An optoelectronic processor for synthetic aperture radar based on adaptive optics technology

Abstract

The present invention relates to a synthetic aperture radar optoelectronic processor based on adaptive optics technology. The processor comprises a SAR pre-processed echo data modulation unit and a sensorless adaptive optics system. The sensorless adaptive optics system includes: a deformable mirror for receiving a laser beam containing modulated information of the SAR pre-processed echo data and reflecting it toward a beam splitter; a beam splitter for transmitting the laser beam containing modulated information of the SAR pre-processed echo data to the deformable mirror, which then receives the reflected beam from the deformable mirror and directs it toward a high-speed camera; a high-speed camera for receiving the laser beam to capture SAR images; and a phase error correction computer for analyzing the SAR image results using an image quality assessment function and, in combination with a stochastic parallel gradient descent algorithm, iteratively adjusting the deformable mirror's mirror shape until preset requirements are met. Compared with existing technologies, the present invention improves the performance of SAR optical processing and offers advantages such as intelligence, versatility, and high precision.

Description

Technical Field

[0001] The present invention relates to the field of synthetic aperture radar imaging technology, and in particular to a synthetic aperture radar optoelectronic processor based on adaptive optics technology. Background Art

[0002] Synthetic aperture radar (SAR) is a practical Earth observation and remote sensing technology. By combining high resolution with all-weather, all-day sensing capabilities, SAR has made significant contributions to both civilian and military applications. With the widespread adoption of SAR technology, generating high-resolution SAR images has become crucial. However, SAR imaging systems are particularly susceptible to phase errors. Phase errors caused by the actual motion of the SAR platform and propagation effects can cause the reconstructed image to be out of focus. These phase errors are also known as propagation disturbances (PDs). Errors due to the actual motion of the SAR platform are related to the uncertainty in the SAR sensor position, which is attributed to the unknown deviation of the SAR platform from its nominal trajectory. In contrast, errors due to propagation effects are random fluctuations in propagation delay caused by atmospheric disturbances. Although the physical origins of these two phase errors are very different, they have similar effects on SAR echo data because they both arise from uncompensated delays in the SAR echoes as they travel back to the SAR sensor.

[0003] SAR echo data is typically processed using either optical or digital processing methods. Due to the large volume of SAR echo data generated, the data is typically broken down into smaller components for separate processing. SAR digital processing typically employs specialized Fast Fourier Transform (FFT) algorithms, processing one dimension at a time. Consequently, digital processing methods are time-consuming and require significant computational processing power. Compared to digital processing, optical processing techniques offer higher processing speeds and lower power consumption. Optical processing has inherent parallel computing capabilities that can be effectively leveraged in SAR echo data processing. It is well known that standard lenses can perform true two-dimensional Fourier transforms at the speed of light without power consumption. Therefore, optical processing techniques reduce processing time and power consumption by simultaneously and instantaneously processing the azimuth and slant range dimensions. The azimuth dimension refers to the direction of the flight trajectory, while the range dimension refers to the direction of the electromagnetic beam.

[0004] In the late 1960s, researchers at the Michigan Environmental Research Institute proposed a tilted-plane optical processor. In this processor, SAR echo data is recorded on black-and-white film. When the film is illuminated by a collimated laser beam, the information contained in the SAR echo data is modulated onto the laser beam. The laser beam then passes through a series of lenses to focus the SAR echo data in two dimensions: azimuth and range. However, because the focal planes for these two dimensions are not in the same position, the input and output planes must be adjusted to obtain a well-focused SAR image.

[0005] While optical processors can reduce processing time and power consumption, they place extremely stringent demands on the precision of the optical path and optical instrumentation. The lenses required in optical processors are complex to manufacture and subject to precision errors. Consequently, complex optical processors require experienced operators to precisely align high-quality lenses on large optical platforms and manipulate optical components to control image quality. Consequently, the imaging process lacks autonomous adaptability and cannot automatically correct for errors and uncertainties.

[0006] With the development of programmable optoelectronic devices, SAR optical processing technology has become increasingly mature. Since 2008, the National Institute of Optics (INO) has collaborated with the European Space Agency (ESA) to develop a real-time spaceborne SAR optoelectronic processor. INO's optoelectronic processor uses a high-resolution spatial light modulator (SLM) to process ASAR echo data carried by the ENVISAT satellite, and achieves better imaging performance than SAR digital processors based on graphics processing units (GPUs) of the same period. In addition, compared with digital processors, INO's optoelectronic processor is more compact and lighter. This processor can be regarded as a miniaturized and improved version of the tilted plane optical processor proposed in 1960, with the same imaging principle. However, the INO optoelectronic processor is not equipped with a phase error correction unit, so it cannot accurately correct the phase error, which to some extent affects the effectiveness of SAR images. To obtain clear SAR images based on an INO optoelectronic processor, a phase error correction method was proposed in the paper "Optronic high-resolution SAR processing with the capability of adaptive phase error compensation" (Y. Gao, C. Lin, R. Guo, et al. IEEE Geosci. Remote Sensing Lett. 13(3), 1–5 (2016)). However, this method is complex to implement and requires an initial calibration of the system before each execution. Furthermore, due to the randomness of propagated disturbances (PDs), setting the threshold for the cyclic judgment condition is difficult, and improper configuration may reduce accuracy.

