Optical system optical axis stability evaluation method and system

Abstract

The application discloses an optical system optical axis stability evaluation method and system, and the optical system comprises at least one optical element. For the optical element, for any motion freedom direction, an optical axis stability error component coefficient of the optical element in the motion freedom direction is obtained, and the optical axis stability error component coefficient describes a movement amount of an image formed by the optical system when the optical element in the motion freedom direction has a unit movement amount. The method comprises the following steps: establishing a structure model of the 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 according to the optical axis stability error component coefficient of each motion freedom direction of the optical element and the rigid body motion vector of the optical element, an optical axis stability error evaluation result of the optical element is obtained, so that the optical axis stability evaluation of the optical system is realized.

Description

Technical Field

[0001] This invention relates to the field of optical systems, and in particular to a method and system for evaluating the optical axis stability of an optical system. Background Technology

[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 equipment. Its optical system is developing towards high resolution, large field of view, long focal length and high integration. Its working environment is also becoming more and more diverse and harsh. Optical detection equipment will be affected by internal and external loads such as gravitational field, temperature change, vibration and so on, which will cause deformation of optical system and supporting structure, and thus affect the optical axis stability of optical system.

[0003] At each stage of optical detection equipment, including preliminary laboratory testing, transportation, launch and on-orbit operation, the relative positions of optical components may be affected by complex environmental factors such as gravity, temperature and micro-vibrations, leading to a decrease in optical axis stability and thus affecting imaging quality.

[0004] To ensure the optical axis stability of optical systems, mechanical and optical compensation techniques are widely used in optical detection equipment. Since the 1990s, the effects of external environmental disturbances on the optical system structure have been reduced by employing mechanical transmission control or selecting low-expansion materials. For example, the design of spaceborne interface components for high-precision space cameras provides crucial support for the optical axis stability of remote sensors; the use of sensors such as gyroscopes, accelerometers, and star sensors for monitoring, and reaction flywheel devices to ensure the pointing accuracy of the space camera's optical axis; the reduction of vibrations during launch and operation through vibration dampers and isolators, while the use of precision actuators (such as piezoelectric ceramic actuators) for fine-tuning to ensure the optical axis stability of the optical system; and the adoption of athermalized designs, such as mechanical passive, optical passive, or hybrid passive designs, to mitigate the influence of external temperature fields, enabling the optical system to maintain excellent optical axis stability over a relatively large temperature range.

[0005] Effective evaluation of the optical axis stability of an optical system is of great significance to optical detection equipment. Accurate evaluation of the optical axis stability of an optical system has extremely important scientific value and significance for fields such as resource exploration, meteorological observation, military imaging reconnaissance, and target tracking and monitoring. Summary of the Invention

[0006] The purpose of this invention is to provide a method and system for evaluating the optical axis stability of an optical system, thereby enabling the evaluation of the optical axis stability of the optical system.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] A method for evaluating the optical axis stability of an optical system, the optical system comprising at least one optical element, including:

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

[0010] A load is applied to the optical system in the structural model to obtain the actual motion vector and rigid body motion vector of the nodes of the optical element, and the rigid body motion vector of the optical element is obtained based on the actual motion vector and rigid body motion vector of the nodes of the optical element.

[0011] The optical axis stability error evaluation result of the optical element is obtained based on the optical axis stability error component coefficients of each degree of freedom of motion of the optical element and the rigid body motion vector of the optical element.

[0012] Specifically, for any optical element in the optical system, based on the imaging relationship of light rays from the optical element to the image plane of the optical system, the amount of motion imaged in the direction of motion is obtained when the optical element generates a motion in that direction. Based on the amount of motion imaged in the direction of motion and the amount of motion of the optical element in that direction, the optical axis stability error component coefficient of the optical element in that direction is obtained. The optical axis stability error component coefficient of the optical element in that direction describes the amount of movement of the image generated by the optical system when the optical element generates a unit amount of motion in that direction.

[0013] Optionally, based on the amount of motion of the image in the direction of motion freedom and the amount of motion of the optical element in the direction of motion freedom, the optical axis stability error component coefficient of the optical element in the direction of motion freedom is obtained, including:

[0014] The optical axis stability error component coefficient of the optical element in the direction of motion is obtained by comparing the amount of motion of the image in the direction of motion with the amount of motion of the optical element in the direction of motion.

