Encoder-based telescope electronic image stabilization method

Abstract

The present application relates to the technical field of image processing, and specifically provides a kind of encoder-based telescope electronic image stabilization method, including collecting target image, target image and corresponding image information are stored to memory according to acquisition sequence, obtain set, from the current time forward to obtain the first target image for image stabilization processing, obtain the encoder value corresponding to frame target image, utilize the encoder value obtained to fit the final estimation guide track of target, according to final estimation guide track, calculate the guide error of target image, according to guide error, calculate the jitter offset corresponding to target image, according to jitter offset, crop target image, and the cropped target image is output to display area.The present application method has obvious effect, does not depend on known guide track, optical and mechanical design, also does not depend on whether there is obvious feature target in target image, and allows adjusting frame frequency and exposure time according to need in observation process, with universal applicability.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of image processing, and specifically provides a telescope electronic image stabilization method based on an encoder. BACKGROUND

[0002] A ground-based photoelectric telescope has multiple guiding modes, including theoretical trajectory guiding, external guiding, and off-target quantity closed-loop guiding. Among them, theoretical trajectory guiding is one of the commonly used modes. Star observation, satellite observation, and space station observation are all based on theoretical orbit models to calculate the observation trajectory. Fixed-point guiding and constant-speed guiding are commonly used for ground and sea surface searches and island observations. In theoretical trajectory guiding, the guiding trajectory has the characteristics of smoothness and accuracy, and usually does not cause image jitter problems. However, when observing, it is difficult to avoid image jitter caused by the interference of strong winds on the telescope. In the external guiding process, due to factors such as the inaccuracy of the guiding trajectory of the guiding source device and the low guiding frequency, the local telescope may experience image jitter. When off-target quantity closed-loop guiding is used, if a large field of view optical system is used for closed-loop guiding and a small field of view optical system is used for imaging, the poor closed-loop tracking accuracy of the large field of view optical system may cause large amplitude jitter in the imaging of the small field of view optical system. Image jitter not only affects the user experience of experimenters, but also has a negative impact on target search, capture, and extraction. Therefore, it is of great significance to study electronic image stabilization methods. Electronic image stabilization, also known as electronic anti-shake (Electronic Image Stabilization, EIS), is a technology that uses image processing algorithms to eliminate video jitter. It is mainly applied to dynamic shooting scenes. Traditional image processing-based stabilization methods include block matching, gray projection, and feature point matching.

[0003] Chinese patent publication number CN117687346A, published on March 12, 2024, and titled "Space image stabilization control system and control method for shipborne photoelectric theodolite" proposes a space image stabilization control system for a shipborne photoelectric theodolite. The system includes a main control module, an inertial navigation module, a servo control module, an encoder module, an image enhancement module, and a control console. It is a multi-system joint control stabilization scheme. However, in a ground-based photoelectric telescope, some devices lack one or more of the above modules. It is not practical to modify a photoelectric telescope that has already been installed and deployed due to high costs.

[0004] Chinese patent publication number CN118334063A, published on July 12, 2024, entitled "An Image Stabilization Method for Ground-Based Telescopes Based on Kernel Correlation Filtering," describes an invention patent application. This method uses kernel correlation filtering to extract target feature regions and calculates jitter compensation by measuring the centroid offset of the target feature regions between adjacent frames, thus achieving electronic image stabilization. However, this method has a problem: not all targets can be effectively extracted using kernel correlation filtering, especially for faint targets or images with strong background noise interference. Kernel correlation filtering is prone to incorrect target extraction, leading to image stabilization failure. Furthermore, when a telescope observes the ground, sea, or islands at a certain rotation speed, the background itself is in motion, making image stabilization methods based on target feature extraction even less suitable.

[0005] Chinese patent publication number CN120495324A, published on August 15, 2025, entitled "Electronic Image Stabilization Method and System for Telescopes Based on Theoretical Guiding Trajectory," proposes an electronic image stabilization method and system based on a theoretical guiding trajectory. This patent achieves good electronic image stabilization when the guiding trajectory is known. However, not all guidance trajectories are known, and even if the target guiding trajectory is known, low trajectory accuracy can still cause significant jitter. Summary of the Invention

[0006] To address the aforementioned problems, this invention provides an encoder-based electronic image stabilization method for telescopes. By utilizing the telescope's historical encoder pointing to fit a smoother final estimated guide trajectory, and then calculating image jitter compensation and cropping through optical system parameters, the electronic image stabilization function is achieved, improving the image stabilization effect. Moreover, this method does not rely on target extraction or known guide trajectories or other information, and has universal applicability.