[0007] In the field of SAR digital processing, the correction technology of PDs phase error has always been a research focus. The paper "Phase gradient autofocus-a robust tool for high resolution SAR phase correction" (DEWahl, PHEichel, DCGhiglia, et al. IEEE Trans. Aerosp. Electron. Syst. 30 (3), 827–835 (1994)) proposed a standard phase gradient autofocus (PGA) algorithm, but this algorithm is only applicable to SAR beamforming mode. Subsequently, several improved versions of PGA algorithms were proposed. In addition to PGA-type algorithms, different autofocus methods based on image quality assessment principles have also been proposed. Currently, the flexibility of digital processing technology in processing phase information enables the development of more powerful autofocus methods than optical processing technology. In addition, research on the impact of atmospheric phase disturbances on SAR imaging and its correction methods is also increasing. However, optical processing technology does not have a suitable PDs correction method, while digital processing technology provides a more mature PDs correction method, which can perform more comprehensive PDs correction, thereby generating higher resolution SAR images. Furthermore, optical processing can compress both the position and distance dimensions simultaneously, whereas digital processing typically operates on a one-dimensional basis. Therefore, the PD correction methods used in digital processing cannot be directly applied to optical processing. Summary of the Invention

[0008] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and provide a synthetic aperture radar optoelectronic processor based on adaptive optics technology to achieve phase error correction of SAR images and improve imaging focusing quality.

[0009] The purpose of the present invention can be achieved by the following technical solutions:

[0010] A synthetic aperture radar optoelectronic processor based on adaptive optics technology includes a SAR pre-processing echo data modulation unit and a sensorless adaptive optics system. The sensorless adaptive optics system includes:

[0011] a deformable mirror, used for receiving the laser beam containing the modulated information of the SAR pre-processed echo data and reflecting it toward the beam splitter;

[0012] A beam splitter is used to transmit the laser beam containing SAR pre-processed echo data modulation information output by the SAR pre-processed echo data modulation unit to the deformable mirror, receive the reflected light beam from the deformable mirror, and then illuminate the high-speed camera;

[0013] a high-speed camera to receive the laser beam and capture SAR images;

[0014] A phase error correction computer is used to receive SAR images transmitted by a high-speed camera, analyze the imaging results of the SAR images using an image quality assessment function, and combine it with a stochastic parallel gradient descent algorithm to iteratively adjust the mirror shape of the deformable mirror until the image quality assessment function converges and the image quality assessment function value meets the preset requirements.

[0015] Furthermore, the image quality assessment function is a Tenengrad function.

[0016] Furthermore, the deformable mirror is a mirror surface that changes shape when a voltage is applied.

[0017] Furthermore, the phase error correction computer generates a Zernike coefficient vector for controlling the mirror shape of the deformable mirror through voltage, and uses a random parallel gradient descent algorithm to iteratively search for the optimal Zernike coefficient vector.

[0018] Furthermore, the process of the stochastic parallel gradient descent algorithm includes the following steps:

[0019] S101: Initialize the Zernike coefficient vector and gain coefficient of the deformable mirror;

[0020] S102: randomly generating a random perturbation signal vector that obeys Bernoulli distribution, that is, increasing and decreasing the random perturbation signal vector with the same amplitude in each iteration process;

[0021] S103: Calculating the variation of the image quality assessment function according to the random disturbance signal vector generated in step S102;

[0022] S104: updating the Zernike coefficient vector according to the change in the gain coefficient, the random perturbation signal vector, and the image quality evaluation function in the current iteration, and using it to control the deformable mirror and calculate the corresponding image quality evaluation function value;

[0023] S105: Determine whether the image quality assessment function value meets the requirement. If so, complete the iterative calculation of the Zernike coefficient vector. If not, return to step S102 for iterative update.

[0024] Furthermore, the deformable mirror has a plurality of actuators that change shape according to voltage, and the deformation of the deformable mirror is a linear superposition of the surface shapes of each actuator under its corresponding voltage.

