Verification method for non-coaxial errors

Abstract

This invention, entitled "A Method for Verifying Non-Coaxial Errors," belongs to the field of optical imaging and geometric correction technology. The technical problem it aims to solve is the geometric distortion in near-field observation images caused by the misalignment of the axis systems of the turntable and the field-of-view adjustment mechanism in existing imaging devices. The technical solution is as follows: S1, Establish a two-dimensional reference coordinate system in the XOY plane, setting the turntable angle as θ_r and the pointing angle of the field-of-view adjustment mechanism as 2*θ_m; S2, Based on the two-dimensional reference coordinate system established in step S1, establish a geometric model from the input quantities θ_r and 2*θ_m to the output quantity, the true field-of-view angle φ1; S3, Obtain the reference image and the original image under non-coaxial motion; S4, Verify the effect of the correction model image: Apply the accurate geometric model and the linear model with errors established in step S2 to process the original image in S3 to obtain geometrically corrected and uncorrected images.

Description

Technical Field

[0001] This invention belongs to the field of optical imaging and geometric correction technology, and specifically relates to a method for verifying non-coaxial errors. Background Technology

[0002] In various space remote sensing applications, imaging devices (including but not limited to imaging spectrometers, multispectral cameras, and scanning imaging systems) typically require ground-based testing to validate their imaging performance. A common method is to use a turntable to simulate platform attitude changes and combine it with a scanning mirror or other field-of-view adjustment mechanism to achieve dynamic pointing verification or motion compensation function verification of the observed target.

[0003] In ideal modeling, it is usually assumed that the rotation axis of the turntable is strictly coincident with the axis of the field adjustment mechanism inside the imaging device (such as the rotation axis of the field adjustment mechanism), thus simplifying the instantaneous field of view of the field adjustment mechanism into a linear superposition relationship between the turntable angle and the pointing angle of the field adjustment mechanism.

[0004] However, in actual engineering implementation, due to mechanical assembly errors, structural layout limitations, and limited installation and adjustment precision, the aforementioned rotation axes often exhibit unavoidable spatial offsets or non-collinearity. This axis inconsistency has a relatively small impact under long-distance observation conditions (such as on-orbit Earth or lunar observations) and can be approximately ignored; however, under close-range ground-based experimental conditions (target distances are typically several meters to tens of meters), this error will be significantly amplified, leading to geometric distortion in near-field observation images.

[0005] The aforementioned errors not only affect the verification of motion compensation function, but also significantly interfere with other imaging tests involving field of view control (such as geometric calibration, spatial resolution testing, and registration accuracy evaluation). Summary of the Invention

[0006] The purpose of this invention is to provide a method for verifying non-coaxial errors, thereby solving the problem of geometric distortion in near-field observation images caused by the misalignment of the axis systems of the turntable and the field-of-view adjustment mechanism in existing ground imaging performance verification tests. This invention provides the following technical solution: A method for verifying non-coaxial errors includes the following steps: S1. Establish a two-dimensional reference coordinate system: Build a ground verification system. Based on the relative positional relationship between the turntable, the field of view adjustment mechanism, the imaging device, and the observation target, establish a fixed three-dimensional rectangular coordinate system O-XYZ. Equivalently represent the spatial positional relationship between the field of view adjustment mechanism and the turntable to a two-dimensional geometric relationship in the XOY plane. Establish a two-dimensional reference coordinate system in the XOY plane, and set the turntable angle as θ_r and the pointing angle of the field of view adjustment mechanism as 2*θ_m. S2. Precise geometric modeling of the field of view: Based on the two-dimensional reference coordinate system established in step S1, and based on the geometric theorem of triangles and the principle of coordinate projection, establish a geometric model from the input quantities θ_r and 2*θ_m to the output quantity true field of view φ1. S3. Using a ground-based verification system, obtain the baseline image of the observed target and the original image under non-coaxial motion. S4. Verification of the effect of the corrected model image: Using the geometric model established in step S2, the original image in step S3 is processed to obtain the geometrically corrected image. By applying the linear relationship φ2=π-θ_r-2*θ_m, the original image in step S3 is processed to obtain an image without geometric correction; The geometrically corrected image, the uncorrected image, and the reference image obtained in step S3 are compared to verify whether the geometric model established in step S2 is correct.

