A real-time single-frame wavefront measurement method and device

Abstract

The application discloses a real-time single-frame wavefront measurement method and device, relates to the technical field of optical measurement and imaging, and comprises the following steps: S1, performing an experiment on a to-be-measured wavefront according to a displacement stage of a shearing interference structure, and acquiring a single-frame interference image containing multiple shearing interference fringes in an arbitrary direction; S2, using a method combining a two-dimensional variational mode decomposition algorithm and a four-step phase-shifting technique to quickly extract phase distribution information; and S3, simultaneously using a differential Zernike polynomial as a base function to reconstruct the wavefront according to the extracted phase distribution information. The method allows collecting a single interference image containing multiple shearing interference fringes in an arbitrary direction in one measurement, can improve the measurement efficiency, and can widen the application potential of the shearing interference method in wavefront analysis.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of optical measurement and imaging technology, in particular to a real-time single-frame wavefront measurement method and device. BACKGROUND

[0002] The lateral shearing interferometry (LSI) technique uses the interference between the wavefront to be measured and the wavefront after lateral translation of itself, does not require a reference wavefront, and can overcome some defects in the structure of off-axis interferometry, and is often used to measure wavefront aberration. The most commonly used core optical element in LSI is a glass plate, a wedge plate, a double prism, and a Wollaston prism. According to different mechanisms, it can be divided into diffraction and non-diffraction. The diffraction method currently uses a multi-wavefront shearing interferometer with a composite grating, which has the disadvantage of high precision requirements for the grating for generating shearing, resulting in high cost. The traditional non-diffraction lateral shearing method generally uses parallel plates, prisms, polarization devices, or some special optical structures to generate lateral shearing. This method can only generate a shearing wavefront in one direction at a time, and often needs to rotate the shearing device to obtain the shearing wavefront in the orthogonal direction, so at least two interference images need to be captured to correctly obtain the wavefront.

[0003] For the problem of extracting phase information from the captured interference image, the fringe projection phase extraction method can be divided into two categories: one is based on single fringe image phase extraction, and the other is based on multiple fringe image phase extraction represented by the phase shift method. In the single projection fringe phase extraction method, the method for extracting the corresponding wavefront is relatively complex, and this complexity is further amplified when dealing with factors such as noise, calibration error, and accurate alignment of optical elements. The single projection fringe phase extraction method includes the use of Fourier transform, continuous wavelet transform, and empirical mode decomposition techniques with spatial carrier frequency. These algorithms have improved in terms of robustness to noise, preservation of image edge details, etc., but still have shortcomings. SUMMARY

[0004] The present application solves the problem of low measurement efficiency of the existing wavefront measurement method, and proposes a real-time single-frame wavefront measurement method and device. The above method allows the acquisition of a single interference image containing multiple arbitrary direction shearing interference fringes in one measurement, which not only improves the measurement efficiency, but also widens the application potential of shearing interferometry in wavefront analysis.

[0005] In order to achieve the above purpose, the present application adopts the following technical scheme: a real-time single-frame wavefront measurement method, comprising the following steps:

[0006] S1, according to the displacement table of the shearing interference structure built, the wavefront to be measured is experimented, and a single frame containing multiple arbitrary direction shearing interference fringe images is obtained;

[0007] S2, a method combining two-dimensional variational mode decomposition algorithm and four-step phase shifting technique is used to quickly extract phase distribution information;

[0008] S3, according to the extracted phase distribution information, a differential Zernike polynomial is used as a base function to reconstruct the wave front.

[0009] In the technical solution, two transverse shear interference fringe images in any direction are simultaneously acquired by the built measuring device, then the shear interference fringe images are processed, the gradient phase information is acquired by combining the effective method of two-dimensional variational mode decomposition and four-step phase shifting technique, and finally the wave front is reconstructed according to the acquired gradient phase information; the above method can effectively separate a single original interference image with multiple arbitrary shear directions, and improve flexibility and applicability.

