An optical remote sensing imaging system and method based on fourier lamination

Abstract

The application discloses an optical remote sensing imaging system and method based on Fourier ptychographic (FP), and the system comprises a sample table, a laser, a plano-concave lens, a linear polaroid, an image sensor and a displacement table; the method comprises the following steps: step 1, obtaining one original low-resolution image corresponding to each angle irradiated by the laser; step 2, processing each original low-resolution image by using a speckle suppression algorithm to obtain a low-resolution intensity image corresponding to each original low-resolution image; and step 3, performing FP synthetic aperture reconstruction on all the low-resolution intensity images to obtain a reconstructed high-resolution image. The application can realize the synthetic aperture imaging of long-distance large-field coherent imaging, and realizes ten-meter imaging of 6 times synthetic aperture reaching 31 mm on a target with a size of 1 m*0.7 m.

Description

Technical Field

[0001] This invention belongs to the field of optical remote sensing information acquisition and processing technology, specifically relating to the application of Fourier stack imaging technology in the field of remote sensing imaging. It provides an optical remote sensing imaging (i.e., FP remote sensing imaging) system and method based on Fourier stack. This technology proves that the application of Fourier stack in the field of synthetic aperture visible light can improve the resolution to the theoretical limit of virtual synthetic aperture, rather than simply suppressing speckle. Background Technology

[0002] Optical remote sensing imaging is an important means and technological supplement to remote sensing. Improving the resolution of space cameras has been a continuous pursuit in the field of high-resolution remote sensing. Spatial resolution is defined as 1.22. λf / D ,in λ The center wavelength, f Focal length D Let's consider the imaging aperture. Increasing the aperture of a space camera, especially the primary mirror, is the most direct way to improve spatial resolution and expand the field of view, according to the formula. However, this introduces geometric aberrations into the optical system, requiring more optical surfaces to optimize these aberrations. This leads to a series of problems, including increased space camera size, cost, and launch risk. Therefore, the single-mirror aperture of a space camera based on a traditional incoherent imaging system cannot be increased indefinitely and is also limited by manufacturing technology.

[0003] Passive optical synthetic aperture cameras can bypass the manufacturing of large-aperture mirrors, but confocal and co-phase relationships between sub-apertures must be guaranteed. For example, the six sub-apertures in Golay6 must achieve strict confocal and co-phase relationships with an accuracy of up to 1 / 10λ to meet imaging requirements. This not only requires extremely high phase detection and attitude control performance, but also demands high platform stability, making widespread engineering application difficult.

[0004] Synthetic Aperture Radar (SAR) is an active, high-resolution radar technology that directly measures the complex amplitude wavefields of sub-apertures using an antenna with a time resolution of picoseconds. This sub-aperture information is then stitched together in the frequency domain to obtain a high-resolution virtual large aperture. Progress has been made in extending the operating wavelength of SAR to the near-infrared band. According to the spatial resolution formula, achieving SAR in the visible light range would provide higher resolution than using microwaves. However, optical bands have frequencies four to five orders of magnitude higher than microwave frequencies. Compared to antennas, optical detectors need to record complex amplitude wavefields at the femtosecond level, which is far beyond the capabilities of modern imaging equipment.

[0005] Fourier ptychography (FP) or Fourier ptychographic microscopy (FPM) is a promising computational imaging technique invented by Zheng and Yang in 2013. It is named after ptychography, proposed by Rodenburg et al. in 2004. FP utilizes coherent illumination to generate a relative shift between the aperture and the object's spectrum, then uses a small-aperture lens to capture a set of low-resolution images corresponding to different parts of the Fourier spectrum. Stitching these low-resolution images reconstructs a high-resolution image corresponding to a larger synthetic aperture. Combining SAR with optical phase retrieval overcomes the trade-off between high resolution and a large field of view in traditional optical imaging. Simultaneously, it recovers aberrations in the optical system, thus achieving digital compensation for aberrations across the entire field of view. Currently, FPM has proven to be not only a powerful tool for addressing field-of-view and resolution constraints but also an example of resolving a range of trade-offs, such as the conflict between angular resolution and spatial resolution.

[0006] In 2014, Dong et al. first reported a conceptual experiment that expanded the application of FPM from microscopic imaging to macroscopic imaging by combining a scanning camera scheme with an FPM algorithm, opening up possibilities for FP technology in industrial inspection or remote imaging. FP is well-suited for space cameras, both of which have large fields of view and require overcoming the resolution limitations of optical systems. This attracted widespread attention, and a series of works on reflective FPM can be referenced. Meanwhile, Holloway et al. reported the concept of FP-based optical synthetic aperture visible light imaging, called SAVI. In 2017, they further refined the SAVI theory and constructed a remote reflective FP imaging device. They extended the imaging distance from 0.7 m to 1.5 m, using a 2.5 mm aperture imaging lens, achieving a synthetic aperture of 15.1 mm. The imaging resolution was improved by 6 times, verifying that reflective FP technology can image general diffuse objects. However, due to the influence of the camera scanning scheme, the field of view always has slight variations, and the ultimately recoverable effective field of view is only the area where all sub-apertures overlap, resulting in low field-of-view utilization of this method. In 2019, we reported a coherent synthetic aperture imaging (CSAI) method based on multi-angle laser illumination. To simulate targets at infinity, a parallel beamtube was used, improving the resolution from 15.6 μm to 3.48 μm (a 4.5-fold increase) with a 12.4 mm field of view. Despite these efforts, a significant scientific question and two major challenges remain to be addressed. First, the multi-angle coherent model of FP is susceptible to distortion by diffuse reflection or the atmosphere, so it is unclear whether the FP model can improve resolution or suppress speckle. Second, the imaging distance is on the meter level, while the field of view diameter is around the centimeter level, significantly limiting its application. Third, the active illumination of this FP requires a darkroom and a high-power laser, making it susceptible to stray light and speckle noise. Summary of the Invention

[0007] The purpose of this invention is to provide an optical remote sensing imaging system and method based on Fourier stacking, in order to solve the problems that existing technologies can only achieve centimeter-level imaging field of view and meter-level imaging distance, and are easily affected by stray light and speckle noise.