[0015] Optionally, the optical system includes first to m optical elements arranged sequentially 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 directions of the degrees of freedom of motion are: translation along the x-axis, translation along the y-axis, rotation about the x-axis, or rotation about the y-axis.

[0017] If m≥2, for the j-th optical element, the motion amount of the j-th optical element in the direction of motion freedom, the first difference, and the transverse magnification of the optical element on the image side of the j-th optical element are multiplied in sequence, and the motion amount of the image in the direction of motion freedom is obtained according to the product. The first difference represents the difference between 1 and the transverse magnification of the j-th optical element, j∈[1,m-1].

[0018] For the m-th optical element, the motion of the image in the direction of the degree of freedom of motion is obtained by multiplying the motion of the m-th optical element in the direction of the degree of freedom of motion with the second difference. The second difference represents the difference between 1 and the transverse magnification of the m-th optical element.

[0019] If m=1, the motion of the image in the direction of the degree of freedom of motion is obtained by multiplying the motion of the m-th optical element in the direction of the degree of freedom of motion with the second difference. The second difference represents the difference between 1 and the vertical magnification of the m-th optical element.

[0020] Optionally, the optical system includes first to m optical elements arranged sequentially 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 motion degree of freedom is the direction of translation along the z-axis:

[0022] If m≥2, for the j-th optical element, the motion amount of the j-th optical element in the direction of the motion degree of freedom, the third difference, and the square of the transverse magnification of the optical element on the image side of the j-th optical element are multiplied in sequence. The motion amount of the image in the direction of the motion degree of freedom is obtained according to the product. The third difference represents the difference between 1 and the square of the transverse magnification of the j-th optical element, j∈[1,m-1].

[0023] For the m-th optical element, the motion of the image in the direction of the motion degree of freedom is obtained by multiplying the motion amount of the m-th optical element in the direction of the motion degree of freedom with the fourth difference value, where the fourth difference value represents the difference between 1 and the square of the transverse magnification of the m-th optical element.

[0024] If m=1, the motion of the image in the direction of the degree of freedom of motion is obtained by multiplying the motion of the m-th optical element in the direction of the degree of freedom of motion with the fourth difference. The fourth difference represents the difference between 1 and the square of the transverse magnification of the m-th optical element.

[0025] Or / and, the direction of motion freedom is the direction of rotation about the z-axis. For the j-th optical element, the motion of the image in the direction of motion freedom is obtained by multiplying the motion of the j-th optical element in the direction of motion freedom by 0, j∈[1,m].

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

[0027] The initial position of the node of the optical element is obtained in the structural model. After applying a load to the optical system, the actual motion vector of the node is obtained. The rigid motion vector of the node is obtained based on the initial position of the node and the influence of the rigid body motion of the optical element on the node's motion.

[0028] Based on the actual motion vector of the node and the rigid motion vector of the node, the rigid motion vector of the optical element is obtained, such that after the optical element moves according to the rigid motion vector of the optical element, the difference between the actual motion vector of the node and the rigid 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 and considering the influence of the rigid body motion of the optical element on the node's motion, using a homogeneous coordinate transformation method in three-dimensional space to obtain the rigid body motion vector of the node, expressed as:

[0030] ;

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

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

[0033] A motion error evaluation function is constructed using the actual motion vector and the rigid body motion vector of the node. The motion error evaluation function describes the sum of the differences between the actual motion vectors and the rigid body motion vectors of the corresponding nodes of the optical element.

[0034] The motion error evaluation function is used to calculate the partial derivatives of the motion quantities in each degree of freedom direction of the optical element, and the partial derivatives are set to 0. The rigid body motion vector of the optical element is obtained by solving the resulting set of equations.

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

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

[0037] Optionally, the evaluation result of the optical axis stability error of the optical element is obtained based on the optical axis stability error component coefficients in each degree of freedom of motion of the optical element and the rigid body motion vector of the optical element, including:

[0038] Based on the rigid body motion vector of the optical element, the optical axis stability error evaluation result of the optical element is obtained using the optical axis stability error evaluation equation. 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 each motion degree of freedom direction of the at least one optical element of the optical system. The motion matrix is ​​formed by the rigid body motion vector of the at least one optical element of the optical system.

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

[0040] Memory, used to store computer programs;

[0041] A processor, configured to execute the computer program to implement the steps of the optical system optical axis stability evaluation method as described in any of the preceding claims.

