A synthetic aperture super-resolution telescope system and imaging method based on incoherent light illumination

By converting incoherent light illumination and multi-channel filters into coherent light signals, and combining overlapping acquisition and computational system reconstruction, the diffraction limit and single-wavelength imaging problems of traditional telescope imaging systems are solved, achieving multi-band super-resolution imaging and improved light energy utilization.

CN118759731BActive Publication Date: 2025-12-26ZHEJIANG UNIV
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Patent Information

Application Number
CN202411049360.0
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2024-08-01
Publication Date
2025-12-26
Estimated Expiration
2044-08-01

AI Technical Summary

Technical Problem

Traditional telescope imaging systems are limited by the diffraction limit, making it impossible to effectively improve spatial resolution by increasing the aperture. Furthermore, existing incoherent illumination super-resolution techniques cannot achieve multi-band imaging.

Method used

An incoherent light source is used in combination with a multi-channel narrowband filter and a pinhole to convert the light into multiple discrete coherent illumination signals. The acquisition position of the telescope system is adjusted by overlapping, and a high-resolution image is reconstructed by a computing system. Multi-color channel multiplexing is achieved by using coherent state multiplexing technology.

Benefits of technology

Multi-band super-resolution imaging was achieved, improving photon utilization and signal-to-noise ratio, avoiding light energy loss of a single wavelength, and obtaining higher spatial resolution images.

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Abstract

The application discloses an imaging system and method of a synthetic aperture super-resolution telescope with incoherent light illumination, comprising an incoherent light source for illuminating a target object, a multi-channel narrow-band filter and a pinhole for filtering light field signals received by the telescope, a telescope optical system for collecting imaging signals, a telescope positioning system for determining the position of the telescope, a displacement platform for moving the telescope, an optical camera for recording imaging signals of the telescope optical system, and a computing system for storing, reconstructing and displaying images. The displacement platform carries the telescope optical system, the multi-channel narrow-band filter, the pinhole, the telescope positioning system, the optical camera and the computing system. The technical scheme can avoid the problem that traditional coherent synthetic aperture imaging can only obtain high-resolution information of a single wavelength, and can also improve the photon utilization rate and signal-to-noise ratio of super-resolution imaging.
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Description

TECHNICAL FIELD

[0001] The application belongs to the field of imaging technology, and particularly relates to a synthetic aperture super-resolution telescope system based on incoherent light illumination and an imaging method. BACKGROUND

[0002] Optical telescope imaging systems are very important long-distance observation imaging devices, and are indispensable devices in the research in the field of remote sensing. In practical applications, people hope to obtain images with high spatial resolution through the optical telescope imaging system, so as to obtain more detailed information about the observed object. However, the spatial resolution of the optical telescope imaging system is limited by the diffraction limit, so that the spatial resolution of an optical telescope imaging system with an aperture A is limited to 1.22λf / A (λ is the wavelength of the incident light wave, and f is the focal length of the imaging system). In order to obtain higher spatial resolution, people build optical telescopes with larger and larger apertures. However, with the increase of the aperture of the optical telescope, the processing difficulty, cost and weight of the optical lens are greatly increased, which makes it limited to obtain increased spatial resolution by increasing the aperture.

[0003] Super-resolution technology can break through the diffraction limit of traditional imaging equipment through some technical means, so as to obtain images with higher spatial resolution. The super-resolution technology in the field of optics has a relatively mature application in microscopic imaging. Structured light illumination super-resolution microscopy and stimulated emission super-resolution microscopy use artificially controlled radiation to illuminate the observed object, and after processing, super-resolution images can be obtained. However, for telescopes, the observed object is far away from the receiving system of the telescope, and it is impossible to use artificially controlled light field for illumination, so it is necessary to develop super-resolution telescope imaging technology based on incoherent light illumination.

[0004] Traditional incoherent optical synthetic aperture imaging is a kind of super-resolution technology, which uses multiple sub-apertures to collect incident light from the target at different angles at the same time. The incident light collected by different apertures is respectively subjected to complex light paths and then interferes and combines on the detector plane, so as to realize super-resolution imaging. In order to obtain a larger aperture, the volume of the imaging system of the traditional incoherent synthetic aperture technology is often very large, and super-resolution and small-volume optical telescopes have always been the goal pursued in the field of remote sensing observation and optical monitoring.

