Wave surface fusion reconstruction method and device

Abstract

The invention discloses a wave surface fusion reconstruction method and device, and relates to the technical field of optical precision measurement. The objective of the invention is to solve the problems of small measurement range and low detection precision caused by limitation of aspheric surface shape detection with complex surface shape and large curvature change in the prior art. Comprising the following steps: according to a Nyquist sampling law, determining a limit resolution point coordinate of a wavefront slope of a to-be-measured aspheric surface shape, according to the limit resolution point coordinate, carrying out girdle division on the wavefront slope of the to-be-measured aspheric surface shape, and according to the size of pixels occupied in a girdle region, determining a shear amount of the girdle region; enabling the to-be-measured aspheric surface subjected to girdle division to pass through an interference device to obtain a shearing interference fringe pattern corresponding to each girdle region, carrying out wrapped phase extraction on the shearing interference fringe patterns to obtain a wrapped phase value, and unpacking the wrapped phase value to obtain a real phase value corresponding to the girdle region; performing differential processing on the real phase value to obtain a phase difference value between adjacent phases, and fitting the phase difference value through a differential Zernike polynomial to obtain an annular zone surface shape corresponding to each annular zone; and splicing the plurality of annular zone surface shapes to obtain a wavefront surface shape with the same size as the surface shape of the aspheric surface to be measured, and fitting the wavefront surface shape through a difference Zernike polynomial to obtain a reconstructed surface shape corresponding to the aspheric surface to be measured.

Description

Technical Field

[0001] The present invention relates to the field of optical precision measurement technology, and more particularly to a wavefront fusion reconstruction method and device. Background Art

[0002] Aspheric optical elements can correct the aberration and chromatic aberration of infrared or visible light imaging systems, increase the field of view, simplify the structure of the optical system, and make the optical design more flexible. In recent years, with the continuous advancement of manufacturing technology and the increasing demand for complex optical surface measurement, especially in the fields of optics and precision machining, aspheric surface shape detection has become increasingly important.

[0003] As one of the effective means of optical detection, lateral shearing interferometry technology has the advantages of low requirements for measurement environment stability, low requirements for light source coherence, strong anti-interference ability, and no need for additional reference surfaces. However, traditional single shearing interferometry technology is limited when dealing with aspheric surfaces, especially when the surface shape is complex and the curvature changes greatly, its measurement accuracy and stability are challenged. Specifically, the curvature of the aspheric ring zone is inconsistent, especially when the asphericity is large, the aberration between the surface and the optimal sphere increases, resulting in dense interference fringes in the edge area of ​​the aspheric surface shape and uneven fringing distribution. Excessive density of interference fringes causes local distortion of the interference pattern and reduces the resolution of the edge fringes, which in turn affects the measurement precision and accuracy. Summary of the Invention

[0004] The embodiments of the present invention provide a wavefront fusion reconstruction method and device for solving the problem that the existing technology has limitations in detecting aspheric surfaces with complex shapes and large curvature variations, resulting in a small measurement range and low detection accuracy.

[0005] An embodiment of the present invention provides a wavefront fusion reconstruction method, comprising:

[0006] According to the Nyquist sampling theorem, the coordinates of the limit resolution point of the wavefront slope of the aspheric surface shape to be measured are determined, the wavefront slope of the aspheric surface shape to be measured is divided into annular zones according to the coordinates of the limit resolution point, and the shear amount of the annular zone area is determined according to the number of pixels occupied by the boundary fringes of the annular zone area; wherein the shear amount determined for each annular zone area is used to analyze the shear interference fringes in the annular zone area;

[0007] The aspheric surface to be measured, which is divided into annular zones, is passed through an interference device to obtain a shearing interference fringe pattern corresponding to each annular zone area, the shearing interference fringe pattern is subjected to wrapped phase extraction to obtain a wrapped phase value, and the wrapped phase value is unwrapped to obtain a true phase value corresponding to the annular zone area;

[0008] Performing differential processing on the true phase value to obtain a phase difference between adjacent phases, and fitting the phase difference by using a differential Zernike polynomial to obtain a ring zone area shape corresponding to each of the ring zones;

[0009] The plurality of annular zone area shapes are spliced ​​to obtain a wavefront shape having the same size as the aspheric surface to be measured, and the wavefront shape is fitted by differential Zernike polynomials to obtain a reconstructed surface shape corresponding to the aspheric surface to be measured.

[0010] Preferably, dividing the wavefront slope of the aspheric surface to be measured into annular zones according to the limiting resolution coordinates, and determining the shearing amount of the annular zones according to the size of the pixels occupied in the annular zones, comprises:

[0011] Dividing the wavefront slope of the aspheric surface to be measured into annular zones according to the coordinates of the limit resolution point to obtain at least an inner annular zone area and an outer annular zone area;

[0012] Determining the area of ​​the inner annular zone and a first shearing amount according to the pixel size occupied by the inner annular zone, wherein the first shearing amount is used to analyze shearing interference fringes included in the inner annular zone;

[0013] The area of ​​the outer annular zone and a second shearing amount are determined according to the size of the pixels occupied by the outer annular zone, and the second shearing amount is used to analyze the shearing interference fringes included in the outer annular zone.

[0014] Preferably, the wavefront slope of the aspheric surface to be measured is as follows:

[0015] W s =2(n(x)-s(x))′| x

[0016] The coordinates of the limit resolution point of the wavefront slope of the aspheric surface to be measured satisfy the following formula:

[0017]

[0018] Among them, W s represents the wavefront slope of the aspheric surface to be measured, n(x) represents the equation of the aspheric surface to be measured, s(x) represents the optimal spherical equation, D represents the aperture of the aspheric surface to be measured, and p represents the number of available pixels of the imaging CCD on the interferometer.

