Method and system for evaluating stability of optical axis of optical system

Abstract

The invention discloses an optical system optical axis stability evaluation method and system, the optical system comprises at least one optical element, for the optical element, for any motion freedom degree direction, the optical axis stability error component coefficient of the optical element in the motion freedom degree direction is obtained; the optical axis stability error component coefficient describes the movement amount of an image formed by the optical system when the optical element generates unit movement amount in the movement freedom degree direction. The method comprises: establishing a structure model of an optical system; applying a load to the optical system in the structure model, obtaining an actual motion vector of a node of the optical element and a rigid body motion vector of the node, and obtaining a rigid body motion vector of the optical element; and obtaining an optical axis stability error evaluation result of the optical element according to the optical axis stability error component coefficient of the optical element in each motion degree-of-freedom direction and the rigid body motion vector of the optical element, thereby realizing optical axis stability evaluation of the optical system.

Description

Technical Field

[0001] The present invention relates to the field of optical systems, and particularly to a method and system for evaluating the optical axis stability of an optical system. Background Art

[0002] With the continuous progress of society and the rapid development of modern technology, people have put forward higher requirements for the imaging quality of optical detection devices. Their optical systems are developing towards high resolution, large field of view, long focal length, and high integration, and their working environments are becoming increasingly diverse and harsh. Optical detection devices will be affected by internal and external loads such as gravitational fields, temperature changes, and vibrations, resulting in deformation of the optical system and supporting structural components, and thus affecting the optical axis stability of the optical system.

[0003] At all stages of optical detection devices, including preliminary laboratory tests, transportation, launch, and on-orbit operation, the relative positions of optical elements may be affected by complex environmental factors such as gravity, temperature, and micro-vibrations, resulting in a decrease in optical axis stability and thus affecting the imaging quality.

[0004] To ensure the optical axis stability of the optical system, mechanical compensation technology and optical compensation technology have been widely applied to optical detection devices. Since the 1990s, the mechanical structure drive control has been adopted or a low-expansion material structure has been selected to weaken the disturbance of the external environment on the optical system structure. For example, the on-orbit interface components of high-precision space cameras are designed to provide important support for the optical axis stability of remote sensors; sensors such as gyroscopes, accelerometers, and star sensors are used for monitoring, and reaction wheel devices are used to ensure the optical axis pointing accuracy of space cameras; vibration dampers and isolators are used to reduce vibrations generated during launch and operation, and at the same time, a precision actuator (such as a piezoelectric ceramic driver) is used for fine-tuning to ensure the optical axis stability of the optical system; in order to weaken the influence of the external temperature field, an athermal design such as mechanical passive, optical passive, or hybrid passive is adopted to enable the optical system to maintain excellent optical axis stability within a certain large temperature change range.

[0005] Effectively evaluating the optical axis stability of the optical system is of great significance to optical detection devices. Evaluating the optical axis stability of the optical system more accurately has extremely important scientific value and great scientific significance in the fields of resource exploration, meteorological observation, military imaging reconnaissance, target tracking and monitoring, etc. Summary of the Invention

[0006] The object of the present invention is to provide a method and system for evaluating the optical axis stability of an optical system, which realizes the evaluation of the optical axis stability of the optical system.

[0007] To achieve the above object, the present invention provides the following technical solutions:

[0008] An optical system optical axis stability evaluation method, the optical system includes at least one optical element, including:

[0009] Establish a structural model of the optical system;

[0010] Apply a load to the optical system in the structural model to obtain the actual motion vector of the nodes of the optical element and the rigid body motion vector of the nodes, and obtain the rigid body motion vector of the optical element according to the actual motion vector of the nodes of the optical element and the rigid body motion vector of the nodes;

[0011] Obtain the optical axis stability error evaluation result of the optical element according to the optical axis stability error component coefficient in each degree of freedom direction of the optical element and the rigid body motion vector of the optical element;

[0012] Wherein, for the optical element of the optical system, for any degree of freedom direction, according to the imaging relationship of the light from the optical element to the image plane of the optical system, when the optical element generates a motion amount in the degree of freedom direction, obtain the motion amount of the image formed in the degree of freedom direction, and according to the motion amount of the image formed in the degree of freedom direction and the motion amount of the optical element in the degree of freedom direction, obtain the optical axis stability error component coefficient of the optical element in the degree of freedom direction, wherein, the optical axis stability error component coefficient of the optical element in the degree of freedom direction describes the movement amount of the image formed by the optical system when the optical element has a unit motion amount in the degree of freedom direction.

[0013] Optionally, obtaining the optical axis stability error component coefficient of the optical element in the degree of freedom direction according to the motion amount of the image formed in the degree of freedom direction and the motion amount of the optical element in the degree of freedom direction includes:

[0014] Obtain the optical axis stability error component coefficient of the optical element in the degree of freedom direction according to the ratio of the motion amount of the image formed in the degree of freedom direction to the motion amount of the optical element in the degree of freedom direction.

[0015] Optionally, the optical system includes first to m optical elements arranged in sequence along the optical axis from the object side to the image side, where m is a positive integer greater than or equal to 1;

[0016] The degree of freedom direction is the direction of translation along the x-axis, the direction of translation along the y-axis, the direction of rotation around the x-axis or the direction of rotation around the y-axis:

[0017] If m ≥ 2, for the j-th optical element, multiply the amount of movement of the j-th optical element in the direction of the degree of freedom of movement, the first difference, and the lateral magnification of the optical element on the image side of the j-th optical element in sequence, and obtain the amount of movement of the image formed in the direction of the degree of freedom of movement according to the obtained product. The first difference represents the difference between 1 and the lateral magnification of the j-th optical element, where j ∈ [1, m - 1];

[0018] For the m-th optical element, obtain the amount of movement of the image formed in the direction of the degree of freedom of movement according to the product of the amount of movement of the m-th optical element in the direction of the degree of freedom of movement and the second difference. The second difference represents the difference between 1 and the lateral magnification of the m-th optical element;

[0019] If m = 1, obtain the amount of movement of the image formed in the direction of the degree of freedom of movement according to the product of the amount of movement of the m-th optical element in the direction of the degree of freedom of movement and the second difference. The second difference represents the difference between 1 and the lateral magnification of the m-th optical element.

