A spherical element surface shape reconstruction system and method based on light field diffraction iteration

Abstract

The application discloses a kind of based on light field diffraction iteration's spherical element surface shape reconstruction system and method, it is related to the detection of spherical element surface shape in optical detection technical field, its purpose is to solve the technical problem of high measurement cost, low measurement efficiency caused by the surface shape measurement method needing reference plane in prior art when spherical element surface shape reconstruction.Light is divided into two ways after spectroscope, one way of transmission light is absorbed by light trap to avoid forming stray light, another way of reflection light is finally recorded diffraction spot map by CCD camera after the spherical mirror to be measured, phase reconstruction algorithm based on light field diffraction iteration is used to realize spherical element surface shape reconstruction, obtain the surface shape distortion containing the error of spherical mirror to be measured, the surface shape distortion not containing the error of spherical mirror to be measured, finally obtain the surface shape error of spherical mirror to be measured, the whole process does not need the surface shape measurement method of reference plane, measurement cost is lower, measurement efficiency is higher, has great application prospect.

Description

Technical Field

[0001] The inventor belongs to the field of optical detection technology, and relates to the detection of the surface shape of spherical elements, and more particularly to a system and method for reconstructing the surface shape of spherical elements based on optical field diffraction iteration. Background Technology

[0002] Large-aperture spherical optical elements are key components of space filters in large laser devices. Their function is to provide a beam transmission path and reference for the main amplification system, filtering out high-frequency components of the Fourier spectrum in the beam, transforming the beam aperture, transmitting the image, and isolating stray light. To ensure smooth beam passage through the aperture and avoid significant wavefront distortion of the main beam after passing through the air filter system, the surface shape quality of the air filter lens must be strictly controlled. Traditional measurement methods utilize interferometry to measure the surface shape of the element. This requires fabricating a standard spherical lens with an F-number matching the spherical mirror under test as a reference surface, causing interference between the reflected light from the spherical mirror under test and the standard spherical mirror. The surface shape of the element is then obtained using a phase reconstruction algorithm.

[0003] Patent application No. 202210344661.0 discloses a super-resolution wafer defect detection system, including an illumination component and an imaging component. The illumination component emits a light source to the imaging component for spot detection. The illumination component includes a laser, which emits a laser beam to a spatial filter. The spatial filter filters the laser beam to generate a filtered beam. The filtered beam passes through a lens and enters a beam splitter, which splits the filtered beam into a first beam and a second beam. The first beam enters a spatial light modulator, which parametrically modulates the first beam. The second beam emitted from the beam splitter enters a first objective lens through an aperture, generating a detection beam. This invention generates a single-point spot through a diffractive optical mechanism. The single-point spot is imaged onto the object surface of the optical system to illuminate the object being imaged. By scanning the object with the single-point spot, image information of the scanned object is acquired, and image reconstruction is performed based on the image information, thereby improving imaging efficiency.

[0004] Patent application number 202111552194.2 also discloses a complex amplitude measurement device and method based on a modulated dual detector. The device includes a laser module, a collimator and beam expander module, a beam splitter, two intensity detectors, a wavefront modulator module, and a control and data processing module. The beam to be measured is split into two beams, one of which is directly recorded by the detector, and the other is modulated by the modulator and then recorded by the detector. The complex amplitude distribution of the beam to be measured can be recovered from the two diffraction spots using a phase iteration recovery algorithm. This method can be used for single-state or multi-state wavefront measurement and can be extended to the measurement of ultrafast phenomena. Due to the introduction of modulation by the modulator, the convergence performance of the recovery algorithm is improved, and the noise level can be effectively reduced. This invention can measure the wavefront complex amplitude distribution under single or multiple modal conditions.

[0005] Patent application number 202111505712.5 also discloses a high-precision online detection device and method for the surface shape of large-aperture optical components. Coherent light generated by a laser is expanded by a beam expander to produce a parallel beam that illuminates the large-aperture optical component. The reflected beam is focused by a focusing lens and then split into two beams by a beam splitter. One beam illuminates an encoding plate, which modulates and encodes the incident light field. A spot detector records the resulting scattered spot. The other beam, perpendicular to the light source, enters another spot detector and records a spot pattern, increasing the information content and improving the accuracy of the calculation. Using the spot intensities recorded by the two spot detectors, an iterative algorithm is used to reconstruct the surface shape distribution of the large-aperture optical component with high precision. This detection method requires no interference optical path, is less affected by the environment, has a simple device structure, and high measurement accuracy, meeting the requirements for online detection of the surface shape of large-aperture optical components.