[0010] The application further provides that the step S2 comprises:

[0011] S21, an optical intensity distribution function of double transverse shear interference in any direction is acquired;

[0012] S22, a two-dimensional variational mode decomposition algorithm is used to express the decomposition process of the multiple interference images acquired in single shooting as a constrained variational problem, and a characteristic modal function is calculated;

[0013] S23, the amplitude distribution of the first fringe and the second fringe on the four channels of the polarization camera polarization array is modulated by four-step phase shifting, and the phase distribution information is extracted.

[0014] The two-dimensional variational mode decomposition algorithm is used to express the decomposition process of the multiple interference images as a constrained variational problem, through the above algorithm, the corresponding characteristic modal function can be obtained by minimizing the energy of each component, and the phase distribution information can be quickly extracted by four-step phase shifting modulation, and real-time imaging is realized.

[0015] The application further provides that the step S3 comprises:

[0016] The difference wave front AW generated by the overlapping area is determined;

[0017] The relationship between the differential wave front and the corresponding differential Zernike polynomial is established, the Zernike polynomial coefficient of the measured wave front is determined by using the least square method, and finally the measured wave front coefficient is solved.

[0018] In the technical solution, the wave front reconstruction process can be completed through the above steps.

[0019] The application is further provided that the light intensity distribution function is represented as the sum of the intensity distribution of an interferogram, the modulation distribution of an incident wave front, and the noise of the interferogram, and the modulation distribution of the incident wave front is the product of the sum of the cosine values of the phase difference of the two groups of shear wave fronts and the modulation state of the incident wave front.

[0020] In the technical solution, the light intensity distribution function of the dual lateral shearing interferometer in any direction is represented before the two-dimensional variational mode decomposition algorithm is used, so as to facilitate the subsequent calculation process.

[0021] The application is further provided that the objective function of the constrained variational problem is represented as the minimum value of the product of the Tikhonov regularization parameter and the square of the gradient norm L 2 , and the constraint condition of the constrained variational problem is that the sum of the decomposed mode functions is equal to the interferogram to be decomposed.

[0022] In the technical solution, the decomposition process of multiple interferograms is represented as a constrained variational problem, and the corresponding characteristic mode functions can be obtained by minimizing the energy generalization of each component through the two-dimensional variational mode decomposition algorithm.

[0023] The application is further provided that the four channels of the polarization camera polarization array are 0°, 45°, 90° and 135° respectively.

[0024] The application is further provided that the wave front to be measured is finally represented as the sum of the products of a series of independent Zernike polynomials and the related weighted coefficients.

[0025] In the technical solution, the wave front reconstruction process of the method is completed by solving the wave front to be measured.

[0026] A real-time single-frame wave front measurement device adopts the real-time single-frame wave front measurement method, and comprises a laser and a beam splitter. The outgoing light path of the laser passes through a beam expander and a linear polarizer in sequence and then irradiates a polarization beam splitter. A first reflecting mirror and a first displacement table are arranged on the two outgoing light paths of the polarization beam splitter respectively. The beam splitter is arranged on one outgoing light path of the polarization beam splitter. A second reflecting mirror and a second displacement table are arranged on the two outgoing light paths of the beam splitter respectively. An image acquisition device is further arranged on one side of the beam splitter.

[0027] In the technical solution, the beam expander, the linear polarizer and the polarization beam splitter are sequentially arranged on the outgoing light path of the laser, the first mirror and the first displacement table are respectively located on two mutually perpendicular outgoing light paths of the polarization beam splitter and are respectively arranged obliquely relative to the outgoing light paths, the beam splitter is located on the outgoing light path of the polarization beam splitter, and similar to the polarization beam splitter, the second mirror and the second displacement table are arranged, the second mirror and the second displacement table are respectively located on two mutually perpendicular outgoing light paths of the beam splitter, and the image acquisition device is located on the outgoing light path of the beam splitter.

[0028] The application further provides that the image acquisition device is arranged on the outgoing light path of the beam splitter away from the second displacement table, and the image acquisition device comprises a zoom lens and a polarization camera.

