A Phase Retrieval Wavefront Detection Method without Support Region Constraint

Abstract

The present invention discloses a phase retrieval wavefront detection method without support region constraint, which can achieve rapid wavefront reconstruction without prior knowledge of the support region. After arbitrarily diffracting a random estimate value to a defocused plane, the wavefront phase of the defocused plane is repeatedly obtained through iteration on the defocused plane, and finally inverse diffraction is performed back to the wavefront to be measured. The present invention replaces the traditional iteration between the wavefront to be measured and the light intensity measurement plane with direct iterative diffraction calculation on the defocused plane, increases the intensity information, improves the tolerance of the algorithm to a loose support region, and further improves the convergence accuracy of the algorithm.

Description

Technical Field

[0001] The present invention relates to the field of optical measurement technologies, and in particular, to a phase retrieval wavefront detection method without support domain constraints. Background Art

[0002] Phase retrieval wavefront detection is a new type of non-interferometric wavefront detection method that has been emerging in recent years. Based on the principle of computational optical imaging, it directly calculates and retrieves wavefront information through the energy distribution of the focal spot. It has a simple structure, does not require the formation of interference fringes, and is suitable for wavefront detection with large relative apertures and high steepness.

[0003] For example, Chinese patent document with publication number CN112629678A discloses a fast phase retrieval method for non-diffracting iterative calculation of a general shape. This method decomposes the wavefront to be measured using numerical orthogonal polynomial modes, then calculates the diffraction basis functions for each term of the numerical orthogonal polynomial based on the fast Fourier transform, and then iteratively solves the coefficient gradient using matrix operations between diffraction planes, achieving high-speed wavefront detection of a general shape.

[0004] Chinese patent document with publication number CN110470245A discloses a phase retrieval method based on the fusion of diffraction information of a Fresnel zone plate. This method uses the diffraction intensity distribution modulated by the Fresnel zone plate for retrieval, and can achieve the reconstruction of a wider frequency band of the wavefront to be measured.

[0005] Phase retrieval is widely applied to fields such as optical detection, imaging, and adaptive optics. However, it is itself an inverse mathematical problem with various unsolved problems. The application of phase retrieval in the optical field and the mutual promotion between different fields have formed a positive feedback iterative process of continuously solving theoretical problems in practice and applying theoretical progress to practice.

[0006] The phase retrieval model establishes an iterative process between the target domain and the Fourier domain, and retrieves the wavefront phase through the measured diffraction intensity, that is, the most classic GS algorithm. Later, Fienup further studied the GS algorithm and developed the ER algorithm and the HIO algorithm, which were applied to the aberration correction of the Hubble Space Telescope. These algorithms have relatively strict requirements for the support domain, and an inaccurately known support domain will reduce the convergence performance of the algorithms. In real practical scenarios, it is very difficult to accurately measure the support domain. Summary of the Invention

[0007] The present invention provides a phase retrieval wavefront detection method without support domain constraints to solve the problem of reduced wavefront reconstruction accuracy caused by the high requirements of traditional phase retrieval wavefront detection methods for the support domain but the difficulty in accurately measuring the support domain, and can improve the wavefront reconstruction accuracy.

[0008] A phase retrieval wavefront detection method without support region constraint, which is applied to the light intensity image acquisition scenario. On the outgoing light path of the laser, a beam expander, a flat plate to be measured, a converging lens, and an image sensor are arranged in sequence. The method includes the following steps:

[0009] S1: Move the image sensor to collect n defocused diffraction spots containing the wavefront error of the flat plate to be measured at different defocus distances;

[0010] S2: Respectively set the focal length f, aperture D, and wavelength λ of the converging lens, and the defocus position z of each defocused diffraction spot, with the optimization step size being h phase , and set the initial complex amplitude g s (x, y) of the measurement plane as an all - one matrix;

