Multi-eye pupil optimization method

Abstract

The invention belongs to the technical field of optics, and particularly relates to a compound eye pupil optimization method. Comprising the following steps: S1, taking an external spherical surface of a regular icosahedron as a sub-eye distribution carrier, and uniformly distributing sub-eyes of the heterogeneous curved surface compound eye system through edge subdivision optimization, multi-direction surface subdivision and clustering and gravity center calculation; and S2, calculating an equivalent inclination angle generated by each sub-eye channel in the optical relay system of the heterogeneous curved surface compound eye system due to pupil shift, and based on the equivalent inclination angle of each sub-eye channel, applying inclination compensation which is equal in size and opposite in direction to each sub-eye on a physical structure so as to realize optical path correction of the heterogeneous curved surface compound eye system. The performance of the heterogeneous curved surface compound eye system can be remarkably improved, the distribution uniformity of sub-eyes is remarkably improved, and the edge imaging quality is greatly improved.

Description

Technical Field

[0001] This invention belongs to the field of optical technology, and in particular relates to a method for optimizing the pupil of a compound eye. Background Technology

[0002] Heterogeneous surface compound eye systems, as an advanced optical imaging architecture, demonstrate enormous application potential and strategic value in multiple high-tech fields due to their unique dual-scale imaging capabilities. The basic working principle of a heterogeneous surface compound eye system is to simultaneously acquire multiple two-dimensional sub-images in different directions using an array composed of multiple sub-eyes. Subsequently, advanced computational imaging algorithms are used to reverse-analyze these sub-images, thereby reconstructing the three-dimensional information of the observation space.

[0003] Existing technologies have significant inherent limitations in achieving uniform sub-eye arrangement. Whether designing a simple ring array or a hexagonal array with improved symmetry, the non-uniformity problem remains far from resolved. Even the current best regular polyhedral subdivision method, while exhibiting perfect symmetry, still suffers from a 130% non-uniformity, which remains a significant source of systematic error for high-precision applications.

[0004] The direct consequence of this non-uniformity is a significant decrease in the stability of the overlapping regions of the sub-eyes' fields of view. In compound eye 3D vision systems, the 3D coordinates of a spatial point are calculated by matching its corresponding points in different sub-eye images (i.e., the principle of triangulation). Stable and uniform field-of-view overlap is a prerequisite for ensuring reliable, multi-view observation of any point in space. When the sub-eyes are unevenly distributed, the field-of-view overlap in some areas is too large, causing data redundancy, while the overlap in other areas is too small, or even blind spots appear. This directly leads to a significant reduction in the accuracy and robustness of 3D information extraction. It can be said that the shortcomings of existing technologies in sub-eye arrangement have become a key bottleneck restricting compound eye systems from moving from "qualitative observation" to "quantitative measurement."

[0005] Existing technologies generally fail to effectively solve or compensate for imaging problems caused by pupil aberration in large field-of-view optical relay systems. The essence of this problem is that, due to the offset of the entrance pupil position in different fields of view, each off-axis sub-eye channel actually sends the beam into the relay system at an angle. This optical "mismatch" introduces a series of defects that severely affect image quality, specifically: image distortion and field-of-view asymmetry, crescent-shaped black borders, imaging of supporting structures, stray light interference, and encroachment by adjacent fields of view. These defects collectively lead to decreased edge field-of-view resolution and reduced signal-to-noise ratio, severely impacting the overall system's imaging quality and data accuracy. Existing technologies lack effective solutions to this problem, mostly employing tolerance or post-processing software correction. However, software correction often fails to perfectly recover lost information and increases the system's computational load. Summary of the Invention

[0006] In view of this, the present invention aims to provide a method for optimizing the pupil of a compound eye, in order to solve the obvious inherent defects of the prior art in achieving uniform sub-eye arrangement and the inability to effectively solve or compensate for the imaging problem caused by the large field-of-view pupil aberration of the optical relay system. The present invention can significantly improve the performance of the heterogeneous curved surface compound eye system, significantly improve the uniformity of sub-eye distribution, and greatly improve the edge imaging quality.

[0007] To achieve the above objectives, the technical solution created by this invention is implemented as follows: A method for optimizing the pupil of a compound eye, used to optimize a heterogeneous curved surface compound eye system, specifically includes the following steps: S1: Using the circumscribing sphere of a regular icosahedron as the carrier for sub-eye distribution, the sub-eyes of the heterogeneous surface compound eye system are uniformly distributed through edge subdivision optimization, multi-directional surface subdivision, and clustering and centroid calculation. S2: Calculate the equivalent tilt angle of each sub-eye channel in the optical relay system of the heterogeneous curved surface compound eye system due to pupil offset, and based on the equivalent tilt angle of each sub-eye channel, apply tilt compensation of equal magnitude and opposite direction to each sub-eye in physical structure to realize optical path correction of the heterogeneous curved surface compound eye system.