[0019] Preferably, the wrapped phase extraction is performed by the following formula:

[0020]

[0021] The true phase value corresponding to the annular zone is obtained by the following formula:

[0022]

[0023] in, Indicates the shear amount as s m When the phase value is wrapped at two-dimensional M×N discrete points, I1, I2, I3, I4 represent the light intensity of the four interference images in the four-step phase shift. represents the true phase value corresponding to the annular region obtained after unwrapping the wrapped phase at two-dimensional M×N discrete points, represents the difference of adjacent elements of the wrapped phase in the x direction, represents the difference of adjacent elements of the wrapped phase in the y direction, Indicates the shear amount as s m The wrapped phase value at the two-dimensional discrete point (m+1,n) when Indicates the shear amount as s m The wrapped phase value at the two-dimensional discrete point (m,n) when Indicates the shear amount as s m The wrapped phase value at the two-dimensional discrete point (m, n+1) when , M represents the number of rows of the discrete two-dimensional matrix, N represents the number of columns of the discrete two-dimensional matrix, m=0,1,…,M-2, n=0,1,…,N-1.

[0024] Preferably, the phase difference between adjacent phases is determined by the following formula:

[0025]

[0026] in, Indicates that the shear amount in the x direction is s m The phase difference between adjacent phases is Indicates that the shear amount in the y direction is s m The phase difference between adjacent phases at the same time, W(x,y) represents the wavefront function to be measured, which describes the wavefront situation at the point (x,y) in the Cartesian coordinate system, s m Indicates the shear amount in the x-direction, J represents the index of the number of terms in the Zernike polynomial, j = 2,…,J, a j represents the coefficient of the j-th Zernike polynomial, Z j (x,y) represents the basis function of the j-th Zernike polynomial, Indicates that the jth item in the x direction has a shear amount of s m The differential Zernike polynomials for , Indicates that the jth item in the y direction has a shear amount of s m The differential Zernike polynomials when Z j (x+s m,y) represents the jth Zernike polynomial at the coordinate (x+s m ,y) point.

[0027] Preferably, the surface shape of the annular zone area corresponding to each of the annular zone areas is determined by the following formula:

[0028] ΔW xm =ΔZ xm a

[0029] ΔW ym =ΔZ ym a

[0030]

[0031] Where ΔW xm Represents the wavefront vector to be measured after discretization in the x direction, ΔW ym represents the wavefront vector to be measured after discretization in the y direction, a represents the Zernike polynomial coefficient vector, represents the Zernike polynomial coefficient vector obtained by the standard least squares method, ΔZ T Denotes the transposed matrix of ΔZ, ΔZ is composed of ΔZ xm and ΔZ ym The discrete matrix (ΔZ T ΔZ) -1 represents ΔZ T The inverse matrix of ΔZ, ΔW represents the combined ΔW xm and ΔW ym The discrete matrix after .

[0032] Preferably, the shapes of the multiple annular zones are spliced ​​using the following formula:

[0033] ΔW r =ΔW1+ΔW2+…ΔW i

[0034] The wavefront shape is fitted by the following formula

[0035]

[0036] Where ΔW r Indicates the differential wavefront of the surface to be measured after splicing, ΔZ T Denotes the transposed matrix of ΔZ, ΔZ is composed of ΔZ xm and ΔZ ym The discrete matrix (ΔZ T ΔZ) -1 represents ΔZ T The inverse matrix of ΔZ, Indicates the solution coefficient, W r(x, y) represents the reconstructed surface shape corresponding to the aspheric surface to be measured.

[0037] An embodiment of the present invention provides a wavefront fusion reconstruction device, comprising:

[0038] a determination unit, configured to determine the coordinates of a limit resolution point of the wavefront slope of the aspheric surface shape to be measured according to the Nyquist sampling theorem, divide the wavefront slope of the aspheric surface shape to be measured into annular zones according to the coordinates of the limit resolution point, and determine a shearing amount for the corresponding annular zone area according to the number of pixels occupied by the boundary fringes of the annular zone area; wherein the shearing amount determined for each annular zone area is used to analyze the shearing interference fringes within the annular zone area;

[0039] A first obtaining unit is configured to obtain a shearing interference fringe pattern corresponding to each annular zone region by passing the aspheric surface to be measured through an interference device, perform wrapped phase extraction on the shearing interference fringe pattern to obtain a wrapped phase value, and unwrap the wrapped phase value to obtain a true phase value corresponding to the annular zone region;

[0040] A second obtaining unit is configured to perform differential processing on the true phase value to obtain a phase difference between adjacent phases, and to fit the phase difference using a differential Zernike polynomial to obtain a ring zone area shape corresponding to each of the ring zones;

[0041] The third obtaining unit is used to splice the surface shapes of multiple annular zones to obtain a wavefront shape of the same size as the surface shape of the aspheric surface to be measured, and fit the wavefront shape through differential Zernike polynomials to obtain a reconstructed surface shape corresponding to the aspheric surface to be measured.

[0042] An embodiment of the present invention provides a computer device, comprising a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes any one of the above-mentioned wavefront fusion reconstruction methods.

[0043] An embodiment of the present invention provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, the processor executes any one of the above-mentioned wavefront fusion reconstruction methods.