[0007] The present invention provides an encoder-based telescope electronic image stabilization method, comprising:

[0008] S1: Acquire target image , target image The corresponding image information is stored in the order of acquisition to obtain a set. ;

[0009] Each time a new frame of the target image is acquired, it and its corresponding image information are stored as an element in a set. The first digit, with a sequence number of 1, is the set. The sequence number of each existing element in the sequence is incremented by 1.

[0010] S2: Get the set The Middle Frame target image Start image stabilization. a sequence number of target images on which a steady image processing is performed:

[0011] obtaining an exposure center time and an encoder value corresponding to the target image of the frame, fitting a preliminary estimated guide trajectory of the target using the obtained exposure center time and encoder value;

[0012] calculating a weight of the encoder value corresponding to the target image of the frame according to the preliminary estimated guide trajectory;

[0013] obtaining a final estimated guide trajectory according to the weight;

[0014] calculating a guide error of the target image according to the final estimated guide trajectory;

[0015] calculating a jitter offset corresponding to the target image according to the guide error;

[0016] clipping the target image according to the jitter offset;

[0017] S3: outputting the clipped target image to a display area.

[0018] Preferably, the image information includes the exposure center time and the encoder value.

[0019] Preferably, the expression of the preliminary estimated guide trajectory is:

[0020] ;

[0021] wherein, , and respectively represent azimuth preliminary estimated guide trajectory coefficients, , and respectively represent pitch preliminary estimated guide trajectory coefficients, represent azimuth, and represent pitch.

[0022] Preferably, the weight of the encoder value corresponding to the target image of the frame and is calculated as:

[0023] ,

[0024] ,

[0025] ,

[0026] wherein, represent the encoder values participating in the calculation of the final estimated trajectory and the weight of represents a weight calculation parameter, and all represent errors.

[0027] Preferably, the expression of the final estimated guide track is:

[0028] ,

[0029] ,

[0030] wherein, represents an arctangent function.

[0031] Preferably, the calculation method of the guide error is:

[0032] ;

[0033] ;

[0034] wherein, represents an azimuth value of the guide error, represents a pitch value of the guide error, represents an encoder value of the target image, represents a final estimated target pointing corresponding to the exposure center moment of the target image on the final estimated guide track.

[0035] Preferably, the calculation method of the jitter offset is:

[0036] :

[0037] ;

[0038] ;

[0039] wherein, represents a horizontal jitter offset, represents a vertical jitter offset, represents an encoder pitch value, represents an angular resolution of the target image in the horizontal direction, represents an angular resolution of the target image in the vertical direction.

[0040] Preferably, the cropping method of the target image is: calculating a cropping region according to the jitter offset, and cropping the target image according to the cropping region; the calculation method of the cropping region is:

[0041] ;

[0042] wherein, represents the coordinate corresponding to the upper left pixel of the target image, , , represents the horizontal clipping ratio, represents the vertical clipping ratio, represents the width of the target image, represents the height of the target image.

[0043] Preferably, the coordinate corresponding to the upper left pixel of the target image is calculated by the following method:

[0044] ;

[0045] ;

[0046] wherein, , .

[0047] Preferably, the coordinate corresponding to the upper left pixel of the target image has a value range satisfying , .

[0048] Compared with the prior art, the present application can achieve the following beneficial effects:

[0049] The present application is directed to the sequence characteristics of the horizon coordinates in the process of telescope observation, and utilizes the historical encoder of the telescope to point to a more smooth final estimated guide trajectory. Then, the image jitter compensation and clipping are calculated through the optical system parameters, so as to realize the electronic image stabilization function. The image stabilization effect of the method is greatly improved compared with the original image sequence. The method does not depend on the target extraction and other information such as known guide trajectory, and does not depend on the complex optical and mechanical design. In addition, the method allows to adjust the frame frequency and exposure time as needed during the observation process, and has universal applicability. BRIEF DESCRIPTION OF DRAWINGS

[0050] Figure 1 is a flow chart of the encoder-based telescope electronic image stabilization method according to an embodiment of the present application;

[0051] Figure 2 is a layout diagram of the encoder-based telescope electronic image stabilization system according to an embodiment of the present application;