[0008] Furthermore, step S1 specifically includes the following steps: S11: Establish a Cartesian coordinate system with the geometric center of the icosahedron as the origin O. Let the radius of the circumscribed sphere of the icosahedron be R, and define the coordinates of each vertex of the icosahedron. S12: Select edge AB on the triangular surface ABC of a regular icosahedron, and select the subdivision point E on edge AB using the following formula. i Subdivision point E i Divide arc AB into S equal parts at the mapping point of the circumsphere of the icosahedron; S13: Repeat step S12 to find the subdivision points corresponding to the selected edges AC and BC on the triangular surface ABC of the regular icosahedron. S14: Take the pairs of subdivision points that are symmetrical about each median of the triangle surface ABC, and connect the pairs of subdivision points along the circumscribing surface of the regular icosahedron. S15: Subdivision point of edge AB Subdivision point of edge AC Symmetrically arranged along the midline set with vertex A, based on subdivision points and subdivision points Solving for the mapping point Mapping point lie in superior:: ; ; in, For vector O , g For coefficients, For vectors , For vector O , For vectors and The angle between the two points, i is the i-th subdivision point, and j is the angle subdivision index; S16: Repeat step S15, based on the subdivision points of edge AB. Subdivision points of edge AC Subdivision points of edge BC Calculate all mapping points; S17: Divide the three nearest mapping points in the three subdivision directions into a cluster, calculate the centroid coordinates of each cluster, and map the centroid coordinates corresponding to each cluster to the position of the circumscribing surface of the icosahedron as the distribution point of each sub-eye on the circumscribing surface of the icosahedron. S18: Repeat steps S12-S17 to obtain the sub-eye distribution points of each triangle surface of the regular icosahedron.

[0009] Furthermore, in step S12, a subdivision point E is selected on edge AB using the following formula. i : ; in, Let k be the vector pointing from the origin to the subdivision point Ei. i For subdivision point E i Position vector coefficients, Let AB be a vector. Let OA be a vector.

[0010] Furthermore, the three subdivision directions include the α subdivision direction, the β subdivision direction, and the γ subdivision direction. In the triangular surface ABC, the subdivision path of the candidate eye mapping point formed by connecting the corresponding subdivision points on edges AB and AC along the circumscribing surface of the icosahedron is taken as the α subdivision direction; the subdivision path of the candidate eye mapping point formed by connecting the corresponding subdivision points on edges BA and BC along the circumscribing surface of the icosahedron is taken as the β subdivision direction; and the subdivision path of the candidate eye mapping point formed by connecting the corresponding subdivision points on edges CA and CB along the circumscribing surface of the icosahedron is taken as the γ subdivision direction.

[0011] Furthermore, in step S16, the formula used to calculate the centroid coordinates of each cluster is as follows: ; in,( , , ), ( , , )and( , , () corresponds to the three nearest mapping points in the three subdivision directions.

[0012] Furthermore, step S2 specifically includes: S21: Calculate the equivalent tilt angle of the current sub-eye channel in the optical relay system of the heterogeneous curved surface compound eye system due to pupil offset using the following formula: ; in, The tilt angle of the current sub-eye. The current pitch angle of the sub-eye. Let be the radius of the first focal surface of the optical relay system. It is the pitch angle. The corresponding pupil center distance; S22: Determine the rotation center point of the current sub-eye. The rotation center point of the current sub-eye is the intersection of the optical axis of the current sub-eye, the principal ray of the 0° field of view of the current sub-eye, and the first focal plane of the optical relay system. S23: Within the plane determined by the optical axis of the current sub-eye and the optical axis of the optical relay system, rotate the current sub-eye around its rotation center point by an angle - This makes the pupil center distance DPC = 0; S24: Replace the current sub-eye with the next sub-eye and repeat steps S21-S23 until all sub-eyes are adjusted and the optical path correction is completed.

[0013] Compared with the prior art, the present invention can achieve the following beneficial effects: (1) The compound eye pupil optimization method described in this invention has poor practicality in terms of the geometric optimization of sub-eye layout. The non-uniformity of the ring array and hexagonal array is as high as 160% and 300%, respectively. The non-uniformity of the regular polyhedral subdivision method, which is the best solution, is still around 130%. This level of non-uniformity will directly lead to the uncertainty of the 3D reconstruction accuracy and increase the burden of subsequent image processing. The spherical lattice homogenization method (GCSH) based on geometric clustering proposed in this invention further reduces the non-uniformity of sub-eye distribution to 116% while fully preserving the regional symmetry. This improvement is not only a numerical improvement, but also means that it provides a more ideal physical basis for subsequent sub-eye calibration and 3D information extraction, thereby directly improving the measurement accuracy and reliability of the system.