[0007] First preferred option: In step S1, a ground verification system is built, which includes a turntable, an imaging device, and a field-of-view adjustment mechanism. Based on the ground verification system, the relative positions of the turntable, the field-of-view adjustment mechanism, the imaging device, and the observation target are as follows: the field-of-view adjustment mechanism is located in the front optical path of the imaging device, the imaging device is mounted on the turntable and rotates with the turntable, the axis of the field-of-view adjustment mechanism and the axis of the turntable are parallel to each other and have a certain spatial offset, and the observation target is located in front of the field-of-view adjustment mechanism.

[0008] Second preferred option: In step S1, a fixed three-dimensional rectangular coordinate system O-XYZ is established: The coordinate system O-XYZ does not change with the rotation of the field of view adjustment mechanism or the turntable, wherein the Z-axis is defined along the axis of the turntable, and its positive direction is from the turntable base to the imaging device base. The Z-axis intersects the upper surface of the turntable at the origin O; The X-axis is located in the plane of the turntable, perpendicular to the Z-axis, and parallel to the plane where the observation target is located. Its positive direction is defined as the direction of rotating 90° counterclockwise from the positive direction of the Z-axis. The Y-axis is determined by the X-axis and Z-axis according to the right-hand rule.

[0009] Third preferred option: In step S1, the spatial positional relationship between the field of view adjustment mechanism and the turntable is equivalent to a two-dimensional geometric relationship in the XOY plane under the following conditions: the axis of the field of view adjustment mechanism and the axis of the turntable have a preset parallel relationship, both axes are parallel to the Z-axis of the coordinate system O-XYZ, and the displacement and attitude deviation of the field of view adjustment mechanism and the turntable in the Z-axis direction are negligible.

[0010] Fourth priority option: In step S1, a two-dimensional reference coordinate system is established in the XOY plane: S11. Take the projection point O_r of the turntable axis in the XOY plane as the origin of the coordinate system O, and O_r is also the center of the turntable; S12. The X-axis and Y-axis directions are defined according to the three-dimensional rectangular coordinate system O-XYZ; S13. The projection point O_m of the field adjustment mechanism axis in the XOY plane moves together with the turntable. O_m is also the center of the field adjustment mechanism. Its trajectory is a circle around the origin O of the coordinate system with a radius of eccentricity r. The eccentricity r is the straight-line distance between the turntable center O_r and the field adjustment mechanism center O_m. S14. Let the extensions of the turntable center O_r and the field of view adjustment mechanism center O_m intersect the observation target at point A, and let the angle between AO_r and the negative X-axis be the turntable angle θ_r; S15. Let point B be the intersection of the field of view of the field adjustment mechanism and the observed target. Point B is the true field of view. The pointing angle 2*θ_m of the field of view adjustment mechanism is the angle between O_mA and O_mB. This angle is an acute angle. S16. Draw BO_m / / B'O through the origin O of the coordinate system, intersecting the observed target at point B'. Point B' is the field of view with geometric distortion, and ∠B'Ox is the field of view angle φ2 without geometric correction.

[0011] Fifth priority option: A geometric model is established from the input quantities θ_r and 2*θ_m to the output quantity, the true field of view angle φ1. The specific derivation includes: S21. Based on the turntable angle θ_r and the target distance H between the origin O of the coordinate system and the observed target, determine the coordinates of point A (x_A, H), where x_A = -H / tanθ_r, and the length of AO is H / sinθ_r; S22. Based on the AO calculated in step S21 and the known eccentricity r, determine the length of AO_m: AO - r; S23. Based on the fact that two lines are parallel, AB / / x-axis, and alternate interior angles are equal, we can obtain ∠BAO = ∠AO - x = θ_r, where -x represents the negative direction of the x-axis; in triangle ABO_m, based on the pointing angle of the field adjustment mechanism 2*θ_m, AO_m, and ∠BAO_m, we can obtain ∠ABO_m = π - 2*θ_m - ∠BAO, and then use the sine theorem to find the distance between AB: AO_m / sin(∠ABO_m) * sin(2*θ_m); S24. Calculate the coordinates (x_B,H) of point B based on the AB distance calculated in step S23, where x_B = x_A + AB; S25. Finally, the true field of view angle φ1 = arctan(H / x_B) is obtained from the coordinates of point B, and the observed target is located in the first quadrant; φ1 = π + arctan(H / x_B), and the observed target is located in the second quadrant.