[0044] An embodiment of the present invention provides a wavefront fusion reconstruction method and device, the method comprising: determining the limit resolution point coordinates of the wavefront slope of the aspheric surface to be measured according to the Nyquist sampling theorem, dividing the wavefront slope of the aspheric surface to be measured into ring zones according to the limit resolution point coordinates, and determining the shear amount of the ring zone area according to the number of pixels occupied by the boundary fringes of the ring zone area; wherein the shear amount determined for each of the ring zone areas is used to analyze the shear interference fringes in the ring zone area; the aspheric surface to be measured that has been divided into ring zones is passed through an interference device to obtain a shear interference fringe pattern corresponding to each ring zone area, and the shear interference fringe pattern is analyzed. The interference fringe pattern is cut to perform wrapped phase extraction to obtain a wrapped phase value, and the wrapped phase value is unpacked to obtain a true phase value corresponding to the annular zone area; the true phase value is differentially processed to obtain a phase difference value between adjacent phases, and the phase difference value is fitted by differential Zernike polynomials to obtain an annular zone area surface shape corresponding to each of the annular zones; a plurality of annular zone area surface shapes are spliced ​​to obtain a wavefront shape of the same size as the aspheric surface shape to be measured, and the wavefront shape is fitted by differential Zernike polynomials to obtain a reconstructed surface shape corresponding to the aspheric surface to be measured. This method achieves flexible and adjustable shearing amount through a shearing device composed of a polarization grating and a plane mirror, can accurately control the interference fringe density according to the measured surface shape, adapt to the measurement requirements of surfaces with different morphologies, and improve the measurement accuracy and applicability; the multi-shearing interference wavefront fusion reconstruction technology proposed by this method can divide different annular regions according to the wavefront slope of the aspheric surface to be measured, select shearing amounts of different sizes for multiple shearing interferences, and thus more comprehensively adapt to the surface shape changes in the central and edge regions of the aspheric surface. This technology can overcome the limitations of traditional single shearing amount technology in processing complex aspheric surfaces; further, the wavefront information of multiple groups of annular regions is restored by using differential Zernike polynomials, and the multiple groups of regional surface shapes are spliced ​​to obtain a matrix of the same size as the original surface shape. The fitting coefficients corresponding to the fused array are solved by re-fitting, and finally the fused surface shape is solved to achieve high-precision surface reconstruction with strong anti-interference ability, avoiding the information loss or inaccurate reconstruction caused by uneven fringe distribution under a single shearing amount, thereby achieving higher measurement accuracy and stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0046] Figure 1A schematic flow chart of a wavefront fusion reconstruction method provided by an embodiment of the present invention;

[0047] Figure 2 Schematic diagram of a multi-shearing interferometry measurement system provided by an embodiment of the present invention;

[0048] Figure 3A A schematic diagram of the original aspheric wavefront simulated by Matlab provided in an embodiment of the present invention;

[0049] Figure 3B A schematic diagram of the aspheric wavefront slope simulated by Matlab provided in an embodiment of the present invention;

[0050] Figure 4 A schematic diagram of the annular zone division result provided by an embodiment of the present invention;

[0051] Figure 5A A schematic diagram of the inner ring area provided in an embodiment of the present invention;

[0052] Figure 5B A schematic diagram of the outer ring area provided in an embodiment of the present invention;

[0053] Figure 6A A schematic diagram of the multi-shear interferometry wavefront fusion reconstruction result provided by an embodiment of the present invention;

[0054] Figure 6B A schematic diagram of a single shear volume wavefront reconstruction result provided by an embodiment of the present invention;

[0055] Figure 7 A schematic structural diagram of a wavefront fusion reconstruction device provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0056] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0057] Figure 1 A schematic diagram of a wavefront fusion reconstruction method provided by an embodiment of the present invention is shown below. Figure 1 The wavefront fusion reconstruction method provided by the embodiment of the present invention is described in detail. Figure 1 As shown, the method mainly includes the following steps:

[0058] Step 101: Determine the coordinates of the limit resolution point of the wavefront slope of the aspheric surface to be measured according to the Nyquist sampling theorem, divide the wavefront slope of the aspheric surface to be measured into annular zones according to the limit resolution point coordinates, and determine the shear amount of the annular zone area according to the number of pixels occupied by the boundary fringes of the annular zone area; wherein the shear amount determined for each annular zone area is used to analyze the shear interference fringes in the annular zone area;

[0059] Step 102: The aspheric surface to be measured, which has been divided into annular zones, is passed through an interferometer to obtain a shearing interference fringe pattern corresponding to each annular zone region, and a wrapped phase extraction is performed on the shearing interference fringe pattern to obtain a wrapped phase value, and the wrapped phase value is unpacked to obtain a true phase value corresponding to the annular zone region.

[0060] Step 103: performing differential processing on the true phase value to obtain a phase difference between adjacent phases, and fitting the phase difference using a differential Zernike polynomial to obtain a ring zone area shape corresponding to each of the ring zones;

[0061] Step 104 , stitching the multiple annular zone area shapes to obtain a wavefront shape of the same size as the aspheric surface to be measured, fitting the wavefront shape by differential Zernike polynomials to obtain a reconstructed shape corresponding to the aspheric surface to be measured.

[0062] In step 101, the aspheric surface shape to be measured is divided into annular zones according to the Nyquist sampling theorem, the coordinates of the limit resolution points of the wavefront slope of the aspheric surface shape to be measured are calculated according to the division formula, and the wavefront slope of the aspheric surface shape to be measured is divided into annular zones according to the coordinates of the limit resolution points to obtain at least an inner annular zone area and an outer annular zone area.

[0063] Specifically, the wavefront slope of the aspheric surface to be measured is as follows:

[0064] W s =2(n(x)-s(x))′| x (1)

[0065] The coordinates of the limit resolution point of the wavefront slope of the aspheric surface to be measured satisfy the following formula:

[0066]

[0067] Among them, W s represents the wavefront slope of the aspheric surface to be measured, s(x) represents the optimal spherical equation, D represents the aperture of the aspheric surface to be measured, ρ represents the number of available pixels of the imaging CCD on the interferometer, and n(x) represents the equation of the aspheric surface to be measured.

[0068]

[0069] Where c represents the inverse of the radius of curvature of the aspheric vertex, k represents the quadratic surface coefficient, k = 1-e 2 , e represents the eccentricity of the aspheric surface.