[0025] Furthermore, the SAR pre-processing echo data modulation unit includes an amplitude modulator and a phase modulator connected to each other, the amplitude modulator receives the output of the synthetic aperture radar for processing, and the output of the phase modulator is directed toward the deformable mirror.

[0026] Furthermore, a 4-f system consisting of multiple lenses is provided between the SAR pre-processing echo data modulation unit and the deformable mirror.

[0027] Furthermore, the 4-f system includes a first lens located at the SAR pre-processing echo data modulation unit and a second lens located at the input end of the deformable mirror.

[0028] Furthermore, the sensorless adaptive optical system is further provided with a reflector and an imaging lens, wherein the input side of the reflector receives the second laser beam and the output side faces the imaging lens, and is used for imaging a point target according to the second laser beam.

[0029] Compared with the prior art, the present invention has the following advantages:

[0030] (1) Based on AO technology, the present invention introduces sensorless adaptive optics (SLAO) into the traditional SAR optoelectronic processor for the first time. A deformable mirror is set to adjust and reflect the laser beam containing the modulation information of the SAR pre-processed echo data. The reflected beam is split by a beam splitter and then collected by a high-speed camera and transmitted to a phase error correction computer. The phase error correction computer uses an image quality evaluation function to analyze the imaging results captured by the high-speed camera and combines it with a stochastic parallel gradient descent algorithm to directly control the deformable mirror. After multiple iterations, the optimal control parameters of the deformable mirror are obtained, the phase error correction of the SAR image is realized, and the imaging focus quality is improved. Compared with traditional processors, it has the following advantages:

[0031] Intelligent: Thanks to SLAO technology, the system can intelligently and automatically complete high-speed phase error correction;

[0032] Versatility: The system can be reprogrammed by selecting different image quality assessment functions to meet the imaging requirements of different SAR echo data;

[0033] High precision: The system can simultaneously achieve precise correction of phase errors (PDs) and optical instrument errors.

[0034] (2) The present invention uses the Tenengrad function based on gradient calculation as the fitness function in the optimization algorithm. The phase error correction computer aims to optimize the Tenengrad value to reach an ideal level, thereby improving image resolution and enhancing image quality.

[0035] In order to control the deformable mirror to complete phase error correction, the image quality evaluation function should meet the requirements of unimodality, high sensitivity and versatility. The present invention uses the Tenengrad function to evaluate resolution test charts and SAR images with different degrees of defocus, and verifies that the function has unimodality, high sensitivity and wide applicability, meeting the standards required for SAR image evaluation functions.

[0036] (3) The proposed scheme was tested on a resolution test image and random phase errors were introduced to investigate the performance of the proposed method. The results showed that the image quality was significantly improved. Finally, SAR imaging processing experiments demonstrated the effectiveness of the SLAO system in adaptively correcting phase errors in SAR images. Due to the high programmability of DM, the proposed system is reconfigurable. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 This is a schematic structural diagram of an optoelectronic processor for a synthetic aperture radar based on adaptive optics technology provided in an embodiment of the present invention;

[0038] Figure 2 A schematic flow chart of a stochastic parallel gradient descent algorithm used by an optoelectronic processor of a synthetic aperture radar based on adaptive optics technology provided in an embodiment of the present invention;

[0039] Figure 3 Schematic diagram of simulation results provided in an embodiment of the present invention, where (a1)–(a4) are a set of resolution test charts with different degrees of defocus. (b1)–(b4) are SAR images under different scenes; (c) is the Tenengrad value of the resolution test chart corresponding to different degrees of defocus; (d) is the Tenengrad value of the SAR image under different scenes.

[0040] Figure 4 Schematic diagram of simulation results provided in an embodiment of the present invention, wherein (a) is the random Zernike coefficient of the initial wavefront aberration; (b) is the sample complex-valued hologram with the initial wavefront aberration; (c) is the corresponding phase plane of the initial wavefront aberration; (d) is the reconstructed hologram after phase error correction in the SLAO system; (e) is the corresponding residual wavefront aberration of (d); and (f) is the phase error correction result.

[0041] Figure 5 This is another structural diagram of an optoelectronic processing system for a synthetic aperture radar based on adaptive optics technology provided in an embodiment of the present invention;

[0042] Figure 6Schematic diagram of phase error correction results after different numbers of correction iterations provided in an embodiment of the present invention, where (a1) is an example of an original SAR image without using the SLAO system; (a2)–(a4) are SAR images of image (a1) after 100, 200, and 500 iterations, respectively (from left to right); (b1) is another example of an original SAR image without using the SLAO system; (b2)–(b4) are SAR images of image (b1) after 100, 200, and 500 iterations, respectively (from left to right); (c1) is the phase plane corresponding to (a1) and (b1); (c2)–(c4) are the corresponding residual wavefront aberrations of (a2)–(a4) and (b2)–(b4), respectively;

[0043] Figure 7 The figure is a schematic diagram of a normalized optimization curve for phase error correction of a SAR optoelectronic processor provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0044] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations.