[0020] Optionally, the optical system includes the first to m-th optical elements arranged in sequence along the optical axis from the object side to the image side, where m is a positive integer greater than or equal to 1;

[0021] The direction of the degree of freedom of movement is the direction of translation along the z-axis:

[0022] If m ≥ 2, for the j-th optical element, multiply the amount of movement of the j-th optical element in the direction of the degree of freedom of movement, the third difference, and the square of the lateral magnification of the optical element on the image side of the j-th optical element in sequence, and obtain the amount of movement of the image formed in the direction of the degree of freedom of movement according to the obtained product. The third difference represents the difference between 1 and the square of the lateral magnification of the j-th optical element, where j ∈ [1, m - 1];

[0023] For the m-th optical element, obtain the amount of movement of the image formed in the direction of the degree of freedom of movement according to the product of the amount of movement of the m-th optical element in the direction of the degree of freedom of movement and the fourth difference. The fourth difference represents the difference between 1 and the square of the lateral magnification of the m-th optical element;

[0024] If m = 1, obtain the amount of movement of the image formed in the direction of the degree of freedom of movement according to the product of the amount of movement of the m-th optical element in the direction of the degree of freedom of movement and the fourth difference. The fourth difference represents the difference between 1 and the square of the lateral magnification of the m-th optical element;

[0025] Or / and, the direction of the degree of freedom of movement is the direction of rotation around the z-axis. For the j-th optical element, obtain the amount of movement of the image formed in the direction of the degree of freedom of movement according to the product of the amount of movement of the j-th optical element in the direction of the degree of freedom of movement and 0, where j ∈ [1, m].

[0026] Optionally, obtaining the rigid body motion vector of the optical element based on the actual motion vector of the node of the optical element and the rigid body motion vector of the node includes:

[0027] Obtaining the initial position of the node of the optical element in the structural model, after applying a load to the optical system, obtaining the actual motion vector of the node, and obtaining the rigid body motion vector of the node based on the initial position of the node combined with the influence of the motion of the node by the optical element moving in a rigid body form;

[0028] Based on the actual motion vector of the node of the optical element and the rigid body motion vector of the node, obtaining the rigid body motion vector of the optical element such that after the optical element moves according to the rigid body motion vector of the optical element, the difference between the actual motion vector of the node and the rigid body motion vector of the corresponding node is minimized.

[0029] Optionally, obtaining the rigid body motion vector of the node includes: based on the initial position of the node, combined with the influence of the motion of the node by the optical element moving in a rigid body form, using the homogeneous coordinate transformation method in three-dimensional space to obtain the rigid body motion vector of the node, expressed as;

[0030] ;

[0031] wherein, the initial position of the i-th node of the optical element in the structural model is , the rigid body motion vector of the i-th node is , the rigid body motion vector of the optical element is expressed as , and i represents the i-th node.

[0032] Optionally, based on the actual motion vector of the node of the optical element and the rigid body motion vector of the node, obtaining the rigid body motion vector of the optical element includes:

[0033] Constructing a motion error evaluation function using the actual motion vector of the node and the rigid body motion vector of the node, and the motion error evaluation function describes the sum of the differences between the actual motion vectors of multiple nodes of the optical element and the rigid body motion vectors of the corresponding nodes;

[0034] Taking the partial derivatives of the motion error evaluation function with respect to the amounts of motion in the directions of each degree of freedom of motion of the optical element respectively, and setting the partial derivatives to 0, and solving the obtained system of equations to obtain the rigid body motion vector of the optical element.

[0035] Optionally, obtaining the evaluation result of the optical axis stability error of the optical element based on the optical axis stability error component coefficients in the directions of each degree of freedom of motion of the optical element and the rigid body motion vector of the optical element includes:

[0036] Based on the rigid body motion vector of the optical element, using the optical axis stability error evaluation equation, an optical axis stability error evaluation result of the optical element is obtained. The optical axis stability error evaluation equation describes that for any direction of the degree of freedom of motion, the optical axis stability error component coefficient in the direction of the degree of freedom of motion of the optical element is multiplied by the amount of motion in the direction of the degree of freedom of motion in the rigid body motion vector of the optical element.

[0037] Optionally, obtaining the optical axis stability error evaluation result of the optical element according to the optical axis stability error component coefficients in the respective directions of the degree of freedom of motion of the optical element and the rigid body motion vector of the optical element includes:

[0038] Based on the rigid body motion vector of the optical element, using the optical axis stability error evaluation equation, an optical axis stability error evaluation result of the optical element is obtained, wherein the optical axis stability error evaluation equation describes the multiplication of an optical axis stability error coefficient matrix and a motion matrix. The optical axis stability error coefficient matrix is formed by the optical axis stability error component coefficients in the respective directions of the degree of freedom of motion of the at least one optical element of the optical system, and the motion matrix is formed by the rigid body motion vectors of the at least one optical element of the optical system.

[0039] An optical axis stability evaluation system for an optical system, comprising:

[0040] A memory for storing a computer program;

[0041] A processor for implementing the steps of the optical axis stability evaluation method for an optical system as described in any one of the above when executing the computer program.

[0042] As can be seen from the above technical solutions, for the optical system optical axis stability evaluation method and system provided by the present invention, the optical system includes at least one optical element. For the optical element of the optical system, for any direction of the degree of freedom of movement, according to the imaging relationship of the light ray from the optical element to the image plane of the optical system, when the amount of movement in the direction of the degree of freedom of movement is generated in the optical element, the amount of movement of the image formed in the direction of the degree of freedom of movement is obtained. According to the amount of movement of the image formed in the direction of the degree of freedom of movement and the amount of movement of the optical element in the direction of the degree of freedom of movement, the optical axis stability error component coefficient of the optical element in the direction of the degree of freedom of movement is obtained. The method includes: establishing a structural model of the optical system; applying a load to the optical system in the structural model to obtain the actual movement vector of the nodes of the optical element and the rigid body movement vector of the nodes, and obtaining the rigid body movement vector of the optical element according to the actual movement vector of the nodes of the optical element and the rigid body movement vector of the nodes; according to the optical axis stability error component coefficients in the respective directions of the degree of freedom of movement of the optical element and the rigid body movement vector of the optical element, obtaining the optical axis stability error evaluation result of the optical element.