[0006] Similar to the aforementioned patents, existing technologies require the fabrication of different high-precision standard spherical mirrors when measuring spherical mirrors with different F-numbers, resulting in high measurement costs and low efficiency. Therefore, a method for absolute surface shape measurement that does not require a reference plane is needed to achieve high-precision reconstruction of the surface shape of spherical components. Summary of the Invention

[0007] The purpose of this invention is to solve the technical problem that existing methods for reconstructing the surface shape of spherical elements require reference planes, resulting in high measurement costs and low measurement efficiency. This invention provides a system and method for reconstructing the surface shape of spherical elements based on optical field diffraction iteration.

[0008] To achieve the above objectives, the present invention specifically adopts the following technical solution:

[0009] A surface shape reconstruction system for spherical elements based on optical field diffraction iteration includes a laser, a collimating lens, a polarizer, lens I, a filter aperture, lens II, a beam splitter, a converging lens, a spherical mirror under test, an imaging lens, a phase-modulated sample, a two-dimensional translation stage, a CCD camera, an optical trap, and a computer; the phase-modulated sample is placed on the two-dimensional translation stage, and the CCD camera is connected to the computer.

[0010] The laser light generated by the laser passes sequentially through a collimating lens, a polarizer, lens I, a filter aperture, and lens II before being incident on a beam splitter and split into two paths. The reflected light from the beam splitter passes through a converging lens and is incident on the spherical mirror under test, where it is reflected. The reflected light from the spherical mirror under test passes through a converging lens, a beam splitter, an imaging lens, and a phase-modulated sample before being incident on a CCD camera. The transmitted light transmitted through the beam splitter is incident on an optical trap and received by the optical trap.

[0011] Furthermore, the converging lens is confocal with the spherical mirror under test.

[0012] Furthermore, the converging lens is a plano-convex lens, with the side of the converging lens closer to the beam splitter being the planar side and the side of the converging lens closer to the spherical mirror under test being the convex side.

[0013] Furthermore, lens I, the filter aperture, and lens II form a collimation system, and the central aperture of the filter aperture has a diameter of less than 30 μm.

[0014] Furthermore, the beam splitter has a beam splitting ratio of 1:1, and the wedge angles of the front and rear surfaces of the beam splitter are greater than 30″.

[0015] Furthermore, the scanning plane of the two-dimensional translation stage is perpendicular to the optical axis of the optical path, and the phase-modulated sample is located between the focal points of the imaging lens and perpendicular to the optical axis of the optical path; the phase-modulated sample is a sample with optical field phase and amplitude modulation and a transmittance greater than 50%.

[0016] A method for reconstructing the surface shape of a spherical element based on optical field diffraction iteration includes the aforementioned system for reconstructing the surface shape of a spherical element based on optical field diffraction iteration, and the specific steps are as follows:

[0017] Step S1: Place the spherical mirror to be tested in the optical path and adjust the spherical mirror to be tested so that the converging lens and the spherical mirror to be tested are confocal.

[0018] Step S2: Control the two-dimensional translation stage to perform scanning. During scanning, ensure that the area of ​​the overlapping region between two adjacent apertures in the scanned image is not less than 50% of the area of ​​a single aperture. The CCD camera saves the diffraction spot pattern of each scanned aperture.

[0019] Step S3: Reconstruct the surface distortion H1(x,y) with systematic error using the diffraction pattern;

[0020] Step S4: Move the spherical mirror to be tested out of the optical path, adjust the converging lens so that the reflected light from the convex surface of the converging lens enters the CCD camera, and the CCD camera obtains the diffraction pattern.

[0021] Step S5: Repeat step S3 to reconstruct the surface distortion H2(x,y) with systematic error;

[0022] Step S6: Calculate the surface shape error H(x,y) of the spherical mirror to be tested:

[0023] H(x,y)=H1(x,y)-H2(x,y).