[0052] Figure 3 is a clipping schematic diagram according to an embodiment of the present application;

[0053] Figure 4 is a theoretical trajectory guide telescope image stabilization effect diagram according to an embodiment of the present application;

[0054] Figure 5 is an encoder-based telescope electronic image stabilization effect diagram provided according to an embodiment of the present application. DETAILED DESCRIPTION

[0055] In order to make the purposes, 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 specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application, and do not constitute a limitation on the present application. In different embodiments, similar elements are associated with similar element labels. In the following embodiments, many details are described in order to make the present application better understood. However, those skilled in the art can easily recognize that some features can be omitted in different cases, or can be replaced by other elements, materials or methods. In some cases, some operations related to the present application are not shown or described in the specification in order to avoid the core part of the present application being overwhelmed by too much description, and it is not necessary for those skilled in the art to describe these related operations in detail according to the description in the specification and general technical knowledge in the art.

[0056] It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other to form various embodiments without conflict. Meanwhile, the steps or actions in the method description can also be sequentially adjusted or adjusted in a manner that is obvious to those skilled in the art. Therefore, the various sequences in the specification and drawings are only for the purpose of clearly describing a certain embodiment, and do not mean that the sequence is necessary, unless otherwise stated that a certain sequence must be followed.

[0057] In the description of the present application, it should be understood that the terms "center", "longitudinal", "transverse", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise" and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, and are only for the purpose of facilitating the description of the present application and simplifying the description, and do not indicate or imply that the device or element indicated must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation on the present application. In addition, the terms "first", "second" and the like are only for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Therefore, the features limited by "first", "second" and the like can explicitly or implicitly include one or more features. In the description of the present application, unless otherwise stated, the meaning of "multiple" is two or more.

[0058] In the description of the present application, it should be noted that unless otherwise explicitly specified and limited, the terms "mounting", "connection", "connecting" should be understood in a broad sense, for example, can be fixed connection, can also be detachable connection, or integrally connected; can be mechanical connection, can also be electrical connection; can be directly connected, can also be indirectly connected through an intermediate medium, can be internal communication of two elements. For those skilled in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0059] The present application will be described in detail below with reference to the accompanying drawings and in conjunction with the embodiments.

[0060] As Figure 1 shown, the present application provides an encoder-based telescope electronic image stabilization method, which is specifically as follows:

[0061] S1: collecting target images , storing the target images and corresponding image information according to the collection sequence to obtain a set ; each time a target image is newly collected, it and the corresponding image information are stored as an element at the head of the set , with a sequence number of 1, and the sequence numbers of the original elements in the set are all increased by 1. During the observation of the target by the telescope, the target images can be collected by the camera. During the collection of the target images, the camera can complete tasks such as receiving the exposure time set by the image system, starting exposure after receiving the trigger signal sent by the digital communication system, ending exposure after the exposure time, and sending the image to the image system. The target images collected by the camera are represented by . Since there are real-time encoder values (azimuth encoder value and elevation encoder value) during the rotation of the telescope, each target image corresponds to an encoder value and a center exposure time. The encoder values (azimuth encoder value and elevation encoder value) and the corresponding center exposure time are collectively referred to as image information, and the image information and the corresponding target image are combined as an element for storage to obtain a set , , wherein represents the sequence number, represents the center exposure time, represents the azimuth encoder value and the elevation encoder value. The elements in the set are stored in the order of the collection of the target images , so as to be used for processing during the stabilization process.

[0062] It should be noted that each newly collected target image at the current time will correspond to the obtained element stored in the set The first sequence number is 1, and the original elements in the set The sequence number of the original element is increased by 1.

[0063] S2: Obtain the set The first frame target image Start the image stabilization process, The sequence number of the target image for which the image stabilization process is performed: obtain the exposure center time and the encoder value corresponding to the frame target image from the current time forward, Fit the preliminary estimated guide trajectory of the target using the obtained exposure center time and encoder value; calculate the weight of the encoder value corresponding to the frame target image based on the preliminary estimated guide trajectory; obtain the final estimated guide trajectory based on the weight; calculate the guide error of the target image based on the final estimated guide trajectory; calculate the jitter offset corresponding to the target image based on the guide error; and crop the target image based on the jitter offset.