[0012] Sixth priority option: Step S3, specifically: Using the ground verification system built in step S1, conduct experiments to obtain a baseline image of the observed target and the original image under non-coaxial motion. The experimental process includes: S31. Start the turntable to rotate counterclockwise at the specified speed; S32. Control the field-of-view adjustment mechanism to rotate clockwise at a specified speed; S33. In the above process, the observed target is imaged to obtain the original image under non-coaxial motion; S34. As a reference, with the turntable stationary, control the field of view adjustment mechanism to rotate at a specified speed to obtain the reference image under the same observation target in step S33.

[0013] Seventh priority option: Step S4, in detail: S41. Take the field of view adjustment mechanism pointing angle 2*θ_m and the turntable angle θ_r acquired in each frame as input; S42. Using the geometric model established in step S2, calculate the true field of view angle φ1; S43. Based on the true field of view φ1, arrange each frame of images according to the angle mapping relationship to generate a geometrically corrected image; S44. Using the linear relationship φ2=π-θ_r-2*θ_m, calculate the field of view φ2 without geometric correction; S45. Based on the uncorrected field of view φ2, arrange each frame of images according to the angle mapping relationship to generate an uncorrected image; S46. Compare the geometrically corrected image, the uncorrected image, and the reference image obtained in step S3 to verify whether the geometric model established in step S2 is correct.

[0014] Eighth priority option: Step S46, in detail: If the geometrically corrected image is highly consistent with the reference image in terms of geometric features, and the uncorrected image deviates from the reference image in terms of geometric features, then it proves that the non-coaxial error of the image has been corrected after the geometric model in step S2.

[0015] The present invention has at least the following beneficial effects: This invention innovatively proposes a method for verifying non-coaxial errors. By modeling a two-dimensional geometric model, the non-coaxial error is corrected, and the effectiveness of the geometric correction model is proved by imaging results. Thus, a systematic method for correction and verification based on non-coaxial errors is proposed, which solves the problem of geometric distortion in near-field observation images caused by the misalignment of the axis systems of the turntable and the field of view adjustment mechanism in ground imaging performance verification tests.

[0016] A correction model based on the non-coaxial error of the imaging device was established, realizing the conversion from the input angle of the turntable and the field of view adjustment mechanism to the actual field of view output angle.

[0017] The image correction effect was verified based on the above correction model, proving the effectiveness of the correction model.

[0018] This invention is not limited to motion compensation, imaging devices, etc. It can be used to correct geometric errors in images whenever there is a misalignment of axes. Attached Figure Description

[0019] Figure 1 This is a flowchart of the overall verification method of the present invention.

[0020] Figure 2 This is a schematic diagram of the ground verification system. Figure 2 The solid black arrows in the diagram represent the rotation direction of the field-of-view adjustment mechanism; the hollow arrows represent the rotation direction of the turntable.

[0021] Figure 3 This is a two-dimensional coordinate geometric model for non-coaxial error correction, with the observed target located in the first quadrant.

[0022] Figure 4 This is a two-dimensional coordinate geometric model for non-coaxial error correction, with the observed target located in the second quadrant.

[0023] Figure 5 This is a comparison image of the reference image, the geometrically corrected image, and the uncorrected image in an embodiment of the present invention.

[0024] Figure label: 1. Turntable; 11. Upper surface of the turntable; 12. Turntable axis; 2. Imaging device; 3. Field of view adjustment mechanism; 31. Field of view adjustment mechanism axis; 4. Observation target. Detailed Implementation

[0025] The following non-limiting embodiments are intended to enable those skilled in the art to gain a more comprehensive understanding of the present invention, but do not limit the invention in any way. The following content is merely an exemplary description of the scope of protection claimed by the present invention, and those skilled in the art can make various changes and modifications to the present invention based on the disclosed content, and such changes should also fall within the scope of protection claimed by the present invention.