[0042] As can be seen from the above technical solution, the optical system optical axis stability evaluation method and system provided by the present invention includes an optical system comprising at least one optical element. For any degree of freedom direction of motion of the optical element, based on the imaging relationship of light rays from the optical element to the image plane of the optical system, the amount of motion imaged in the degree of freedom direction when the optical element generates motion is obtained. Based on the amount of motion imaged in the degree of freedom direction and the amount of motion of the optical element in the degree of freedom direction, the optical axis stability error component coefficient of the optical element in the degree of freedom direction is obtained. The method includes: establishing a structural model of the optical system; applying loads to the optical system in the structural model to obtain the actual motion vectors and rigid body motion vectors of the nodes of the optical element, and obtaining the rigid body motion vector of the optical element based on the actual motion vectors and rigid body motion vectors of the nodes; and obtaining the optical axis stability error evaluation result of the optical element based on the optical axis stability error component coefficients in each degree of freedom direction of motion and the rigid body motion vector of the optical element.

[0043] The optical system optical axis stability evaluation method and system of the present invention establishes a structural model of the optical system and obtains the optical axis stability error component coefficients of the optical element in the direction of motion degree of freedom based on the imaging relationship of light from the optical element to the image plane of the optical system. After simulating the application of load to the optical system in the structural model, the rigid body motion vector of the optical element is obtained, and then the optical axis stability error evaluation result of the optical element is obtained, thus realizing the evaluation of the optical axis stability of the optical system. Attached Figure Description

[0044] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0045] Figure 1 A flowchart of an optical system optical axis stability evaluation method provided in an embodiment of the present invention;

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

[0047] Figure 3 To Figure 2 The structural model of the optical system shown is established;

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

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

[0050] 101-Primary mirror, 102-Secondary mirror, 103-Third mirror, 104-Folding mirror, 105-Detector. Detailed Implementation

[0051] To enable those skilled in the art to better understand the technical solutions of this invention, the technical solutions of the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of this invention.

[0052] For reference Figure 1 , Figure 1 A flowchart of an optical system optical axis stability evaluation method is provided as an embodiment. The optical system includes at least one optical element, and the optical system optical axis stability evaluation method includes the following steps:

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

[0054] The structural model of an optical system reflects the arrangement and structure of optical elements within the system. In this model, the optical elements are divided into multiple nodes.

[0055] S12: Apply a load to the optical system in the structural model to obtain the actual motion vector and rigid body motion vector of the nodes of the optical element, and obtain the rigid body motion vector of the optical element based on the actual motion vector and rigid body motion vector of the nodes of the optical element.

[0056] In the structural model, a load is applied to the optical system. 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 of the nodes.

[0057] In this embodiment, the optical element is considered to 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] The rigid body motion vector of the optical element is obtained from the motion vectors of its nodes. The motion vector of a node includes the amount of motion of the node in each degree of freedom. The rigid body motion vector of the optical element includes the amount of motion of the optical element in each degree of freedom.

[0059] S13: Based on the optical axis stability error component coefficients of each degree of freedom of motion of the optical element and the rigid body motion vector of the optical element, obtain the evaluation result of the optical axis stability error of the optical element.

[0060] Specifically, for any optical element in the optical system, based on the imaging relationship of light rays from the optical element to the image plane of the optical system, the amount of motion imaged in the direction of motion is obtained when the optical element generates a motion in that direction. Based on the amount of motion imaged in the direction of motion and the amount of motion of the optical element in that direction, the optical axis stability error component coefficient of the optical element in that direction is obtained. The optical axis stability error component coefficient of the optical element in that direction describes the amount of movement of the image generated by the optical system when the optical element generates a unit amount of motion in that direction.

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

[0062] After obtaining the rigid body motion vector of the optical element using the structural model of the optical system, the optical axis stability error evaluation result of the optical element can be obtained based on the rigid body motion vector of the optical element and the optical axis stability error component coefficients in each degree of freedom direction of the optical element. Therefore, the optical axis stability evaluation method of the optical system in this embodiment establishes a structural model of the optical system, obtains the optical axis stability error component coefficients in the degree of freedom direction of the optical element based on the imaging relationship of light rays from the optical element to the image plane of the optical system, simulates 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 obtains the optical axis stability error evaluation result of the optical element, thus realizing the evaluation of the optical axis stability of the optical system.