[0029] In the technical solution, the image acquisition device can simultaneously acquire the positions of two groups of transverse shearing interference beams and simultaneously obtain two transverse shearing interference fringe images in any direction.

[0030] The application further provides that a quarter-wave plate is further arranged between the image acquisition device and the beam splitter.

[0031] In the technical solution, the quarter-wave plate and the image acquisition device are located on the outgoing light path of the beam splitter.

[0032] The application can bring the following beneficial effects:

[0033] The real-time single-frame wavefront measurement method can obtain gradient phase information by combining two-dimensional variational modal decomposition and four-step phase shifting technology, can effectively separate a single original interference image with multiple arbitrary shearing directions, and improves flexibility and applicability.

[0034] The real-time single-frame wavefront measurement device can acquire an interference image containing multiple shearing interference fringes in any direction, integrates the interference characteristics of polarized light, adopts flexible and customizable shearing, and has high flexibility. BRIEF DESCRIPTION OF DRAWINGS

[0035] Figure 1 is a schematic view of a real-time single-frame wavefront measurement device of the application.

[0036] Figure 2 is a schematic view of the geometric relationship of the wavefront shearing interference ray tracing to be measured.

[0037] Figure 3 is a schematic view of the double transverse shearing wavefront pattern acquired by the image acquisition device.

[0038] Figure 4Fig. 1 is a schematic diagram of wrapped interference fringe patterns of two arbitrary shearing directions extracted by the phase extraction algorithm of the present application.

[0039] Reference signs:

[0040] 1. Laser 2, beam expander 3, linear polarizer 4, first displacement table 5, first mirror 6, polarization beam splitter 7, beam splitter 8, quarter wave plate 9, zoom lens 10, polarization camera 11, second displacement table 12, second mirror. DETAILED DESCRIPTION

[0041] In order to make the objectives, technical solutions and advantages of the present application clearer, further detailed description will be given below in combination with the drawings and examples. It should be understood that the specific embodiments described herein are only the best mode of the present application, which are used to explain the present application and do not limit the protection scope of the present application. All other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the present application.

[0042] Example 1

[0043] The present embodiment provides a real-time single-frame wavefront measurement device, which refers to Figure 1 which mainly comprises a laser 1, a beam expander 2, a linear polarizer 3, a first displacement table 4, a first mirror 5, a polarization beam splitter 6, a beam splitter 7, a quarter wave plate 8, a zoom lens 9, a polarization camera 10, a second displacement table 11 and a second mirror 12.

[0044] Referring to Figure 1 , the outgoing light path of the laser 1 is sequentially irradiated to the polarization beam splitter 6 after passing through the beam expander 2 and the linear polarizer 3, and the first mirror 5 and the first displacement table 4 are respectively arranged on the two outgoing light paths of the polarization beam splitter 6; the beam splitter 7 is arranged on one outgoing light path of the polarization beam splitter 6, and the second mirror 12 and the second displacement table 11 are respectively arranged on the two outgoing light paths of the beam splitter 7, and an image acquisition device is further arranged on one side of the beam splitter 7.

[0045] More specifically, the first mirror 5 and the first displacement table 4 are respectively arranged on the two perpendicular outgoing light paths of the polarization beam splitter 6, and are respectively arranged obliquely relative to the outgoing light paths.

[0046] The second mirror 12 and the second displacement table 11 are respectively arranged on the two mutually perpendicular outgoing light paths of the beam splitter 7.

[0047] The image acquisition device is specifically arranged on the outgoing light path of the beam splitter 7 away from the second displacement table 11, and the above-mentioned image acquisition device mainly comprises a zoom lens 9 and a polarization camera 10.

[0048] A quarter wave plate 8 is arranged between the image acquisition device and the beam splitter 7.

[0049] In the technical solution, the image acquisition device can simultaneously acquire the positions of two groups of transverse shearing interference beams and simultaneously obtain two transverse shearing interference fringe images in any direction.