[0043] The optical system optical axis stability evaluation method and system of the present invention establish a structural model of the optical system and obtain the optical axis stability error component coefficient of the optical element in the direction of the degree of freedom of movement according to the imaging relationship of the light ray from the optical element to the image plane of the optical system. After simulating the application of a load to the optical system in the structural model, the rigid body movement vector of the optical element is obtained, and then the optical axis stability error evaluation result of the optical element is obtained, realizing the evaluation of the optical axis stability of the optical system. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0045] Figure 1 It is a flowchart of an optical system optical axis stability evaluation method provided by an embodiment of the present invention;

[0046] Figure 2 It is a schematic diagram of an optical system according to an embodiment of the present invention;

[0047] Figure 3 For Figure 2 The structural model established for the optical system shown;

[0048] Figure 4 It is a flowchart of the method for obtaining the rigid body movement vector of the optical element in the optical system optical axis stability evaluation method according to an embodiment of the present invention.

[0049] The reference numerals in the accompanying drawings of the specification include:

[0050] 101 - primary mirror, 102 - secondary mirror, 103 - tertiary mirror, 104 - folding mirror, 105 - detector. Detailed implementation manners

[0051] In order to enable those skilled in the art to better understand the technical solutions in the present invention, the following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without making creative efforts shall fall within the protection scope of the present invention.

[0052] Reference can be made to Figure 1 , Figure 1 which is a flowchart of a method for evaluating the optical axis stability of an optical system provided for an embodiment. The optical system includes at least one optical element, and the method for evaluating the optical axis stability of the optical system includes the following steps:

[0053] S11: Establish a structural model of the optical system.

[0054] The structural model of the optical system reflects the arrangement positions of the optical elements in the optical system and the structures of the optical elements. In the structural model of the optical system, the optical elements of the optical system are divided into multiple nodes.

[0055] S12: Apply a load to the optical system in the structural model to obtain the actual motion vectors of the nodes of the optical elements and the rigid body motion vectors of the nodes, and obtain the rigid body motion vectors of the optical elements according to the actual motion vectors of the nodes of the optical elements and the rigid body motion vectors of the nodes.

[0056] Simulate applying a load to the optical system in the structural model. Under the applied load, the optical elements of the optical system will move, and the motion vectors of the nodes of the optical elements are obtained. The motion vectors of the nodes reflect the motion conditions of the nodes.

[0057] In this embodiment, it is considered that the optical elements move in the form of a rigid body, and the rigid body motion vector of the optical element refers to the motion vector of the optical element moving in the form of a rigid body.

[0058] Obtain the rigid body motion vectors of the optical elements according to the motion vectors of the nodes of the optical elements. The motion vectors of the nodes include the amounts of motion of the nodes in the directions of each degree of freedom of motion. The rigid body motion vectors of the optical elements include the amounts of motion of the optical elements in the directions of each degree of freedom of motion.

[0059] S13: Obtain the evaluation result of the optical axis stability error of the optical element according to the optical axis stability error component coefficients in the directions of various degrees of freedom of movement of the optical element and the rigid body motion vector of the optical element.

[0060] Among them, for the optical element of the optical system, for any direction of degree of freedom of movement, according to the imaging relationship of light from the optical element to the image plane of the optical system, when the optical element generates a movement amount in the direction of the degree of freedom of movement, obtain the movement amount of the imaged image in the direction of the degree of freedom of movement. According to the movement amount of the imaged image in the direction of the degree of freedom of movement and the movement amount of the optical element in the direction of the degree of freedom of movement, obtain the optical axis stability error component coefficient of the optical element in the direction of the degree of freedom of movement. Among them, the optical axis stability error component coefficient of the optical element in the direction of the degree of freedom of movement describes the movement amount of the image formed by the optical system when the optical element has a unit movement amount in the direction of the degree of freedom of movement.

[0061] For any optical element of the optical system, for any direction of degree of freedom of movement, the optical axis stability error component coefficient corresponding to any direction of degree of freedom of movement of the optical element can be obtained.

[0062] After obtaining the rigid body motion vector of the optical element by using the structural model of the optical system, the evaluation result of the optical axis stability error of the optical element can be obtained according to the rigid body motion vector of the optical element and the optical axis stability error component coefficients in the directions of various degrees of freedom of movement of the optical element. Therefore, the optical axis stability evaluation method of the optical system in this embodiment realizes the evaluation of the optical axis stability of the optical system by establishing the structural model of the optical system, obtaining the optical axis stability error component coefficients of the optical element in the direction of the degree of freedom of movement according to the imaging relationship of light from the optical element to the image plane of the optical system, simulating the application of load to the optical system in the structural model to obtain the rigid body motion vector of the optical element, and then obtaining the evaluation result of the optical axis stability error of the optical element.

[0063] In some embodiments, establishing the structural model of the optical system includes: establishing the optical system and establishing the structural model according to the design index requirements of the optical system. According to the design index requirements of the optical system, determine the number of optical elements included in the optical system, the optical structure of the optical elements, and the arrangement of the optical elements along the optical path. Exemplarily, optical design software can be used to design the optical system according to the design index requirements.

[0064] Further, a structural model of the optical system can be established based on the established optical system. The structural model of the optical system reflects the structures of the optical elements of the optical system, the arrangement positions of the optical elements in the optical system, and may also include the support structural members of the optical elements. Exemplarily, computer-aided design (CAD) software can be used to establish the structural model of the optical system.

[0065] In some embodiments, the structural model can be divided into finite elements. When performing the finite element division, the quality of the mesh division will directly affect the calculation scale, calculation speed, and the accuracy of the evaluation results obtained through subsequent numerical calculations.