[0005] In order to solve the problem of small volume super-resolution of optical telescope, aperture scanning Fourier ptychographic imaging technology is invented. The principle is to use coherent light to illuminate the target, then move the optical imaging system to capture the high frequency information of the target at each angle, then perform spectrum splicing in the Fourier domain to expand the spectrum range, and finally synthesize a high resolution image. However, this technology has two technical problems. First, it needs to use coherent light to actively illuminate the sample, but the real telescope imaging cannot achieve this requirement. Second, the coherent light needed belongs to a single pure state, which cannot realize multi-band super-resolution imaging. For the actual target, only high-resolution information of a single wavelength can be obtained, and other band information is lost. According to statistical optics, for partially coherent light or incoherent light, it can be described by superposition of multiple completely coherent light states. SUMMARY

[0006] In view of the above, the purpose of the present application is to provide an imaging system and method of synthetic aperture super-resolution telescope with incoherent light illumination to solve the above technical problems.

[0007] In order to achieve the above-mentioned purpose of the application, the imaging system of synthetic aperture super-resolution telescope with incoherent light illumination provided by the embodiment comprises:

[0008] A light source, which is an incoherent light source, is used to illuminate the target;

[0009] A telescope system, which is internally integrated with a multi-channel narrow-band filter for spectral filtering of the light field signal received by the telescope and a pinhole for spatial filtering, generates an imaging signal composed of multiple discrete coherent light illuminated light field signals after filtering;

[0010] An optical camera arranged at the output end of the telescope system is used to record the imaging signal and form a low-resolution image;

[0011] A positioning system is used to determine the collection position of the telescope system;

[0012] A displacement system is used to load the telescope optical system, the positioning system, the optical camera and the computing system, and is also used to adjust the collection position of the telescope system for the next imaging in an overlapping manner according to the current collection position of the telescope system, so that the telescope system switches the angle to collect the imaging signal of the target;

[0013] A computing system is used to store the low-resolution image, and reconstruct and visualize the high-resolution image based on multiple low-resolution images.

[0014] Preferably, the light source is sunlight, a wide-spectrum LED light source or an ultra-continuous laser.

[0015] Preferably, the telescope system is a refractive telescope, a reflective telescope or a catadioptric telescope system.

[0016] Preferably, the positioning system employs GPS.

[0017] Preferably, for the telescope system, the light field signal of the non-coherent light source illumination is converted into the superposition of multiple discrete coherent light illumination light field signals by multi-channel narrow-band filter and pinhole when imaging:

[0018]

[0019] wherein I i represents the light field signal of the non-coherent light corresponding to the i-th imaging angle of the telescope relative to the target object, I ji represents the light field signal of the coherent light illumination corresponding to the j-th channel of the multi-channel narrow-band filter, and n represents the total number of channels of the multi-channel narrow-band filter.

[0020] Preferably, when the telescope system is collecting observations, the collection position of the telescope system is adjusted by overlapping, so that the aperture trajectory of the telescope system is distributed on a spherical surface centered on the target object, and there is overlap between multiple aperture positions.

[0021] Preferably, the displacement system includes a mechanical guide rail, a vehicle, an airplane, a ship, or a satellite.

[0022] Preferably, in the computing system, the reconstruction of the high-resolution image based on multiple low-resolution images includes:

[0023] Step 1, initialize the image I h as a historical high-resolution image; convert multiple low-resolution images in the spatial domain into multiple spectral images in the frequency domain, wherein the spectral image includes an intensity image and a phase image;

[0024] Step 2, simulate to generate simulated low-resolution images of different spectral channels corresponding to the current collection position

[0025] Step 3, superimpose the simulated low-resolution images of different spectral channels to obtain a simulated superposition image wherein i represents the imaging angle index, j represents the channel index, and n represents the total number of channels;

[0026] Step 4, then use the simulated superposition image to update the intensity value I ji of each spectral channel corresponding to the intensity image, to obtain the updated intensity value of each spectral channel and use I ji ′ to update the low-resolution target value to perform superposition to obtain a real superposition intensity image the real superposition intensity image Ii ′ The high-resolution spectrum corresponding to the current acquisition position of the phase map is converted into a high-resolution map in the spatial domain, and the high-resolution map corresponding to the current acquisition position is updated into the historical high-resolution map;