[0026] Example like Figure 1 As shown, this invention proposes a method for verifying non-coaxial errors, comprising the following steps: S1: Establish a two-dimensional reference coordinate system like Figure 2 As shown, a ground verification system is constructed, which includes a turntable 1, an imaging device 2, and a field-of-view adjustment mechanism 3. The relative positional relationship between the turntable 1, the imaging device 2, the field-of-view adjustment mechanism 3, and the observation target 4 is determined. The field-of-view adjustment mechanism 3 is located in the front optical path of the imaging device 2. The imaging device 2 is mounted on the turntable 1 and rotates with the turntable 1. The axis 31 of the field-of-view adjustment mechanism and the axis 12 of the turntable have a certain spatial offset. The observation target 4 is located in front of the field-of-view adjustment mechanism 3.

[0027] Based on the relative positions of the turntable 1, imaging device 2, field-of-view adjustment mechanism 3, and observation target 4, a fixed three-dimensional rectangular coordinate system O-XYZ is first established. This coordinate system O-XYZ does not change with the rotation of the turntable 1 or the field-of-view adjustment mechanism 3. The Z-axis is defined along the turntable axis 12, with its positive direction pointing from the base of the turntable 1 to the base of the imaging device 2. The Z-axis intersects the upper surface 11 of the turntable at the origin O. The X-axis lies within the upper surface 11 of the turntable, perpendicular to the Z-axis, and parallel to the plane containing the observation target 4. Its positive direction is defined as a 90° counterclockwise rotation from the positive direction of the Z-axis. The Y-axis is determined by the X-axis and Z-axis according to the right-hand rule.

[0028] In this invention, the turntable axis 12 and the field of view adjustment mechanism axis 31 have a preset parallel relationship, and both are parallel to the Z-axis of the above coordinate system O-XYZ.

[0029] Under the structural conditions corresponding to the aforementioned ground verification system, the motion of the turntable 1 and the field-of-view adjustment mechanism 3 mainly occurs within the XOY plane, and their displacement and attitude deviation in the Z-axis direction are negligible relative to the working accuracy of the ground verification system. Therefore, the spatial relationship between the turntable 1 and the field-of-view adjustment mechanism 3 can be described as an equivalent two-dimensional geometric relationship within the XOY plane. In the XOY two-dimensional plane, the axis 31 of the field-of-view adjustment mechanism and the axis 12 of the turntable can be equivalent to two point coordinates, and the observed target 4 can be equivalent to a line parallel to the X-axis.

[0030] like Figure 3 , Figure 4As shown, a two-dimensional reference coordinate system is established in the XOY plane, specifically as follows: S11. Take the projection point O_r of the turntable axis 12 in the XOY plane as the origin O of the coordinate system. O_r coincides with O and O_r is also the center of the turntable.

[0031] S12. The X-axis and Y-axis directions are still defined according to the three-dimensional rectangular coordinate system O-XYZ described above.

[0032] S13. The projection point O_m of the field adjustment mechanism axis 31 in the XOY plane moves together with the turntable 1. O_m is also the center of the field adjustment mechanism. Its trajectory is a circle around the origin O with a radius of eccentricity r. The eccentricity r is the straight-line distance between the turntable center O_r and the field adjustment mechanism center O_m.

[0033] S14. Let the extensions of the turntable center O_r and the field of view adjustment mechanism center O_m intersect the observation target 4 at point A, and let the angle between AO_r and the negative X-axis be the turntable angle θ_r.

[0034] S15. Let point B be the intersection of the field of view of the field adjustment mechanism and the observed target 4. Point B is the true field of view. The pointing angle 2*θ_m of the field of view adjustment mechanism is the angle between O_mA and O_mB, which is an acute angle.