[0014] (2) The compound eye pupil optimization method described in this invention provides a practical solution to the problem of large field-of-view pupil aberration in optical relay systems, filling a gap in the prior art. Existing technologies have failed to effectively overcome a series of imaging defects caused by pupil position shift. These defects, such as field-of-view asymmetry, morphological distortion, crescent-shaped black borders, and increased stray light, severely limit the effective field of view and imaging quality of the system. The sub-eye tilt angle compensation method proposed in this invention, through a "reverse tilt" physical compensation mechanism, effectively eliminates all of the above imaging defects. Furthermore, experiments have shown that the optimized prototype completely solves persistent problems such as image quality degradation, crescent-shaped black borders, imaging of the supporting structure, and intrusion into the high-resolution (HD) sub-eye field of view, resulting in a qualitative improvement in the image quality of the edge field of view.

[0015] (3) The compound eye pupil optimization method described in this invention, through the synergistic application of the GCSH method and the tilt compensation method, has achieved a breakthrough in the macroscopic performance indicators of the heterogeneous compound eye array at the system level. The total field of view of the dual-scale coverage of the heterogeneous curved surface compound eye system has been expanded from the original 142° to 155°. This 13° field of view gain is essentially achieved by improving the imaging quality of the edge field of view, "unlocking" the originally unusable physical field of view into a usable field of view, greatly enhancing the detection and monitoring capabilities of the system, and significantly improving the edge resolution of the compound eye, which is the most powerful proof of the advantages of this invention. In the resolution test, the optimized prototype reduced the resolution drop by 66% in the edge field of view area, whether it was the wide-angle (WA) sub-eye or the high-definition (HD) sub-eye. This data clearly shows that structural optimization plays a decisive role in improving the imaging quality of the large field of view system. It not only makes the image "look better" but also effectively improves the system's ability to resolve details.

[0016] (4) The compound eye pupil optimization method described in this invention has made significant progress in terms of sub-eye distribution uniformity and imaging quality compared with the existing best technology. More importantly, it provides an unprecedented high-quality data source for subsequent practical applications (such as sub-eye calibration and image reconstruction) through structural optimization. The proposed optimization strategy has wide applicability and is expected to become the design standard for future high-performance compound eye cameras, especially those equipped with complex optical relay systems. Attached Figure Description

[0017] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments and descriptions of the invention are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 A schematic flowchart illustrating the compound eye pupil optimization method described in an embodiment of the present invention; Figure 2 The diagram illustrates the subdivision results obtained by the spherical lattice homogenization method based on geometric clustering as described in the embodiments of the present invention. The diagram shows: (a) a conceptual diagram of subdivision of a traditional icosahedron; (b) a schematic diagram of spherical mapping for subdivision of a traditional icosahedron; (c) a schematic diagram of the GCSH algorithm subdividing the edges of a icosahedron; (d) the optimized result of the GCSH algorithm subdividing the edges of a icosahedron; (e) a schematic diagram of the GCSH algorithm subdividing the interior surface of a icosahedron; (f) the spatial average value of each group; and (g) a comparison of the results of traditional icosahedron subdivision and the GCSH algorithm. Figure 3 This invention provides a statistical table of the angles between the lines connecting adjacent subdivision points and the center of the sphere in the traditional icosahedral subdivision and the GCSH algorithm, as described in the embodiments of the present invention. Figure 4 A comparison chart of the optimization results of GCSH at different subdivision frequencies as described in the embodiments of the present invention; Figure 5 A schematic diagram of tilt compensation for the sub-eye and optical relay system described in an embodiment of the present invention; Figure 6 The graph showing the relationship between the pitch angle and tilt angle of the sub-eye and the optical relay system described in the embodiment of the present invention. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not constitute a limitation thereof.

[0019] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0020] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on this invention. Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, features defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0021] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0022] Heterogeneous curved compound eye systems can simultaneously achieve rapid searching of a large field of view and high-resolution local detailing, effectively resolving the inherent contradiction between field of view and resolution in traditional optical systems. Its core application areas, such as wide-area surveillance, machine vision, and rapid target localization and tracking, all have an urgent need for this dual capability. For example, in wide-area surveillance, the system needs to continuously scan a wide area to detect abnormal events, while simultaneously magnifying suspicious targets to obtain clear details for identification and judgment.