[0050] In the technical solution, the quarter wave plate 8 and the image acquisition device are located on the exit light path of the beam splitter 7.

[0051] In the technical solution, the beam expander 2, the linear polarizer 3, and the polarization beam splitter 6 are sequentially arranged on the exit light path of the laser 1, the first mirror 5 and the first displacement table 4 are respectively located on two mutually perpendicular exit light paths of the polarization beam splitter 6 and are respectively arranged to be inclined relative to the exit light paths, the beam splitter 7 is located on the exit light path of the polarization beam splitter 6 and is similar to the polarization beam splitter 6, and the beam splitter 7 is provided with a second mirror 12 and a second displacement table 11, the second mirror 12 and the second displacement table 11 are respectively located on two mutually perpendicular exit light paths of the beam splitter 6, and the image acquisition device is located on the exit light path of the beam splitter 7.

[0052] In the embodiment, the distance from the direct light and the reflected light at the polarization beam splitter 6 to the center of the first mirror 5 and the first displacement table is 111 mm and 88 mm respectively.

[0053] In the embodiment, the distance from the direct light and the reflected light at the beam splitter 7 to the center of the second mirror 12 and the second displacement table 11 is 73 mm and 70 mm respectively, and the distance can also be set according to actual requirements.

[0054] In the embodiment, the angle between the first mirror 5 at the polarization beam splitter 6 and the horizontal direction is 68°.

[0055] In the embodiment, the angle between the second mirror 12 at the beam splitter 7 and the horizontal direction is 24°.

[0056] In the embodiment, the beam diameter of the laser 1 is 5 mm.

[0057] The working principle of the real-time single-frame wavefront measurement device is described as follows: the light emitted from the laser 1 is optimized at the front end, and uniform linearly polarized light is obtained after passing through the linear polarizer 3. Then the linearly polarized light source can be vertically incident on the polarizing beam splitter 6, and then the direction of the transmission axis is adjusted by the first displacement table 4. Then the light is divided into reflected s wave and transmitted p wave by the polarizing beam splitter 6. Then the light meets again at the polarizing beam splitter 6 to form the first lateral shearing interference. The interference light, i.e. p wave and s wave, is divided into two p waves and two s waves after passing through the lateral shearing interference system composed of two displacement tables and one non-polarizing beam splitter 7. Then the light beam passes through the quarter wave plate 8 with the fast axis at 45° to the polarization direction, and is modulated into two left-handed circularly polarized light and two right-handed circularly polarized light. The left-handed circularly polarized light and the right-handed circularly polarized light interfere with each other.

[0058] Based on the above working principle, the wavefront to be measured is represented as:

[0059] E=Aexp[iW1]

[0060] Wherein, A represents the amplitude, and W1 represents the phase delay of the p wave.

[0061] Each element in the device is substituted into the corresponding Jones matrix and vector expression for calculation. For details, refer to the following formula:

[0062]

[0063] Wherein, W1 and W2 represent the phase delay of the p wave and the s wave respectively; A represents the amplitude; E represents the Jones matrix representation of each element, wherein QWP represents the quarter wave plate, M1 and M2 represent the mirror and the adjustable mirror respectively; PBS represents the polarizing beam splitter. The polarization states of E1 and E2 are orthogonal to each other, which meets the orthogonal polarization state.

[0064] Since the orthogonal polarization states do not produce interference patterns, the light beam needs to pass through the image sensor array of the polarization camera 10 to produce interference. The basic principle of the polarization camera 10 used in the present application is to cover a mask plate made by special process on the imaging array surface, which is composed of 2x2 array of 4 polarization pixels. The polarization angle of adjacent polarization pixels is 45°. The light beam will interfere in four directions, and four interference fringes with obvious phase shift can be observed on the polarization camera 10. The Jones vector of E1 and E2 after passing through the imaging array surface of the polarization camera is specifically represented as:

[0065]

[0066] Wherein, W1 and W2 represent the phase delay of the p wave and the s wave respectively; and α represents the polarization angle of the polarization camera imaging array, which is 0°, 45°, 90° and 135° respectively.