[0035] S16. Draw BO_m / / B'O through the origin O of the coordinate system, intersecting the observed target 4 at point B'. Point B' is the field of view with geometric distortion, and ∠B'Ox is the field of view angle φ2 without geometric correction.

[0036] S2: Accurate geometric modeling of the true field of view φ1 Based on the two-dimensional reference coordinate system established in step S1, and using the geometric theorems of triangles and the principle of coordinate projection, a geometric model is established from the input quantity (turntable angle θ_r, field of view adjustment mechanism pointing angle 2*θ_m) to the output quantity (true field of view angle φ1); the specific derivation includes: S21. Based on the turntable angle θ_r and the target distance H (the target distance H is the perpendicular distance between the observed target 4 and the X-axis, i.e., the distance between the origin O of the coordinate system and the observed target 4), determine the coordinates of point A (x_A, H), where x_A = -H / tanθ_r, and the length of AO is H / sinθ_r.

[0037] S22. Based on the AO calculated in step S21 and the known eccentricity r, determine the length of AO_m: AO-r. S23. Based on the fact that two lines are parallel (AB / / x-axis) and alternate interior angles are equal, we can obtain ∠BAO = ∠AO - x = θ_r, where -x represents the negative x-axis direction. In triangle ABO_m, based on the pointing angle of the field adjustment mechanism (2*θ_m), AO_m, and ∠BAO_m, we get ∠ABO_m = π - 2*θ_m - ∠BAO. Then, using the sine theorem, we can find the distance between AB: AO_m / sin(∠ABO_m) * sin(2*θ_m).

[0038] S24. Calculate the coordinates (x_B,H) of point B based on the AB distance calculated in step S23, where x_B = x_A + AB.

[0039] S25. Finally, the true field of view angle φ1 = arctan(H / x_B) is obtained from the coordinates of point B, indicating that the observed target is located in the first quadrant; φ1 = π + arctan(H / x_B), indicating that the observed target is located in the second quadrant. This angle is a function of θ_r, 2*θ_m, r, and the target distance H, rather than a simple linear superposition of π - θ_r - 2*θ_m.

[0040] S3: Image data acquired based on the ground verification system The experiment was conducted using the ground verification system built in step S1 to obtain the baseline image of the observed target and the original image under non-coaxial motion. The experimental procedure is as follows: S31. Start turntable 1 to rotate counterclockwise at the specified speed.

[0041] S32. Control the field of view adjustment mechanism 3 to rotate clockwise at a specified speed.

[0042] S33. In the above process, the observed target 4 is imaged to obtain the original image under non-coaxial motion.

[0043] S34. As a reference, with the turntable 1 stationary, control the field-of-view adjustment mechanism 3 to rotate at a specified speed to acquire the reference image under the same observed target 4 as in step S33, such as... Figure 5 As shown.

[0044] S4: Verification of the image effect of the calibration model: Using the geometric model established in step S2, the original image in step S3 is processed to obtain a geometrically corrected image; using the linear relationship φ2=π-θ_r-2*θ_m, the original image in step S3 is processed to obtain an uncorrected image. The geometrically corrected image, the uncorrected image, and the reference image obtained in step S3 are compared to verify whether the geometric model established in step S2 is correct.

[0045] Step S4, in detail: S41. Take the field of view adjustment mechanism pointing angle 2*θ_m and the turntable angle θ_r acquired in each frame as input.

[0046] S42. Using the geometric model established in step S2, calculate the true field of view angle φ1.

[0047] S43. Based on the true field of view φ1, arrange each frame of images according to the angle mapping relationship to generate a geometrically corrected image, such as... Figure 5 As shown.

[0048] S44. Using the linear relationship φ2=π-θ_r-2*θ_m, calculate the field of view φ2 without geometric correction; S45. Based on the uncorrected field of view φ2, arrange each frame of images according to the angle mapping relationship to generate an uncorrected image, such as... Figure 5 As shown; S46. Compare the geometrically corrected image and the uncorrected image with the reference image obtained in step S3.

[0049] Step S46, in detail: Verification: If the geometrically corrected image is highly consistent with the reference image in terms of geometric features, and the uncorrected image deviates from the reference image in terms of geometric features, then it proves that the non-coaxial error of the image has been corrected after the geometric model in step S2.