[0023] This purely visual detection scheme not only possesses strong environmental adaptability but also offers significant advantages in cost control and system integration compared to systems relying on lidar. However, the overall detection performance of the system, especially the reliability and accuracy of its output data, is closely coupled with two core elements: the accuracy of the compound eye camera parameter model and the intrinsic quality of the output images. Therefore, any technological breakthroughs aimed at improving these two aspects will directly drive the deployment and development of this technology in practical applications.

[0024] In the physical implementation of a compound eye system, the spatial arrangement of the sub-eyes on a curved substrate determines the system's performance. An ideal arrangement should balance the uniformity of the field of view coverage with the symmetry of the array structure. Uniformity ensures the stability of the overlapping areas between sub-eyes, which is crucial for subsequent accurate 3D information extraction; while symmetry greatly simplifies the design complexity and operating cost of subsequent processing algorithms such as image stitching and calibration. Currently, there are three main sub-eye distribution schemes in the industry, but all have limitations to varying degrees.

[0025] The simplest arrangement is a circular array, with sub-eyes distributed along concentric rings. Its advantage lies in its simplicity of design and manufacturing. However, its structural drawbacks are also quite obvious: firstly, the unevenness of its sub-eye distribution is as high as approximately 160%, leading to extremely unstable field-of-view overlap; secondly, the structure lacks regional symmetry, imposing a heavy computational burden on subsequent image processing. This initial "simplicity" actually shifts the complexity to the software layer, increasing the overall operating cost of the system.

[0026] To address the symmetry issue, researchers introduced hexagonal tiling. Hexagonal tiling is the geometry that achieves the densest tiling on a plane. However, problems arise when mapping this planar structure to a sphere. Due to topological constraints, it is impossible to perfectly tile a sphere with regular hexagons. In practical tiling, as the eye positions approach the sphere's "equator," the spacing between adjacent eyes inevitably decreases, even leading to physical interference. This causes the non-uniformity to increase dramatically, surging to approximately 300%, making it impractical for applications requiring high-precision, uniform coverage.

[0027] The most advanced method currently available is based on the icosahedron, as it is the closest shape to a sphere among all regular polyhedra. The implementation involves first subdividing each equilateral triangle surface of the icosahedron, and then projecting all the resulting vertices onto the circumscribing sphere of the icosahedron; these projection points are the locations of the sub-eyes. The greatest advantage of this method is that it achieves absolutely strict regional symmetry, inheriting the inherent symmetry properties of the icosahedron. Simultaneously, it significantly reduces the non-uniformity of the sub-eye distribution to approximately 130%. Although this is the best solution currently available, a 130% non-uniformity still represents a significant source of error for high-precision 3D measurement applications.

[0028] Besides the geometric issues of sub-eye arrangement, existing compound eye systems also generally face a key technical bottleneck stemming from the optical physics level: the large field-of-view pupil aberration of the optical relay system. In a typical compound eye camera design, the light rays acquired by all the sub-eyes are not directly imaged onto their respective sensors, but are first imaged through a shared, large field-of-view optical relay system (usually a complex lens group similar to a fisheye lens).

[0029] Pupil aberration, specifically entrance pupil position shift, refers to the change in the axial position of the entrance pupil corresponding to the principal ray at different field of view angles within an optical relay system. For a sub-eye at the center of the field of view, its optical axis coincides with the optical axis of the optical relay system, and light rays are incident normally. However, for sub-eyes at the edge of a large field of view, their principal rays enter the optical relay system at a larger angle, causing a shift in the entrance pupil position of the optical relay system. This effect results in the edge sub-eyes actually facing the optical relay system in a "tilted" posture, leading to a series of chain-reaction imaging defects.

[0030] These defects include: asymmetrical field of view of sub-images; morphological distortion of image content; a significant increase in stray light within the compound eye system; and ultimately, a severe decrease in imaging resolution. These problems work together to significantly impair the imaging quality and data accuracy of the compound eye system. At a deeper level, there is a negative synergistic effect between the geometric defects in sub-eye arrangement and the optical defects in pupil aberration. A sub-eye located at the edge due to uneven arrangement has a lower weight in its contribution to 3D reconstruction due to its poor position, and it happens to be the sub-eye most severely affected by pupil aberration. This "double whammy" effect causes a precipitous drop in the performance of the compound eye system at the edge of the field of view, severely limiting the effective field of view and overall reliability of the entire compound eye system. Therefore, a systematic optimization scheme that can simultaneously solve the problems of geometric arrangement and optical matching is crucial for promoting the mature application of compound eye technology.

[0031] To fundamentally overcome the two major technical defects mentioned above, this invention performs synergistic optimization at both the geometric layout and optical path levels, thereby systematically improving the imaging quality, effective field of view, and final detection accuracy of the heterogeneous curved surface compound eye system.