[0067] Therefore, the light intensity distribution of the final light beam falling on the polarization camera array is specifically represented as:

[0068]

[0069] The light intensity distribution of the interference of the other two beams of left and right circularly polarized light is the same as I a_1 The light intensity distribution of the double interference fringes received by the polarization camera is shown as follows. When α is 0°, 45°, 90°, and 135°, the phase shift amounts of 0, π / 2, π, and 3π / 2 can be simultaneously generated on the imaging array surface of the polarization camera, four-step phase shift is realized, phase distribution information is quickly extracted, and real-time imaging is realized,

[0070]

[0071] wherein A represents the amplitude; ΔW1 represents the differential phase W1-W2; NOISE represents the noise; and α represents the polarization angle of the imaging array of the polarization camera.

[0072] Embodiment 2

[0073] The embodiment provides a real-time single-frame wavefront measurement device, which mainly comprises a laser 1, a beam expander 2, a linear polarizer 3, a first displacement table 4, a first mirror 5, a polarization beam splitter 6, a beam splitter 7, a quarter-wave plate 8, a zoom lens 9, a polarization camera 10, a second displacement table 11, and a second mirror 12. With continuous reference to Figure 1 , the outgoing light path of the laser 1 passes through the beam expander 2 and the linear polarizer 3 in sequence and is incident on the polarization beam splitter 6, the first mirror 5 and the first displacement table 4 are respectively arranged on the two outgoing light paths of the polarization beam splitter 6; the beam splitter 7 is arranged on one of the outgoing light paths of the polarization beam splitter 6, the second mirror 12 and the second displacement table 11 are respectively arranged on the two outgoing light paths of the beam splitter 7, and an image acquisition device is further arranged on one side of the beam splitter 7.

[0074] More specifically, the first mirror 5 and the first displacement table 4 are respectively arranged on the two perpendicular outgoing light paths of the polarization beam splitter 6, and are respectively arranged obliquely relative to the outgoing light paths.

[0075] The second mirror 12 and the second displacement table 11 are respectively arranged on the two perpendicular outgoing light paths of the beam splitter 7.

[0076] The image acquisition device is specifically arranged on the outgoing light path of the beam splitter 7 away from the second displacement table 11, and the above-mentioned image acquisition device mainly comprises the zoom lens 9 and the polarization camera 10.

[0077] The quarter-wave plate 8 is arranged between the image acquisition device and the beam splitter 7.

[0078] In the technical solution, the image acquisition device can simultaneously acquire the positions of the two groups of transverse shearing interference light beams and simultaneously obtain two transverse shearing interference fringe images in any direction.

[0079] In the technical solution, the quarter-wave plate 8 and the image acquisition device are located on the exit light path of the beam splitter 7.

[0080] In the technical solution, the beam expander 2, the linear polarizer 3, and the polarization beam splitter 6 are sequentially arranged on the exit light path of the laser 1, the first mirror 5 and the first displacement stage 4 are respectively located on two mutually perpendicular exit light paths of the polarization beam splitter 6 and are respectively arranged to be inclined with respect to the exit light paths, the beam splitter 7 is located on the exit light path of the polarization beam splitter 6 and is similar to the polarization beam splitter 6, and the second mirror 12 and the second displacement stage 11 are arranged, the second mirror 12 and the second displacement stage 11 are respectively located on two mutually perpendicular exit light paths of the beam splitter 6, and the image acquisition device is located on the exit light path of the beam splitter 7.

[0081] In the embodiment, the distance from the direct light and the reflected light at the polarization beam splitter 6 to the center of the first mirror 5 and the first displacement stage is 111 mm and 88 mm, respectively.

[0082] In the embodiment, the distance from the direct light and the reflected light at the beam splitter 7 to the center of the second mirror 12 and the second displacement stage 11 is 73 mm and 70 mm, respectively, and can be arranged according to actual requirements.