[0050] Finally, it should be noted that the above content is only used to illustrate the technical solution of the present invention, and is not intended to limit the scope of protection of the present invention. Simple modifications or equivalent substitutions made by those skilled in the art to the technical solution of the present invention do not depart from the essence and scope of the technical solution of the present invention.

Claims

1. A method for checking for non-coaxial errors, characterized in that: Includes the following steps: S1. Establish a two-dimensional reference coordinate system: Build a ground verification system. Based on the relative positional relationship between the turntable, the field of view adjustment mechanism, the imaging device, and the observation target, establish a fixed three-dimensional rectangular coordinate system O-XYZ. Equivalently represent the spatial positional relationship between the field of view adjustment mechanism and the turntable to a two-dimensional geometric relationship in the XOY plane. Establish a two-dimensional reference coordinate system in the XOY plane, and set the turntable angle as θ_r and the pointing angle of the field of view adjustment mechanism as 2*θ_m. S2. Precise geometric modeling of the field of view: Based on the two-dimensional reference coordinate system established in step S1, and based on the geometric theorem of triangles and the principle of coordinate projection, establish a geometric model from the input quantities θ_r and 2*θ_m to the output quantity true field of view φ1. S3. Using a ground-based verification system, obtain the baseline image of the observed target and the original image under non-coaxial motion. S4. Verification of the effect of the corrected model image: Using the geometric model established in step S2, the original image in step S3 is processed to obtain the geometrically corrected image. By applying the linear relationship φ2=π-θ_r-2*θ_m, the original image in step S3 is processed to obtain an image without geometric correction; The geometrically corrected image, the uncorrected image, and the reference image obtained in step S3 are compared to verify whether the geometric model established in step S2 is correct.

2. The method for checking non-coaxial errors according to claim 1, characterized in that: In step S1, a ground verification system is built, which includes a turntable, an imaging device, and a field-of-view adjustment mechanism. Based on the ground verification system, the relative positions of the turntable, the field-of-view adjustment mechanism, the imaging device, and the observation target are as follows: the field-of-view adjustment mechanism is located in the front optical path of the imaging device, the imaging device is mounted on the turntable and rotates with the turntable, the axis of the field-of-view adjustment mechanism and the axis of the turntable are parallel to each other and have a certain spatial offset, and the observation target is located in front of the field-of-view adjustment mechanism.

3. The method for checking non-coaxial errors according to claim 2, characterized in that: In step S1, a fixed three-dimensional rectangular coordinate system O-XYZ is established: The coordinate system O-XYZ does not change with the rotation of the field of view adjustment mechanism or the turntable, wherein the Z-axis is defined along the axis of the turntable, and its positive direction is from the turntable base to the imaging device base. The Z-axis intersects the upper surface of the turntable at the origin O; The X-axis is located in the plane of the turntable, perpendicular to the Z-axis, and parallel to the plane where the observation target is located. Its positive direction is defined as the direction of rotating 90° counterclockwise from the positive direction of the Z-axis. The Y-axis is determined by the X-axis and Z-axis according to the right-hand rule.

4. The method for checking non-coaxial errors according to claim 3, characterized in that: In step S1, the spatial positional relationship between the field of view adjustment mechanism and the turntable is equivalent to a two-dimensional geometric relationship in the XOY plane under the following conditions: the axis of the field of view adjustment mechanism and the axis of the turntable have a preset parallel relationship, both axes are parallel to the Z-axis of the coordinate system O-XYZ, and the displacement and attitude deviation of the field of view adjustment mechanism and the turntable in the Z-axis direction are negligible.