[0063] In some implementations, establishing a structural model of the optical system includes: establishing the optical system and its structural model based on the design specifications of the optical system. Based on the design specifications of the optical system, the number of optical elements, the optical structure of the optical elements, and the arrangement of the optical elements along the optical path are determined. Optical design software can be used, for example, to design the optical system according to the design specifications.

[0064] Furthermore, 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 structure of the optical elements, the arrangement of the optical elements in the optical system, and may also include supporting structural components for the optical elements. For example, computer-aided design (CAD) software can be used to establish the structural model of the optical system.

[0065] In some implementations, the structural model can be meshed using finite element methods. The quality of the mesh generation during finite element meshing directly affects the computational scale, computational speed, and the accuracy of the evaluation results obtained through subsequent numerical calculations.

[0066] For example, refer to Figure 2 and Figure 3 , Figure 2 This is a schematic diagram of an optical system according to one embodiment. Figure 3 To Figure 2 The structural model of the optical system shown is established. Figure 2 A solid line with an arrow indicates the direction of light propagation, such as... Figure 2 As shown, in this embodiment, the optical system includes a primary mirror 101, a secondary mirror 102, a third mirror 103, a folding mirror 104, and a detector 105. Light rays from an object are reflected sequentially by the primary mirror 101, secondary mirror 102, third mirror 103, and folding mirror 104 before being imaged onto the detector 105. The detector 105 can be positioned on the image plane. Figure 3 The diagram shows the structural model of the established optical system, which illustrates the structure of each mirror and the supporting structural components of the mirrors.

[0067] Optical systems can experience optical misalignment due to internal and external loads causing deviations in optical components, ultimately leading to a decrease in imaging quality. This embodiment uses a mathematical model to analyze the variation in optical axis stability error, thereby exploring optical axis stability.

[0068] When the disturbance to the optical system is very small, any higher-order aberrations 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] Where L0 represents the ideal size of the optical axis, ΔU represents the rigid body motion of the optical element, and ∂L / ∂U represents the first-order partial derivative of L with respect to U, i.e., the sensitivity coefficient matrix. ∂L / ∂U contains all wavefront data of the optical system and includes two parts: optical sensitivity and wavefront aberration sensitivity. Optical sensitivity can be used to calculate the optical axis stability error, and wavefront aberration sensitivity can be used to calculate aberrations. In this embodiment, the method for analyzing optical axis stability only uses the optical sensitivity coefficient. O(2) represents the higher-order changes of the optical axis.

[0071] For any direction of motion freedom, based on the imaging relationship of light rays from the optical element to the image plane of the optical system, the amount of motion imaged in that direction when the optical element generates motion in that direction is obtained. Based on the amount of motion imaged in that direction and the amount of motion of the optical element in that direction, the optical axis stability error component coefficient of the optical element in that direction is obtained. For example, the optical element has six degrees of freedom, 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 instance, the optical system includes m optical elements, where m is a positive integer greater than or equal to 1. For translation along the x-axis, the amount of motion of the j-th optical element in that direction is represented as Tx. j The amount of motion of the image along the x-axis translation direction is represented by T´x j According to T'x j and Tx j The optical axis stability error component coefficient of the j-th optical element along the x-axis translation direction can be obtained, j∈[1,m].

[0072] In some embodiments, obtaining the optical axis stability error component coefficient of the optical element in the direction of motion freedom, based on the amount of motion imaged in the direction of motion freedom and the amount of motion of the optical element in the direction of motion freedom, includes: obtaining the optical axis stability error component coefficient of the optical element in the direction of motion freedom based on the ratio of the amount of motion imaged in the direction of motion freedom to the amount of motion of the optical element in the direction of motion freedom. Obtaining the ratio of the amount of motion imaged in the direction of motion freedom to the amount of motion of the optical element in the direction of motion freedom, and obtaining the optical axis stability error component coefficient of the optical element in the direction of motion freedom based on the ratio. For example, the amount of motion of the j-th optical element in the translational direction along the x-axis is denoted as Tx. j The amount of motion of the image along the x-axis translation direction is represented by T´x j The ratio of the two is expressed as T´x j / Tx j According to T'x j / Tx jThe optical axis stability error component coefficient of the j-th optical element along the x-axis translation direction can be obtained, j∈[1,m].

[0073] In some embodiments, the optical system includes first to m optical elements arranged sequentially 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 directions of the degrees of freedom of motion are the direction of translation along the x-axis, the direction of translation along the y-axis, the direction of rotation about the x-axis, or the direction of rotation about the y-axis;

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

[0075] For the m-th optical element, the motion of the image in the direction of the motion degree of freedom is obtained by multiplying the motion amount of the m-th optical element in the direction of the motion degree of freedom with the second difference. The second difference represents the difference between 1 and the vertical magnification of the m-th optical element.