[0064] The image stabilization process can start from a target image according to actual user needs, which is referred to as the frame in the embodiment of the present application, and is represented as , The sequence number is assumed to start the image stabilization process from the target image , and in the image stabilization process, the frame target image is processed every time a new frame of target image is obtained. The image stabilization process is as follows:

[0065] Since the motion trajectory of the target is unknown, the target motion trajectory needs to be fitted first. The encoder values within a time period of are taken from the current time forward to obtain the encoder values corresponding to the frame target image, including the azimuth encoder value and the pitch encoder value, and the estimated trajectory of the target is fitted using the obtained encoder values. It should be noted that the frame target image needs to satisfy , that is, the multiple encoder values obtained from the current time forward need to pass through the time at which the target image is stabilized. After fitting, the preliminary estimated guide trajectory of the target is obtained:

[0066] ;

[0067] Wherein, , And represent the azimuth preliminary estimated guide trajectory coefficients, , and respectively represent the pitch preliminary estimation guide trajectory coefficient, represents the azimuth, represents the pitch.

[0068] Solve the azimuth preliminary estimation guide trajectory coefficient and the pitch preliminary estimation guide trajectory coefficient to obtain the final estimation trajectory. The embodiment of the present application adopts the least square method to solve the azimuth preliminary estimation guide trajectory coefficient and the pitch preliminary estimation guide trajectory coefficient.

[0069] Since the telescope is dithered and there is no orbit true value, there is no target to help the image stabilization, so the accuracy requirement for the orbit prediction is higher, and therefore high-precision trajectory fitting is required. The preliminary estimation guide trajectory is used to obtain the weight of the encoder value in the time period . The and in each are respectively calculated as the weight in the preliminary estimation guide trajectory, and the specific solving method is as follows:

[0070] The error absolute value and of each encoder value is calculated by using the preliminary estimation guide trajectory:

[0071] ,

[0072] ,

[0073] wherein, and respectively represent the preliminary azimuth estimation value and the preliminary pitch estimation value obtained by the preliminary estimation guide trajectory at the time .

[0074] Then, the errors and are calculated:

[0075] ,

[0076] wherein, represents that the error value is used for the weight calculation, represents the minimum error limit value, represents the maximum error limit value, represents the error or , and are empirical values, which are used to prevent the abnormal error from affecting the accuracy of the next trajectory fitting.

[0077] Computing weights and :

[0078] ,

[0079] ,

[0080] ,

[0081] wherein, denotes the weight of and participating in the final estimated trajectory calculation, denotes the weight calculation parameter, which is an empirical value. In the embodiments of the present application, , , .

[0082] According to the above-mentioned weights, the final estimated guide trajectory with higher accuracy is recalculated:

[0083] For each group of and , the three-dimensional Cartesian coordinate vector is calculated:

[0084] ,

[0085] Let , , , wherein, , and all represent the calculation process matrix, denotes the normalized time of . By solving using the weighted least squares solution, can be expressed as:

[0086] ,

[0087] wherein, and all represent the calculation process matrix.

[0088] The angle between the large arc of the spherical segment is represented as , then:

[0089] ,

[0090] wherein, denotes the three components in the three-dimensional Cartesian coordinate system, denotes the calculation process data.

[0091] Finally, a more accurate final estimated guide trajectory is obtained:

[0092] ,

[0093] ,

[0094] in, This represents the arctangent function.

[0095] There is often an error between the actual movement of the target and the final estimated guided trajectory. In this embodiment of the invention, this is referred to as the guidance error, which is calculated as follows:

[0096] ;

[0097] ;

[0098] in, This indicates the azimuth value of the guidance error. The pitch value represents the guidance error. This represents the encoder value of the target image. This represents the final estimated target orientation corresponding to the exposure center time of the target image on the final estimated guide trajectory, i.e., the exposure center time of the target image. Substitute the final estimated guide trajectory into the corresponding coordinate values. This is for the final estimation of the target direction. The unit of guidance error is "degree".

[0099] After obtaining the guidance error, the jitter offset of the target image is then calculated based on the telescope optical system parameters. Jitter offset The calculation method is as follows:

[0100] :

[0101] ;

[0102] ;

[0103] Wherein, the image angular resolution is a parameter of the telescope optical system, which is a known quantity, expressed as: , This represents the angular resolution of the target image in the horizontal direction (corresponding to the orientation in the horizon coordinate system). This represents the angular resolution of the target image in the vertical direction (corresponding to the pitch in the horizon coordinate system). and All units are Arcseconds per pixel (AJ / pixel) means that each pixel is represented by an arcsecond. This indicates the horizontal jitter offset. represents a vertical jitter offset, represents an encoder pitch value.