[0070] It should be noted that, in the embodiment of the present invention, the aspheric surface shape obtained by simulation through formula (3) is subtracted from the optimal spherical surface to generate the aspheric wavefront image. Figure 3A , the aspheric wavefront slope satisfies like Figure 3B , the slope of the aspheric wavefront is substituted for the entrance diameter D and the number of imaging pixels ρ, and the limit value of the path difference change rate is calculated to be 0.39×10 -3 mm / pixel, this value is the ordinate corresponding to the limit resolution point, the x-axis represents the normalized aperture, and the abscissa of the point is the corresponding normalized aperture value. Figure 3B The path difference change rate curve of the aspheric surface shown divides the wavefront slope at the limit resolution point, and the pixel values ​​of the inner and outer ring areas can be calculated.

[0071] Furthermore, the shearing amount of the annular zone is determined based on the size of the pixels occupied within the annular zone. Specifically, when the pixels of the boundary fringes of the inner annular zone meet the resolvable condition, the area of ​​the inner annular zone and a first shearing amount are determined, and the first shearing amount is used to resolve the shearing interference fringes included in the inner annular zone. When the pixels of the boundary fringes of the outer annular zone meet the resolvable condition, the area of ​​the zone and a second shearing amount are determined, and the second shearing amount is used to resolve the shearing interference fringes included in the outer annular zone.

[0072] In an embodiment of the present invention, the boundary stripes are the outermost stripes representing the boundary of the inner annular area (outer annular area). The boundary stripes of each annular area need to meet the analytical conditions. The analytical conditions here can be determined according to the sampling theorem. Specifically, according to the sampling theorem, each stripe only needs to include 2 pixels to losslessly reconstruct the original signal. In practical applications, considering the influence of noise and adjustment errors, the number of pixels included in each stripe can be increased. In an embodiment of the present invention, when each stripe occupies a width of at least 5 pixels, it can be used to display the position of a stripe, and this position is the boundary of the decomposable stripe. In an embodiment of the present invention, the boundary stripes of the annular area occupying 5 pixels are the analytical conditions.

[0073] In practical applications, the shearing amount determined for each annular zone is used to analyze the shearing interference fringes within the annular zone. The first shearing amount s1 can be selected to analyze the shearing interference fringes included in the inner annular zone, and the second shearing amount s2 can be selected to analyze the shearing interference fringes included in the outer annular zone. The annular zone division result is as follows: Figure 5A and 5B shown.

[0074] The interference device used in the method provided in the embodiment of the present invention is as follows Figure 2 As shown, it mainly includes a laser light source 1, a beam expansion and collimation system 2, a first beam splitter prism 3, a standard mirror 4, an aspheric surface to be measured 5, a second beam splitter prism 6, a polarization grating 7, a plane mirror 8, an imaging lens 9, a polarization camera 10, and an electronic control unit 11. Specifically, the laser light source 1 emits a parallel light beam, which passes through the beam expansion and collimation system 2 and then to the first beam splitter prism 3. After passing through the standard mirror 4, it is incident on the aspheric surface to be measured 5. The test wavefront returned from the surface of the optical element passes through the second beam splitter prism 6 and is incident on the adjustable shearing device composed of the polarization grating 7 and the plane mirror 8. The reflected light is incident on the target surface of the polarization camera through the imaging lens to collect four shearing interference patterns with different phase shifts.

[0075] In this interferometer, the reflective lateral shearing device composed of the polarization grating 7 and the plane mirror 8 is used to split a beam of light into two beams, and make the two beams of light produce lateral displacement (that is, shear), thereby forming interference fringes; the polarization grating 7 and the plane mirror 8 are arranged on an electrically controlled displacement stage, which is a high-precision mobile platform with a movement accuracy that can reach the micron or even nanometer level; the automatic control unit 11 is composed of a motor, a controller and a sensor. The function of the automatic control unit 11 is to drive the electrically controlled displacement stage to change the relative position between the polarization grating and the mirror. The automatic control unit 11 realizes precise control of the distance between the polarization grating and the mirror by controlling the electrically controlled displacement stage, flexibly adjusts the amount of shear, and realizes multiple shear interference measurements.

[0076] In step 102, based on Figure 2 The interference device shown performs shear interference on the aspheric surface to be measured that has been divided into annular zones, and obtains a shear interference fringe pattern corresponding to each annular zone area. Specifically, the four interference images obtained by a polarization camera are measured at one time, and the phase difference of the four interference images is The four-step phase shifting technology is used for phase extraction. The electric-controlled translation stage is connected to the reflective transverse shearing device to obtain multiple sets of shear interference with adjustable shearing amount. I1 and I2 are the intensities of the two shearing beams respectively. The two beams can interfere to form interference fringes. The phase information under different shearing amounts is given by express.

[0077]

[0078] The phase obtained by the four-step phase shift method is obtained by the inverse tangent function, and the phase difference is:

[0079]

[0080] Furthermore, the sheared interference fringe pattern is wrapped for phase extraction to obtain the wrapped phase value, and the wrapped phase value is unwrapped to obtain the real phase value corresponding to the annular area. Specifically, the unwrapping is because the main value phase obtained by the phase shift algorithm is not a real continuous phase, and the unwrapping algorithm is used to process it to obtain the real continuous phase information. The unwrapping operation is performed based on the weighted iterative discrete cosine transform least squares method, assuming is the unpacked phase at two-dimensional M×N discrete points, The corresponding wrapped phase is as follows:

[0081]

[0082] Furthermore, the phase difference needs to meet the following conditions:

[0083]

[0084] In practical applications, first define the wrapping operator The details are as follows:

[0085]

[0086] In the embodiment of the present invention, the difference between adjacent elements of the wrapped phase in the x direction and the difference between adjacent elements of the wrapped phase in the y direction can be defined, and then the least square method can be used to solve The specific formula is as follows

[0087]

[0088]

[0089] in, Indicates the shear amount as s m When the phase value is wrapped at two-dimensional M×N discrete points, I(0°), I(45°), I(90°), and I(135°) represent the light intensity of the four interference images in the four-step phase shift. represents the true phase value corresponding to the annular region obtained after unwrapping the wrapped phase at two-dimensional M×N discrete points, represents the difference of adjacent elements of the wrapped phase in the x direction, represents the difference of adjacent elements of the wrapped phase in the y direction, Indicates the shear amount as s m The wrapped phase value at the two-dimensional discrete point (m+1,n) when Indicates the shear amount as s m The wrapped phase value at the two-dimensional discrete point (m,n) when Indicates the shear amount as s mThe wrapped phase value at the two-dimensional discrete point (m, n+1) when , M represents the number of rows of the discrete two-dimensional matrix, N represents the number of columns of the discrete two-dimensional matrix, m=0,1,…,M-2; b=0,1,…,N-1.