[0008] To achieve the above-mentioned technical objectives, the present invention employs the following technical solution:

[0009] On one hand, this invention provides an optical remote sensing imaging system based on Fourier stacks, comprising a sample stage, a laser, a plano-concave lens, a linear polarizer, an image sensor, and a displacement stage; wherein: The sample stage is used to place the sample, and the sample stage is located within the field of view of the image sensor and within the illumination range of the laser; The laser is used to emit a spherical wavefront to illuminate the sample on the sample stage; the laser is fixed by the displacement stage; The plano-concave lens is located at the light-emitting end of the laser; The linear polarizer is located at the front end of the image sensor; The displacement stage is used to fix the laser and drive the laser to move, so that the laser can irradiate the sample on the sample stage from different angles. The image sensor is used to acquire a raw, low-resolution image at each angle of laser illumination.

[0010] On the other hand, the present invention provides an optical remote sensing imaging method based on Fourier stacks. This method is based on the optical remote sensing imaging system based on Fourier stacks of the present invention, and specifically includes the following steps: Step 1: The laser generates a diverging spherical wavefront to illuminate the diffused object. The light reflected from the object is captured by the camera. The laser is moved by the movement of the displacement stage so that it illuminates the object from different angles. During this process, the image sensor acquires a raw low-resolution image corresponding to each angle illuminated by the laser. Step 2: Process each original low-resolution image obtained in Step 1 using the speckle suppression algorithm to obtain a low-resolution intensity image after speckle noise suppression for each original low-resolution image. Step 3: Perform FP synthetic aperture reconstruction on all the low-resolution intensity images obtained in Step 2 after speckle noise suppression to obtain the reconstructed high-resolution image, including the following sub-steps: Step 3.1: Initialize the pupil of the optical remote sensing imaging system based on Fourier stacks using the following formula. Determine the number of reconstruction iterations Where M is the set total number of iterations; use any low-resolution intensity image obtained in step 2 after speckle suppression. Upsampling is performed to obtain the Fourier spectrum corresponding to the sample. The initial value;

[0011] Where, vector Represents frequency domain coordinates, Indicates the diameter of the pupil; Step 3.2: Calculate the light field guess corresponding to the s-th low-resolution image using the following formula. ; , in, For spatial coordinates, This is the sequence number of the low-resolution image. The relative spectral shift caused by the linear phase of the light source. The location of the laser. To illuminate the wave vector, This represents the distance between the laser's location and the sample. for The spectrum of the position corresponding to the s-th low-resolution image; Step 3.3: Update the result obtained in step 3.2 using the following formula. The light field guess corresponding to the updated s-th low-resolution image is obtained. ; , in, This is the s-th low-resolution intensity image obtained in step 2 after speckle suppression; Step 3.4, use the following formula to calculate the Fourier spectrum corresponding to the sample. Update the spectral position corresponding to the s-th low-resolution image;

[0012]

[0013] in, The Fourier spectrum corresponding to the updated sample. For the updated pupil function, Describes the complex conjugate function. It is a function for maximizing the value; Step 3.5: Traverse the N low-resolution images, that is, repeat steps 3.2 to 3.4 until all N low-resolution images have been traversed, and complete the update of the spectral positions corresponding to all low-resolution images. Step 3.6: Iterate through the number of iterations, i.e., repeat steps 3.2 to 3.5, until convergence or m = M, completing the set number of iterations M. Calculate the Fourier spectrum of the sample obtained in the last iteration. Perform the inverse Fourier transform and take the square, i.e. This yields a reconstructed high-resolution intensity image of the sample.

[0014] Furthermore, the number of iterations M can be between 20 and 100.

[0015] Furthermore, in step 2, the processing of each low-resolution image obtained in step 1 includes the following sub-steps: Step 2.1, use the following formula to process the original low-resolution image. Taking the logarithm, we obtain the additive speckle noise model:

[0016] in, It is an intensity image without speckle distortion. It is speckle noise. yes The logarithm of It is the logarithm of speckle noise; Step 2.2, use the following formula to calculate the logarithm of the speckle noise in Step 2.1. The estimated speckle noise is obtained by performing an estimation. : , in It's a BM3D noise reduction operation; Step 2.3, use the following formula to evaluate the estimated speckle noise obtained in Step 2.2. Perform the transformation to obtain : , in This is a function that performs the following processing on variable v: ; Step 2.4, construct the new image logarithm of speckle noise intensity using the following formula: ; Step 2.5: The logarithm of the final denoised intensity image is obtained using the following formula. : ; Step 2.6: Obtain the final denoised low-resolution intensity image using the following formula. ; .

[0017] Thirdly, the present invention provides an optical remote sensing imaging method based on the Rayleigh limit, comprising the following steps: Step 1: Calculate the Rayleigh limit of the optical remote sensing imaging system based on Fourier stacking of the present invention under speckle effect using the following formula, as the theoretical resolution; , in, It's the wavelength. D It is the diameter of the image sensor lens; Step two: Execute the optical remote sensing imaging method based on Fourier stacking of the present invention, and then calculate the contrast of the reconstructed high-resolution image obtained in step three of the method using the following formula. In the optical remote sensing imaging method based on Fourier stacks, the original low-resolution image acquired in step 1 is a USAF image: , in, For contrast, W and B These represent the average intensity values ​​of the foreground and background in the reconstructed USAF image, respectively. Step 3: Set the threshold of the contrast curve obtained in Step 2, and calculate the minimum resolvable linewidth of the reconstructed high-resolution image at the threshold. Compare the minimum resolvable linewidth with the theoretical resolution obtained in Step 1. If the minimum resolvable linewidth is close to the theoretical resolution, retain the current imaging system parameters. Otherwise, further adjust the imaging system parameters and return to Step 1 until the minimum resolvable linewidth is close to the theoretical resolution.