[0024] Furthermore, in step S3, the specific steps for reconstructing the surface distortion are as follows:

[0025] Step S3-1: The complex amplitude of the probe light incident on the phase-modulated sample is... Complex amplitude of phase-modulated sample Assign an initial random guess;

[0026] Where r0 represents the displacement vector in the x0y0 plane, m represents the iteration number, and S j This represents the scan displacement vector corresponding to the j-th scan region;

[0027] Step S3-2, convert the complex amplitude Complex amplitude Multiplying them together yields the complex amplitude of the outgoing wave.

[0028]

[0029] Step S3-3, convert the complex amplitude of the outgoing wave The transmission distance Z is transferred to the CCD recording plane to obtain the complex amplitude of the optical field.

[0030]

[0031] in, This represents Fresnel diffraction propagation, Z represents the propagation distance, and m represents the number of iterations;

[0032] Step S3-4, the diffraction spot I in the diffraction pattern recorded by the CCD camera j Replace the square root value of (r) The modulus remains unchanged while the phase remains constant, forming a new complex amplitude value.

[0033] Step S3-5, convert the complex amplitude value The beam propagates backward Z to the sample plane, and the complex amplitude of the emitted light is obtained.

[0034]

[0035] in, This represents the inverse Fresnel diffraction propagation algorithm, where Z represents the propagation distance and m represents the number of iterations.

[0036] Step S3-6: Update the complex amplitude of the object surface. and probe optical recovery amplitude

[0037]

[0038]

[0039] Where α and β are constants, taking positive numbers between 0 and 1. They represent Conjugate;

[0040] In step S3-7, the two-dimensional translation stage moves to the next position, which overlaps with the previously scanned area. Steps S3-4 to S3-6 are repeated to obtain an accurate convergence result; the final complex amplitude after convergence is obtained. probe optical recovery amplitude And from the final complex amplitude probe optical recovery amplitude The phase is extracted to obtain the surface distortion H1(x,y).

[0041] Furthermore, in steps S3-7, equation (1.1) is used as the convergence criterion for the iteration. When Er is less than the requirement of the convergence criterion, the iteration loop is exited.

[0042]

[0043] in, I represents the CCD complex amplitude calculated in the j-th region during the m-th iteration. j (r) represents the light intensity distribution recorded by the CCD in the j-th region, and (x, y) represent the image plane coordinates, respectively.

[0044] The beneficial effects of this invention are as follows:

[0045] In this invention, the laser beam is split into two paths after passing through a beam splitter. One path of transmitted light is absorbed by an optical trap to avoid the formation of stray light, while the other path of reflected light passes through the spherical mirror under test and is finally recorded by a CCD camera as a diffraction pattern (the diffraction pattern is also known as a light intensity pattern). A phase reconstruction algorithm based on optical field diffraction iteration is used to reconstruct the surface shape of the spherical element, obtaining the surface distortion containing the error of the spherical mirror under test and the surface distortion without the error of the spherical mirror under test, and finally obtaining the surface error of the spherical mirror under test. The entire process does not require a surface shape measurement method with a reference plane, resulting in lower measurement costs and higher measurement efficiency. Furthermore, the method described in this application has advantages such as high measurement accuracy, simple measurement method, good measurement repeatability, and large dynamic range, and has great application prospects. Attached Figure Description

[0046] Figure 1 This is the optical path diagram of the present invention;

[0047] Figure 2 This is a scanning path diagram of the two-dimensional translation stage in this invention;

[0048] Figure 3 This invention uses a CCD camera to capture the diffraction pattern of each scanning aperture.

[0049] Figure 4 This is a schematic diagram of reconstructing the shape of the spherical mirror under test in this invention;

[0050] The attached figures are labeled as follows: 101-Laser, 102-Collimating lens, 103-Polarizer, 104-Lens I, 105-Filter aperture, 106-Lens II, 107-Beam splitter, 108-Converging lens, 109-Spherical mirror under test, 110-Imaging lens, 111-Phase modulation sample, 112-Two-dimensional translation stage, 113-CCD camera, 114-Optical trap, 115-Computer. Detailed Implementation

[0051] This embodiment provides a spherical element surface shape reconstruction system based on optical field diffraction iteration, which includes a laser 101, a collimating lens 102, a polarizer 103, a lens I 104, a filter aperture 105, a lens II 106, a beam splitter 107, a converging lens 108, a spherical mirror under test 109, an imaging lens 110, a phase modulation sample 111, a two-dimensional translation stage 112, a CCD camera 113, an optical trap 114, and a computer 115; the phase modulation sample 111 is placed on the two-dimensional translation stage 112, and the CCD camera 113 is connected to the computer 115.