[0104] After the above calculation, the target image is jitter-compensated and cropped, as shown in the following formula (3) : Figure 3 The cropping method is as follows: the cropping area is calculated according to the jitter offset , and the target image is cropped according to the cropping area . The calculation method of the cropping area is as follows:

[0105] The width of the target image collected by the camera is set as , and the height is set as . The cropping area is defined as , wherein represents the coordinates of the upper left pixel of the target image, , , represents a horizontal cropping ratio, represents a vertical cropping ratio, and the value range satisfies , .

[0106] The calculation method of the coordinates of the upper left pixel of the target image is as follows:

[0107] ,

[0108] ,

[0109] wherein , .

[0110] The calculation method of the above coordinates has limited the value of the coordinates , so that the out-of-bound situation of cropping is avoided. The target image is cropped according to the cropping area obtained by calculation, and the cropped target image is obtained.

[0111] S3: output the cropped target image to the display area.

[0112] The cropped target image is output to the display area. After the above image stabilization process is completed for each frame of the collected target image in the order of collection, the target image is output to the display area frame by frame, and continuous and image-stabilized target observation results can be obtained.

[0113] As shown in the following formula (4) : Figure 2As shown, in order to realize the above-mentioned encoder-based telescope electronic image stabilization method, the embodiment of the present application further provides an image stabilization system, comprising: an image system, a digital communication system, a time system terminal, a telescope, the telescope is provided with an azimuth encoder, a pitch encoder and a camera, the azimuth encoder and the pitch encoder provide the azimuth direction and the pitch direction of the telescope. The image system performs the following tasks: setting the exposure time for the camera as needed, receiving the camera image, sending the frame frequency and the exposure time to the digital communication system as needed, receiving the time, the azimuth encoder direction and the pitch encoder direction latched by the digital communication system, and performing electronic image stabilization processing. The camera can perform the following tasks: receiving the exposure time set by the image system, starting exposure after receiving the trigger signal sent by the digital communication system, ending exposure after the exposure time, sending the image to the image system, and the like. The digital communication system performs the following tasks: receiving the frame frequency and the exposure time sent by the image system; sending an external trigger signal such as a rising edge or a falling edge to the camera according to the frame frequency; reading the time information from the time system terminal, the azimuth encoder direction from the azimuth encoder, and the pitch encoder direction from the pitch encoder at the exposure time after triggering the camera exposure; and sending the time information, the azimuth encoder direction and the pitch encoder direction to the image system. The time information in the working process of the image stabilization system is provided by the time system terminal.

[0114] In addition, the start time of each new trigger cycle of the frame frequency , the digital communication system provides an external trigger signal to the camera, and the camera starts exposure, then at , the digital communication system obtains the time, the azimuth encoder direction and the pitch encoder direction from the time system, the azimuth encoder and the pitch encoder, and sends them to the image system, and at , the camera stops exposure after the time forwardly moves for the length of the exposure time, and sends the image to the image system, and the image system starts the electronic image stabilization process.

[0115] In order to verify the effect of the method of the present application, the following experiment is performed:

[0116] The peak signal-to-noise ratio (PSNR) is commonly used as an index to evaluate the effect of image stabilization, and the basic principle is to compare the square mean of the pixel difference between two adjacent images. However, due to the obvious noise of the infrared camera image, it will affect the evaluation of the peak signal-to-noise ratio, so the present application uses the jitter amplitude of the target centroid with obvious characteristics to evaluate the image stabilization effect of the present application. The target centroid is used only for evaluating the image stabilization effect, and the target centroid does not need to be extracted in the actual use.

[0117] In a strong wind weather, a telescope is used for observation experiment, the experiment uses a aperture telescope, and a short-wave infrared camera is configured, the observation field of view of the telescope is​ , the image resolution is , the horizontal and vertical angular resolutions are .

[0118] As shown in Figure 4 , the tracking observation of the International Space Station (ISS) is performed using a theoretical orbit to guide a telescope, a weighted centroid algorithm is used to calculate the pixel centroid of the target, and the difference between the centroids of adjacent frames is used as the evaluation criterion for the image jitter amplitude. The absolute values of the horizontal and vertical direction jitter amplitudes of the target in the image are both more than , wherein the horizontal jitter amplitude RMS is , and the vertical jitter amplitude RMS is .