[0018] Compared with the prior art, the present invention has the following technical effects: 1. In the field of remote sensing, the FP model is easily affected by diffuse reflection or atmospheric damage, thus only achieving centimeter-level imaging field of view and meter-level imaging distance. The imaging system of the present invention can overcome this limitation.

[0019] 2. Since active photodetectors require darkrooms and high-power lasers and are easily affected by stray light and speckle noise, the imaging system and method of this invention can effectively solve these problems.

[0020] 3. In this study, it was found that FP can improve the resolution to the theoretical limit of synthetic aperture rather than simply suppress speckle effect. Therefore, in response to the problem of unclear FP imaging mechanism, this invention proposes the Rayleigh limit to solve the problem, and achieves imaging at a distance of 10 meters with a synthetic aperture of 31 mm, which is 6 times larger than the synthetic aperture, on a target with a size of 1 m × 0.7 m.

[0021] In summary, this invention enables synthetic aperture imaging for long-distance, large-field-of-view coherent imaging. The results of the embodiments demonstrate that this invention effectively suppresses speckle noise and improves image quality, and the resulting synthetic aperture quantitatively verifies the proposed resolution limit. The proposed resolution limit is of great significance for predicting and evaluating the performance of practical coherent imaging systems (such as laser imaging and laser displays). Attached Figure Description

[0022] Figure 1This invention presents an optical remote sensing imaging system and principle based on Fourier stacking. (a) The proposed long-range FP coherent imaging mechanism involves illuminating the target with a divergent laser beam to increase the field of view, and recording the object's reflection by the sensor through an imaging lens. Since the numerical aperture of the imaging system is fixed, the image obtained on the sensor plane has a finite resolution. By moving the laser with an xy-motion platform, the captured original image sequence is shown in Figure (b-1). (b-2) shows the blurred and degraded speckles. (b-3) is the result of FP reconstruction based on the captured original image sequence, which significantly reduces the speckle size and improves the resolution. (b-4) is the result of further using a speckle suppression algorithm.

[0023] Figure 2 This is a comparison of two typical FP remote imaging mechanisms. (a, b) Camera scanning and its reduced field of view, (c, d) Laser scanning and its reduced field of view.

[0024] Figure 3 This is a comparison of three FP remote sensing imaging illumination schemes: (a) focused illumination, (b) quasi-plane wave illumination, and (c) divergent illumination. For simplicity, the object's horizontal plane coordinates are represented as follows: x The laser is located x s At this location, the distance from the center of the object is z s object distance z o Image distance z I Satisfies the laws of geometric optics lenses. ,in f It is the focal length.

[0025] Figure 4 This is a simulation comparison of synthetic aperture imaging based on different phase terms of FP. Taking the intensity of USAF (United States Air Force, resolution plate) image samples as an example, (a) Fourier spectrum (a-1), original image (a-2), and synthetic aperture image (a-3) when the phase term is zero; (b) Fourier spectrum (b-1), original image (b-2), and synthetic aperture image (b-3) when the phase term is a quadratic phase; (c) Fourier spectrum (c-1), original image (c-2), and synthetic aperture image (c-3) when the phase term is a mixture of quadratic phase and random phase.

[0026] Figure 5This is a schematic diagram of the speckle suppression algorithm in the method of this invention. Flowchart (left) and speckle suppression simulation (right). (b) The speckle image is obtained based on the (a) Ground Truth (GT) simulation with a negative exponential distribution. (d) The speckle suppression algorithm in this invention outperforms the (c) BM3D algorithm in terms of quantitative SSIM, PSNR, and visual quality. (The second row of the right image is an enlarged version of the red box in (a) that corresponds one-to-one with the first row of the right image.) Figure 6 Super-resolution coherent imaging at a distance of 10 meters was performed on a landscape painting target. (a-1) Imaging setup, (a-2) Target. The imaging area is a portion of the target image, measuring 1m × 0.7m. (b) Low-resolution original image and strong speckles in the red and yellow framed areas (b-1, b-2). After 6x super-resolution processing using FP, the resolution of the reconstructed image (c) and the magnified red and yellow framed areas (c-1, c-2) are significantly improved, and the speckle size is reduced. Further speckle suppression processing is applied to the FP reconstructed image to reduce the intensity variation in the speckle area, resulting in a smooth despecimen image (d) and magnified red and yellow framed areas (d-1, d-2). The brightness of (b-2), (c-2), and (d-2) is adjusted to obtain better visualization results.

[0027] Figure 7 This is a 10-meter distance super-resolution coherent imaging performed on a custom resolution target. (a) Ground truth (GT) of the self-designed resolution target including different resolution maps; (a-1, a-2) are magnified views of the red and yellow boxed areas. (b) The original image captured by the imaging; (b-1, b-2) are magnified views of the red and yellow boxed areas. (c) The FP super-resolution reconstructed image; (c-1, c-2) are magnified views of the red and yellow boxed areas. (d) The FP reconstruction result after speckle suppression; (d-1, d-2) are magnified views of the red and yellow boxed areas. The brightness adjustments in (b-2), (c-2), and (d-2) are for better visualization of the 10-meter distance super-resolution coherent imaging on the resolution target.