[0076] If m=1, the motion of the image in the direction of the degree of freedom of motion is obtained by multiplying the motion of the m-th optical element in the direction of the degree of freedom of motion with the second difference. The second difference represents the difference between 1 and the vertical magnification of the m-th optical element.

[0077] For example, if m≥2, for the j-th optical element, j∈[1,m-1], the motion of the image 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 formula:

[0078] ; (2)

[0079] ; (3)

[0080] ; (4)

[0081] ; (5)

[0082] Among them, T´x j Tx represents the amount of motion of the image along the x-axis translation direction. j Let T'y represent the amount of motion of the j-th optical element in the translational direction along the x-axis. j Ty represents the amount of motion of the image along the y-axis translation direction. j R'x represents the amount of motion of the j-th optical element in the y-axis translation direction. jRx represents the amount of motion of the image in the direction of rotation about the x-axis. j R'y represents the amount of motion of the j-th optical element in the direction of rotation about the x-axis. j Ry represents the amount of motion of the image in the direction of rotation about the y-axis. j M represents the amount of motion of the j-th optical element in the direction of rotation about the y-axis. j M represents the transverse magnification of the j-th optical element. j+1 Let (j+1) denote the transverse magnification of the (j+1)th optical element, and (1.0) denote the transverse magnification of the detector of the optical system.

[0083] For the m-th optical element, the motion of the image formed along the x-axis translation direction, along the y-axis translation direction, and around the x-axis rotation direction, and around the y-axis rotation direction, can be obtained according to the following formula:

[0084] ; (6)

[0085] ; (7)

[0086] ; (8)

[0087] ; (9)

[0088] Among them, T´x m Tx represents the amount of motion of the image along the x-axis translation direction. m T'y represents the amount of motion of the m-th optical element in the translational direction along the x-axis. m Ty represents the amount of motion of the image along the y-axis translation direction. m R'x represents the amount of motion of the m-th optical element in the y-axis translation direction. m Rx represents the amount of motion of the image in the direction of rotation about the x-axis. m R'y represents the amount of motion of the m-th optical element in the direction of rotation about the x-axis. m Ry represents the amount of motion of the image in the direction of rotation about the y-axis. m M represents the amount of motion of the m-th optical element in the direction of rotation about the y-axis. m Let (1.0) represent the vertical magnification of the m-th optical element, and let (1.0) represent the vertical magnification of the detector of the optical system.

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

[0090] In some embodiments, the optical system includes first to m optical elements arranged sequentially 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 motion degree of freedom is the direction of translation along the z-axis.

[0091] If m≥2, for the j-th optical element, the motion amount of the j-th optical element in the direction of the motion degree of freedom, the third difference, and the square of the transverse magnification of the optical element on the image side of the j-th optical element are multiplied in sequence, and the resulting product is used as the motion amount of the image in the direction of the motion degree of freedom. The third difference represents the difference between 1 and the square of the transverse magnification of the j-th optical element, j∈[1,m-1].

[0092] For the m-th optical element, the motion of the image in the direction of the motion degree of freedom is obtained by multiplying the motion amount of the m-th optical element in the direction of the motion degree of freedom with the fourth difference value, where the fourth difference value represents the difference between 1 and the square of the transverse magnification of the m-th optical element.

[0093] If m=1, the motion of the image in the direction of the motion degree of freedom is obtained by multiplying the motion amount of the m-th optical element in the direction of the motion degree of freedom with the fourth difference value, where the fourth difference value represents the difference between 1 and the square of the transverse magnification of the m-th optical element.

[0094] For example, if m≥2, for the j-th optical element, j∈[1, m-1], the amount of motion of the image along the z-axis translation direction can be obtained according to the following formula:

[0095] ; (10)

[0096] Among them, T´z j Tz represents the amount of motion of the image along the z-axis translation direction. j M represents the amount of motion of the j-th optical element in the translational direction along the z-axis. j M represents the transverse magnification of the j-th optical element. j+1 Let (j+1) denote the transverse magnification of the (j+1)th optical element, and (1.0) denote the transverse magnification of the detector of the optical system.