[0032] The invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0033] like Figure 1 As shown, this invention proposes a method for optimizing the pupil of a compound eye, used to optimize a heterogeneous curved surface compound eye system, specifically including the following steps: S1: Using the circumscribing sphere of a regular icosahedron as the carrier for sub-eye distribution, the sub-eyes of the heterogeneous surface compound eye system are uniformly distributed through edge subdivision optimization, multi-directional surface subdivision, and clustering and centroid calculation. S2: Calculate the equivalent tilt angle of each sub-eye channel in the optical relay system of the heterogeneous curved surface compound eye system due to pupil offset, and based on the equivalent tilt angle of each sub-eye channel, apply tilt compensation of equal magnitude and opposite direction to each sub-eye in physical structure to realize optical path correction of the heterogeneous curved surface compound eye system.

[0034] It should be noted that the present invention aims to provide a systematic optimization method for the pupil of a compound eye. This method does not address a single problem, but rather performs synergistic optimization at both the geometric layout and optical path levels. Its specific objectives can be broken down into the following two points: 1. A novel sub-eye layout optimization method is proposed: This method aims to significantly improve the uniformity of sub-eye distribution on curved surfaces through innovative geometric design, while fully preserving the excellent regional symmetry brought about by the regular polyhedral subdivision method. The Geometric Clustering-based Spherical Homogenization (GCSH) method for optimizing sub-eye layout aims to lay a better physical foundation at the geometric level for high-precision 3D information extraction of heterogeneous surface compound eye systems.

[0035] 2. A targeted imaging compensation method is proposed: This method aims to accurately eliminate the equivalent tilt effect introduced by the pupil offset of the optical relay system, and the resulting series of imaging defects. By performing physical and precise compensation for each sub-eye, the optical path is corrected at its source, restoring the imaging quality of the edge field of view.

[0036] By combining the two methods described above, this invention provides a comprehensive upgrade to the structure of the heterogeneous curved compound eye system, thereby systematically improving its imaging quality, effective field of view, and final detection accuracy, enabling it to better meet the application requirements of high precision and high reliability.

[0037] like Figures 2-3 As shown, in some embodiments, step S1 specifically includes the following steps: S11: Establish a Cartesian coordinate system with the geometric center of the icosahedron as the origin O. Let the radius of the circumscribed sphere of the icosahedron be R, and define the coordinates of each vertex of the icosahedron. S12: Select edge AB on the triangular surface ABC of a regular icosahedron, and select the subdivision point E on edge AB using the following formula. i Subdivision point E i Divide arc AB into S equal parts at the mapping point of the circumsphere of the icosahedron; S13: Repeat step S12 to find the subdivision points corresponding to the selected edges AC and BC on the triangular surface ABC of the regular icosahedron. S14: Take the pairs of subdivision points that are symmetrical about each median of the triangle surface ABC, and connect the pairs of subdivision points along the circumscribing surface of the regular icosahedron. S15: Subdivision point of edge AB Subdivision point of edge AC Symmetrically arranged along the midline set with vertex A, based on subdivision points and subdivision points Solving for the mapping point Mapping point lie in superior:: ; ; in, For vector O , g For coefficients, For vectors , For vector O , For vectors and The angle between the two points, i is the i-th subdivision point, and j is the angle subdivision index; S16: Repeat step S15, based on the subdivision points of edge AB. Subdivision points of edge AC Subdivision points of edge BC Calculate all mapping points; S17: Divide the three nearest mapping points in the three subdivision directions into a cluster, calculate the centroid coordinates of each cluster, and map the centroid coordinates corresponding to each cluster to the position of the circumscribing surface of the icosahedron as the distribution point of each sub-eye on the circumscribing surface of the icosahedron. S18: Repeat steps S12-S17 to obtain the sub-eye distribution points of each triangle surface of the regular icosahedron.

[0038] In some embodiments, in step S12, a subdivision point E is selected on edge AB using the following formula. i : ; in, Let k be the vector pointing from the origin to the subdivision point Ei. i For subdivision point E i Position vector coefficients, Let AB be a vector. Let OA be a vector.

[0039] It should be noted that in the constraint i>1, j ∈ [1, i-1], the physical meaning of j is the angular subdivision index within a specific sector. The first level of subdivision (defined by i): First, on two sides (e.g., AB and AC) of the triangular facet of the regular icosahedron, a pair of corresponding subdivision points are determined by index i. and These two points and the origin O form a sector O. .

[0040] Second subdivision (defined by j): Next, denser points are generated within this sector. Formula The function is to divide the total included angle θ of this sector into i equal parts, and then take the index j from the first part to the (i-1)th part to generate i-1 uniformly distributed mapping points at the angle.