[0028] Figure 8The resolution limits under different synthetic apertures are characterized by the reconstruction results of the target using USAF resolution. (a) Original image with an original aperture of 5 mm, and reconstructed images with synthetic apertures SA of 10 mm, 18 mm, and 35 mm. (b) Enlarged area of ​​each bar group in (a), with the blue dashed line as the boundary of resolvable features; features below this line are resolvable. (c) Quantitative comparison curves of reconstruction effects at synthetic apertures SA of 18 mm and 35 mm (vertical axis represents contrast, horizontal axis represents the manually selected stripe group position on USAF). (d) Comparison of the resolution reconstructed using this invention with theoretical predictions. The red asterisk indicates the limit resolution of the image recovered by the reconstruction and speckle suppression methods in this invention under different synthetic apertures, and the blue curve represents the resolution limit proposed in this invention (horizontal axis is synthetic aperture, vertical axis is minimum resolvable linewidth).

[0029] Figure 9 This is the result of the super-resolution imaging analysis of the present invention. (a) is... Figure 7 (a) shows the magnified resolution bar image in the lower right corner, (a-1) the ground truth (GT) image, (a-2) the original image, (a-3) the pre-processor (FP) reconstructed image, and (a-4) the result of further speckle suppression after FP reconstruction. (b) shows magnified areas selected by different colors in Figure (a) to compare the resolution of GT, the original image, FP reconstruction, and the result of further speckle suppression after FP reconstruction. The resolution of the original image is 0.25 lp / mm, which is improved to 1.4 lp / mm after FP reconstruction and speckle reduction.

[0030] Figure 10 This is a comparison between SAVI and the imaging method of this invention. Both schemes use similar parameters. A camera with an aperture of 2.34 mm is placed one meter away from the object. A 26×26 image grid is captured with 78% overlap, and the synthetic aperture is 14.84 mm. (a, b, c) are the low-resolution image, reconstructed image, and denoised image using the imaging mechanism of this invention, respectively. (d, e, f) are the low-resolution image, reconstructed image, and denoised image using the SAVI scheme, respectively. The method of this invention has significant advantages. Detailed Implementation

[0031] like Figure 1 As shown in (a), the optical remote sensing imaging system based on Fourier stacking provided by this invention includes a sample stage, a laser, a plano-concave lens, a linear polarizer, an image sensor, and a displacement stage. The laser is fixed by the displacement stage, and the sample stage is located within the field of view of the image sensor and within the laser's illumination range. The plano-concave lens is located at the laser's output end (for generating a diverging beam), and the linear polarizer is located at the front end of the image sensor.

[0032] Due to camera scanning scheme ( Figure 2 (a,b) The camera lens required to achieve far-field diffraction must be very small. For imaging scenarios at a distance of ten meters, the maximum diameter of the camera lens is only 1.6 millimeters, which is much smaller than that of commonly used commercial cameras. At the same time, the scanning of the camera will produce different fields of view, resulting in a limited field of view in the effective area. Figure 2 (b) Therefore, the system of the present invention employs a laser scanning scheme ( Figure 2 (c,d)). Laser scanning solutions are widely used due to their large field of view. There are three illumination methods; the SAVI mentioned in the background section uses focused illumination. Figure 3 (a)); Quasi-plane wave illumination is frequently used in the field of FPM ( Figure 3 (b) Since these two types of illumination require the use of condenser lenses or collimating lenses in their optical path design, their field of view is limited. Furthermore, the shifted light source needs to illuminate the object from different angles, making these two solutions impractical for long-distance remote sensing imaging. Therefore, this invention employs a third type of divergent illumination (…). Figure 3 (c) Since no additional mirror is needed, the imaging field of view and distance can be greatly increased.

[0033] Based on the Fourier layer-based optical remote sensing imaging system of the present invention, the present invention provides the following Fourier layer-based optical remote sensing imaging method, which specifically includes the following steps: Step 1: The laser generates a diverging spherical wavefront that illuminates the diffused object. The light reflected from the object is captured by the camera. A displacement stage moves the laser to illuminate the object from different angles. During this process, the image sensor acquires a raw low-resolution image corresponding to each angle of laser illumination, such as... Figure 1 As shown in (b - 1).

[0034] No. s Original low-resolution image obtained from each illumination angle The formation process is as follows: spherical light field emitted by a laser Distance Illumination is applied to the surface of the sample object, forming a light field on the sample surface. ,Then Distance After a distance Upon reaching the image sensor, according to the laws of geometric optics lenses... : (1) in, Represents image plane coordinates, Represents the object plane coordinates; This represents the inverse Fourier transform. Indicates Fourier transform; For the pupil function of the imaging system; in, This represents the second phase term from the target object to the image sensor lens. To illuminate the wave vector, It is the imaginary unit; Among them, the light field of the target object surface for: (2) in, For the target complex amplitude, For the target amplitude, It is the random phase generated on the surface of the target object due to random height fluctuations; in, for: (3) in, It is a constant phase term. and These are linear phase terms and quadratic phase terms. This indicates the location of the laser source.

[0035] make Indicates the complex amplitude of the sample target: (4) Formula (1) can be further calculated as follows: (5) in, For the target amplitude of the sample The corresponding Fourier spectrum, The relative spectral shift caused by the linear phase of the light source; movement of the light source will change the linear phase. , making the complex amplitude The position of the pupil changes, resulting in a low-resolution intensity image containing speckle noise being acquired at the image sensor. .

[0036] According to formula (5), the phase of the target is a mixture of the secondary phase from the illumination path and the imaging lens and the random phase from the rough surface. In coherent imaging, the target amplitude is usually of primary concern. However, when the aperture is limited, the phase term has a profound impact on the image. Therefore, using a resolution board (United States Air Force, USAF) image as the target, simulations of three phase terms—empty phase, secondary phase term, and mixed phase term—are performed and explained below: Empty phase (also called zero phase) is represented by a plane wave whose Fourier spectrum is simulated as follows: Figure 4As shown in (a-1), a peak can be observed at the DC component, with attenuation at higher spatial frequencies. (Original image) Figure 4 (a-2) are the bright field and dark field images extracted from the DC component and high frequency of the spectrum, respectively. High-resolution image reconstruction is performed based on these original images. Figure 4 (a-3)).

