to a minimum value, and updating the initial clipping amount, specifically comprises:
Sequentially obtaining a first wavefront to be measured, a first transverse shearing interference pattern, a first simulation phase and a neighborhood error value according to the initial phase and the neighborhood shearing quantity of the initial shearing quantity;
And selecting a neighborhood error value or an initial error value with the minimum value according to the magnitudes of the neighborhood error values and the initial error value, and updating the initial clipping amount by using the neighborhood clipping amount or the initial clipping amount with the minimum value.
5. The method of claim 1, wherein determining an iterative wavefront to be measured, determined based on the initial or neighborhood shearing amount corresponding to the minimum value, as an exact reconstructed wavefront when the minimum value is less than a threshold value, specifically comprises:
if a neighborhood error value or an initial error value with a minimum value is smaller than a set threshold value, determining a neighborhood shearing amount or an initial shearing amount according to the minimum value, and determining an iteration wavefront to be measured determined based on the neighborhood shearing amount or the initial shearing amount as an accurate reconstruction wavefront.
6. A transverse shearing interference wavefront reconstruction device, comprising:
The obtaining unit is used for performing phase unwrapping on the initial transverse shearing interference image obtained based on the transverse shearing interference device to obtain an initial phase, and fitting the initial phase and the initial shearing quantity through a differential Zernike polynomial to obtain an initial wavefront to be measured after fitting;
The first determining unit is used for generating a simulated transverse shearing interference image based on transverse shearing interference of the initial wavefront to be detected and the initial shearing quantity, and performing phase unwrapping on the simulated transverse shearing interference image to obtain a simulated phase;
The second determining unit is used for determining a plurality of neighborhood error values corresponding to the initial error values based on a neighborhood optimization method, and selecting the initial shearing quantity corresponding to the minimum value or the neighborhood shearing quantity to update the initial shearing quantity;
the first determining unit is specifically configured to:
And respectively obtaining an x-direction error function, a y-direction error function and a total error function based on the initial phase and the simulation phase through the following formulas, and determining an initial error value corresponding to the initial shearing quantity according to the total error function, wherein the x-direction error function, the y-direction error function and the total error function are shown as follows:
Wherein E x denotes an x-direction error function, E y denotes a y-direction error function, E denotes a total error function, Δw x (x, y) is an x-direction initial unwrapping phase, Δw 'x (x, y) is an x-direction simulated unwrapping phase, Δw y (x, y) is a y-direction initial unwrapping phase, Δw' y (x, y) is a y-direction simulated unwrapping phase, n x denotes the number of points involved in calculation in the x-direction, and n y denotes the number of points involved in calculation in the y-direction.
7. A computer device comprising a memory and a processor, the memory storing a computer program which, when executed by the processor, causes the processor to perform the transverse shear interference wavefront reconstruction method according to any one of claims 1-5.
8. A computer readable storage medium, characterized in that a computer program is stored, which computer program, when being executed by a processor, causes the processor to perform the transverse shearing interferometry wavefront reconstruction method according to any of claims 1-5.
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