[0027] Step 5, using I ji ′ The real superposition intensity map I is obtained by superposition The real superposition intensity map I is obtained by superposition i ′ The high-resolution spectrum corresponding to the current acquisition position of the phase map is converted into a high-resolution map in the spatial domain, and the high-resolution map corresponding to the current acquisition position is updated into the historical high-resolution map;

[0028] The current acquisition position of the telescope system is switched, and step 2 is executed until the historical high-resolution map obtained when convergence is achieved is taken as the final reconstructed high-resolution map.

[0029] To achieve the above-mentioned purposes, the application further provides an imaging method of a synthetic aperture super-resolution telescope under non-coherent light illumination, wherein the method adopts the imaging system and comprises the following steps:

[0030] Step 1', determining the distance and angle corresponding relationship of the telescope relative to the target object, and adjusting the angle of the telescope system to face the target object;

[0031] Step 2', adjusting the position of the telescope to (x1, y1, z1), and recording the low-resolution map I i through the optical camera after filtering by the multi-channel narrow-band filter and the pinhole, wherein the position information (x1, y1, z1) is determined and recorded by the positioning system;

[0032] Step 3', switching the position of the telescope to (x n ,y n ,z n ), and recording the low-resolution map I n through the optical camera after filtering by the multi-channel narrow-band filter and the pinhole, wherein the position information (x n ,y n ,z n ) is determined and recorded by the positioning system;

[0033] Step 4', repeating step 3' until a plurality of low-resolution maps in the spatial domain are obtained;

[0034] Step 5', reconstructing the high-resolution map based on the plurality of low-resolution maps to obtain a high-resolution map in the spatial domain.

[0035] Compared with the prior art, the application has at least the following beneficial effects:

[0036] The application first proposes a multi-color channel multiplexing synthetic aperture super-resolution imaging based on coherent state multiplexing in incoherent light illumination, which avoids the traditional coherent synthetic aperture imaging that can only obtain high-resolution information of a single wavelength. In addition, coherent state multiplexing avoids the loss of optical energy caused by single-channel narrowband filtering, thereby improving the photon utilization rate and signal-to-noise ratio of super-resolution imaging. BRIEF DESCRIPTION OF DRAWINGS

[0037] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or prior art description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0038] Figure 1 Fig. 1 is a structural schematic diagram of an imaging system of a synthetic aperture super-resolution telescope of incoherent light illumination proposed in the embodiments of the present application;

[0039] Figure 2 Fig. 2 is a position distribution side view of a telescope system proposed in the embodiments of the present application;

[0040] Figure 3 Fig. 3 is a position distribution top view of a telescope system proposed in the embodiments of the present application;

[0041] Figure 4 Fig. 4 is a flowchart of a super-resolution image reconstruction method proposed in the embodiments of the present application;

[0042] Figure 5 Fig. 5 is a flowchart of an imaging method proposed in the embodiments of the present application;

[0043] Figure 6 Fig. 6 is a schematic diagram of a super-resolution telescope result obtained by simulation of the coherent state multiplexing technology proposed in the embodiments of the present application;

[0044] Figure 7 Fig. 7 is a reconstructed image corresponding to different bandwidth filters obtained by simulation of the coherent state multiplexing technology proposed in the embodiments of the present application;

[0045] Figure 8 Fig. 8 is a gray scale curve diagram at the red dotted line in the reconstructed image corresponding to different bandwidth filters and a resolution change curve diagram with bandwidth in the embodiments of the present application. DETAILED DESCRIPTION

[0046] In order to make the objects, technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and do not limit the protection scope of the present application.

[0047] As shown in the embodiment, the imaging system of the synthetic aperture super-resolution telescope with incoherent light illumination provided by the embodiment comprises a light source 200, a target object 201, a telescope system 202, a multi-channel narrow-band filter 203, an aperture 204, an optical camera 205, a computing system 206, a positioning system 207, and a displacement system 208. Figure 1

[0048] The light source 200 is an incoherent light source for illuminating the target object 201, which can be sunlight, or a wide-spectrum LED light source or super-continuous laser.