[0052] Lens I104 and lens II106 are confocal, achieving parallel light output. Converging lens 108 is confocal with the spherical mirror under test 109, allowing the light beam to return along the same path after passing through the spherical mirror. The parallel light formed by the laser through lens II106 is split into two paths by beam splitter 107. One path is reflected as the measurement light, and the other path is transmitted and absorbed by light trap 114 to avoid the formation of stray light.

[0053] The converging lens 108 is a plano-convex lens. The side of the converging lens 108 closest to the beam splitter 107 is the planar side, and the side of the converging lens 108 closest to the spherical mirror 109 under test is the convex side.

[0054] Lens I104, filter aperture 105, and lens II106 form a collimation system, and the central aperture of filter aperture 105 is less than 30μm.

[0055] The beam splitter 107 has a beam splitting ratio of 1:1, and the wedge angles of the front and rear surfaces of the beam splitter are greater than 30″.

[0056] The scanning plane (i.e. the moving plane) of the two-dimensional translation stage 112 is perpendicular to the optical axis of the optical path. The phase-modulated sample 111 is located between the imaging lens 110 and the focal point of the imaging lens 110 and is perpendicular to the optical axis of the optical path. The phase-modulated sample 111 is a sample with optical field phase and amplitude modulation and a transmittance greater than 50%.

[0057] like Figure 1 As shown, the specific optical path of this reconstruction system is as follows:

[0058] The laser generated by laser 101 passes sequentially through collimating lens 102, polarizer 103, lens I 104, filter aperture 105, and lens II 106 before being incident on beam splitter 107 and split into two paths. The reflected light from beam splitter 107 passes through converging lens 108 and is incident on the spherical mirror 109 under test, where it is reflected. The reflected light from the spherical mirror 109 passes through converging lens 108, beam splitter 107, imaging lens 110, and phase-modulated sample 111 before being incident on CCD camera 113. The diffraction pattern recorded by CCD camera 113 is input into computer 115 for reconstructing the surface profile. The transmitted light transmitted through beam splitter 107 is incident on optical trap 114 and received by optical trap 114.

[0059] When using this spherical element surface reconstruction system for reconstruction, the specific steps are as follows:

[0060] Step S1: Place the spherical mirror 109 to be tested in the optical path and adjust the spherical mirror 109 to make the converging lens 108 and the spherical mirror 109 confocal.

[0061] Among them, the spherical mirror to be tested 109 is a concave spherical mirror with an aperture of 100mm and a focal length of 1000mm, and the phase modulation sample 111 is a bee's wing.

[0062] Step S2: Control the two-dimensional translation stage 112 to perform scanning. During scanning, ensure that the area of ​​the overlapping region between two adjacent apertures in the scanned image is not less than 50% of the area of ​​a single aperture. The CCD camera 113 saves the diffraction spot pattern of each scanned aperture.

[0063] Two-dimensional translation stage 112 according to Figure 2 The path shown is scanned in a 5x5 array with an overlap of 70% and a scanning aperture of 2mm. Based on this, the CCD camera 113 acquires diffraction patterns for each scanning aperture, as shown below. Figure 3 As shown, the diffraction pattern here is the intensity pattern, and the same applies below.

[0064] Step S3: Reconstruct the surface distortion H1(x,y) with systematic errors using the diffraction pattern.

[0065] The specific steps for reconstructing surface distortion are as follows:

[0066] Step S3-1: The complex amplitude of the probe light incident on the phase-modulated sample (111) is... Complex amplitude of phase-modulated sample 111 Assign an initial random guess;

[0067] Where r0 represents the displacement vector in the x0y0 plane, m represents the iteration number, and S j This represents the scan displacement vector corresponding to the j-th scan region;

[0068] Step S3-2, convert the complex amplitude Complex amplitude Multiplying them together yields the complex amplitude of the outgoing wave.

[0069]

[0070] Step S3-3, convert the complex amplitude of the outgoing wave The transmission distance Z is transferred to the CCD recording plane to obtain the complex amplitude of the optical field.

[0071]

[0072] in, This represents Fresnel diffraction propagation, Z represents the propagation distance, and m represents the number of iterations;

[0073] Steps S3-4: The diffraction spot I in the diffraction pattern recorded by the CCD camera 113... j Replace the square root value of (r) The modulus remains unchanged while the phase remains constant, forming a new complex amplitude value.