[0037] The second phase term uses spherical waves to transmit through the object. In FPM, spherical waves are usually approximated as quasi-plane waves within a small region of the object. The Fourier spectrum of the object is as follows: Figure 4 As shown in (b-1), its Fourier spectrum differs significantly from that corresponding to the empty phase. This is because the quadratic phase term introduces light waves exceeding the maximum incident angle of the numerical aperture, resulting in a simulated original image ( Figure 4 (b-2) presents a partially bright field and a partially dark field. During its reconstruction, the field of view is increased as the resolution improves and the numerical aperture increases (4(b-3)).

[0038] The mixed phase term, containing random phase and quadratic phase, has the following Fourier spectrum: Figure 4 As shown in (c-1), due to the dominance of random phase and the uniform spread of the spectrum in the Fourier domain, the spectrum does not exhibit any meaningful structure. The original image obtained from the simulation is as follows. Figure 4 As shown in (c-2), the presence of blobules reduces image quality, and the reconstruction result is as follows. Figure 4 As shown in (c-3).

[0039] As shown above, the simulation of the phase term demonstrates that the remote sensing FP technology significantly expands the field of view and improves resolution.

[0040] Step 2: Due to speckle effects, the original low-resolution image exhibits blurring and degradation, such as... Figure 1 As shown in (b-2). Here, the speckle suppression algorithm is applied to each original low-resolution image obtained in step 1 to obtain a speckle-suppressed low-resolution intensity image corresponding to each original low-resolution image, in order to improve image quality. Figure 1 (as shown in (b-4)).

[0041] Speckle patterns are not traditional noise; rather, their intensity is random due to the random phase distortion of the intensity field. (Speckle intensity image) probability distribution Follows a negative exponential distribution ,in This represents the intensity image before speckle distortion. The speckle intensity image can be directly represented as a multiplicative noise model. ,in It is speckle noise, and its probability distribution is... for This invention proposes the following speckle suppression algorithm, such as... Figure 5 As shown, step 2, processing each low-resolution image obtained in step 1, includes the following sub-steps: Step 2.1: Process the original low-resolution image (i.e., the speckle intensity image). (Coordinates omitted) Taking the logarithm, we obtain the additive speckle noise model: (6) in, It is an intensity image without speckle distortion. It is speckle noise. yes The logarithm of It is the logarithm of speckle noise. The probability distribution of speckle noise is non-Gaussian, therefore the classic Gaussian denoising algorithm cannot be applied to the suppression and removal of speckle noise.

[0042] Step 2.2, calculate the logarithm of the speckle noise in Step 2.1. The estimated speckle noise is obtained by performing an estimation. : (7) in It's a BM3D noise reduction operation; Step 2.3, the estimated speckle noise obtained in Step 2.2 Perform the transformation to obtain : (8) in This is a function that performs the following processing on variable v: (9) Step 2.4: Construct a new image logarithm of speckle noise intensity using formula (14); (10) Step 2.5: Obtain the final logarithm of the denoised intensity image using formula (15). ; (11) Step 2.6: Obtain the final low-resolution intensity image after speckle suppression according to formula (16). ; (12).

[0043] Step 3: Process all the low-resolution intensity images obtained in Step 2 after speckle suppression. FP synthetic aperture reconstruction is performed to obtain a reconstructed high-resolution image, thereby reducing speckle size and improving resolution. Figure 1 (b-3) includes the following sub-steps: Step 3.1: Initialize the pupil of the imaging system of the present invention using formula (13). Determine the number of reconstruction iterations Where M is the set total number of iterations (20~100); use any low-resolution intensity image obtained in step 2 after speckle suppression (preferably one with a normal incidence illumination angle). Upsampling is performed to obtain the Fourier spectrum corresponding to the sample. The initial value; (13) Where, vector Represents frequency domain coordinates, This indicates the diameter of the pupil.

[0044] Step 3.2: Calculate the light field guess corresponding to the s-th low-resolution image using formula (14). ; (14) in, For spatial coordinates, This is the sequence number of the low-resolution image. The relative spectral shift caused by the linear phase of the light source. The location of the laser. To illuminate the wave vector, This represents the distance between the laser's location and the sample. for The spectrum of the position corresponding to the s-th low-resolution image.

[0045] Step 3.3, update the result obtained in step 3.2 using formula (15). The light field guess corresponding to the updated s-th low-resolution image is obtained. ; (15) in, (Coordinates are omitted in step 2 and are abbreviated as) () represents the s-th low-resolution intensity image obtained in step 2 after speckle suppression; Step 3.4, use formula (16) to calculate the Fourier spectrum of the sample. Update the spectral position corresponding to the s-th low-resolution image; (16) (17) in, The Fourier spectrum corresponding to the updated sample. For the updated pupil function, Describes the complex conjugate function. It is a function for maximizing the value; Step 3.5: Traverse the N low-resolution images, that is, repeat steps 3.2 to 3.4 until all N low-resolution images have been traversed (the traversal order can be 1 to N, or a center circle or Z-shape), to complete the update of the spectral positions corresponding to all low-resolution images; Step 3.6: Iterate through the iterations, i.e., repeat steps 3.2 to 3.5, until convergence or m=M, completing the set number of iterations. Calculate the Fourier spectrum of the sample obtained in the last iteration. Perform the inverse Fourier transform and take the square, i.e. The reconstructed high-resolution intensity image of the sample is obtained; where convergence means that the error matrix is ​​continuously less than a set threshold and remains unchanged, and the threshold is determined according to the convergence situation.

[0046] Based on the Fourier stack-based optical remote sensing imaging method of the present invention, the present invention provides an optical remote sensing imaging method based on the Rayleigh limit. This method determines whether the imaging method of the present invention has reached the system limit based on a new imaging system limit (Rayleigh limit), thereby adjusting the results of the Fourier stack-based optical remote sensing imaging method of the present invention.