[0090] In step 103, the true phase value obtained in step 102 is subjected to differential processing to obtain the phase difference between adjacent phases. The phase difference is fitted by differential Zernike polynomials to obtain the surface shape of the annular zone corresponding to each annular zone. Specifically:

[0091] The differential Zernike polynomial fitting algorithm is used to restore the surface shape of the annular zone, and multiple groups of surface shapes ΔW with different shear magnitudes are obtained. m (m=1,2,3...). Zernike wavefront fitting uses Zernike polynomials as basis functions to characterize the wavefront to be measured. Expanding the wavefront W(x,y) to be measured in the Cartesian coordinate system into the first J fringe Zernike polynomials, we can obtain the following expression:

[0092]

[0093] Where Z j (x,y) represents the basis function of the j-th Zernike polynomial, a j represents the coefficient of the j-th Zernike polynomial. The summation starts from the second term because the first term represents the constant term. Since the lateral shearing interferometry measures the difference of the wavefront in the shear direction, the constant term cannot be measured by shearing interferometry. From the above formula, we can see that the wavefront to be measured with different shear amounts in the x and y directions is and It can be expressed as:

[0094]

[0095] in, Indicates that the jth item in the x direction has a shear amount of s m The differential Zernike polynomials for , Indicates that the jth item in the y direction has a shear amount of s m The differential Zernike polynomials at the time, W(x,y) represents the wavefront function to be measured, describing the wavefront situation at the point (x,y) in the Cartesian coordinate system, s m Indicates the shear amount in the x-direction, J represents the index of the number of terms in the Zernike polynomial, j = 2,…,J, a j represents the coefficient of the j-th Zernike polynomial, Z j (x,y) represents the basis function of the j-th Zernike polynomial.

[0096] Furthermore, the jth item in the x direction has a shear amount of s m The differential Zernike polynomials when the j-th term in the y direction is sheared with s m The differential Zernike polynomials for are as follows:

[0097]

[0098] Furthermore, the differential wavefront under the same set of shear Combined into a discrete matrix:

[0099] ΔW xm =ΔZ xma (17)

[0100] ΔW ym =ΔZ ym a (18)

[0101] Where ΔZ xm and ΔZ ym Represent the differential Zernike polynomial expressions in the x and y directions respectively. Further, the differential wavefront ΔW under the same set of shear amounts is xm , ΔW ym Combined into a discrete matrix ΔW, ΔZ xm and ΔZ ym Combined into the same discrete matrix ΔZ, specifically:

[0102]

[0103] Furthermore, the Zernike coefficient vector can be obtained by solving the equation using the standard least squares method as shown below The area of ​​the annular region ΔW can be fitted.

[0104]

[0105] Where ΔW xm Represents the wavefront vector to be measured after discretization in the x direction, ΔW ym represents the wavefront vector to be measured after discretization in the y direction, a represents the Zernike polynomial coefficient vector, represents the Zernike polynomial coefficient vector obtained by the standard least squares method, ΔZ T Denotes the transposed matrix of ΔZ, ΔZ is composed of ΔZ xm and ΔZ ym The discrete matrix (ΔZ T ΔZ) -1 represents ΔZ T The inverse matrix of ΔZ, ΔW represents the combined ΔW xm and ΔWym The discrete matrix after .

[0106] In step 104, the surface shapes of the multiple annular zones are spliced ​​together to obtain a wavefront shape of the same size as the surface shape of the aspheric surface to be measured. The wavefront shape is fitted by differential Zernike polynomials to obtain a reconstructed surface shape corresponding to the aspheric surface to be measured. Specifically, the surface shapes of the multiple annular zones are spliced ​​together using the following formula to obtain a differential wavefront of the wavefront to be measured:

[0107] ΔW r =ΔW1+ΔW2+…ΔW i (twenty two)

[0108] The differential wavefront of the wavefront to be measured is as follows:

[0109]

[0110] Furthermore, the surface shapes of multiple annular zones are fitted again, and the coefficients can be obtained by solving the equation using the standard least squares method. Then By substituting the following formula, we can obtain the reconstructed surface shape corresponding to the aspheric surface to be measured:

[0111]

[0112] Where ΔW r Indicates the differential wavefront of the surface to be measured after splicing, ΔZ T Denotes the transposed matrix of ΔZ, ΔZ is composed of ΔZ xm and ΔZ ym The discrete matrix (ΔZ T ΔZ) -1 represents ΔZ T The inverse matrix of ΔZ, Indicates the solution coefficient, W r (x, y) represents the reconstructed surface shape corresponding to the aspheric surface to be measured.

[0113] In summary, the method provided by the embodiments of the present invention proposes a multi-shear wavefront fusion reconstruction technique. To address the problem that the surface shape of aspheric surfaces often varies significantly between the center and edge regions, this method divides the aspheric surface into different annular zones based on the slope of the wavefront, selects shear amounts of different sizes, performs multiple shear interferences, and uses differential Zernike polynomials to restore the surface shape of the annular zones. The surface shapes of the annular zones are then fused to obtain the final surface shape. This method overcomes the limitations of traditional single shear amount technology when processing aspheric surfaces with large curvature variations, further enables the detection of large or complex aspheric surfaces, and achieves high-precision reconstruction of the wavefront to be measured.