[0049] The telescope system 202 is directed to the target object 201 illuminated by the light source and collects imaging signals. The telescope system 202 can be a refractive telescope, or a reflective telescope or catadioptric telescope system, including but not limited to a Newtonian telescope, a Galilean telescope, a Cassegrain telescope, a Schmidt telescope, a Maksutov telescope.

[0050] The multi-channel narrow-band filter 203 and the aperture 204 are placed in the middle of the telescope optical system 202, for spectral filtering and spatial filtering of the light field signals received by the telescope, and the filtered imaging signals are composed of multiple discrete coherent light illumination light field signals:

[0051]

[0052] wherein I i represents the light field signal of the incoherent light corresponding to the i-th imaging angle of the telescope relative to the target object, I ji represents the light field signal of the coherent light illumination corresponding to the j-th channel of the multi-channel narrow-band filter, and n represents the total number of channels of the multi-channel narrow-band filter.

[0053] The optical camera 205 is arranged at the output end of the telescope system, for recording the imaging signals and forming a low-resolution image in the spatial domain. The positioning system 207 is used to determine the collection position of the telescope system, which can be a global positioning system (GPS), and specifically records and feeds back the spatial information of the telescope system 202, which is used to control the displacement system 208 to move to the next step.

[0054] ​The displacement system 208 is used for loading the telescope optical system 202, the positioning system 207, the optical camera 205 and the computing system 206, which can be a mechanical guide rail, or a vehicle, an airplane, a ship, a satellite, etc. The displacement system 208 is also used for adjusting the collection position of the telescope system 202 in the next imaging in an overlapping manner according to the current collection position of the telescope system 202, so that the telescope system 202 switches the angle to collect the imaging signal of the target object, that is, to collect the coherent imaging signal of multiple angles.

[0055] The computing system 206 is used for storing the low-resolution images and reconstructing and visualizing the high-resolution image based on multiple low-resolution images, that is, reconstructing the multi-channel super-resolution image through the coherent state multiplexing algorithm.

[0056] In a specific application, as shown in Figure 2 and Figure 3 , the incoherent illumination light is irradiated to the target object 201 at a certain angle, and D is the distance from the telescope system 202 to the target object 201. The aperture A and the distance D determine the numerical aperture NA of the telescope optical system 202:

[0057] NA = sin (A / 2D)

[0058] The telescope system 202 with an aperture A is moved from position 1 to position 2, and the target object 201 is photographed respectively to obtain the low-resolution intensity images of different angles, which correspond to the spectral information of different positions in the spectrum of the target object, as shown in Figure 3 The circle part is the spectrum corresponding to the low-resolution image of each position, and the radius is NA. The essence of super-resolution imaging recovery corresponds to the expansion of the spectrum collection range of the target object, that is, the spectra corresponding to different low-resolution images are spliced in the spectral region. In order to realize iterative convergence in the reconstruction process, a certain overlap rate needs to be met between the adjacent collected spectra.

[0059] In the computing system 206, the reconstruction of the high-resolution image based on multiple low-resolution images is performed, as shown in Figure 4 The reconstruction process of the high-resolution image with phase is given, including the following steps:

[0060] Step 1, initialize the image I h as the historical high-resolution image; convert the multiple low-resolution images in the spatial domain into multiple spectral images in the frequency domain, wherein the spectral image includes an intensity image and a phase image;

[0061] Step 2, simulate to generate a simulated low-resolution image of different spectral channels corresponding to the current collection position

[0062] Step 3, superimpose the simulated low-resolution images of different spectral channels to obtain a simulated superimposed image where i denotes the imaging angle index, j denotes the channel index, and n denotes the total number of channels;

[0063] Step 4, then use the simulation overlay The intensity value I of each spectral channel is updated for the corresponding intensity map ji to obtain the updated intensity value of each spectral channel And use I ji ′ Update the low-resolution target value Overlay to obtain the real overlay intensity map I The real overlay intensity map I i ′ The high-resolution spectrum map in the frequency domain corresponding to the current acquisition position is composed of the phase map, and then converted into a high-resolution map in the spatial domain, and the high-resolution map corresponding to the current acquisition position is updated into the historical high-resolution map.