[0097] For the m-th optical element, the amount of motion of the image along the z-axis translation direction can be obtained according to the following formula:

[0098] ; (11)

[0099] Among them, T´z m Tz represents the amount of motion of the image along the z-axis translation direction. m M represents the amount of motion of the m-th optical element in the translational direction along the z-axis. mLet (1.0) represent the vertical magnification of the m-th optical element, and let (1.0) represent the vertical magnification of the detector of the optical system.

[0100] In some embodiments, the optical system includes first to m optical elements arranged sequentially 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 motion freedom is the direction of rotation about the z-axis, and for the j-th optical element, the motion of the image in the direction of motion freedom is obtained by multiplying the motion of the j-th optical element in the direction of motion freedom by 0, where j∈[1,m].

[0101] For example, for the j-th optical element, j∈[1, m], the amount of motion of the image in the rotational direction along the z-axis can be obtained according to the following formula:

[0102] ;(12)

[0103] Among them, R´z j Rz represents the amount of motion of the image in the direction of rotation about the z-axis. j Let (1,0) represent the amount of motion of the j-th optical element in the direction of rotation about the z-axis, and let (1,0) represent the transverse magnification of the detector of the optical system.

[0104] When using the above formula for calculation, if the motion of the optical element in the corresponding degree of freedom direction is a unit motion, then the value obtained by calculating according to the formula can represent the optical axis stability error component coefficient of the optical element in that degree of freedom direction.

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

[0106] S131: Obtain the initial position of the node of the optical element in the structural model, apply a load to the optical system, obtain the actual motion vector of the node, and obtain the rigid motion vector of the node based on the initial position of the node and the influence of the node's motion on the optical element moving in a rigid body form.

[0107] The load applied to the optical system is simulated in the structural model. Under the action of the applied load, the optical elements of the optical system will move, and the actual motion vector of the nodes of the optical elements is obtained.

[0108] Based on the initial position of the node, and considering the influence of the node's motion on the rigid body motion of the optical element, the rigid body motion vector of the node is obtained.

[0109] S132: Based on the actual motion vector of the node of the optical element and the rigid body motion vector of the node, obtain 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.

[0110] For the obtained 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 node is minimized after the optical element moves from the initial state according to the rigid body motion vector.

[0111] In some implementations, obtaining the rigid body motion vector of the node includes: based on the initial position of the node and considering the influence of the node's motion on the rigid body motion of the optical element, obtaining the rigid body motion vector of the node using a homogeneous coordinate transformation method in three-dimensional space.

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

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

[0114] ; (13)

[0115] Wherein, in the structural model, the initial position of the i-th node of the optical element is The rigid body motion vector of the i-th node is The rigid body motion vector of the optical element is expressed as: , where i represents the i-th node.

[0116] The following formula can be used to calculate using homogeneous coordinate transformation in three-dimensional space:

[0117] ;(14)

[0118] Wherein, in the structural model, the initial position of the i-th node of the optical element is The rigid body motion vector of the i-th node is The rigid body motion vector of the optical element is expressed as: , where i represents the i-th node. Formula (13) can be obtained from formula (14).

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

[0120] (15)

[0121] 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 based on the actual motion vector of the node and the rigid body motion vector of the node includes: constructing a motion error evaluation function using the actual motion vector of the node and the rigid body motion vector of the node, the motion error evaluation function describing 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 the partial derivative of the motion error evaluation function with respect to the motion quantity in each motion degree of freedom direction of the optical element, setting the partial derivative to 0, and solving the resulting 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 an optical element and the rigid body motion vectors of the corresponding nodes. The difference between the actual motion vectors of a node and the rigid body motion vectors of the corresponding nodes can be the sum of the squares of the differences of the nodes in each degree of freedom direction. The square of the difference of a node in any degree of freedom direction represents the square of the difference between the amount of motion of the node's actual motion vector in that degree of freedom direction and the amount of rigid body motion of the node's rigid body motion vector in that degree of freedom direction. For example, the motion error evaluation function can be expressed as:

[0126] ; (17)

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

[0128] The rigid body motion vector of the optical element is obtained by taking the partial derivatives of the motion error evaluation function with respect to the motion quantities in each degree of freedom of the optical element, and setting the partial derivatives to zero. The rigid body motion vector of the optical element can be calculated using finite element analysis. For small optical elements, their elastic deformation is negligible, so a coupled single-point model with 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-scale optical elements, so 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 the multiple nodes of the optical element, and the least squares method is applied to obtain the equally weighted multi-node surface rigid body motion.