[0045] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention as claimed, but rather merely represents selected embodiments of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without creative effort shall fall within the scope of protection of the present invention.

[0046] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, it does not need to be further defined or explained in subsequent drawings.

[0047] Example 1

[0048] Adaptive optics (AO) is a technology used to correct optical aberrations, and was originally used to correct the blurring effect of ground-based telescope images caused by atmospheric turbulence. PDs (propagation disturbances) also include atmospheric phase disturbances. Although AO technology is mainly used to deal with atmospheric turbulence, the two phase errors in PDs have similar effects on SAR echo data. In addition, AO technology can also correct the accuracy of the optical path. The performance of high-resolution SAR images is very sensitive to PDs, and high-resolution optical processing depends on high-fidelity focusing. Therefore, in order to improve the performance of SAR optical processing, the present invention, based on AO technology, introduces sensorless adaptive optics (SLAO) into traditional SAR optoelectronic processors for the first time.

[0049] This embodiment provides a synthetic aperture radar optoelectronic processor based on adaptive optics technology, including a SAR pre-processing echo data modulation unit and a sensorless adaptive optics system. The sensorless adaptive optics system includes:

[0050] a deformable mirror (DM) for receiving the laser beam containing the modulated information of the SAR pre-processed echo data and reflecting it toward the beam splitter;

[0051] a beam splitter configured to transmit the laser beam containing SAR pre-processed echo data modulation information output by the SAR pre-processed echo data modulation unit to the deformable mirror, receive the reflected beam from the deformable mirror, and then direct it toward the high-speed camera; wherein the SAR pre-processed echo data modulation information is data obtained by pre-processing and modulating the original SAR echo data;

[0052] a high-speed camera (HSC) for receiving the first laser beam to capture a SAR image;

[0053] A phase error correction computer (PECC) is used to receive SAR images transmitted by a high-speed camera, analyze the imaging results of the SAR image using an image quality assessment function, and combine it with a stochastic parallel gradient descent algorithm to iteratively adjust the mirror shape of the deformable mirror until the image quality assessment function converges and the image quality assessment function value meets the preset requirements, thereby completing phase error correction and improving imaging focus quality.

[0054] This new SAR optoelectronic processor has the following advantages over traditional processors:

[0055] Intelligent: Thanks to SLAO technology, the system can intelligently and automatically complete high-speed phase error correction.

[0056] Versatility: The system can be reprogrammed by selecting different image quality assessment functions to meet the imaging requirements of different SAR echo data.

[0057] High precision: The system can simultaneously achieve precise correction of phase errors (PDs) and optical instrument errors.

[0058] Figure 1 and Figure 5 Both show the functional block diagrams of high-resolution SAR optoelectronic processors. Both optical path forms can meet the processing requirements of this solution.

[0059] Figure 1 In the process, the laser beam containing the modulation information of the SAR pre-processed echo data is first irradiated to the deformable mirror (DM), then reflected to the beam splitter, and then reflected by the beam splitter to the high-speed camera.

[0060] Figure 5 In the process, the laser beam containing the SAR pre-processed echo data modulation information first passes through the beam splitter, is reflected by the beam splitter and illuminates the deformable mirror (DM), and then reflects the deformable mirror (DM) and illuminates the beam splitter, and is transmitted through the beam splitter to the high-speed camera.

[0061] Traditional optical processors are only capable of performing matched filtering processing on raw SAR echo data based on theoretical estimates. However, this method ignores the impact of propagation disturbances (PDs) and optical processor precision errors on the effectiveness of high-resolution SAR images. This scheme transmits the laser carrier signal to the deformable mirror (DM). The laser beam is split into two beams by a beam splitter (BS), and the clarity of the SAR image captured by the high-speed camera (HSC) reflects the current performance of the system. The SPGD algorithm is executed on a phase error correction computer (PECC) to generate a set of Zernike coefficients that represent compensated Zernike wavefronts based on image quality, thereby controlling the DM to achieve wavefront phase error correction.

[0062] The system is also reconfigurable. Due to the programmability of DM, by selecting different image quality evaluation functions, the corresponding compensated Zernike wavefront can be obtained for the phase error information of different modes and SAR systems.

[0063] Specifically, a deformable mirror is a mirror that changes shape when a voltage is applied. It has multiple actuators that change shape according to the voltage. The deformation of the deformable mirror is the linear superposition of the surface shapes of each actuator under its corresponding voltage.