[0114] In order to more clearly introduce a multi-shear interference wavefront fusion reconstruction method provided by an embodiment of the present invention, the following is combined with Figures 3A to 5B Taking θ as an example, the wavefront fusion reconstruction method is introduced.

[0115] Example 1

[0116] Generate wavefront model: Characterize the aspheric surface shape according to the quadratic surface formula, give specific surface parameters, and use MATLAB simulation to generate a wavefront model with specific aspheric surface characteristics, such as Figure 3A and Figure 3B As shown:

[0117] Divide the annular area: The slope distribution of the simulated aspheric wavefront in different areas is as follows Figure 4 As shown in Figure 2, the coordinates of the limit resolution points calculated according to the Nyquist theorem are used to divide the annular zone into zones.

[0118] Determine the shear amount and the size of the annulus: Match the appropriate shear amount to each annulus area. By simulating the shear interference fringe density under different shear amounts, select the appropriate shear amount to ensure that the shear interference fringe pattern of each annulus area can be analyzed. Calculate the number of pixels occupied by the inner and outer annulus areas to obtain the size of the annulus area. Figure 5A and 5B shown.

[0119] Extract and unpack phase: Generate lateral shearing interferograms under different shear amounts, extract phase and perform unpacking processing: Use a four-step phase shifting algorithm to extract the phase information of the wavefront to be measured from the interference image obtained by simulation.

[0120] Phase unpacking based on weighted iterative DCT least squares algorithm: The extracted wrapped phase is unpacked using the weighted iterative DCT (discrete cosine transform) least squares algorithm to obtain multiple sets of differential phases. These differential phases can reflect the phase changes of the measured wavefront in different regions.

[0121] Fitting and restoring the surface shape: Differential Zernike polynomial fitting is used to restore the surface shape. The differential Zernike polynomial fitting algorithm is used to process the differential phase data obtained in step 5 and fit the surface shape of the inner and outer ring areas.

[0122] Wavefront fusion processing: The restored local area surface shapes are spliced ​​into a complete wavefront shape matrix. The spliced ​​surface shape is re-fitted through a wavefront fusion algorithm based on differential Zernike polynomials to optimize the transition boundary of the spliced ​​area.

[0123] The final result is obtained: the best fitting coefficient obtained by the least squares method is used to solve the final fusion surface shape and obtain a high-precision wavefront reconstruction result with an error of PV = 1.0636e-10λ and RMS = 4.6828e-11λ. The reconstructed surface shape after surface shape restoration is as follows: Figure 6A and 6B shown.

[0124] Example 2

[0125] Step 201: wavefront ring division:

[0126] In step 2011, assume that the aperture of the aspheric surface to be measured is D = 100 mm, the number of available pixels of the imaging CCD on the interferometer is p = 1024, the wavelength λ = 0.6328 μm, and the equation of the aspheric surface to be measured is shown in formula (3). Assuming that the quadratic surface coefficient k = -3.5 (paraboloid), the inverse of the radius of curvature of the aspheric surface vertex c = 1 / 100, the optimal spherical surface equation s(x) can be determined based on the characteristics of the aspheric surface.

[0127] Step 2012: The slope of the wavefront returned from the image plane is: W s =2(n(x)-s(x))′| x , according to formula (2), the coordinates of the limit resolution point can be determined.

[0128] Specifically, the equation of the aspheric surface to be measured is first derived, and the coordinate value of the limit resolution point that satisfies the wavefront slope is found through numerical calculation, and the normalized aperture value corresponding to the limit resolution point is set to x0=0.6.

[0129] Step 2013: Divide the aspheric surface to be measured into an inner ring zone and an outer ring zone according to the coordinates of the limit resolution point. To meet the distinguishability principle, select a larger shearing amount s1 = 20 pixels; the outer ring Since it is unsolvable, a smaller clipping amount s2 = 8 pixels is selected.

[0130] Step 202: Phase extraction and unpacking:

[0131] Step 221: Use a polarization camera to measure four phase differences at once. The interference image of the four images is I1, I2, I3, and I4. According to the four-step phase shift method formula Calculating the wrapping phase

[0132] Assuming that at a certain point, I1 = 100, I2 = 80, I3 = 60, I4 = 120, then according to the four-step phase shift formula we can get:

[0133] The above calculation is performed for each pixel in the interference image to obtain the wrapped phase matrix Wrapping Phase Matrix It is a two-dimensional matrix of M×N (assuming M=10, N=10).

[0134] Step 2022, set is the wrapped phase matrix, is the corresponding unwrapping phase. First, define the wrapping operator F, The differences of adjacent elements in the x-direction and y-direction of the wrapping phase are calculated using formulas (9) and (10).

[0135] Then, we use the least squares method to solve By minimizing the objective function:

[0136]

[0137] When the objective function E reaches its minimum value, we get This is the unpacked phase of the area, that is, the true phase value.

[0138] Step 203: Regional surface restoration:

[0139] Step 2031: Expand the wavefront to be measured into the first N=36 fringe Zernike polynomials in the Cartesian coordinate system. The wavefronts to be measured with different shear magnitudes in the x-direction and y-direction are shown in formulas (13) and (14), respectively. The j-th term in the x-direction is m The differential Zernike polynomials when the j-th term in the y direction is sheared with s m The differential Zernike polynomials for are shown in formulas (15) and (16) respectively.

[0140] Furthermore, the differential wavefront under the same set of shear Combined into a discrete matrix:

[0141] ΔW xm =ΔZ xm a (17)

[0142] ΔW ym =ΔZ ym a (18)

[0143] Where ΔZ xm and ΔZ ym Represent the differential Zernike polynomial expressions in the x and y directions respectively. Further, the differential wavefront ΔW under the same set of shear amounts is xm , ΔW ym Combined into a discrete matrix ΔW, ΔZ xm and ΔZym Combined into the same discrete matrix ΔZ, specifically:

[0144]

[0145] Furthermore, the standard least squares method is used to solve the equation: According to the obtained Zernike coefficient The surface shape ΔW of the annular zone can be fitted.