[0066] Exemplarily, reference can be made to Figure 2 and Figure 3 , Figure 2 which is a schematic diagram of an optical system of an embodiment, Figure 3 for Figure 2 the structural model established for the optical system shown. Figure 2 The solid lines with arrows in Figure 2 indicate the light propagation direction. As shown in Figure 3 , in this embodiment, the optical system includes a primary mirror 101, a secondary mirror 102, a tertiary mirror 103, a folding mirror 104, and a detector 105. The light of the object is reflected by the primary mirror 101, the secondary mirror 102, the tertiary mirror 103, and the folding mirror 104 in sequence and then imaged onto the detector 105. The detector 105 can be arranged on the image plane. As shown in

[0067] Due to the action of internal and external loads, the optical system will cause deviations of the optical elements, resulting in optical misalignment, and ultimately affecting the degradation of the imaging quality of the optical system. The method of this embodiment analyzes the change amount of the optical axis stability error by establishing a mathematical model to explore the optical axis stability.

[0068] When the perturbation received by the optical system is very small, any high-order aberration of the optical system can be ignored, and the first-order Taylor expansion of the optical path matrix L can be expressed as:

[0069] ; (1)

[0070] Wherein, L0 represents the size of the optical axis in the ideal case of the optical system, ΔU represents the rigid body movement amount of the optical element, ∂L / ∂U represents the first-order partial derivative of L with respect to U, that is, the sensitivity coefficient matrix. ∂L / ∂U contains all the wavefront data of the optical system, and ∂L / ∂U includes two parts: optical sensitivity and wavefront difference sensitivity. The optical sensitivity can be used to calculate the optical axis stability error, and the wavefront difference sensitivity can be used to calculate the aberration. The method of this embodiment analyzes the optical axis stability only using the optical sensitivity coefficient. O(2) represents the high-order variation amount of the optical axis.

[0071] For any direction of the degree of freedom of movement, according to the imaging relationship of the light ray from the optical element to the image plane of the optical system, when obtaining the movement amount of the optical element in the direction of the degree of freedom of movement, the movement amount of the image formed in the direction of the degree of freedom of movement is obtained. According to the movement amount of the image formed in the direction of the degree of freedom of movement and the movement amount of the optical element in the direction of the degree of freedom of movement, the optical axis stability error component coefficient of the optical element in the direction of the degree of freedom of movement is obtained. Exemplarily, the degrees of freedom of movement of the optical element are six, including translation along the x-axis, translation along the y-axis, translation along the z-axis, rotation about the x-axis, rotation about the y-axis, and rotation about the z-axis. For example, the optical system includes m optical elements, where m is a positive integer greater than or equal to 1. For the translation direction along the x-axis, the movement amount of the j-th optical element in the translation direction along the x-axis is denoted as Tx j , and the movement amount of the image formed in the translation direction along the x-axis is denoted as T´x j , according to T´x j and Tx j , the optical axis stability error component coefficient of the j-th optical element in the translation direction along the x-axis can be obtained, where j ∈ [1, m].

[0072] In some embodiments, obtaining the optical axis stability error component coefficient of the optical element in the direction of the degree of freedom of movement according to the movement amount of the image formed in the direction of the degree of freedom of movement and the movement amount of the optical element in the direction of the degree of freedom of movement includes: obtaining the optical axis stability error component coefficient of the optical element in the direction of the degree of freedom of movement according to the ratio of the movement amount of the image formed in the direction of the degree of freedom of movement to the movement amount of the optical element in the direction of the degree of freedom of movement. Obtain the ratio of the movement amount of the image formed in the direction of the degree of freedom of movement to the movement amount of the optical element in the direction of the degree of freedom of movement, and obtain the optical axis stability error component coefficient of the optical element in the direction of the degree of freedom of movement according to the ratio. Exemplarily, the movement amount of the j-th optical element in the translation direction along the x-axis is denoted as Tx j , and the movement amount of the image formed in the translation direction along the x-axis is denoted as T´x j , and their ratio is denoted as T´x j / Tx j , according to T´x j / Tx jThe coefficient of the optical axis stability error component in the translational direction of the j-th optical element along the x-axis can be obtained, where j ∈ [1, m].

[0073] In some embodiments, the optical system includes first to m-th optical elements arranged in sequence along the optical axis from the object side to the image side, where m is a positive integer greater than or equal to 1, and the direction of the degree of freedom of movement is the translational direction along the x-axis, the translational direction along the y-axis, the rotational direction about the x-axis, or the rotational direction about the y-axis;

[0074] If m ≥ 2, for the j-th optical element, the amount of movement of the j-th optical element in the direction of the degree of freedom of movement, the first difference, and the lateral magnification of the optical element on the image side of the j-th optical element are multiplied in sequence, and the amount of movement of the image formed in the direction of the degree of freedom of movement is obtained according to the obtained product. The first difference represents the difference between 1 and the lateral magnification of the j-th optical element, where j ∈ [1, m - 1];

[0075] For the m-th optical element, the amount of movement of the image formed in the direction of the degree of freedom of movement is obtained according to the product of the amount of movement of the m-th optical element in the direction of the degree of freedom of movement and the second difference. The second difference represents the difference between 1 and the lateral magnification of the m-th optical element.

[0076] If m = 1, the amount of movement of the image formed in the direction of the degree of freedom of movement is obtained according to the product of the amount of movement of the m-th optical element in the direction of the degree of freedom of movement and the second difference. The second difference represents the difference between 1 and the lateral magnification of the m-th optical element.