[0064] The SPGD algorithm is an adaptive optical correction method. It estimates the gradient of the control signal based on the relationship between the change in performance indicators and the change in control signals, and iteratively searches for the optimal system performance indicator in the direction of gradient descent. The corresponding algorithm process includes:

[0065] S101: Initialize the Zernike coefficient vector and gain coefficient of the deformable mirror;

[0066] S102: randomly generating a random perturbation signal vector that obeys Bernoulli distribution, that is, increasing and decreasing the random perturbation signal vector with the same amplitude in each iteration process;

[0067] S103: Calculating the variation of the image quality assessment function according to the random disturbance signal vector generated in step S102;

[0068] S104: updating the Zernike coefficient vector according to the change in the gain coefficient, the random perturbation signal vector, and the image quality evaluation function in the current iteration, and using it to control the deformable mirror and calculate the corresponding image quality evaluation function value;

[0069] In the kth iteration, the Zernike coefficient vector ρ of the compensated Zernike wavefront (k) ={ρ1,ρ2,···,ρm} (k) The calculation formula is as follows:

[0070] ρ (k) =ρ (k-1) +γ·Δρ (k) ΔJ (k)

[0071] Where Δρ (k) ={Δρ1,Δρ2,···,Δρm} (k) is the random perturbation signal vector applied in the kth iteration. The values ​​of Δρi are independent of each other and follow a Bernoulli distribution, i.e. the components have equal amplitudes and the probability of positive and negative signs is 50%. ΔJ (k) is the change of fitness function, and γ is the gain coefficient. In this embodiment, the system performance index is optimized towards the maximum value, so γ takes a positive value. The flow chart of SPGD algorithm in SLAO system is as follows: Figure 2 shown.

[0072] S105: Determine whether the image quality assessment function value meets the requirement. If so, complete the iterative calculation of the Zernike coefficient vector. If not, return to step S102 for iterative update.

[0073] For the image quality assessment function, before using the SPGD algorithm to control the SLAO system, a correlation must be established between the fitness function and the system performance evaluation index. In this system, the Tenengrad function, which is based on gradient calculation, is preferably used as the fitness function in the optimization algorithm. In image processing, a clearly focused image typically has sharper edges, so its gradient value is larger. The Tenengrad function uses the Sobel operator to extract the gradient values ​​of the image horizontally and vertically. The following Sobel operator template, represented by Gx and Gy, is used to detect image edges:

[0074]

[0075] The gradient of an image at any point can be expressed as:

[0076]

[0077] G x (x,y)=G x *I(x,y),G y (x,y)=G y *I(x,y)

[0078] Therefore, the Tenengrad value of this image is defined as follows:

[0079]

[0080] Where n is the total number of identifiable pixels.

[0081] Therefore, the Tenengrad function is preferably selected as the fitness function of the SPGD algorithm. The SLAO system aims to optimize the Tenengrad value to reach an ideal level, thereby improving image resolution and enhancing image quality.

[0082] Validity of Tenengrad function:

[0083] In order to control the deformable mirror (DM) to complete phase error correction, the image quality evaluation function should meet the following requirements:

[0084] 1. Unimodality: The SAR optoelectronic processor has a uniquely determined focus position for a given SAR echo signal. Therefore, the image quality evaluation function should also have a unique maximum value.

[0085] 2. High sensitivity: Since the image quality assessment function is used for fine phase error correction, it should have high sensitivity to be able to distinguish minute scattering differences.

[0086] 3. Universality: The texture features of different observation targets in SAR images are different. Therefore, the image quality assessment function should not be affected by the image content.

[0087] This embodiment performs simulation evaluation on a variety of test charts. In the simulation, a set of wavefront aberrations is obtained by multiplying a single Zernike mode aberration (defocus) with a set of symmetrical arithmetic progression coefficients around the origin. Figure 3 (a1)– Figure 3 As shown in (a4), these wavefront aberrations are introduced into the resolution test chart (1951USAF resolution target, negative). The Tenengrad function is used to evaluate this set of resolution test charts with different degrees of defocus, and the results are shown in Figure 3In addition, using the above method, a set of wavefront aberrations are introduced into four SAR images of different scenes, as shown in (c). Figure 3 (b1)– Figure 3 As shown in (b4), four sets of images are generated, and their image quality shows a unimodal variation. The image quality of these four sets of SAR images is then evaluated using the Tenengrad function. As the degree of defocus decreases, the image quality of Figure 3 The Tenengrad value shown in (b1) increases to 0.8796, which is 9.4 times the original Tenengrad value of 0.0932. Figure 3 (b2)– Figure 3 (b4) shows a similar trend. The normalized evaluation curve based on the Tenengrad value of 0.8796 is shown in Figure 3 As shown in (d), the Tenengrad value trends of these four groups of SAR images can be observed more intuitively.