[0041] Furthermore, geometrically speaking, the centroid, determined by three points on the sphere, lies on the plane defined by these three points, inside the sphere. After calculating the coordinates (X, Y, Z) of the centroid inside the sphere using a formula, this point needs to be projected back onto the sphere from the origin (the center of the sphere) to obtain the final distribution points of the sub-eyes. The algorithm first generates three sets of slightly biased "candidate points" on the sphere using different rules, and then obtains a more centered and uniform final position by taking the spatial average of these three sets of points (i.e., calculating the centroid before projection).

[0042] In some embodiments, the three subdivision directions include an α subdivision direction, a β subdivision direction, and a γ subdivision direction. In the triangular surface ABC, the subdivision path of the candidate eye mapping point formed by connecting the corresponding subdivision points on edges AB and AC along the circumscribing surface of the icosahedron is taken as the α subdivision direction; the subdivision path of the candidate eye mapping point formed by connecting the corresponding subdivision points on edges BA and BC along the circumscribing surface of the icosahedron is taken as the β subdivision direction; and the subdivision path of the candidate eye mapping point formed by connecting the corresponding subdivision points on edges CA and CB along the circumscribing surface of the icosahedron is taken as the γ subdivision direction.

[0043] In some embodiments, the formula used to calculate the centroid coordinates of each cluster in step S16 is: ; in,( , , ), ( , , )and( , , () corresponds to the three nearest mapping points in the three subdivision directions.

[0044] This invention employs a Geometric Clustering-based Spherical Homogenization (GCSH) method to address the core problem of uneven sub-eye distribution. The GCSH algorithm improves upon the existing best icosahedral subdivision method by introducing a geometric design strategy based on multi-directional subdivision and centroid averaging. While maintaining the inherent symmetry of the icosahedron, it effectively reduces the non-uniformity of sub-eye distribution from 130% in traditional methods to 116%. This purely geometric optimization not only improves the physical uniformity of the layout but also simplifies the complexity of subsequent image processing algorithms due to its preservation of excellent regional symmetry.

[0045] The core objective of the GCSH algorithm is to optimize the traditional icosahedral subdivision method to obtain a more uniformly distributed sub-eye lattice on a sphere. The essence of this method lies in its pure geometric design philosophy, avoiding complex iterative solutions or parameter optimization processes, thus achieving determinism and efficiency.

[0046] Establish a Cartesian coordinate system with the geometric center O of the icosahedron as the origin, and define the coordinates of the three vertices of the surface of the icosahedron under discussion as follows: ; in , R is the radius of the circumsphere of the icosahedron. The entire optimization process of GCSH follows three basic principles and three basic steps, transforming the traditional method's subdivision of "faces" into the optimization of "edges" and the fusion of multi-directional "projections": 1. Optimize edge subdivision points: First, subdivide each edge of the icosahedron. To ensure that the spacing of these subdivision points projected onto the circumscribed sphere is strictly equal, their positions need to be optimized. Taking the center of the icosahedron as the origin, the position vector of the optimized subdivision point E on any edge AB can be obtained by solving for a specific coefficient k. The solution is obtained using the formula: ; A series of k values ​​can be obtained, thus dividing the sector OAB into s equal parts according to the angle. These optimized points are then mapped onto the circumsphere, correcting the large inhomogeneity produced by the traditional method near the vertices of the icosahedron.

[0047] 2. Multi-directional surface subdivision: Using the optimized edge mapping points as a reference, the surface of the icosahedron is subdivided along three edge directions, resulting in three different sets of subdivision points. For example, when subdividing along a certain direction, a pair of optimized points located on two different edges are connected, and the resulting spherical arc is divided at equal angles to determine the mapping points inside the surface.

[0048] Taking subdivision direction α as an example, and Given a pair of optimized corresponding points on edges AB and AC, connect the two points along the sphere to obtain an arc. As shown by the solid black arc in Figure (e). Arc Together with the origin O, they form a sector Assume point G is located at... The coordinates of point G, the mapping point on the map, are as follows: ; Where g is the coefficient to be solved, To uniformly subdivide this sector, the position of point G needs to satisfy the following: ; in, For vectors and The included angle. For each subdivision direction, there are s-1 such sectors, as shown by the black dotted line in Figure (e). Each sector needs to be divided in this way.

[0049] Next, clustering and centroid calculation are performed: Since the three sets of points obtained by subdividing along each edge direction do not overlap, the three nearest subdivision points in different subdivision directions are grouped into a cluster. The centroid of each cluster is calculated as the final optimized point position for GCSH.