[0083] In the embodiment, the angle between the first mirror 5 at the polarization beam splitter 6 and the horizontal direction is 68°.

[0084] In the embodiment, the angle between the second mirror 12 at the beam splitter 7 and the horizontal direction is 24°.

[0085] In the embodiment, the beam diameter of the laser 1 is 5 mm.

[0086] On the basis of the embodiment 1, the embodiment proposes a real-time single-frame wavefront measurement method, which mainly includes the following steps.

[0087] Step S1, the displacement stage of the completed shearing interference structure is used to experiment on the wavefront to be measured, and a single frame including multiple shearing interference fringe images in any direction is obtained.

[0088] Step S2, after obtaining the shearing interference fringe image, the phase distribution information is quickly extracted by combining the two-dimensional variational mode decomposition algorithm and the effective method of four-step phase shifting technology.

[0089] Step S3, according to the phase distribution information obtained in step S2, and using differential Zernike polynomials as the base function to reconstruct the wavefront.

[0090] For step S1, the displacement table mainly includes a first displacement table 4 and a second displacement table 11, and the displacement table mainly consists of a rotary displacement table and an angular displacement table, which can realize 360° rotation of the mirror, ±5° pitch adjustment, and can be adjusted through a differential head. Figure 2 According to the geometric relationship of the shear interferometric ray tracing of the to-be-measured wavefront, the size of the shear quantity can be calculated; in addition, the shear direction can be obtained by edge detection on the two decomposed fringe patterns,

[0091]

[0092] Where oo1 and α are the distance from the direct light mirror to the center of the beam splitter prism and the angle with the x-axis; oo2 and β are the distance from the deflected light mirror to the center of the beam splitter prism and the angle with the x-axis. x Where oo1 and α are the distance from the direct light mirror to the center of the beam splitter prism and the angle with the x-axis; oo2 and β are the distance from the deflected light mirror to the center of the beam splitter prism and the angle with the x-axis.

[0093] For step S2, it mainly includes the following sub-steps.

[0094] Step S21, first, the light intensity distribution function of the double lateral shear interference in any direction is obtained; for the above light intensity distribution function, it is the sum of the modulation distribution of the incident wavefront, the interference pattern noise and the intensity distribution of the interference pattern, wherein the modulation distribution of the incident wavefront is the product of the sum of the cosine values of the phase difference of the two groups of shear wavefronts and the modulation state of the incident wavefront.

[0095] In this technical solution, before the two-dimensional variational modal decomposition algorithm is used, the light intensity distribution function of the double lateral shear interference in any direction is represented, so as to facilitate the subsequent calculation process.

[0096] In this embodiment, the light intensity distribution function can be specifically represented as:

[0097] I(x,y)=I a (x,y)+I b (x,y){cos[ΔW1(x,y)]+cos[ΔW2(x,y)]}+n

[0098] Where I a (x,y) represents the intensity distribution of the interference pattern, I b (x,y) represents the modulation state of the incident wavefront; ΔW1(x,y) and ΔW2(x,y) are the phase difference of the two groups of shear wavefronts, and n is the interference pattern noise.

[0099] Step S22, secondly, the two-dimensional variational mode decomposition algorithm is adopted, and a decomposition process of the plurality of interferograms captured in a single shot is expressed as a constrained variational problem to obtain a characteristic modal function. Specifically, an objective function of the constrained variational problem is expressed as a minimum value of a product of a Tikhonov regularization parameter and a square of a gradient norm L 2 , and a constraint condition of the constrained variational problem is that a sum of the decomposed modal functions is equal to the interferogram to be decomposed.

[0100] In more detail, the two-dimensional variational mode decomposition (2DVMD) is a newly proposed adaptive signal analysis method, which is established on the basis of variational method and Wiener filtering, and can adaptively separate several signals with different modes, i.e., can obtain a band-limited eigenmodal function. First, for each eigenmodal u k , an analytical signal is calculated by Hilber transform, and a one-sided spectrum is obtained. Second, for each one-sided spectrum modal, each frequency spectrum is moved to a "baseband" by mixing an exponential modulation term with a center frequency w k . Finally, a bandwidth is estimated by a H 1 igh smoothing (L 2 norm) of the demodulated signal.