[0146] Step 204: Wavefront fusion and reconstruction:

[0147] Step 2041. Combine the multiple sets of regional shapes obtained in step 203 to obtain a matrix W with the same size as the original shape. r (x, y), the differential wavefront of the surface to be measured after splicing is expressed as:

[0148]

[0149] Where ΔW r is a column vector, representing the differential wavefront of the surface to be measured after splicing, ΔZ represents the differential wavefront of the surface to be measured after splicing, Indicates the solution coefficient.

[0150] The surface shapes of the multiple ring zones after splicing are fitted again, and the standard least squares method is used to solve the equation:

[0151]

[0152] The coefficients obtained will be Substituting the above equation, the wavefront to be measured is obtained, thereby realizing the reconstruction of the wavefront to be measured based on the lateral shearing interferogram of multiple shear quantities.

[0153] Based on the same inventive concept, an embodiment of the present invention provides a wavefront fusion reconstruction device. Since the principle of solving the technical problem of the device is similar to that of a wavefront fusion reconstruction method, the implementation of the device can refer to the implementation of the method, and the repeated parts will not be repeated.

[0154] like Figure 7 As shown, the apparatus includes a determining unit 701 , a first obtaining unit 702 , a second obtaining unit 703 and a third obtaining unit 704 .

[0155] A determination unit 701 is configured to determine the coordinates of a limit resolution point of the wavefront slope of the aspheric surface to be measured according to the Nyquist sampling theorem, divide the wavefront slope of the aspheric surface to be measured into annular zones according to the coordinates of the limit resolution point, and determine a shearing amount of the annular zone according to the number of pixels occupied by the boundary fringes of the annular zone; wherein the shearing amount determined for each annular zone is used to analyze shear interference fringes within the annular zone;

[0156] A first obtaining unit 702 is configured to obtain a shearing interference fringe pattern corresponding to each annular zone region by passing the aspheric surface to be measured through an interferometer, perform wrapped phase extraction on the shearing interference fringe pattern to obtain a wrapped phase value, and unwrap the wrapped phase value to obtain a true phase value corresponding to the annular zone region;

[0157] The second obtaining unit 703 is configured to perform differential processing on the true phase value to obtain a phase difference between adjacent phases, and to fit the phase difference using a differential Zernike polynomial to obtain a ring zone area shape corresponding to each of the ring zones;

[0158] The third obtaining unit 704 is used to splice the multiple annular zone area shapes to obtain a wavefront shape of the same size as the aspheric surface to be measured, and fit the wavefront shape through differential Zernike polynomials to obtain a reconstructed surface shape corresponding to the aspheric surface to be measured.

[0159] It should be understood that the units included in the above-described wavefront fusion reconstruction device are merely logical divisions based on the functions implemented by the device. In actual applications, the above-described units can be superimposed or separated. Furthermore, the functions implemented by the wavefront fusion reconstruction device provided in this embodiment correspond one-to-one with the wavefront fusion reconstruction method provided in the above-described embodiment. A more detailed processing flow implemented by this device has been described in detail in the above-described method embodiment 1 and will not be described in detail here.

[0160] Another embodiment of the present invention also provides a computer device, which includes: a processor and a memory; the memory is used to store computer program code, and the computer program code includes computer instructions; when the processor executes the computer instructions, the electronic device performs the various steps of the wavefront fusion reconstruction method shown in the above method embodiment.

[0161] Another embodiment of the present invention further provides a computer-readable storage medium, which stores computer instructions. When the computer instructions are executed on a computer device, the computer device executes each step of the wavefront fusion reconstruction method shown in the above method embodiment.

[0162] Although the preferred embodiments of the present invention have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0163] Obviously, those skilled in the art may make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if such changes and modifications fall within the scope of the claims and their equivalents, the present invention is intended to include such changes and modifications.

Claims

1. A wavefront fusion reconstruction method, characterized in that: include: According to the Nyquist sampling theorem, the coordinates of the limit resolution point of the wavefront slope of the aspheric surface shape to be measured are determined, the wavefront slope of the aspheric surface shape to be measured is divided into annular zones according to the coordinates of the limit resolution point, and the shear amount of the annular zone area is determined according to the number of pixels occupied by the boundary fringes of the annular zone area; wherein the shear amount determined for each annular zone area is used to analyze the shear interference fringes in the annular zone area; The aspheric surface to be measured, which is divided into annular zones, is passed through an interference device to obtain a shearing interference fringe pattern corresponding to each annular zone area, the shearing interference fringe pattern is subjected to wrapped phase extraction to obtain a wrapped phase value, and the wrapped phase value is unwrapped to obtain a true phase value corresponding to the annular zone area; Performing differential processing on the true phase value to obtain a phase difference between adjacent phases, and fitting the phase difference by using a differential Zernike polynomial to obtain a ring zone area shape corresponding to each of the ring zones; The plurality of annular zone area shapes are spliced ​​to obtain a wavefront shape having the same size as the aspheric surface to be measured, and the wavefront shape is fitted by differential Zernike polynomials to obtain a reconstructed surface shape corresponding to the aspheric surface to be measured.

2. The method according to claim 1, wherein The step of dividing the wavefront slope of the aspheric surface to be measured into annular zones according to the limiting resolution coordinates, and determining the shearing amount of the annular zones according to the number of pixels occupied by the boundary fringes of the annular zones, comprises: Dividing the wavefront slope of the aspheric surface to be measured into annular zones according to the coordinates of the limit resolution point to obtain at least an inner annular zone area and an outer annular zone area; When the number of pixels of the boundary fringes of the inner annular zone meets the resolvable condition, determining the area of ​​the inner annular zone and a first shearing amount, wherein the first shearing amount is used to resolve the shearing interference fringes included in the inner annular zone; When the number of pixels of the boundary fringes of the outer annular zone meets the analysis condition, the area of ​​the outer annular zone and the second shearing amount are determined, and the second shearing amount is used to analyze the shearing interference fringes included in the outer annular zone.