[0077] Exemplarily, if m ≥ 2, for the j-th optical element, where j ∈ [1, m - 1], the amounts of movement of the image formed in the translational direction along the x-axis, the translational direction along the y-axis, the rotational direction about the x-axis, and the rotational direction about the y-axis can be obtained according to the following formulas:

[0078] ; (2)

[0079] ; (3)

[0080] ; (4)

[0081] ; (5)

[0082] where T´x j represents the amount of movement of the image formed in the translational direction along the x-axis, Tx j represents the amount of movement of the j-th optical element in the translational direction along the x-axis, T´y j represents the amount of movement of the image formed in the translational direction along the y-axis, Ty j represents the amount of movement of the j-th optical element in the translational direction along the y-axis, R´x jIndicates the amount of movement of the imaged object in the direction of rotation about the x-axis, Rx j Indicates the amount of movement of the j-th optical element in the direction of rotation about the x-axis, R´y j Indicates the amount of movement of the imaged object in the direction of rotation about the y-axis, Ry j Indicates the amount of movement of the j-th optical element in the direction of rotation about the y-axis, M j Indicates the transverse magnification of the j-th optical element, M j+1 Indicates the transverse magnification of the (j + 1)-th optical element, and (1.0) indicates the transverse magnification of the detector of the optical system.

[0083] For the m-th optical element, the amounts of movement of the imaged object in the directions of translation along the x-axis, translation along the y-axis, rotation about the x-axis, and rotation about the y-axis can be obtained according to the following formulas:

[0084] ; (6)

[0085] ; (7)

[0086] ; (8)

[0087] ; (9)

[0088] where, T´x m Indicates the amount of movement of the imaged object in the direction of translation along the x-axis, Tx m Indicates the amount of movement of the m-th optical element in the direction of translation along the x-axis, T´y m Indicates the amount of movement of the imaged object in the direction of translation along the y-axis, Ty m Indicates the amount of movement of the m-th optical element in the direction of translation along the y-axis, R´x m Indicates the amount of movement of the imaged object in the direction of rotation about the x-axis, Rx m Indicates the amount of movement of the m-th optical element in the direction of rotation about the x-axis, R´y m Indicates the amount of movement of the imaged object in the direction of rotation about the y-axis, Ry m Indicates the amount of movement of the m-th optical element in the direction of rotation about the y-axis, M m Indicates the transverse magnification of the m-th optical element, and (1.0) indicates the transverse magnification of the detector of the optical system.

[0089] When calculating using the above formulas, if the amount of movement of the optical element in the direction of the corresponding degree of freedom of movement is a unit amount of movement, then the value obtained by calculation according to the formula can represent the coefficient of the optical axis stability error component of the optical element in the direction of this degree of freedom of movement.

[0090] In some embodiments, the optical system includes first to mth optical elements sequentially arranged along the optical axis from the object side to the image side, where m is a positive integer greater than or equal to 1; the direction of the degree of freedom of movement is the direction of translation along the z-axis:

[0091] If m≥2, for the jth optical element, multiply the amount of movement of the jth optical element in the direction of the degree of freedom of movement, the third difference, and the square of the lateral magnification of the optical element on the image side of the jth optical element in sequence, and use the obtained product as the amount of movement of the imaged object in the direction of the degree of freedom of movement. The third difference represents the difference between 1 and the square of the lateral magnification of the jth optical element, and j∈[1, m - 1];

[0092] For the mth optical element, obtain the amount of movement of the imaged object in the direction of the degree of freedom of movement according to the product of the amount of movement of the mth optical element in the direction of the degree of freedom of movement and the fourth difference. The fourth difference represents the difference between 1 and the square of the lateral magnification of the mth optical element;

[0093] If m = 1, obtain the amount of movement of the imaged object in the direction of the degree of freedom of movement according to the product of the amount of movement of the mth optical element in the direction of the degree of freedom of movement and the fourth difference. The fourth difference represents the difference between 1 and the square of the lateral magnification of the mth optical element.

[0094] Exemplarily, if m≥2, for the jth optical element, j∈[1, m - 1], the amount of movement of the imaged object in the direction of translation along the z-axis can be obtained according to the following formula:

[0095] ; (10)

[0096] where, T´z j represents the amount of movement of the imaged object in the direction of translation along the z-axis, Tz j represents the amount of movement of the jth optical element in the direction of translation along the z-axis, M j represents the lateral magnification of the jth optical element, M j+1 represents the lateral magnification of the j + 1th optical element, and (1.0) represents the lateral magnification of the detector of the optical system.

[0097] For the mth optical element, the amount of movement of the imaged object in the direction of translation along the z-axis can be obtained according to the following formula:

[0098] ; (11)

[0099] where, T´z m represents the amount of movement of the imaged object in the direction of translation along the z-axis, Tz m represents the amount of movement of the mth optical element in the direction of translation along the z-axis, M mrepresents the lateral magnification of the m-th optical element, and (1.0) represents the lateral magnification of the detector of the optical system.

[0100] In some embodiments, the optical system includes first to m-th optical elements arranged in sequence along the optical axis from the object side to the image side, where m is a positive integer greater than or equal to 1; the direction of the degree of freedom of movement is the direction of rotation about the z-axis. For the j-th optical element, the amount of movement of the imaged object in the direction of the degree of freedom of movement is obtained according to the product of the amount of movement of the j-th optical element in the direction of the degree of freedom of movement and 0, where j ∈ [1, m].

[0101] Exemplarily, for the j-th optical element, where j ∈ [1, m], the amount of movement of the imaged object in the direction of rotation about the z-axis can be obtained according to the following formula:

[0102] ; (12)

[0103] where, R´z j represents the amount of movement of the imaged object in the direction of rotation about the z-axis, Rz j represents the amount of movement of the j-th optical element in the direction of rotation about the z-axis, and (1.0) represents the lateral magnification of the detector of the optical system.

[0104] When calculating using the above formula, if the amount of movement of the optical element in the corresponding direction of the degree of freedom of movement is a unit amount of movement, then the value calculated according to the formula can represent the coefficient of the optical axis stability error component of the optical element in the direction of the degree of freedom of movement.

[0105] In some embodiments, obtaining the rigid body motion vector of the optical element according to the actual motion vector of the node of the optical element and the rigid body motion vector of the node includes the following steps, which can be referred to Figure 4 as shown Figure 4 is a flowchart of the method for obtaining the rigid body motion vector of the optical element in the method for evaluating the optical axis stability of an optical system in an embodiment:

[0106] S131: Obtain the initial position of the node of the optical element in the structural model. After applying a load to the optical system, obtain the actual motion vector of the node, and obtain the rigid body motion vector of the node according to the initial position of the node combined with the influence of the node motion by the rigid body motion of the optical element.