[0050] The coordinates of the final optimized point are: ; like Figure 4 As shown, the optimization performance of GCSH is compared at seven subdivision frequencies: s = 3, 6, 9, 12, 15, 18, and 21. The exact coordinates of the subdivision points on the entire sphere can be obtained using the Rodriguez rotation formula and the rotational symmetry of the icosahedron. In summary, the GCSH algorithm exhibits excellent optimization performance at any subdivision frequency, sufficient to guide the uniform arrangement of heterogeneous surface compound eye structures.

[0051] In some embodiments, step S2 specifically includes: S21: Calculate the equivalent tilt angle of the current sub-eye channel in the optical relay system of the heterogeneous curved surface compound eye system due to pupil offset using the following formula: ; in, The tilt angle of the current sub-eye. The current pitch angle of the sub-eye. Let be the radius of the first focal surface of the optical relay system. It is the pitch angle. The corresponding pupil center distance; S22: Determine the rotation center point of the current sub-eye. The rotation center point of the current sub-eye is the intersection of the optical axis of the current sub-eye, the principal ray of the 0° field of view of the current sub-eye, and the first focal plane of the optical relay system. S23: Within the plane determined by the optical axis of the current sub-eye and the optical axis of the optical relay system, rotate the current sub-eye around its rotation center point by an angle - This makes the pupil center distance DPC = 0; S24: Replace the current sub-eye with the next sub-eye and repeat steps S21-S23 until all sub-eyes are adjusted and the optical path correction is completed.

[0052] The sub-eye tilt angle compensation method for pupil shift aims to solve the image quality degradation problem caused by large-field-of-view pupil aberration in optical relay systems. Its core idea is to transform the complex optical aberration problem into a more manageable geometric problem. First, the equivalent optical tilt angle generated by pupil shift at each sub-eye channel is accurately calculated. Then, in the physical structural design, an equal-sized but opposite-direction tilt compensation is applied to each sub-eye. This ingenious "reverse tilt" compensation mechanism can actively correct the optical path of each sub-eye entering the optical relay system, fundamentally eliminating or greatly mitigating a series of defects such as image quality degradation, image distortion, stray light, and field-of-view encroachment.

[0053] This method aims to eliminate the tilt effect caused by the large field-of-view pupil aberration of the optical relay system, requiring different degrees of tilt compensation for each sub-eye channel. For any sub-eye channel, its tilt angle t is a function of the pitch angle φ, which can be calculated using the following formula: ; Where r is the radius of the first-order focal surface. It is the pitch angle. The corresponding pupil center distance.

[0054] The sub-eye tilt compensation method for pupil shift involves, in terms of physical structure, rotating all sub-eyes around point N (the intersection of the sub-eye optical axis, the 0° field principal ray, and the first focal plane) within the plane determined by their optical axes and the optical relay system's optical axis. This makes DPC equal to 0, thus completing the compensation for tilt.

[0055] like Figures 5-6 As shown, P is the entrance pupil of the optical relay system, A is the sub-eye, and the tilt angle t and pitch angle are... The relationship curves show that when the pitch angle is less than 20°, the tilt angle increases almost linearly with a slope of approximately 0.224. The tilt angle reaches its maximum value of 9.152° at a pitch angle of 56.8°. Since tilt exists in all sub-eyes except the center, and is particularly pronounced in the central region of the field of view, compensation for it is both necessary and meaningful.

[0056] These two algorithms, addressing the problem from geometric and optical perspectives respectively, work together to systematically improve the performance of compound eye systems. The structural optimization method proposed in this invention possesses good versatility; its design principles and implementation algorithms can be widely applied to other types of compound eye cameras, especially those equipped with complex optical relay systems, providing a clear and effective path for technological development in this field.

[0057] This invention applies the two optimization methods described above to the redesign and manufacturing of heterogeneous compound eye arrays. The proposed methods have been verified through detailed simulation analysis and the manufacturing and testing of prototypes. A series of comparative experiments, including blank scene imaging, field-of-view testing, resolution testing, and real-scene imaging, all demonstrate that the optimized prototype exhibits significant improvements in sub-eye distribution uniformity, field-of-view range, image morphology control, and resolution. Furthermore, the original imaging defects are perfectly eliminated, proving the effectiveness and practicality of the technical solution of this invention.

[0058] It should be understood that the various forms of processes shown above can be used to reorder, add, or delete steps. For example, the steps described in this invention disclosure can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this invention can be achieved, and this is not limited herein.