[0011] S3: Set the pixel size Δd u ×Δd v and the number of pixels M 0 ×N 0 of the image sensor, crop and normalize the j - th collected diffraction spot to obtain an effective spot with dimensions M×M

[0012] S4: Based on the scalar diffraction theory, diffract the initial complex amplitude g s (x, y) of the measurement plane to the j - th defocus plane to obtain the diffraction light field of the j - th defocus plane. The formula is:

[0013]

[0014] and replace the amplitude with the j - th effective spot obtained after S3 processing to obtain the diffraction light field after amplitude replacement

[0015] S5: For the j - th defocus plane, use the diffraction spot of the k - th defocus plane to calculate the phase gradient, where k≠j, and optimize the phase of the estimated complex amplitude to obtain the optimized diffraction light field The formula is:

[0016]

[0017] S6: Diffract the diffraction of the j - th defocus plane calculated in S5 to the next defocus plane, the j'- th defocus plane. The formula is:

[0018]

[0019] and perform symbol replacement j′ = j, and replace the amplitude with the diffraction spot after S3 processing

[0020] ​

[0021] S7: Increment the iteration count t by 1, and repeat steps S5 - S6 until t ≥ T, where T represents the total number of iterations;

[0022] S8: From the j-th defocused plane, inverse-diffract the optimized diffracted light field calculated in S5 back to the wavefront to be measured, obtaining the reconstructed light field.

[0023] Furthermore, in step S3, the centroid method is used to crop the j-th diffracted light spot collected.

[0024] In step S4, the scalar diffraction theory is Fresnel diffraction.

[0025] In step S4, the formula for amplitude replacement using the j-th effective light spot obtained after processing by S3 is:

[0026]

[0027] where arg[ ] represents the phase extraction operation, is the diffracted light field after amplitude replacement.

[0028] In step S4, the j-th defocused plane is the first defocused plane.

[0029] In step S5, the objective function for phase gradient calculation is:

[0030]

[0031] where and are and the normalized intensity of I j (u, v), is the intensity value of the diffracted light spot on the j-th defocused plane calculated using the diffracted light spot on the k-th diffracted plane; W jk (u, v) is the weight parameter used to remove pixels with low signal-to-noise ratio.

[0032] In step S5, the method for phase gradient calculation is:

[0033]

[0034] where Im[] represents the imaginary part extraction, is calculated through the following formula

[0035]

[0036]

[0037] Where, Δz jk is the distance between the j-th diffraction surface and the k-th diffraction surface, and G jk (u, v) represents the complex amplitude of the j-th defocused plane calculated from the diffraction spot of the k-th diffraction surface.

[0038] In step S8, the formula for calculating the reconstructed light field is:

[0039]

[0040] Where, Δz 1j is the distance between the 1st diffraction surface and the j-th diffraction surface.

[0041] Compared with the prior art, the present invention has the following beneficial effects:

[0042] The present invention directly calculates and reconstructs the phase iteratively on the diffraction surface, and can achieve high-precision wavefront reconstruction without support domain constraint. The iterative wavefront reconstruction method is combined with a non-linear optimization algorithm to accelerate the wavefront phase reconstruction process, and the disordered use of diffraction spots will accelerate the algorithm convergence process. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 is a schematic diagram of a device for a phase recovery wavefront detection method without support domain constraint in an embodiment of the present invention;

[0044] Figure 2 is a flowchart of a phase recovery wavefront detection method without support domain constraint in an embodiment of the present invention;

[0045] Figure 3 is a recovery result diagram of applying the method of the present invention in an embodiment. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0046] The present invention will be further described in detail below with reference to the drawings and embodiments. It should be noted that the following embodiments are intended to facilitate the understanding of the present invention and do not limit it in any way.

[0047] As Figure 1 shown, as an example of light intensity map acquisition, a beam expander 2, a to-be-tested flat plate 3, a converging lens 4, and an image sensor 5 are sequentially arranged on the outgoing light path of a laser 1, and the image sensor 5 is fixed on a precision guide rail 6.