[0088] therefore, Figure 3 Shows that the Tenengrad function meets the criteria required for SAR image evaluation functions, including unimodal, high sensitivity, and universality.

[0089] Optionally, the SAR pre-processing echo data modulation unit includes an amplitude modulator and a phase modulator connected to each other, which perform amplitude modulation and phase modulation in sequence. The amplitude modulator receives the output of the synthetic aperture radar for processing, and the output of the phase modulator is directed toward the deformable mirror.

[0090] Optionally, a 4-f system consisting of multiple lenses is further provided between the SAR pre-processing echo data modulation unit and the deformable mirror.

[0091] The 4-f system includes a first lens located at a SAR pre-processing echo data modulation unit and a second lens located at an input end of a deformable mirror.

[0092] Optionally, the sensorless adaptive optical system is further provided with a reflector and an imaging lens, wherein the input side of the reflector receives the second laser beam, and the output side faces the imaging lens, and is used for imaging a point target according to the second laser beam.

[0093] This embodiment also conducts a SAR imaging processing experiment on the above-mentioned synthetic aperture radar optoelectronic processor to verify its effectiveness. The specific process is as follows:

[0094] 1. Theoretical basis of high-resolution SAR optical imaging

[0095] After the ideal SAR echo signal is demodulated, the received baseband signal of the point target can be expressed as:

[0096]

[0097] where τ and t represent range time and azimuth time, respectively; A is the reflection coefficient of the point target; ωr(·) and ωa(·) are the range and azimuth envelopes, respectively; f0 is the carrier frequency; c is the speed of light; K r and K a Represent the linear modulation rate of distance and azimuth respectively; t c is the moment when the beam center passes through the point target; R(t) is the instantaneous slant range between the antenna phase center and the target. For a point target, R(t) can be expressed as:

[0098]

[0099] Using the parabola approximation, R(t) can be expressed as:

[0100]

[0101] After the two-dimensional Fourier transform operation, the two-dimensional spectrum of the ideal received baseband signal can be obtained as follows:

[0102]

[0103] Where Vr is the equivalent radar platform velocity; R0 is the slant range at the aperture center; A0 is a constant; W r (·) and W a (·) are the range and azimuth envelopes in the two-dimensional frequency domain; f τ and f t are the distance and orientation variables in the two-dimensional frequency domain, respectively.

[0104] Assume f0>>|f τ |,

[0105]

[0106] Therefore, in the preprocessing stage, the phase correction filter based on theoretical estimation can be expressed as:

[0107]

[0108] PDs (propagation disturbances) are caused by uncompensated delays in radar echoes returning to the SAR sensor, typically due to atmospheric disturbances or uncompensated platform motion. The effects of PDs can be accounted for in the data by defining the following equation as a representation of the data including PDs, denoted as α(P,t).

[0109] s pd (τ,t)=s i (τ,t)e jα(P,t)

[0110] Where P is a pulse target.

[0111] 2. Modeling of deformable mirror

[0112] This embodiment uses a continuous surface deformable mirror (DM) with 69 actuators as a wavefront corrector. A DM is a mirror that changes shape when a voltage is applied, compensating for phase errors by producing the desired surface shape. When a unit voltage is applied to a specific actuator, the deformation produced by the DM surface is a function of the actuator's influence, typically approximated by a Gaussian function of the following form:

[0113]

[0114] Where (x,y) is any position on the DM, (x i ,yi) is the position of the i-th actuator, d is the spacing between actuators, σ is the coupling coefficient between actuators, and α is the Gaussian exponent.

[0115] Therefore, when using a 69-unit DM, the matrix of the influence function can be expressed as:

[0116] δ=(δ1δ2…δ 69 )

[0117] Due to the independent control of each actuator in the DM, the deformation of the DM surface is the linear superposition of the surface shapes of each actuator under its corresponding voltage, which can be expressed as:

[0118] φ=δv

[0119] Where υ is the control voltage of each actuator, v=(v1,v2,···,v 69 )T.

[0120] Expand each influence function into a Zernike polynomial, and the i-th influence function can be expressed as:

[0121] δ i =za i

[0122] Where z is a set of Zernike terms, z=(z1,z2,···,z m ); and a i is a set of Zernike coefficients, a i =(ai1,ai2,···,ai m )T.

[0123] The DM surface deformation based on Zernike polynomial expansion can be expressed as:

[0124] φ=zη

[0125] Among them, η is a set of Zernike coefficients, η=(ηi1,ηi2,···,ηi m )T.