[0129] In some embodiments, obtaining the optical axis stability error evaluation result of the optical element based on the optical axis stability error component coefficients of each degree of freedom of motion of the optical element and the rigid body motion vector of the optical element includes: using the optical axis stability error evaluation equation to obtain the optical axis stability error evaluation result of the optical element based on the rigid body motion vector of the optical element, wherein the optical axis stability error evaluation equation describes multiplying the optical axis stability error component coefficient of the optical element in the direction of motion freedom of any degree of freedom by the amount of motion in the direction of motion freedom of the rigid body motion vector of the optical element.

[0130] In some embodiments, obtaining the optical axis stability error evaluation result of the optical element based on the optical axis stability error component coefficients in each degree of freedom direction of the optical element and the rigid body motion vector of the optical element includes: obtaining the optical axis stability error evaluation result of the optical element using the optical axis stability error evaluation equation based on the rigid body motion vector of the optical element, wherein 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 each degree of freedom direction of the 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.

[0131] For example, the optical axis stability error coefficient matrix [L] Img It can be represented as:

[0132] (18)

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

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

[0135] (19)

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

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

[0138] Memory, used to store computer programs;

[0139] A processor is configured to execute the computer program to implement the steps of the optical system optical axis stability evaluation method as described in any of the above embodiments.

[0140] The optical system optical axis stability evaluation system of this embodiment establishes a structural model of the optical system and obtains the optical axis stability error component coefficients of the optical element in the direction of motion degree of freedom based on the imaging relationship of light from the optical element to the image plane of the optical system. After simulating the application of load to the optical system in the structural model, the rigid body motion vector of the optical element is obtained, and then the optical axis stability error evaluation result of the optical element is obtained, thus realizing the evaluation of the optical axis stability of the optical system.

[0141] In some implementations, the optical axis stability error evaluation equation can be constructed using the second type of response (DRESP2) in finite element software. This allows for the online evaluation of the optical sensitivity coefficient (i.e., the optical axis stability error component coefficient) and the rigid body displacement information in the six degrees of freedom of each optical element within the finite element solver. In other words, it obtains the optical axis stability error caused by static load conditions and identifies the optical axis sensitive optical elements. This can serve as an auxiliary judgment basis for subsequent redesign of the optomechanical structure and subsequent processing and assembly.

[0142] The optical axis stability evaluation method and system of this embodiment first establishes the optical system and structural model of the space camera; secondly, it constructs the optomechanical constraint equations of the space camera in the mechanical coordinate system, and obtains the optical sensitivity coefficient matrix of each optical element in six degrees of freedom based on the optomechanical constraint equations of the space camera system; thirdly, it constructs the finite element model of the space camera optomechanical system based on the optomechanical model, and sets the static load to be analyzed; fourthly, it constructs an online evaluation method for the optical axis stability of the space camera in the static environment at the finite element solver level through the second type of response (DRESP2); finally, it analyzes the optical axis stability error of the space camera under load, and determines the sensitive optical elements according to the contribution of the space camera optical elements.

[0143] The optical system optical axis stability evaluation method and system of this embodiment are intended to analyze the optical axis stability error of the optical system under static load. This method provides an evaluation basis for the redesign and topology optimization of the optical-mechanical structure of a space camera, and can also provide an auxiliary assembly and adjustment benchmark for the initial successful assembly and testing of the system.

[0144] The foregoing has provided a detailed description of the optical axis stability evaluation method and system for an optical system provided by this invention. Specific examples have been used to illustrate the principles and implementation methods of this invention. The descriptions of the embodiments above are merely for the purpose of helping to understand the method and core ideas of this invention. It should be noted that those skilled in the art can make various improvements and modifications to this invention without departing from its principles, and these improvements and modifications also fall within the protection scope of the claims of this invention.