5. The method for checking non-coaxial errors according to claim 4, characterized in that: In step S1, a two-dimensional reference coordinate system is established in the XOY plane: S11. Take the projection point O_r of the turntable axis in the XOY plane as the origin of the coordinate system O, and O_r is also the center of the turntable; S12. The X-axis and Y-axis directions are defined according to the three-dimensional rectangular coordinate system O-XYZ; S13. The projection point O_m of the field adjustment mechanism axis in the XOY plane moves together with the turntable. O_m is also the center of the field adjustment mechanism. Its trajectory is a circle around the origin O of the coordinate system with a radius of eccentricity r. The eccentricity r is the straight-line distance between the turntable center O_r and the field adjustment mechanism center O_m. S14. Let the extensions of the turntable center O_r and the field of view adjustment mechanism center O_m intersect the observation target at point A, and let the angle between AO_r and the negative X-axis be the turntable angle θ_r; S15. Let point B be the intersection of the field of view of the field adjustment mechanism and the observed target. Point B is the true field of view. The pointing angle 2*θ_m of the field of view adjustment mechanism is the angle between O_mA and O_mB. This angle is an acute angle. S16. Draw BO_m / / B'O through the origin O of the coordinate system, intersecting the observed target at point B'. Point B' is the field of view with geometric distortion, and ∠B'Ox is the field of view angle φ2 without geometric correction.

6. The method for checking non-coaxial errors according to claim 5, characterized in that: A geometric model is established from the input quantities θ_r and 2*θ_m to the output quantity, the true field of view angle φ1. The specific derivation includes: S21. Based on the turntable angle θ_r and the target distance H between the origin O of the coordinate system and the observed target, determine the coordinates of point A (x_A, H), where x_A = -H / tanθ_r, and the length of AO is H / sinθ_r; S22. Based on the AO calculated in step S21 and the known eccentricity r, determine the length of AO_m: AO-r; S23. Based on the fact that two lines are parallel, AB / / x-axis, and alternate interior angles are equal, we can obtain ∠BAO = ∠AO - x = θ_r, where -x represents the negative direction of the x-axis; in triangle ABO_m, based on the pointing angle of the field adjustment mechanism 2*θ_m, AO_m, and ∠BAO, we can obtain ∠ABO_m = π - 2*θ_m - ∠BAO, and then use the sine theorem to find the distance between AB: AO_m / sin(∠ABO_m) * sin(2*θ_m); S24. Calculate the coordinates (x_B,H) of point B based on the AB distance calculated in step S23, where x_B = x_A + AB; S25. Finally, the true field of view angle φ1 = arctan(H / x_B) is obtained from the coordinates of point B, and the observed target is located in the first quadrant; φ1 = π + arctan(H / x_B), and the observed target is located in the second quadrant.

7. The method for verifying non-coaxial errors according to claim 6, characterized in that: In step S3, the ground verification system built in step S1 is used to conduct experiments to obtain the reference image of the observed target and the original image under non-coaxial motion. The experimental process includes: S31. Start the turntable to rotate counterclockwise at the specified speed; S32. Control the field-of-view adjustment mechanism to rotate clockwise at a specified speed; S33. In the above process, the observed target is imaged to obtain the original image under non-coaxial motion; S34. As a reference, with the turntable stationary, control the field of view adjustment mechanism to rotate at a specified speed to obtain the reference image under the same observation target in step S33.

8. The method for verifying non-coaxial errors according to claim 7, characterized in that: Step S4, in detail: S41. Take the field of view adjustment mechanism pointing angle 2*θ_m and the turntable angle θ_r acquired in each frame as input; S42. Using the geometric model established in step S2, calculate the true field of view angle φ1; S43. Based on the true field of view φ1, arrange each frame of images according to the angle mapping relationship to generate a geometrically corrected image; S44. Using the linear relationship φ2=π-θ_r-2*θ_m, calculate the field of view φ2 without geometric correction; S45. Based on the uncorrected field of view φ2, arrange each frame of images according to the angle mapping relationship to generate an uncorrected image; S46. Compare the geometrically corrected image, the uncorrected image, and the reference image obtained in step S3 to verify whether the geometric model established in step S2 is correct.

9. The method for verifying non-coaxial errors according to claim 8, characterized in that: Step S46, in detail: If the geometrically corrected image is highly consistent with the reference image in terms of geometric features, and the uncorrected image deviates from the reference image in terms of geometric features, then it proves that the non-coaxial error of the image has been corrected after the geometric model in step S2.

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