[0047] First, the limits of the new imaging system mentioned above are defined: The Rayleigh criterion has been widely used in resolution estimation for incoherent imaging. Two incoherent point sources separated by the Rayleigh limit are only resolvable; when the two sources are coherent and in phase, they are indistinguishable; however, when the two sources are out of phase (i.e., offset by π radians), they are completely "resolvable." In reflective coherent imaging, speckle patterns generated by random phases from microscopically rough surfaces degrade image quality and resolution; these random phases fluctuate significantly within the phase range of -π to π. A conservative approach to defining the resolution limit is to consider the worst-case scenario, namely, two points with the same phase, where a superimposed intensity profile is easily formed. Theoretically, from the superimposed image, it can be calculated that when the center tilt angle intensity is 81% of the maximum intensity on either side, the angular distance between the two points is... Therefore, the Rayleigh limit of a coherent imaging system under speckle effect is defined as: (18) in, It's the wavelength. D It is the diameter of the image sensor lens.

[0048] An optical remote sensing imaging method based on the Rayleigh limit specifically includes the following steps: Step 1: According to formula (18), calculate the Rayleigh limit of the optical remote sensing imaging system based on Fourier stacks of the present invention under speckle effect, as the theoretical resolution ( Figure 8 (d) marked in blue); (18) in, It's the wavelength. D It is the diameter of the image sensor lens.

[0049] Step two, execute the optical remote sensing method based on Fourier stacking of the present invention, and then use the following formula to calculate the contrast of the reconstructed high-resolution image sample obtained in step 3 of the method (in this embodiment, the original low-resolution image acquired in step 1 is a USAF image). Figure 8 (c) Contrast curve: (19) in, For contrast, W and B These are the average intensity values ​​of the foreground and background (shown in the example as three white bars and two black bars in the same group of lines) on the reconstructed USAF image; Step 3: Set the threshold of the contrast curve obtained in Step 2, and calculate the minimum resolvable linewidth of the reconstructed high-resolution image at the threshold. Figure 8 (d) marked in red) (This threshold can ensure that the reconstructed high-resolution image is resolvable, and it is 0.1 in Example 3); compare the minimum resolvable linewidth with the theoretical resolution obtained in step 1 to determine whether the imaging method of the present invention can approach or reach the system limit level, so as to analyze the imaging system parameters of the method of the present invention: if the minimum resolvable linewidth is close to the theoretical resolution, it indicates that the imaging system of the present invention has a significant effect; otherwise, further adjust the imaging system parameters and return to step 1 until the former approaches the theoretical resolution. The degree of closeness is determined according to the actual requirements.

[0050] The above technical solution actually proposes a theoretical limit to address the problem of unclear FP imaging mechanism, clarifying that FP can improve resolution to the theoretical limit of synthetic aperture, rather than simply suppressing speckle effect.

[0051] To verify the reliability and effectiveness of the system and method of the present invention, the following embodiments are conducted: Example 1: Verification of long-distance imaging of a landscape painting sample at 10m using the imaging system and method according to the present invention. Settings: such as Figure 6As shown in (a-1). A wavelength of 532 nm was used. nm Illumination is provided by a single-mode laser, using a plano-concave lens (focal length -10). mm This produces a diverging beam. The maximum power of the laser is 100. mW A two-dimensional translation platform (Zolix, PSA050-11-X) is used to move the laser source. The image sensor (IMX178) has a size of 2048×3056 pixels and a pixel pitch of 2.4 μm, and uses a 75nm process. mm Focal length and 5 mm Imaging is performed using a lens with a specific aperture size. The sensor's full field of view is... In addition, a linear polarizer is placed in front of the camera to filter out non-interference light. The target image is a large landscape painting. Figure 6 (a-2)). Based on the system conditions, a portion of the sample (~1m × 0.7m) was imaged as follows. Figure 6 As shown in (b), the prototype system aperture was set to 5 mm, the laser source was translated by 0.875 mm per step, and the overlap rate was 82.5%. By acquiring 31x31 low-resolution images, a maximum synthetic aperture of 31 mm could be achieved, which is 6 times the lens aperture.

[0052] analyze Figure 6 (b) Due to the rough surface of the image, severe spots can be observed. Furthermore, due to the limitation of the aperture size, significant blurring and diffraction appear in parts of the original image under magnification. Figure 6 (b-1, b-2) further reduced image quality. FP reconstruction and speckle suppression were performed based on the acquired 31x31 low-resolution images. Figure 6 (c) It can be seen that, compared with the original capture with an aperture of 5 mm, the FP synthetic aperture reconstruction with an aperture of 31 mm produces finer resolution and smaller spots. For example, it can be observed that... Figure 6 (c1) The fine structure of the building and Figure 6 The leaf patterns in (c2), these patterns are in Figure 6 (b1) and Figure 6 It is indistinguishable from the original capture of (b2). From Figure 6 (d) It can be seen that by applying the speckle suppression algorithm proposed in this invention, speckle suppression of speckle patterns can be achieved, thereby significantly improving visual quality.

[0053] Example 2: Verification of long-distance imaging of a custom resolution sample at 10m using the imaging system and method according to the present invention. Setup: Use a custom-defined resolution sample as the target, measuring 42cm × 29.7cm, and place it 10 meters away from the camera. The resolution target includes several different types of commonly used resolution images, such as... Figure 7 As shown in (a), by translating the laser source and acquiring 27×27 low-resolution images, the maximum achievable synthetic aperture is 27.75 mm, which is 5.6 times the aperture diameter. The remaining system settings are the same as in Example 1.