[0107] Simulate applying a load to the optical system in the structural model. Under the applied load, the optical elements of the optical system will move, and obtain the actual motion vector of the nodes of the optical elements.

[0108] According to the initial position of the node, combined with the influence of the node motion by the rigid body motion of the optical element, obtain the rigid body motion vector of the node.

[0109] S132: Obtain the rigid body motion vector of the optical element based on the actual motion vector of the node of the optical element and the rigid body motion vector of the node, such that after the optical element moves according to the rigid body motion vector of the optical element, the difference between the actual motion vector of the node and the rigid body motion vector of the corresponding node is minimized.

[0110] For the obtained rigid body motion vector of the optical element, after the optical element moves from the initial state according to this rigid body motion vector, the difference between the actual motion vector of the node and the rigid body motion vector of the node is minimized.

[0111] In some embodiments, obtaining the rigid body motion vector of the node includes: based on the initial position of the node, combined with the influence of the motion of the node by the rigid body motion of the optical element, using the homogeneous coordinate transformation method in three-dimensional space to obtain the rigid body motion vector of the node.

[0112] In practical applications, the actual displacement of the node represents the actual motion vector of the node, the rigid body displacement of the node represents the rigid body motion vector of the node, and the actual displacement or rigid body displacement of the node includes the displacement amount along the x-axis, the displacement amount along the y-axis, and the displacement amount along the z-axis.

[0113] Obtaining the rigid body motion vector of the node using the homogeneous coordinate transformation method in three-dimensional space can be expressed as:

[0114] ; (13)

[0115] wherein, the initial position of the i-th node of the optical element in the structure model is , the rigid body motion vector of the i-th node is , the rigid body motion vector of the optical element is expressed as , and i represents the i-th node.

[0116] The homogeneous coordinate transformation method in three-dimensional space can be calculated according to the following relational expression:

[0117] ; (14)

[0118] wherein, the initial position of the i-th node of the optical element in the structure model is , the rigid body motion vector of the i-th node is , the rigid body motion vector of the optical element is expressed as , and i represents the i-th node. Formula (13) can be obtained according to formula (14).

[0119] In the homogeneous coordinate transformation method in three-dimensional space, the initial position of the node is After rigid body displacement, the node positions are The homogeneous transformation matrix A is expressed as:

[0120] . (15)

[0121] Among them, since Rx, Ry, and Rz are very small, sinRx≈Rx, cosRx≈1, and so on.

[0122] Through homogeneous coordinate transformation, we can obtain:

[0123] . (16)

[0124] In some embodiments, obtaining the rigid body motion vector of the optical element according to the actual motion vector of the nodes of the optical element and the rigid body motion vector of the nodes includes: constructing a motion error evaluation function using the actual motion vector of the nodes and the rigid body motion vector of the nodes, where the motion error evaluation function describes the sum of the differences between the actual motion vectors of multiple nodes of the optical element and the rigid body motion vectors of the corresponding nodes; taking partial derivatives of the motion error evaluation function with respect to the motion amounts in the respective motion degrees of freedom directions of the optical element, and setting the partial derivatives to 0, and solving the obtained system of equations to obtain the rigid body motion vector of the optical element.

[0125] The motion error evaluation function describes the sum of the differences between the actual motion vectors of multiple nodes of the optical element and the rigid body motion vectors of the corresponding nodes. The difference between the actual motion vector of a node and the rigid body motion vector of the corresponding node can be the sum of the squares of the differences in each motion degree of freedom direction of the node. The square of the difference in any motion degree of freedom direction of the node represents the square of the difference between the motion amount of the actual motion vector of the node in the motion degree of freedom direction and the rigid body motion amount of the rigid body motion vector of the node in the motion degree of freedom direction. Exemplarily, the motion error evaluation function can be expressed as:

[0126] ; (17)

[0127] Among them, the actual motion vector of the i-th node of the optical element is , and the rigid body motion vector of the i-th node is , where i represents the i-th node of the optical element.

[0128] By taking partial derivatives of the motion error evaluation function with respect to the motion amounts in the respective motion degrees of freedom directions of the optical element, and setting the partial derivatives to 0, the rigid body motion vector of the optical element is solved and obtained. The rigid body motion vector of the optical element can adopt a finite element analysis calculation method. For small optical elements, their elastic deformation can be ignored, so a single-point model with coupled and concentrated mass can be used to represent the rigid body motion. However, for large optical systems such as space cameras, the optical elements used are mostly meter-level optical elements, and rigid body motion needs to be considered. In this embodiment, the least squares method is used to obtain the rigid body motion vector of the optical element based on the motion vectors of multiple nodes of the optical element, and the least squares method is applied to obtain the rigid body motion of the multi-node surface with equal weights.

[0129] In some embodiments, obtaining the evaluation result of the optical axis stability error of the optical element according to the optical axis stability error component coefficients in the respective motion degrees of freedom directions of the optical element and the rigid body motion vector of the optical element includes: using the optical axis stability error evaluation equation according to the rigid body motion vector of the optical element to obtain the evaluation result of the optical axis stability error of the optical element, where the optical axis stability error evaluation equation describes that for any motion degree of freedom direction, multiplying the optical axis stability error component coefficient in the motion degree of freedom direction of the optical element by the motion amount in the motion degree of freedom direction in the rigid body motion vector of the optical element.

[0130] In some embodiments, obtaining the evaluation result of the optical axis stability error of the optical element according to the optical axis stability error component coefficients in the respective motion degrees of freedom directions of the optical element and the rigid body motion vector of the optical element includes: using the optical axis stability error evaluation equation according to the rigid body motion vector of the optical element to obtain the evaluation result of the optical axis stability error of the optical element, where the optical axis stability error evaluation equation describes the multiplication of the optical axis stability error coefficient matrix and the motion matrix, the optical axis stability error coefficient matrix is formed by the optical axis stability error component coefficients in the respective motion degrees of freedom directions of the at least one optical element of the optical system, and the motion matrix is formed by the rigid body motion vectors of the at least one optical element of the optical system.