[0064] Step 5, use I ji ′ Overlay to obtain the real overlay intensity map I The real overlay intensity map I i ′ The high-resolution spectrum map in the frequency domain corresponding to the current acquisition position is composed of the phase map, and then converted into a high-resolution map in the spatial domain, and the high-resolution map corresponding to the current acquisition position is updated into the historical high-resolution map.

[0065] Switch the current acquisition position of the telescope system, jump to execute step 2, until the historical high-resolution map obtained when converging is used as the final reconstructed high-resolution map.

[0066] As shown in Figure 5 , the embodiment also provides an imaging method of a synthetic aperture super-resolution telescope with incoherent light illumination, which adopts the imaging system described above, and includes the following steps:

[0067] Step 1', determine the distance and angle corresponding relationship of the telescope relative to the target object, and adjust the angle of the telescope system to face the target object;

[0068] Step 2', adjust the position of the telescope to (x1, y1, z1), and record the low-resolution map I i filtered by the multi-channel narrow-band filter and the pinhole through the optical camera, wherein the position information (x1, y1, z1) is determined and recorded through the positioning system;

[0069] Step 3', switch the position of the telescope to (x n , y n , z n), by optical camera recording low resolution images filtered by multi-channel narrow band filters and pinhole n where position information (x n ,y n ,z n ) is determined and recorded by a positioning system;

[0070] Step 4', repeat step 3' until a plurality of low resolution images in spatial domain are obtained;

[0071] Step 5', reconstruct high resolution image based on the plurality of low resolution images to obtain high resolution image in spatial domain, the specific reconstruction process adopts steps 1-5.

[0072] Figure 6 is a super-resolution telescope result schematic diagram simulated by the coherent state multiplexing technology proposed in the embodiments of the present application, specifically, a true value image is used to generate a series of low resolution images by algorithm to simulate images taken by telescopes at different angles, and then the low resolution images are restored to high resolution images by algorithm, analysis of the image shows that the proposed phase recovery algorithm based on coherent state can decompose non-coherent mixed state into multiple coherent states, and restore high resolution image through iteration, and the decomposed low resolution images and high resolution images of each waveband are as follows Figure 6 .

[0073] Figure 7 is a reconstructed image corresponding to different bandwidth filters simulated by the coherent state multiplexing technology proposed in the embodiments of the present application, analysis of the image shows that as the bandwidth of the filter increases, the contrast of the reconstructed image decreases. When the bandwidth of the filter is greater than 100 nm, the reconstructed image appears a large degree of blur, and the detailed information of the detection target cannot be obtained.

[0074] Figure 8 is a gray scale curve graph at the red dashed line and a resolution change curve graph of the reconstructed image corresponding to different bandwidth filters of Figure 7 in the embodiments of the present application, analysis of the image shows that as the spectral bandwidth increases, the resolution value constantly rises, and the resolution capability constantly decreases.

[0075] The above specific embodiments have described the technical solutions and beneficial effects of the present application in detail, it should be understood that the above description is only the most preferred embodiment of the present application, and is not used to limit the present application, any modification, supplement and equivalent replacement, etc. made within the principle range of the present application shall be included in the protection scope of the present application.

Claims

1. An imaging system of a synthetic aperture super-resolution telescope with non-coherent illumination, characterized in that, The method comprises the following steps: a light source, which is a non-coherent light source, is used to illuminate a target object; a telescope system, which is internally integrated with a multi-channel narrow-band filter and a pinhole for spatial filtering of a light field signal received by the telescope, and the filtered light field signal is composed of multiple discrete coherent light illumination imaging signals; an optical camera is arranged at the output end of the telescope system, and is used to record the imaging signals and form a low-resolution image; a positioning system is used to determine the collection position of the telescope system; a displacement system is used to load the telescope optical system, the positioning system, the optical camera and the computing system, and is also used to adjust the collection position of the telescope system in the next imaging in an overlapping manner according to the current collection position of the telescope system, so that the telescope system switches the angle to collect the imaging signal of the target object; a computing system is used to store the low-resolution image, and reconstruct and visualize a high-resolution image based on multiple low-resolution images.