[0126] The known deformation can be expanded according to the Zernike polynomial to obtain the Zernike coefficient of each term. i =za i and φ=zη, the corresponding control voltage can be obtained:

[0127] v=a + η

[0128] Among them, a+ is the pseudo-inverse matrix of a, a=(a1,a2,···,a 69 ).

[0129] When using DM for phase error correction, the principle of phase unwrapping is employed. The deformation of the DM surface changes the optical distance of points on the laser beam cross section, thereby correcting the phase error. Since the beam is reflected from the DM after phase error correction, the relationship between the corrected phase and the DM deformation is as follows:

[0130]

[0131] Here, λ is the wavelength of the laser beam.

[0132] 3. Analysis of the effectiveness of SLAO in phase error correction

[0133] In the simulation process of correcting the phase error introduced by SLM in the SLAO system, a negative 1951 USAF test pattern was used as a sample. The complex-valued hologram of the sample was obtained by using the Gerchberg-Saxton (GS) algorithm, and the phase error was deliberately introduced by adding a phase mask to the phase of the hologram. A set of initial Zernike coefficients were randomly generated, see Figure 4 Among them, the 3rd to 14th Zernike polynomials are modeled as wavefront aberrations, see Figure 4 (a) in the figure. After the wavefront aberration is introduced, the quality of the reconstructed image obtained using the Fresnel back-propagation algorithm is severely degraded. Figure 4 (b) and Figure 4 (c) in the figure shows the original image and the wavefront aberration. It can be noted that the fifth pair of lines (line width 39.4 μm) in the fourth group of the resolution map cannot be distinguished. The reconstructed hologram after phase error correction and its corresponding residual wavefront aberration are shown in Figure 4 (d) and Figure 4(e) in the figure. After phase error correction, the resolution of the reconstructed image is significantly improved, and the second pair of lines in the fifth group (line width 27.8μm) becomes clearly visible. The Tenengrad value of the original image is 0.8563, which is used to verify the performance of the SLAO system in subsequent simulations. After 300 iterations, the Tenengrad value increased from 0.8563 to 2.6596, an increase of 3.1 times. This clearly shows that the SLAO system is able to adequately correct most phase errors. Figure 4 (f) in Figure 3 shows the normalized optimization curve based on the Tenengrad value of 2.6596 to more intuitively observe the characteristics of the SLAO system.

[0134] 4. SAR echo data imaging processing based on SLAO system

[0135] Figure 5 The structure diagram and photos of the experimental platform for a SAR imaging system based on the established SLAO system are presented. This platform is used to study and verify improvements in SAR imaging quality in practical application systems. After collimation, the laser beam (532 nm) passes through a digital micromirror device (DMD, DLP6500FLQ) and a phase-only spatial light modulator (SLM, GAEA-2, Holoeye). The amplitude and phase information of the theoretically processed SAR echo data are modulated onto the laser beam. The SLM is placed in a conjugate plane with the DMD. Lenses L3 and L4 form a 4-f system. The laser beam is reflected by the DM and then imaged by the HSC through the 4-f system. The HSC is located in a conjugate plane with the SLM. Both the DM and the HSC are controlled by the PECC, which performs an iterative phase error correction process.

[0136] Figure 6 The original SAR image and its corresponding phase plane are shown when the SLAO system is not used. Figure 6 (a1) in Figure 6 (c1) in the figure. The SAR images and the corresponding residual wavefront aberrations after different iterations of the SLAO system are shown in Figure 6 (a2) in Figure 6 (a4) Figure 6 (b2) in Figure 6 (b4) and Figure 6 (c2) in – Figure 6(c4) in the figure. The initial SAR image has a Tenengrad value of 0.1889, and the image quality is not ideal. The SPGD algorithm controls the DM to gradually correct the phase error. The optimization curve begins to converge after 500 iterations, and the Tenengrad value increases from 0.1889 to 0.9774, which is 5.2 times higher than before compensation. The whole process takes 46.39 seconds. The standardized optimization curve based on the Tenengrad value of 0.9774 is shown in the figure. Figure 7 As shown in Figure 2. In addition, the maximum sharpness function and the minimum entropy function are selected to evaluate the performance of the SAR image before and after correction. The evaluation results are shown in Table 1. It can be concluded from Table 1 that the phase error compensation of the SLAO system can improve the performance of the SAR image.