[0074] Step S3-5, convert the complex amplitude value By propagating the beam in reverse Z to the sample plane, a more accurate complex amplitude of the sample output light can be obtained.

[0075]

[0076] in, This represents the inverse Fresnel diffraction propagation algorithm, where Z represents the propagation distance and m represents the number of iterations.

[0077] Step S3-6: Update the complex amplitude of the object surface. and probe optical recovery amplitude

[0078]

[0079] Where α and β are constants, taking positive numbers between 0 and 1. They represent Conjugate;

[0080] complex amplitude Complex amplitude Extract the phase from the image and then extract the phase. This yields H1(x,y).

[0081] In step S3-7, the two-dimensional translation stage 112 moves to the next position, which overlaps with the previous scan area. Steps S3-4 to S3-6 are repeated to obtain an accurate convergence result; the final complex amplitude after convergence is obtained. probe optical recovery amplitude And from the final complex amplitude probe optical recovery amplitude Extract the phase and then extract the phase. This yields the surface distortion H1(x,y).

[0082] In steps S3-7, equation (1..3) is used as the convergence criterion for the iteration. When Er is less than the requirement of the convergence criterion, the iteration loop is exited.

[0083]

[0084] in, I represents the CCD complex amplitude calculated in the j-th region during the m-th iteration. j (r) represents the light intensity distribution recorded by the CCD in the j-th region, and (x, y) represent the image plane coordinates, respectively.

[0085] Step S4: Move the spherical mirror (109) to be tested out of the optical path, adjust the converging lens (108) so that the reflected light from the convex surface of the converging lens (108) enters the CCD camera (113) and the CCD camera (113) obtains the diffraction pattern.

[0086] Step S5, the method for reconstructing and obtaining the surface distortion H2(x,y) is the same as the method for reconstructing and obtaining the surface distortion H1(x,y); that is, repeat step S3 (including steps S3-1 to S3-7) to reconstruct and obtain the surface distortion H2(x,y) with systematic error.

[0087] Step S6: Calculate the surface shape error H(x,y) of the spherical mirror (109) to be tested;

[0088] H(x,y)=H1(x,y)-H2(x,y);

[0089] in, Figure 4 That is, the surface shape of the spherical mirror (109) to be tested.

Claims

1. A spherical element surface shape reconstruction system based on optical field diffraction iteration, characterized in that: The system includes a laser (101), a collimating lens (102), a polarizer (103), a lens I (104), a filter (105), a lens II (106), a beam splitter (107), a converging lens (108), a spherical mirror to be tested (109), an imaging lens (110), a phase modulation sample (111), a two-dimensional translation stage (112), a CCD camera (113), an optical trap (114), and a computer (115). The phase modulation sample (111) is placed on the two-dimensional translation stage (112), and the CCD camera (113) is connected to the computer (115). The laser generated by the laser (101) passes sequentially through a collimating lens (102), a polarizer (103), a lens I (104), a filter aperture (105), and a lens II (106) before being incident on a beam splitter (107) and split into two paths. The reflected light reflected by the beam splitter (107) passes through a converging lens (108) and is incident on the spherical mirror under test (109) and is reflected. The reflected light from the spherical mirror under test (109) passes through the converging lens (108), the beam splitter (107), the imaging lens (110), and the phase-modulated sample (111) before being incident on a CCD camera (113). The transmitted light transmitted through the beam splitter (107) is incident on an optical trap (114) and received by the optical trap (114).

2. The spherical element surface shape reconstruction system based on optical field diffraction iteration as described in claim 1, characterized in that: The converging lens (108) and the spherical mirror (109) under test are confocal.

3. The spherical element surface shape reconstruction system based on optical field diffraction iteration as described in claim 2, characterized in that: The converging lens (108) is a plano-convex lens. The side of the converging lens (108) closer to the beam splitter (107) is the planar side, and the side of the converging lens (108) closer to the spherical mirror (109) under test is the convex side.

4. The spherical element surface shape reconstruction system based on optical field diffraction iteration as described in claim 1, characterized in that: Lens I (104), filter aperture (105), and lens II (106) form a collimation system, and the central aperture of filter aperture (105) is less than 30 μm.