2. The imaging system of a synthetic aperture super resolution telescope with incoherent illumination of claim 1, wherein, The light source is sunlight, a wide-spectrum LED light source or an ultra-continuous laser.

3. The imaging system of a synthetic aperture super resolution telescope with incoherent illumination of claim 1, wherein, The telescope system is a refractive telescope, a reflective telescope or a catadioptric telescope system.

4. The imaging system of a synthetic aperture super resolution telescope with incoherent illumination of claim 1, wherein, The positioning system uses GPS.

5. The imaging system of a synthetic aperture super resolution telescope with incoherent illumination of claim 1, wherein, When the telescope system is imaging, the multi-channel narrow-band filter and the pinhole are used to convert the light field signal illuminated by the non-coherent light source into the superposition of multiple discrete coherent light illumination light field signals: wherein I i represents the light field signal of the incoherent light corresponding to the i-th imaging angle of the telescope relative to the target object, I ji represents the light field signal of the coherent light illumination corresponding to the j-th channel of the multi-channel narrow-band filter, and n represents the total number of channels of the multi-channel narrow-band filter.

6. The imaging system of a synthetic aperture super resolution telescope with incoherent illumination of claim 1, wherein, When the telescope system is observing and collecting, the collection position of the telescope system is adjusted in an overlapping manner, so that the aperture trajectory of the telescope system is distributed on a spherical surface with the target object as the center, and there is an overlap between multiple aperture positions.

7. The imaging system of a synthetic aperture super resolution telescope with incoherent illumination of claim 1, wherein, The displacement system includes a mechanical guide rail, a vehicle, an airplane, a ship or a satellite.

8. The imaging system of a synthetic aperture super resolution telescope with incoherent illumination of claim 1, wherein, In the computing system, the reconstruction of the high-resolution image based on multiple low-resolution images comprises: Step 1, initialize image I h As a historical high-resolution image; convert a plurality of low-resolution images in a spatial domain to a plurality of spectral images in a frequency domain, wherein the spectral images include intensity images and phase images; Step 2, simulation generates simulated low resolution images for different spectral channels corresponding to the current acquisition location Step 3, simulated low resolution image of superimposed different spectral channels Obtaining a simulated superimposed image where i denotes an imaging angle index, j denotes a channel index, and n denotes a total number of channels. Step 4, next use the simulation overlay map The intensity value I of each spectral channel is updated on the corresponding intensity map ji , to obtain the updated intensity value of each spectral channel And use I ji ′ Update the low-resolution target value Overlay to obtain the real overlay intensity map Convert the real overlay intensity map I i ′ The high-resolution spectrum map corresponding to the current acquisition position in the frequency domain is composed of the phase map, and is converted into a high-resolution map in the spatial domain. The high-resolution map corresponding to the current acquisition position is updated into the historical high-resolution map. Step 5, using I ji ′ Performing superposition to obtain a real superposition intensity map The real superposition intensity map I i ′ A high-resolution spectrum map in the frequency domain corresponding to the current acquisition position is composed with the phase map, and is converted into a high-resolution map in the spatial domain. The high-resolution map corresponding to the current acquisition position is updated into the historical high-resolution map. switching the current collection position of the telescope system and jumping to step 2 until the historical high-resolution image obtained when convergence is achieved is used as the final reconstructed high-resolution image.

9. An imaging method of a synthetic aperture super resolution telescope with incoherent illumination, characterized in that, The method uses the imaging system of any one of claims 1-8, and comprises the following steps: Step 1', determining the distance and angle correspondence of the telescope relative to the target object, adjusting the angle of the telescope system to face the target object; Step 2', adjusting the position of the telescope to (xl,yl,zi), recording a low resolution image I through the optical camera filtered by the multi-channel narrow band filter and the pinhole i where the position information (xl,yl,zi) is determined and recorded by the positioning system; Step 3', switching the position of the telescope to (x n ,y n ,z n ), recording the low-resolution image I n filtered through the multi-channel narrow-band filter and pinhole by the optical camera, where the position information (x n ,y n ,z n ) is determined and recorded by the positioning system; Step 4', repeating step 3' until multiple low-resolution images in the spatial domain are obtained; Step 5', reconstructing a high-resolution image based on multiple low-resolution images to obtain a high-resolution image in the spatial domain.

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