[0137] Table 1 Comparison of SAR image indicators before and after phase correction

[0138]

[0139] In summary, this paper combines a traditional SAR optoelectronic processor with an adaptive optical phase correction system (SLAO) to develop a SAR optoelectronic processor with adaptive phase error correction. First, the Tenengrad function was used to evaluate resolution test patterns and SAR images with varying degrees of defocus, verifying the function's unimodality, high sensitivity, and wide applicability. Subsequently, the SPGD algorithm, a numerical method for solving multidimensional unconstrained optimization problems, was used to estimate the gradient of the performance evaluation function for each perturbation and optimize the control variables along the gradient direction to search for the optimal solution of the performance evaluation function. Experiments were conducted on resolution test patterns and with the introduction of random phase errors to investigate the performance of this scheme. Results showed significant improvements in image quality. Finally, SAR imaging processing experiments demonstrated the effectiveness of the SLAO system in adaptively correcting phase errors in SAR images. Due to the high programmability of the DM, the proposed system is reconfigurable. Different image quality evaluation functions can be selected to obtain compensated Zernike wavefronts with corresponding phase error information for different modes and SAR systems.

[0140] The above describes in detail the preferred embodiments of the present invention. It should be understood that those skilled in the art can make numerous modifications and variations based on the concepts of the present invention without inventive effort. Therefore, any technical solutions that can be derived by those skilled in the art through logical analysis, reasoning, or limited experimentation based on the concepts of the present invention and the prior art should be within the scope of protection defined by the claims.

Claims

1. A synthetic aperture radar optoelectronic processor based on adaptive optics technology, characterized in that: The system comprises a SAR pre-processing echo data modulation unit and a sensorless adaptive optical system, wherein the sensorless adaptive optical system comprises: a deformable mirror, used for receiving the laser beam containing the modulated information of the SAR pre-processed echo data and reflecting it toward the beam splitter; A beam splitter is used to transmit the laser beam containing SAR pre-processed echo data modulation information output by the SAR pre-processed echo data modulation unit to the deformable mirror, receive the reflected light beam from the deformable mirror, and then illuminate the high-speed camera; a high-speed camera to receive the laser beam and capture SAR images; A phase error correction computer receives SAR images transmitted by a high-speed camera, analyzes the imaging results of the SAR images using an image quality assessment function, and combines this with a stochastic parallel gradient descent algorithm to iteratively adjust the shape of the deformable mirror until the image quality assessment function converges and the image quality assessment function value meets preset requirements. The image quality assessment function is a Tenengrad function; The deformable mirror is a mirror that changes shape when a voltage is applied; The phase error correction computer generates a Zernike coefficient vector for controlling the mirror shape of the deformable mirror through voltage, and adopts a random parallel gradient descent algorithm to iteratively search for the optimal Zernike coefficient vector.

2. The optoelectronic processor for synthetic aperture radar based on adaptive optics technology according to claim 1, characterized in that: The process of the stochastic parallel gradient descent algorithm includes the following steps: S101: Initialize the Zernike coefficient vector and gain coefficient of the deformable mirror; S102: randomly generating a random perturbation signal vector that obeys Bernoulli distribution, that is, increasing and decreasing the random perturbation signal vector with the same amplitude in each iteration process; S103: Calculating the variation of the image quality assessment function according to the random disturbance signal vector generated in step S102; S104: updating the Zernike coefficient vector according to the change in the gain coefficient, the random perturbation signal vector, and the image quality evaluation function in the current iteration, and using it to control the deformable mirror and calculate the corresponding image quality evaluation function value; S105: Determine whether the image quality assessment function value meets the requirement. If so, complete the iterative calculation of the Zernike coefficient vector. If not, return to step S102 for iterative update.

3. The optoelectronic processor for synthetic aperture radar based on adaptive optics technology according to claim 1, characterized in that: The deformable mirror has a plurality of actuators that change shape according to voltage, and the deformation of the deformable mirror is a linear superposition of the surface shape of each actuator under its corresponding voltage.

4. The optoelectronic processor for synthetic aperture radar based on adaptive optics technology according to claim 1, characterized in that: The SAR pre-processing echo data modulation unit includes an amplitude modulator and a phase modulator connected to each other. The amplitude modulator receives the output of the synthetic aperture radar for processing, and the output of the phase modulator is directed toward the deformable mirror.

5. The optoelectronic processor for synthetic aperture radar based on adaptive optics technology according to claim 1, characterized in that: A 4-f system consisting of multiple lenses is also provided between the SAR pre-processing echo data modulation unit and the deformable mirror.

6. The optoelectronic processor for synthetic aperture radar based on adaptive optics technology according to claim 5, characterized in that: The 4-f system includes a first lens located at a SAR pre-processing echo data modulation unit and a second lens located at an input end of a deformable mirror.

7. The optoelectronic processor for synthetic aperture radar based on adaptive optics technology according to claim 1, characterized in that: The sensorless adaptive optical system is further provided with a reflector and an imaging lens. The input side of the reflector receives the second laser beam, and the output side faces the imaging lens, and is used to perform point target imaging according to the second laser beam.

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