[0131] Exemplarily, the optical axis stability error coefficient matrix [L] Img can be expressed as:

[0132] . (18)

[0133] Wherein, represents the optical axis stability error component coefficient in the first degree of freedom direction of the first optical element, represents the optical axis stability error component coefficient in the nth degree of freedom direction of the first optical element, The coefficient of the optical axis stability error component in the first degree-of-freedom direction of the m-th optical element The coefficient of the optical axis stability error component in the n-th degree-of-freedom direction of the m-th optical element

[0134] The motion matrix of the optical system is expressed as {X} Optics , and the optical axis stability error evaluation equation of the optical system can be expressed as:

[0135] . (19)

[0136] In this embodiment, the optical system can be a space camera, and can be exemplarily applied to Figure 2 and Figure 3 the off-axis three-mirror space camera shown

[0137] This embodiment also provides an optical system optical axis stability evaluation system, including:

[0138] A memory for storing a computer program;

[0139] A processor for implementing the steps of the optical system optical axis stability evaluation method as described in any one of the above embodiments when executing the computer program

[0140] The optical system optical axis stability evaluation system of this embodiment realizes the evaluation of the optical axis stability of the optical system by establishing a structural model of the optical system, obtaining the coefficient of the optical axis stability error component of the optical element in the direction of the degree of freedom of motion according to the imaging relationship of the light from the optical element to the image plane of the optical system, simulating the rigid body motion vector of the optical element after applying a load to the optical system in the structural model, and then obtaining the evaluation result of the optical axis stability error of the optical element

[0141] In some embodiments, the optical axis stability error evaluation equation can be constructed by the second type of response (DRESP2) in finite element software to realize the online evaluation inside the finite element solver of the optical sensitivity coefficient (i.e., the coefficient of the optical axis stability error component) and the rigid body displacement information of each optical element in six degrees-of-freedom directions, that is, to obtain the optical axis stability error caused by the static load condition and find out the optical axis sensitive optical elements, which can be used as an auxiliary judgment basis for the subsequent re-optimization design of the opto-mechanical structure and subsequent processing and alignment

[0142] The method and system for evaluating the optical axis stability of the optical system in this embodiment first establish the optical system and structural model of the space camera. Secondly, the opto-mechanical constraint equations of the space camera in the mechanical coordinate system are constructed, and the optical sensitivity coefficient matrix in the six-degree-of-freedom directions of each optical element is obtained based on the opto-mechanical constraint equations of the space camera system. Thirdly, a finite element model of the opto-mechanical system of the space camera is constructed based on the opto-mechanical model, and the static loads to be analyzed are set. Fourthly, an online evaluation method for the optical axis stability at the finite element solver level of the space camera in the static environment is constructed through the second type of response (DRESP2). Finally, the optical axis stability error of the space camera under the action of the load is analyzed, and the sensitive optical elements are determined according to the contribution degree of the optical elements of the space camera.

[0143] The method and system for evaluating the optical axis stability of the optical system in this embodiment aim to analyze the optical axis stability error of the optical system under the action of static loads. This method provides an evaluation basis for the re-optimization design and progressive optimization of the opto-mechanical structure of the space camera, and can also provide an auxiliary alignment benchmark for the initial successful assembly and testing of the system.

[0144] The above has introduced in detail a method and system for evaluating the optical axis stability of an optical system provided by the present invention. Specific examples are used in this article to elaborate on the principle and implementation manner of the present invention. The description of the above embodiments is only used to help understand the method and its core idea of the present invention. It should be noted that for those of ordinary skill in the art of this technology, without departing from the principle of the present invention, several improvements and modifications can still be made to the present invention, and these improvements and modifications also fall within the protection scope of the claims of the present invention.

Claims

1. A method for evaluating optical axis stability of an optical system, wherein the optical system comprises at least one optical element, characterized in that: include: Establishing a structural model of the optical system; Applying loads to the optical system in the structural model to obtain actual motion vectors of nodes of the optical element and rigid body motion vectors of nodes, and obtaining rigid body motion vectors of the optical element according to the actual motion vectors of the nodes of the optical element and the rigid body motion vectors of the nodes; Obtaining an optical axis stability error evaluation result of the optical element according to the optical axis stability error component coefficients of each motion degree of freedom direction of the optical element and the rigid body motion vector of the optical element; Among them, for the optical element of the optical system, for any direction of movement freedom, according to the imaging relationship of light from the optical element to the image plane of the optical system, when the optical element generates the amount of movement in the direction of movement freedom, the amount of movement imaged in the direction of movement freedom is obtained, and according to the amount of movement imaged in the direction of movement freedom and the amount of movement of the optical element in the direction of movement freedom, the optical axis stability error component coefficient of the optical element in the direction of movement freedom is obtained, wherein the optical axis stability error component coefficient of the optical element in the direction of movement freedom describes the amount of movement imaged by the optical system when the optical element undergoes a unit amount of movement in the direction of movement freedom.

2. The optical axis stability evaluation method of an optical system according to claim 1, characterized in that: According to the imaged motion amount in the direction of the motion freedom and the motion amount of the optical element in the direction of the motion freedom, obtaining the optical axis stability error component coefficient of the optical element in the direction of the motion freedom comprises: According to the ratio of the imaged motion amount in the direction of the motion freedom degree to the motion amount of the optical element in the direction of the motion freedom degree, the optical axis stability error component coefficient of the optical element in the direction of the motion freedom degree is obtained.