[0048] As Figure 2 shown, a phase recovery wavefront detection method without support domain constraint includes the following steps:

[0049] S1: Move the image sensor to collect n defocused diffraction spots containing the wavefront error of the to-be-tested flat plate at different defocus distances.

[0050] S2: Set the focal length f, aperture D, and wavelength λ of the converging lens, and the defocus position z of each defocus diffraction spot k , with the optimization step size being h phase , and set the initial solution g s (x,y) of the measurement plane as a matrix of all ones

[0051] S3: Set the pixel size Δd u × Δd v and the number of pixels M 0 × N 0 , crop and normalize the j-th collected diffraction spot based on the centroid method to obtain an effective spot with dimensions M×M

[0052] S4: Based on the Fresnel diffraction theory, diffract the initial solution g s (x,y) of the measurement plane to the first defocus plane to obtain the diffraction light field of the first defocus plane. The formula is as follows

[0053]

[0054] and replace the amplitude with the j-th effective spot obtained after processing by S3 to obtain the diffraction light field after amplitude replacement The formula is as follows

[0055]

[0056] In the formula, arg[ ] represents the phase extraction operation

[0057] S5: For the j-th defocus plane, use the diffraction spot of the k-th defocus plane to calculate the phase gradient, where k≠j, and optimize the phase of the estimated complex amplitude to obtain the optimized diffraction light field The formula is as follows

[0058]

[0059] The objective function for calculating the phase gradient is

[0060]

[0061] In the formula and are and I j (u,v)'s normalized intensity, is the intensity value of the diffraction spot of the j-th defocus plane calculated using the diffraction spot of the k-th diffraction plane; W jk (u,v) is the weight parameter used to remove low signal-to-noise ratio pixel points

[0062] The method for calculating the phase gradient is as follows:

[0063]

[0064] In the formula, Im[] represents taking the imaginary part, It is calculated through the following formula

[0065]

[0066]

[0067] In the formula, Δz jk is the distance between the j-th diffraction surface and the k-th diffraction surface, and G jk (u, v) represents the complex amplitude of the j-th defocused plane calculated from the diffraction spot of the k-th diffraction surface.

[0068] S6: Calculate the diffraction of the j-th defocused plane obtained in S5 to the next defocused plane, the j'-th defocused plane. The formula is:

[0069]

[0070] And perform symbol substitution j′ = j, and use the diffraction spot processed by S3 for amplitude substitution

[0071]

[0072] S7: The iteration number t = t + 1, and repeat steps S5 - S6 until t ≥ T, where T represents the total number of iterations;

[0073] S8: From the j-th defocused plane, inverse diffract the optimized diffraction light field obtained in S5 back to the wavefront to be measured, and obtain the reconstructed light field. The formula is:

[0074]

[0075] In the formula, Δz 1j is the distance between the first diffraction surface and the j-th diffraction surface.

[0076] The following gives a specific embodiment of the method of the present invention to illustrate the technical effects of the method.

[0077] Here, the focal length is selected as f = 1079.41mm, z 1 , z 2 , z 3 = [-10, -15, -20]mm, the aperture D = 22.9mm, the total number of iterations N for wavefront detection = 5000, and the effective spot sampling number is 1024×1024.

[0078] In this embodiment, three defocused diffraction images are collected for the phase and amplitude reconstruction of the wavefront, and the selected diffraction calculation model is the Fresnel diffraction model. Figure 3 This is the recovery result graph of the method proposed by the present invention. Among them, (a1) and (a2) are the initial values used for the recovered phase and amplitude of the method proposed by the present invention, (b1) and (b2) are the recovered phase and amplitude of the method proposed by the present invention, and (c1) and (c2) are the phase and amplitude of the real graph. It can be seen from the figure the effectiveness of the method proposed in this paper.