5. The spherical element surface shape reconstruction system based on optical field diffraction iteration as described in claim 1, characterized in that: The beam splitter (107) has a beam splitting ratio of 1:1 and the wedge angles of the front and rear surfaces of the beam splitter are greater than 30″.

6. The spherical element surface shape reconstruction system based on optical field diffraction iteration as described in claim 1, characterized in that: The scanning plane of the two-dimensional translation stage (112) is perpendicular to the optical axis of the optical path. The phase-modulated sample (111) is located between the focal points of the imaging lens (110) and the imaging lens (110) and is perpendicular to the optical axis of the optical path. The phase-modulated sample (111) is a sample with optical field phase and amplitude modulation and a transmittance greater than 50%.

7. A method for reconstructing the surface shape of a spherical element based on optical field diffraction iteration, characterized in that, The system for reconstructing the surface shape of a spherical element based on optical field diffraction iteration, as described in any one of claims 1-6, comprises the following steps: Step S1: Place the spherical mirror (109) to be tested in the optical path and adjust the spherical mirror (109) to be tested so that the converging lens (108) and the spherical mirror (109) are confocal. Step S2: Control the two-dimensional translation stage (112) to perform scanning. During scanning, ensure that the area of ​​the overlapping region between two adjacent apertures in the scanned image is not less than 50% of the area of ​​a single aperture. The CCD camera (113) saves the diffraction spot pattern of each scanned aperture. Step S3: Reconstruct the surface distortion H1(x,y) with systematic error using the diffraction pattern; Step S4: Move the spherical mirror (109) to be tested out of the optical path, adjust the converging lens (108) so that the reflected light from the convex surface of the converging lens (108) enters the CCD camera (113) and the CCD camera (113) obtains the diffraction pattern. Step S5: Repeat step S3 to reconstruct the surface distortion H2(x,y) with systematic error; Step S6, calculate the surface shape error H(x,y) of the spherical mirror (109) to be tested: H(x,y)=H1(x,y)-H2(x,y).

8. The method for reconstructing the surface shape of a spherical element based on optical field diffraction iteration as described in claim 7, characterized in that: In step S3, the specific steps for reconstructing surface distortion are as follows: Step S3-1: The complex amplitude of the probe light incident on the phase-modulated sample (111) is... Complex amplitude of phase-modulated sample (111) Assign an initial random guess; Where r0 represents the displacement vector in the x0y0 plane, m represents the iteration number, and S j This represents the scan displacement vector corresponding to the j-th scan region; Step S3-2, convert the complex amplitude Complex amplitude Multiplying them together yields the complex amplitude of the outgoing wave. Step S3-3, convert the complex amplitude of the outgoing wave The transmission distance Z is transferred to the CCD recording plane to obtain the complex amplitude of the optical field. in, This represents Fresnel diffraction propagation, Z represents the propagation distance, and m represents the number of iterations; Step S3-4, the diffraction spot I in the diffraction pattern recorded by the CCD camera (113) j Replace the square root value of (r) The modulus remains unchanged while the phase remains constant, forming a new complex amplitude value. Step S3-5, convert the complex amplitude value The beam propagates backward Z to the sample plane, and the complex amplitude of the emitted light is obtained. in, This represents the inverse Fresnel diffraction propagation algorithm, where Z represents the propagation distance and m represents the number of iterations. Step S3-6: Update the complex amplitude of the object surface. and probe optical recovery amplitude Where α and β are constants, taking positive numbers between 0 and 1. They represent Conjugate; In step S3-7, the two-dimensional translation stage (112) moves to the next position, which overlaps with the previous scan area. Steps S3-4 to S3-6 are repeated to obtain an accurate convergence result; the final complex amplitude after convergence is obtained. probe optical recovery amplitude And from the final complex amplitude probe optical recovery amplitude The phase is extracted to obtain the surface distortion H1(x,y).

9. The method for reconstructing the surface shape of a spherical element based on optical field diffraction iteration as described in claim 8, characterized in that: In steps S3-7, equation (1.1) is used as the convergence criterion for the iteration. When Er is less than the requirement of the convergence criterion, the iteration loop is exited. in, I represents the CCD complex amplitude calculated in the j-th region during the m-th iteration. j (r) represents the light intensity distribution recorded by the CCD in the j-th region, and (x, y) represent the image plane coordinates, respectively.

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