3. The method according to claim 1, wherein The wavefront slope of the aspheric surface to be measured is as follows: W s =2(n(x)-s(x))′| x The coordinates of the limit resolution point of the wavefront slope of the aspheric surface to be measured satisfy the following formula: Among them, W s represents the wavefront slope of the aspheric surface to be measured, n(x) represents the equation of the aspheric surface to be measured, s(x) represents the optimal spherical equation, D represents the aperture of the aspheric surface to be measured, and p represents the number of available pixels of the imaging CCD on the interferometer.

4. The method according to claim 1, wherein The wrapped phase is extracted using the following formula: The true phase value corresponding to the annular zone is obtained by the following formula: in, Indicates the shear amount as s m When the phase value is wrapped at two-dimensional M×N discrete points, I1, I2, I3, I4 represent the light intensity of the four interference images in the four-step phase shift. represents the true phase value corresponding to the annular region obtained after unwrapping the wrapped phase at two-dimensional M×N discrete points, represents the difference of adjacent elements of the wrapped phase in the x direction, represents the difference of adjacent elements of the wrapped phase in the y direction, Indicates the shear amount as s m The wrapped phase value at the two-dimensional discrete point (m+1,n) when Indicates the shear amount as s m The wrapped phase value at the two-dimensional discrete point (m,n) when Indicates the shear amount as s m The wrapped phase value at the two-dimensional discrete point (m, n+1) when , M represents the number of rows of the discrete two-dimensional matrix, N represents the number of columns of the discrete two-dimensional matrix, m=0,1,…,M-2, n=0,1,…,N-1.

5. The method according to claim 1, wherein The phase difference between adjacent phases is determined by the following formula: in, Indicates that the shear amount in the x direction is s m The phase difference between adjacent phases is Indicates that the shear amount in the y direction is s m The phase difference between adjacent phases at the same time, W(x,y) represents the wavefront function to be measured, which describes the wavefront situation at the point (x,y) in the Cartesian coordinate system, s m Indicates the shear amount in the x-direction, J represents the index of the number of terms in the Zernike polynomial, j = 2,…,J, a j represents the coefficient of the j-th Zernike polynomial, Z j (x,y) represents the basis function of the j-th Zernike polynomial, Indicates that the jth item in the x direction has a shear amount of s m The differential Zernike polynomials for , Indicates that the jth item in the y direction has a shear amount of s m The differential Zernike polynomials when Z j (x+s m ,y) represents the jth Zernike polynomial at the coordinate (x+s m ,y) point.

6. The method according to claim 1, wherein The shape of the annular zone area corresponding to each annular zone area is determined by the following formula: ΔW xm =ΔZ xm a ΔW ym =ΔZ ym a Where ΔW xm Represents the wavefront vector to be measured after discretization in the x direction, ΔW ym represents the wavefront vector to be measured after discretization in the y direction, a represents the Zernike polynomial coefficient vector, represents the Zernike polynomial coefficient vector obtained by the standard least squares method, ΔZ T Denotes the transposed matrix of ΔZ, ΔZ is composed of ΔZ xm and ΔZ ym The discrete matrix (ΔZ T ΔZ) -1 represents ΔZ T The inverse matrix of ΔZ, ΔW represents the combined ΔW xm and ΔW ym The discrete matrix after .

7. The method according to claim 1, wherein The following formula is used to stitch together the multiple annular zone area shapes: ΔW r =ΔW1+ΔW2+…ΔW i The wavefront shape is fitted by the following formula Where ΔW r Indicates the differential wavefront of the surface to be measured after splicing, ΔZ T Denotes the transposed matrix of ΔZ, ΔZ is composed of ΔZ xm and ΔZ ym The discrete matrix (ΔZ T ΔZ) -1 represents ΔZ T The inverse matrix of ΔZ, Indicates the solution coefficient, W r (x, y) represents the reconstructed surface shape corresponding to the aspheric surface to be measured.

8. A wavefront fusion reconstruction device, characterized in that: include: a determination unit, configured to determine the coordinates of a limit resolution point of the wavefront slope of the aspheric surface shape to be measured according to the Nyquist sampling theorem, divide the wavefront slope of the aspheric surface shape to be measured into annular zones according to the coordinates of the limit resolution point, and determine a shearing amount of the annular zone region according to the number of pixels occupied by the boundary fringes of the annular zone region; wherein the shearing amount determined for each annular zone region is used to analyze shear interference fringes within the annular zone region; A first obtaining unit is configured to obtain a shearing interference fringe pattern corresponding to each annular zone region by passing the aspheric surface to be measured through an interference device, perform wrapped phase extraction on the shearing interference fringe pattern to obtain a wrapped phase value, and unwrap the wrapped phase value to obtain a true phase value corresponding to the annular zone region; A second obtaining unit is configured to perform differential processing on the true phase value to obtain a phase difference between adjacent phases, and to fit the phase difference using a differential Zernike polynomial to obtain a ring zone area shape corresponding to each of the ring zones; The third obtaining unit is used to splice the surface shapes of multiple annular zones to obtain a wavefront shape of the same size as the surface shape of the aspheric surface to be measured, and fit the wavefront shape through differential Zernike polynomials to obtain a reconstructed surface shape corresponding to the aspheric surface to be measured.

9. A computer device, characterized in that: The computer device includes a memory and a processor, the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the wavefront fusion reconstruction method according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that A computer program is stored, and when the computer program is executed by a processor, the processor is caused to execute the wavefront fusion reconstruction method according to any one of claims 1 to 7.

Images