[0119] As shown in Figure 5 , a comparative experiment is performed using the method of the present application, and the parameter values are , , wherein the horizontal jitter amplitude RMS is , and the vertical jitter amplitude RMS is , and the optimization effect is significant.

[0120] Although the embodiments of the present application have been shown and described above, it should be understood that the above-described embodiments are exemplary and should not be construed as limiting the present application. Those skilled in the art can make changes, modifications, replacements and variations to the above-described embodiments within the scope of the present application.

[0121] The specific embodiments of the present application described above do not constitute a limitation on the scope of protection of the present application. Any various other corresponding changes and modifications made according to the technical concept of the present application should be included in the scope of protection of the claims of the present application.

Claims

1. An encoder-based telescope electronic image stabilization method, characterized in that, The method comprises the following steps: S1: collect target images store the target images and corresponding image information according to the collection sequence to obtain a collection ; Each time a target image is newly captured, it is stored in the set as an element together with corresponding image information The sequence number of the first element in the set is 1 The sequence numbers of the original elements in the set are all incremented by 1 S2: Acquire set In the middle Frame target image Start the image stabilization process, Sequence number indicating the target image on which the image stabilization process is performed: acquire from the current time forward an exposure center time and an encoder value corresponding to the frame target image, fit a preliminary estimate of the target's intended trajectory using the acquired exposure center time and encoder value Based on the preliminary estimate of the trajectory, calculate a weight of an encoder value corresponding to the frame target image; a weight of an encoder value corresponding to the frame target image and the calculation formula is; ， ， ， wherein, represents the weight of the and weight of the represents a weight computation parameter, and both represent an error; According to the weight, the final estimated guide track is recalculated: For each set and , calculate its three-dimensional Cartesian coordinate vector : ， Let , , where , and are the process matrices, is the normalized time of . The solution is obtained by weighted least squares and can be expressed as: ， wherein and both represent a calculation process matrix; The segment spherical large arc angle is expressed as Then, there are: ， wherein, denotes three components in a three-dimensional Cartesian coordinate system, denotes calculation process data; According to the weight, the final estimated guide track is obtained; the final estimated guide track is obtained: ， ， wherein denotes the arctangent function; According to the final estimated guide track, the guide error of the target image is calculated; According to the guide error, the jitter offset corresponding to the target image is calculated; According to the jitter offset, the target image is cropped; S3: output the cropped target image to the display area.

2. The encoder-based telescope electronic image stabilization method of claim 1, wherein, The image information includes exposure center time and encoder value.

3. The encoder-based telescope electronic image stabilization method of claim 1, wherein, The expression of the preliminary estimated guide track is: ； wherein, , and respectively represent azimuth preliminary estimation guide trajectory coefficients, , and respectively represent pitch preliminary estimation guide trajectory coefficients, represents azimuth, represents pitch.

4. The encoder-based telescope electronic image stabilization method of claim 1, wherein, The calculation method of the guide error is: ； ； wherein, represents an azimuth value of a guidance error, represents a pitch value of a guidance error, represents an encoder value of a target image, represents a final estimated target pointing corresponding to an exposure center time of a target image on a final estimated guidance trajectory.

5. The encoder-based telescope electronic image stabilization method of claim 1, wherein, The dither offset The calculation method is: ： ； ； wherein, represents a horizontal dither offset, represents a vertical dither offset, represents an encoder pitch value, represents an angular resolution of the target image in horizontal direction, represents an angular resolution of the target image in vertical direction.

6. The encoder-based telescope electronic image stabilization method of claim 1, wherein, The cropping method of the target image is: according to the jitter offset, the cropping area is calculated, and the target image is cropped according to the cropping area; the calculation method of the cropping area is: ； wherein, represents the coordinates of the top-left pixel of the target image, , , represents the horizontal cropping ratio, represents the vertical cropping ratio, represents the width of the target image, represents the height of the target image.

7. The encoder-based telescope electronic image stabilization method of claim 5, wherein, The target image upper left corner pixel corresponding coordinate The calculation method is: ； ； wherein , .

8. The encoder-based telescope electronic image stabilization method of claim 7, wherein, The target image upper left corner pixel corresponding coordinate The value range of the target image upper left corner pixel corresponding coordinate satisfies , .

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