[0079] The above-described embodiments have detailed the technical solutions and beneficial effects of the present invention. It should be understood that the above are only specific embodiments of the present invention and are not used to limit the present invention. Any modifications, supplements, and equivalent replacements made within the scope of the principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A phase retrieval wavefront detection method without support region constraint, which is applied to the light intensity image acquisition scenario. On the outgoing light path of the laser, a beam expander, a flat plate to be measured, a converging lens, and an image sensor are arranged in sequence. Characterized in that, This method includes the following steps: S1: Move the image sensor to collect n defocused diffraction spots containing the wavefront error of the flat plate to be measured at different defocus distances. S2: Set the focal length f, aperture D, and wavelength λ of the converging lens respectively, and the defocus position z of each defocused diffraction spot k , with the optimization step size being h phase , and set the initial complex amplitude g s (x, y) as a matrix of all ones; S3: Set the pixel size Δd of the image sensor u ×Δd v and the number of pixels M 0 ×N 0 , crop and normalize the j-th diffracted light spot collected to obtain an effective light spot with dimensions M×M S4: Based on the scalar diffraction theory, the initial complex amplitude g s (x, y) of the measurement plane is diffracted to the j-th defocus plane to obtain the diffracted light field of the j-th defocus plane. The formula is as follows: The j-th effective light spot obtained after being processed by S3 Perform amplitude substitution to obtain the diffracted light field after amplitude substitution S5: For the j-th defocus plane, use the diffraction spot of the k-th defocus plane to calculate the phase gradient, where k ≠ j, and optimize the phase of the estimated complex amplitude to obtain the optimized diffraction light field. The formula is as follows: where arg() represents the phase-taking operation, and E jk represents the objective function for phase gradient calculation; S6: Calculate the diffraction on the j-th defocus plane obtained in S5 to the j'-th defocus plane of the next defocus plane. The formula is: And perform symbol substitution j' = j, and use the diffraction spot after being processed by S3 for amplitude substitution S7: Increment the iteration count t by 1, and repeat steps S5 - S6 until t ≥ T, where T represents the total number of iterations. S8: From the j-th defocus plane, the optimized diffracted light field calculated in S5 is inverse-diffracted back to the wavefront to be measured, obtaining the reconstructed light field.

2. The phase retrieval wavefront detection method without support region constraint according to claim 1, Characterized in that, In step S3, the centroid method is used to crop the j-th collected diffraction spot.

3. The phase retrieval wavefront detection method without support region constraint according to claim 1, Characterized in that, In step S4, the scalar diffraction theory is Fresnel diffraction.

4. The phase retrieval wavefront detection method without support region constraint according to claim 1, Characterized in that, In step S4, the j-th effective light spot obtained after being processed by S3 The formula for amplitude replacement is as follows: where arg[ ] represents the phase-taking operation, is the diffracted light field after amplitude substitution.

5. The phase retrieval wavefront detection method without support region constraint according to claim 1, Characterized in that, In step S4, the j-th defocus plane is the first defocus plane.

6. The phase retrieval wavefront detection method without support region constraint according to claim 1, Characterized in that, In step S5, the objective function for phase gradient calculation is: In the formula, and are and I j the normalized intensities of the diffraction spot intensity value of the j-th defocused plane calculated from the diffraction spot of the k-th diffraction plane; W jk (u, v) is a weight parameter used to remove pixel points with low signal-to-noise ratio.

7. The phase retrieval wavefront detection method without support region constraint according to claim 6, Characterized in that, In step S5, the method for phase gradient calculation is: where Im[] represents taking the imaginary part, is calculated by the following formula where, Δz jk is the distance between the j-th diffraction surface and the k-th diffraction surface, and G jk (u, v) represents the complex amplitude of the j-th defocused plane calculated from the diffraction spot of the k-th diffraction surface.

8. The phase retrieval wavefront detection method without support region constraint according to claim 1, Characterized in that, In step S8, the formula for calculating the reconstructed light field is: where Δz 1j is the distance between the first diffraction plane and the j-th diffraction plane.

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