[0054] Imaging results as follows Figure 7 As shown. Figure 7 (b) The raw image captured by the imaging system has a lower resolution due to aperture limitations, and its image quality is significantly lower than the real image due to speckle (e.g., Figure 7 (b-1,b-2) compared to Figure 7 (Ground Truth of (a-1, a-2)). After FP reconstruction, the image resolution is greatly improved, such as Figure 7 As shown in (c), the speckle is still present in the reconstructed image, but its size has been significantly reduced, resulting in higher spatial resolution. The effect after applying the speckle suppression algorithm of this invention is as follows: Figure 7 As shown in (d), the effect of speckle is significantly eliminated, the contrast is improved, and the same resolution improvement as the traditional FP algorithm is maintained.

[0055] Example 3: The imaging system according to the present invention tests the proposed resolution limit at different apertures. Setup: To quantitatively study resolution performance, negative images from the USAF were imaged. A smooth layer of white paint was sprayed onto the chrome-plated surface, and the target was imaged through the back of a glass plate to preserve the high-resolution characteristics of the image. Since the USAF is 18mm × 18mm in size, the imaging distance was shortened to 1 meter. z =1m), and only 1 / 16 of the camera's field of view is used. The aperture is set to 5mm. The laser source is translated 1mm per step, with an overlap rate of 80%. 31x31 low-resolution images are acquired, and the maximum synthesized aperture is 35mm.

[0056] like Figure 8 (a) shows the original image captured by the imaging system and the reconstructed image. Due to the surface roughness of the white bars, we can observe spots that degrade image quality and resolution. High-resolution images were reconstructed using a sequence of 31x31 captured images at different synthetic apertures. Figure 8 (a) shows the reconstructions with synthesized apertures SA of 10 mm, 18 mm and 35 mm. It can be seen that as the synthesized aperture increases, the speckle size decreases, resulting in higher spatial resolution. Figure 8 (a) shows the proposed speckle suppression algorithm on the right side of the reconstruction results. It can be observed that the speckle suppression algorithm helps to remove speckle effects and improve performance. Figure 8(b) shows the original captured images and reconstructed images at four locations (1,5), (2,4), (3,3), and (4,4) with SA values ​​of 5mm, 10mm, 18mm, and 35mm, where (1,5) represents group 1 and element 5. It can be seen that as the synthetic aperture increases, the speckle size decreases and the spatial resolution improves. The speckle suppression algorithm improves image quality by reducing speckle variation, thus helping to visually distinguish white bars. The blue dashed line represents the boundary of resolvable features; features below this line are resolvable.

[0057] Resolution performance is quantitatively evaluated by calculating the contrast ratio for each group, which is defined as: (18) in, W and B These are the average intensity values ​​for the three white bars and two black bars in the same group, respectively. Regions were manually located on high-resolution images from USAF and scaled proportionally to the correct size for each test image. Figure 8 (c) Comparison of reconstructed images with SA=18mm and SA=35mm. It can be seen that the contrast improves with increasing synthetic aperture SA. Furthermore, a contrast threshold was set to determine the limiting resolution of the SA image in the contrast map. Since the limit calculated according to the Rayleigh standard is approximately 0.1, the contrast threshold was also set to 0.1. Then, the minimum resolvable linewidth for various synthetic apertures was calibrated as follows: Figure 8 The position of the red star in (d) indicates that the experimental resolution has reached the limit in formula (17). Figure 8 (d) The blue line is horizontal.

[0058] Figure 9 Quantitatively demonstrating the super-resolution performance of the method of the present invention (by...) Figure 7 (a) The image is magnified from the lower right corner. Under the given imaging parameters, the minimum resolvable linewidth of the original image is 1.7 mm. From... Figure 9 As can be seen from the original image in (b), reconstructing the synthetic aperture image from the original image significantly improves the resolution, reduces the speckle size, and further smooths the speckle by combining it with the speckle suppression algorithm. Figure 9 As can be seen in (b), after using FP for super-resolution processing, the minimum resolvable linewidth is 0.357 mm, which is at least 4.7 times higher than the original image.

[0059] Example 4: Comparison of the imaging mechanism of the imaging system of the present invention with the SAVI imaging mechanism Compared to the camera scanning scheme of SAVI, the imaging system of this invention can provide a larger field of view. First, the SAVI setup was experimentally replicated, and a convex lens with a diameter of 2 inches and a focal length of 300 mm was inserted between the laser and the target to compensate for the second phase in SAVI. The distance for the replication experiment was one meter. After passing through the compensating lens, the illumination was focused and produced a spot of approximately 21 mm on the object; obviously, the spot size is limited by the diameter of the compensating lens. The camera was mounted on a translation stage, and the Fourier spectrum of the object was scanned after movement. The camera was positioned 0.5 mm apart to ensure a 78% overlap, acquiring a 26 × 26 grid image, and synthesizing an aperture of 14.84 mm. The SAVI experimental results are as follows... Figure 10 As shown in (df).

[0060] To ensure a fair comparison, this invention maintains the exact same configuration as SAVI, except that the compensating lens in SAVI is replaced with a plano-concave lens (6mm diameter, -6mm focal length) to produce a spherical diverging beam. The diverging beam illuminates the entire object measuring 62mm × 92mm. The light source is translated using a translation stage. The step increment is set to 0.5mm, with an overlap of 78%. A synthetic aperture of 14.84mm is achieved by recording 26 × 26 images. Experimental results are as follows... Figure 10 As shown in (ac). With SAVI ( Figure 10 Compared to (df), the present invention significantly improves FOV (by 6 times).

[0061] In summary, the optical remote sensing imaging system and method based on Fourier stacking proposed in this invention can achieve synthetic aperture imaging for long-distance, large-field-of-view coherent imaging. The results of the embodiments show that the imaging system and method of this invention can effectively suppress speckle noise and improve image quality, and the resulting synthetic aperture quantitatively verifies the proposed resolution limit. Furthermore, 10-meter imaging with a synthetic aperture of 31 mm (6 times the size of the original) was achieved on an object measuring 1 m × 0.7 m. The proposed resolution limit is of great significance for predicting and evaluating the performance of practical coherent imaging systems (such as laser imaging and laser displays).