[0059] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A method for optimizing the pupil of a compound eye, used to optimize a heterogeneous curved surface compound eye system, characterized in that, Specifically, the steps include the following: S1: Using the circumscribing sphere of a regular icosahedron as the carrier for sub-eye distribution, the sub-eyes of the heterogeneous surface compound eye system are uniformly distributed through edge subdivision optimization, multi-directional surface subdivision, and clustering and centroid calculation. S2: Calculate the equivalent tilt angle of each sub-eye channel in the optical relay system of the heterogeneous curved surface compound eye system due to pupil offset, and based on the equivalent tilt angle of each sub-eye channel, apply tilt compensation of equal magnitude and opposite direction to each sub-eye in physical structure to realize optical path correction of the heterogeneous curved surface compound eye system.

2. The method for optimizing the pupil of a compound eye according to claim 1, characterized in that, Step S1 specifically includes the following steps: S11: Establish a Cartesian coordinate system with the geometric center of the icosahedron as the origin O. Let the radius of the circumscribed sphere of the icosahedron be R, and define the coordinates of each vertex of the icosahedron. S12: Select edge AB on the triangular surface ABC of a regular icosahedron, and select the subdivision point E on edge AB using the following formula. i Subdivision point E i Divide arc AB into S equal parts at the mapping point of the circumsphere of the icosahedron; S13: Repeat step S12 to find the subdivision points corresponding to the selected edges AC and BC on the triangular surface ABC of the regular icosahedron. S14: Take the pairs of subdivision points that are symmetrical about each median of the triangle surface ABC, and connect the pairs of subdivision points along the circumscribing surface of the regular icosahedron. S15: Subdivision point of edge AB Subdivision point of edge AC Symmetrically arranged along the midline set with vertex A, based on subdivision points and subdivision points Solving for the mapping point Mapping point lie in superior:: ； ； in, For vector O , g For coefficients, For vectors , For vector O , For vectors and The angle between the two points, i is the i-th subdivision point, and j is the angle subdivision index; S16: Repeat step S15, based on the subdivision points of edge AB. Subdivision points of edge AC Subdivision points of edge BC Calculate all mapping points; S17: Divide the three nearest mapping points in the three subdivision directions into a cluster, calculate the centroid coordinates of each cluster, and map the centroid coordinates corresponding to each cluster to the position of the circumscribing surface of the icosahedron as the distribution point of each sub-eye on the circumscribing surface of the icosahedron. S18: Repeat steps S12-S17 to obtain the sub-eye distribution points of each triangle surface of the regular icosahedron.

3. The method for optimizing the pupil of a compound eye according to claim 2, characterized in that, In step S12, the subdivision point E is selected on edge AB using the following formula. i : ； in, Let k be the vector pointing from the origin to the subdivision point Ei. i For subdivision point E i Position vector coefficients, Let AB be a vector. Let OA be a vector.

4. The method for optimizing the pupil of a compound eye according to claim 2, characterized in that, The three subdivision directions include the α subdivision direction, the β subdivision direction, and the γ subdivision direction. In the triangular surface ABC, the subdivision path of the candidate eye mapping point formed by connecting the corresponding subdivision points on edges AB and AC along the circumscribing surface of the regular icosahedron is taken as the α subdivision direction; the subdivision path of the candidate eye mapping point formed by connecting the corresponding subdivision points on edges BA and BC along the circumscribing surface of the regular icosahedron is taken as the β subdivision direction; and the subdivision path of the candidate eye mapping point formed by connecting the corresponding subdivision points on edges CA and CB along the circumscribing surface of the regular icosahedron is taken as the γ subdivision direction.

5. The method for optimizing the pupil of a compound eye according to claim 4, characterized in that, In step S16, the formula used to calculate the centroid coordinates of each cluster is: ； in,( , , ), ( , , )and( , , () corresponds to the three nearest mapping points in the three subdivision directions.

6. The method for optimizing the pupil of a compound eye according to claim 4, characterized in that, Step S2 specifically includes: S21: Calculate the equivalent tilt angle of the current sub-eye channel in the optical relay system of the heterogeneous curved surface compound eye system due to pupil offset using the following formula: ； in, The tilt angle of the current sub-eye. The current pitch angle of the sub-eye. Let be the radius of the first focal surface of the optical relay system. It is the pitch angle. The corresponding pupil center distance; S22: Determine the rotation center point of the current sub-eye. The rotation center point of the current sub-eye is the intersection of the optical axis of the current sub-eye, the principal ray of the 0° field of view of the current sub-eye, and the first focal plane of the optical relay system. S23: Within the plane determined by the optical axis of the current sub-eye and the optical axis of the optical relay system, rotate the current sub-eye around its rotation center point by an angle - This makes the pupil center distance DPC = 0; S24: Replace the current sub-eye with the next sub-eye and repeat steps S21-S23 until all sub-eyes are adjusted and the optical path correction is completed.

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