3. The optical axis stability evaluation method of an optical system according to claim 1, characterized in that: The optical system comprises first to mth optical elements arranged in sequence along the optical axis from the object side to the image side, where m is a positive integer greater than or equal to 1; The direction of the degree of freedom of motion is the direction of translation along the x-axis, the direction of translation along the y-axis, the direction of rotation around the x-axis, or the direction of rotation around the y-axis: If m≥2, for the jth optical element, the amount of motion of the jth optical element in the direction of the motion freedom, the first difference, and the vertical axis magnification of the optical element on the image side of the jth optical element are multiplied in sequence, and the amount of motion of the image in the direction of the motion freedom is obtained according to the obtained product, the first difference represents the difference between 1 and the vertical axis magnification of the jth optical element, j∈[1, m-1]; For the m-th optical element, the imaged motion amount in the direction of the motion freedom is obtained according to the product of the motion amount of the m-th optical element in the direction of the motion freedom and the second difference, wherein the second difference represents the difference between 1 and the vertical axis magnification of the m-th optical element; If m=1, the imaged motion amount in the direction of the motion freedom is obtained based on the product of the motion amount of the mth optical element in the direction of the motion freedom and the second difference, where the second difference represents the difference between 1 and the vertical axis magnification of the mth optical element.

4. The optical axis stability evaluation method of an optical system according to claim 1, characterized in that: The optical system comprises first to mth optical elements arranged in sequence along the optical axis from the object side to the image side, where m is a positive integer greater than or equal to 1; The direction of the degree of freedom of motion is the direction of translation along the z-axis: If m≥2, for the j-th optical element, the amount of motion of the j-th optical element in the direction of the motion freedom, the third difference, and the square of the vertical axis magnification of the optical element on the image side of the j-th optical element are multiplied in sequence, and the amount of motion of the image in the direction of the motion freedom is obtained according to the obtained product, wherein the third difference represents the difference between 1 and the square of the vertical axis magnification of the j-th optical element, j∈[1, m-1]; For the m-th optical element, the imaged motion amount in the direction of the motion freedom is obtained according to the product of the motion amount of the m-th optical element in the direction of the motion freedom and a fourth difference, wherein the fourth difference represents a difference between 1 and the square of the vertical axis magnification of the m-th optical element; If m=1, the amount of motion of the image in the direction of the degree of freedom of motion is obtained according to the product of the amount of motion of the m-th optical element in the direction of the degree of freedom of motion and the fourth difference, wherein the fourth difference represents the difference between 1 and the square of the vertical axis magnification of the m-th optical element; Or / and, the direction of the degree of freedom of movement is the direction of rotation around the z-axis. For the j-th optical element, the amount of motion of the image in the direction of the degree of freedom of movement is obtained according to the product of the amount of motion of the j-th optical element in the direction of the degree of freedom of movement and 0, j∈[1,m].

5. The optical axis stability evaluation method of an optical system according to claim 1, characterized in that: Obtaining the rigid body motion vector of the optical element according to the actual motion vector of the node of the optical element and the rigid body motion vector of the node comprises: The initial position of the node of the optical element is obtained in the structural model, and after applying a load to the optical system, the actual motion vector of the node is obtained, and the rigid body motion vector of the node is obtained according to the initial position of the node combined with the influence of the optical element moving in a rigid body form on the motion of the node; The rigid body motion vector of the optical element is obtained according to the actual motion vector of the node of the optical element and the rigid body motion vector of the node, so that after the optical element moves according to the rigid body motion vector of the optical element, the difference between the actual motion vector of the node and the rigid body motion vector of the corresponding node is minimized.

6. The optical axis stability evaluation method of an optical system according to claim 5, characterized in that: Obtaining the rigid body motion vector of the node comprises: according to the initial position of the node, in combination with the influence of the motion of the node being affected by the motion of the optical element in the form of a rigid body, obtaining the rigid body motion vector of the node using a homogeneous coordinate transformation method in a three-dimensional space, expressed as; ； Wherein, the initial position of the i-th node of the optical element in the structural model is , the rigid body motion vector of the i-th node is , the rigid body motion vector of the optical element is expressed as , i represents the i-th node.

7. The optical axis stability evaluation method of an optical system according to claim 5, characterized in that: According to the actual motion vector of the node of the optical element and the rigid body motion vector of the node, obtaining the rigid body motion vector of the optical element comprises: Constructing a motion error evaluation function using the actual motion vector of the node and the rigid body motion vector of the node, wherein the motion error evaluation function describes the sum of the differences between the actual motion vectors of a plurality of nodes of the optical element and the rigid body motion vectors of the corresponding nodes; The motion error evaluation function is partially derived for the motion amount in each motion freedom direction of the optical element, and the partial derivative is set to 0. The rigid body motion vector of the optical element is obtained by solving the obtained equation group.

8. The optical axis stability evaluation method of an optical system according to claim 1, characterized in that: According to the optical axis stability error component coefficients of each motion freedom direction of the optical element and the rigid body motion vector of the optical element, obtaining the optical axis stability error evaluation result of the optical element comprises: According to the rigid body motion vector of the optical element, an optical axis stability error evaluation equation is used to obtain an optical axis stability error evaluation result of the optical element. The optical axis stability error evaluation equation describes, for any direction of movement freedom, multiplying the optical axis stability error component coefficient of the optical element in the direction of the movement freedom by the movement amount in the rigid body motion vector of the optical element in the direction of the movement freedom.

9. The optical axis stability evaluation method of an optical system according to claim 1, characterized in that: According to the optical axis stability error component coefficients of each motion freedom direction of the optical element and the rigid body motion vector of the optical element, obtaining the optical axis stability error evaluation result of the optical element comprises: According to the rigid body motion vector of the optical element, an optical axis stability error evaluation equation is used to obtain an optical axis stability error evaluation result of the optical element, wherein the optical axis stability error evaluation equation describes the multiplication of an optical axis stability error coefficient matrix and a motion matrix, the optical axis stability error coefficient matrix is ​​formed by the optical axis stability error component coefficients in each direction of motion freedom of the at least one optical element of the optical system, and the motion matrix is ​​formed by the rigid body motion vector of the at least one optical element of the optical system.

10. An optical system optical axis stability evaluation system, characterized in that: include: Memory for storing computer programs; A processor, configured to implement the steps of the optical axis stability evaluation method of an optical system as claimed in any one of claims 1 to 9 when executing the computer program.

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