Claims

1. A Fourier-layers-based optical remote sensing imaging method, characterized in that, This method is based on a Fourier layer-based optical remote sensing imaging system, which includes a sample stage, a laser, a plano-concave lens, a linear polarizer, an image sensor, and a displacement stage. Specifically: the sample stage is used to place samples, and is located within the field of view of the image sensor and the illumination range of the laser; the laser emits a spherical wavefront to illuminate the samples on the sample stage; the laser is fixed by the displacement stage; the plano-concave lens is located at the laser's output end; the linear polarizer is located at the front end of the image sensor; the displacement stage is used to fix the laser and drive it to move, allowing the laser to illuminate the samples on the sample stage from different angles; the image sensor is used to acquire one raw low-resolution image at each angle of laser illumination. Specifically, the steps include the following: Step 1: The laser generates a diverging spherical wavefront to illuminate the diffused object. The light reflected from the object is captured by the camera. The laser is moved by the movement of the displacement stage so that it illuminates the object from different angles. During this process, the image sensor acquires a raw low-resolution image corresponding to each angle illuminated by the laser. Step 2: Process each original low-resolution image obtained in Step 1 using the speckle suppression algorithm to obtain a speckle-suppressed low-resolution intensity image corresponding to each original low-resolution image. Step 3: Perform FP synthetic aperture reconstruction on all the low-resolution intensity images obtained in Step 2 after speckle noise suppression to obtain the reconstructed high-resolution image, including the following sub-steps: Step 3.1: Initialize the pupil of the optical remote sensing imaging system based on Fourier stacks using the following formula. Determine the number of reconstruction iterations Where M is the set total number of iterations; use any low-resolution intensity image obtained in step 2 after speckle suppression. Upsampling is performed to obtain the Fourier spectrum corresponding to the sample. The initial value; where the vector denotes the frequency domain coordinate, denotes the pupil diameter; Step 3.2, compute the light field guess corresponding to the s-th low resolution image using the following formula ; ， in, For spatial coordinates, This is the sequence number of the low-resolution image. The relative spectral shift caused by the linear phase of the light source. The location of the laser. To illuminate the wave vector, This represents the distance between the laser's location and the sample. for The spectrum of the position corresponding to the s-th low-resolution image; Step 3.

3. Update the result of step 3.2 with the following formula , to obtain the updated light field guess corresponding to the s-th low resolution image ; ， in, This is the s-th low-resolution intensity image obtained in step 2 after speckle suppression; Step 3.4, updating the Fourier spectrum position corresponding to the sample using the formula updating the spectrum position corresponding to the s-th low resolution image; wherein, is the Fourier spectrum corresponding to the updated sample, is the updated pupil function, denotes the complex conjugate function, is the maximum function; Step 3.5: Traverse the N low-resolution images, that is, repeat steps 3.2 to 3.4 until all N low-resolution images have been traversed, and complete the update of the spectral positions corresponding to all low-resolution images. Step 3.6: Iterate through the number of iterations, i.e., repeat steps 3.2 to 3.5, until convergence or m = M, completing the set number of iterations M. Calculate the Fourier spectrum of the sample obtained in the last iteration. Perform the inverse Fourier transform and take the square, i.e. This yields a reconstructed high-resolution intensity image of the sample.

2. The Fourier-Stack-Based optical remote sensing imaging method according to claim 1, wherein, The number of iterations M ranges from 20 to 100.

3. The Fourier-Stack-Based optical remote sensing imaging method according to claim 1, wherein, Step 2, the processing of each low-resolution image obtained in step 1, includes the following sub-steps: Step 2.

1. Apply to the original low resolution image Taking the logarithm gives the additive speckle noise model: wherein, is the intensity image without speckle destruction, is the speckle noise, is the logarithm of, is the speckle noise logarithm; Step 2.

2. Estimate the speckle noise using the log of the speckle noise from Step 2.1 :​ ， wherein is the BM3D denoising operation; Step 2.

3. Estimate the speckle noise from the estimate obtained in step 2.2 using the following formula Performing a transformation, we obtain : ， wherein is a function that processes the variable v as follows: ； Step 2.4, construct the new image logarithm of speckle noise intensity using the following formula: ； Step 2.5, the final denoised intensity image log is obtained using the following formula : ； Step 2.

6. The final denoised low resolution intensity image is obtained using the following equation ; 。 4. A method of optical remote sensing imaging based on Rayleigh limit, characterized in that, Includes the following steps: Step 1: Calculate the Rayleigh limit of the optical remote sensing imaging system based on Fourier stacks under speckle effect using the following formula, as the theoretical resolution; ， wherein, is the wavelength, D is the image sensor lens diameter; Step two, performing the Fourier-layers-based optical remote sensing imaging method according to any one of claims 1-3, and then calculating the contrast of the reconstructed high-resolution image obtained in step 3 by using the following formula wherein the original low-resolution image collected in step 1 of the Fourier-layers-based optical remote sensing imaging method is a USAF image: ， wherein, is the contrast, W and B are the average intensity values of the foreground and background on the reconstructed USAF image, respectively. Step 3: Set the threshold of the contrast curve obtained in Step 2, and calculate the minimum resolvable linewidth of the reconstructed high-resolution image at the threshold. Compare the minimum resolvable linewidth with the theoretical resolution obtained in Step 1. If the minimum resolvable linewidth is close to the theoretical resolution, retain the current imaging system parameters. Otherwise, further adjust the imaging system parameters and return to Step 1 until the minimum resolvable linewidth is close to the theoretical resolution.

Images