[0101] The Fourier property is used to define the 2D analytical signal u k , and specific reference is made to the following formula:

[0102]

[0103] wherein * represents convolution, δ(t) represents Dirac function, is a partial derivative with respect to time t, is a center frequency.

[0104] The two-dimensional variational mode decomposition algorithm is used to express a decomposition process of the plurality of interferograms captured in a single shot as a constrained variational problem:

[0105]

[0106] wherein α k is a Tikhonov regularization parameter, is a square of a gradient norm L 2 , u k =(u1,u2,…u k ) is a decomposed modal function; U AS,K (x) represents a complex analytical signal composed of u k and a Hilbert transform thereof, <w k ,X> represents a frequency wave number domain, and f represents an interferogram to be decomposed.

[0107] First, the minimization problem of u k is solved:

[0108]

[0109] where α is a regularization function and λ is a Lagrange multiplier. This will result in the following Wiener-Filter:

[0110]

[0111] where and are the Fourier transforms of f(w), u(w) and λ(w), respectively, and n is the iteration time.

[0112] Second, the minimization problem of is solved, as follows:

[0113]

[0114] which is expressed in the Fourier frequency domain as:

[0115]

[0116] The solution is:

[0117]

[0118] where is the modal power and the first moment on the half-plane Ω k . The Lagrange multiplier λ is updated by standard gradient ascent with a fixed time step γ:

[0119]

[0120] After several iterations, the energy functional minimization is achieved and the individual modal components are obtained.

[0121] Using the above algorithm, the corresponding characteristic modal functions u k are obtained by minimizing the energy generalization of each component, as follows:

[0122]

[0123] Finally, the amplitude distribution of the first and second fringes on the four channels of the polarization camera polarization array is extracted using four-step phase shift modulation to obtain the phase distribution information. Specifically, the amplitude distribution of the first and second fringes on the 0°, 45°, 90° and 135° channels of the polarization camera polarization array is further modulated using four-step phase shift modulation, which can be referred to as the following formula:

[0124]

[0125] For step S3, the wavefront to be measured can be finally expressed as a sum of a series of independent Zernike polynomials multiplied by the relevant polynomial weight coefficients.

[0126] In more detail, the differential wavefront AW generated by the overlapping area can be specifically referred to as follows:

[0127]

[0128] where θ is the shearing direction (the angle between the shearing wavefront defined by the wavefront to be measured and the z-axis), S is the shearing amount; and ΔZ is the expression of the differential Zernike basis function.

[0129] After the shearing direction θ and the shearing amount S are determined as known quantities through the above-mentioned geometric calculation, the relationship between the differential wavefront and the corresponding differential Zernike polynomials can be established by solving the wavefront coefficients to be measured, and is specifically referred to as follows:

[0130]

[0131] where each of ΔZ1 and ΔZ2 represents the value of the Zernike differential polynomial of order N 2 .

[0132] The Zernike polynomial coefficients of the wavefront to be measured are determined by using the least square method, and are specifically expressed as follows:

[0133]

[0134] The wavefront to be measured can be expressed as a sum of a series of independent Zernike polynomials multiplied by the relevant polynomial weight coefficients, and the formula is specifically expressed as follows:

[0135]

[0136] where Z j (x, y) is the jth term of the Zernike polynomial, and the vector a j represents the weight coefficient of the relevant polynomial.

[0137] Referring to Figure 3 , the schematic diagram of the double-lateral shearing wavefront pattern collected by the image acquisition device is shown, and in this embodiment, the single frame of the interference fringe image containing any two shearing directions collected by the image acquisition device is shown.

[0138] Referring to Figure 4 , by performing phase extraction on the Figure 3 interference fringe image, the wrapped interference fringe pattern of two arbitrary shearing directions and the image background obtained by the algorithm of this embodiment are shown.

[0139] Finally, it should be pointed out that the above embodiments are only used to illustrate the technical solutions of the present application but not to limit. Although the present application is explained in detail with reference to the embodiments, those skilled in the art should understand that the technical solutions of the present application can be modified or replaced equivalently without departing from the spirit and scope of the present application, and all of them should be covered in the scope of the claims of the present application.

Claims

1. A real-time single-frame wavefront measurement method, characterized in that, The method comprises the following steps: S1, obtaining a single frame containing multiple arbitrary direction shearing interference fringe images according to the displacement table of the built shearing interference structure for the wavefront to be measured; the shearing interference structure comprises a laser, a polarizer, two sets of components composed of a polarization beam splitter, a mirror, a displacement table, a quarter-wave plate, and a polarization camera; S2, extracting phase distribution information quickly by using a method combining a two-dimensional variational mode decomposition algorithm and a four-step phase shifting technique; S3, reconstructing the wavefront according to the extracted phase distribution information while using a differential Zernike polynomial as a base function.

2. The method of claim 1, wherein, The step S2 comprises: S21, obtaining a light intensity distribution function in an arbitrary direction of double lateral shearing interference; S22, expressing the decomposition process of multiple interference patterns obtained in a single shooting as a constrained variational problem by using a two-dimensional variational mode decomposition algorithm, and calculating feature modal functions; S23, using four-step phase shift modulation to extract phase distribution information from the amplitude distribution of the first fringe and the second fringe on the four channels of the polarization camera polarization array.

3. The method of claim 2, wherein, The step S3 comprises: determining a differential wavefront ΔW generated by the overlapping area; establishing a relationship between the differential wavefront and the corresponding differential Zernike polynomial; determining the Zernike polynomial coefficients of the wavefront to be measured by using a least square method, and finally solving the wavefront coefficients to be measured.

4. The method of claim 2, wherein, The light intensity distribution function is expressed as the sum of the intensity distribution of the interference pattern, the modulation distribution of the incident wavefront, and the noise of the interference pattern, and the modulation distribution of the incident wavefront is the product of the sum of the cosine values of the phase difference of the two sets of shearing wavefronts and the modulation state of the incident wavefront.

5. The method of claim 2, wherein, The objective function of the constrained variational problem is expressed as the minimum of the product of a Tikhonov regularization parameter and the square of the gradient norm L 2 The constraint condition of the constrained variational problem is that the sum of the decomposed modal functions equals the interferogram to be decomposed.

6. The method of claim 2, wherein, The four channels of the polarization camera polarization array are 0°, 45°, 90°, and 135°, respectively.

7. The method of claim 1, wherein, The wavefront to be measured is finally expressed as the sum of the product of a series of independent Zernike polynomials and the related multiple weighting coefficients.

8. A real-time single-frame wavefront measurement device, employing a real-time single-frame wavefront measurement method according to any one of claims 1-7, characterized in that, The device comprises a laser (1) and a beam splitter (7), the outgoing light path of the laser (1) passes through a beam expander (2) and a linear polarizer (3) in sequence and then is directed to a polarization beam splitter (6), a first mirror (5) and a first displacement table (4) are arranged on the two outgoing light paths of the polarization beam splitter (6), respectively; the beam splitter (7) is arranged on one outgoing light path of the polarization beam splitter (6), a second mirror (12) and a second displacement table (11) are arranged on the two outgoing light paths of the beam splitter (7), respectively, and an image acquisition device is further arranged on one side of the beam splitter (7).

9. A real-time single-frame wavefront measurement device according to claim 8, wherein, The image acquisition device is arranged on the outgoing light path of the beam splitter (7) away from the second displacement table (11), and the image acquisition device comprises a zoom lens (9) and a polarization camera (10).

10. A real-time single-frame wavefront measurement device according to claim 8 or 9, wherein, A quarter-wave plate (8) is further arranged between the image acquisition device and the beam splitter (7).

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