Claims

1. A method for evaluating the optical axis stability of an optical system, wherein the optical system includes at least one optical element, characterized in that, include: Establish a structural model of the optical system; A load is applied to the optical system in the structural model to obtain the actual motion vector and rigid body motion vector of the nodes of the optical element, and the rigid body motion vector of the optical element is obtained based on the actual motion vector and rigid body motion vector of the nodes of the optical element. The optical axis stability error evaluation result of the optical element is obtained based on the optical axis stability error component coefficients of each degree of freedom of motion of the optical element and the rigid body motion vector of the optical element. Specifically, for the optical element of the optical system, for any direction of motion freedom, based on the imaging relationship of light rays from the optical element to the image plane of the optical system, the amount of motion imaged in the direction of motion freedom when the optical element generates a motion in the direction of motion freedom is obtained. Based on the amount of motion imaged in the direction of motion freedom and the amount of motion of the optical element in the direction of motion freedom, the optical axis stability error component coefficient of the optical element in the direction of motion freedom is obtained. The optical axis stability error component coefficient of the optical element in the direction of motion freedom describes the amount of movement that occurs when the optical element generates a unit amount of motion in the direction of motion freedom. The optical system includes first to m optical elements arranged sequentially along the optical axis from the object side to the image side, where m is a positive integer greater than or equal to 1; If m≥2, for the j-th optical element, j∈[1, m-1], if the direction of the motion degree of freedom 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, then the motion amount of the j-th optical element in the direction of motion degree of freedom, the first difference, and the transverse magnification of the optical element on the image side of the j-th optical element are multiplied sequentially, and the resulting product is used to obtain the motion amount of the image in the direction of motion degree of freedom. The first difference represents the difference between 1 and the transverse magnification of the j-th optical element. If the direction of motion degree of freedom is the direction of translation along the z-axis, then the motion amount of the j-th optical element in the direction of motion degree of freedom, the third difference, and the square of the transverse magnification of the optical element on the image side of the j-th optical element are multiplied sequentially, and the resulting product is used to obtain the motion amount of the image in the direction of motion degree of freedom. The third difference represents the difference between 1 and the square of the transverse magnification of the j-th optical element. If m ≥ 2, for the m-th optical element, if the direction of motion freedom is translation along the x-axis, translation along the y-axis, rotation around the x-axis, or rotation around the y-axis, then the motion of the image in the direction of motion freedom is obtained by multiplying the motion of the m-th optical element in the direction of motion freedom by a second difference, where the second difference represents the difference between 1 and the transverse magnification of the m-th optical element; if the direction of motion freedom is translation along the z-axis, then the motion of the image in the direction of motion freedom is obtained by multiplying the motion of the m-th optical element in the direction of motion freedom by a fourth difference, where the fourth difference represents the difference between 1 and the square of the transverse magnification of the m-th optical element; When m=1, if the direction of motion freedom is translation along the x-axis, translation along the y-axis, rotation around the x-axis, or rotation around the y-axis, then the motion of the image in the direction of motion freedom is obtained by multiplying the motion of the m-th optical element in that direction of motion freedom by a second difference, where the second difference represents the difference between 1 and the transverse magnification of the m-th optical element; if the direction of motion freedom is translation along the z-axis, then the motion of the image in that direction of motion freedom is obtained by multiplying the motion of the m-th optical element in that direction of motion freedom by a fourth difference, where the fourth difference represents the difference between 1 and the square of the transverse magnification of the m-th optical element; Or / and, the direction of the motion degree of freedom is the direction of rotation about the z-axis. For the j-th optical element, the motion amount of the image in the direction of the motion degree of freedom is obtained by multiplying the motion amount of the j-th optical element in the direction of the motion degree of freedom by 0, j∈[1,m].

2. The method for evaluating the optical axis stability of an optical system according to claim 1, characterized in that, Based on the amount of motion of the image in the direction of motion freedom and the amount of motion of the optical element in the direction of motion freedom, the optical axis stability error component coefficient of the optical element in the direction of motion freedom is obtained, including: The optical axis stability error component coefficient of the optical element in the direction of motion is obtained by comparing the amount of motion of the image in the direction of motion with the amount of motion of the optical element in the direction of motion.

3. The method for evaluating the optical axis stability of an optical system according to claim 1, characterized in that, Obtaining the rigid motion vector of the optical element based on the actual motion vector of the node and the rigid motion vector of the node includes: The initial position of the node of the optical element is obtained in the structural model. After applying a load to the optical system, the actual motion vector of the node is obtained. The rigid motion vector of the node is obtained based on the initial position of the node and the influence of the rigid body motion of the optical element on the node's motion. Based on the actual motion vector of the node and the rigid motion vector of the node, the rigid motion vector of the optical element is obtained, such that after the optical element moves according to the rigid motion vector of the optical element, the difference between the actual motion vector of the node and the rigid motion vector of the corresponding node is minimized.

4. The method for evaluating the optical axis stability of an optical system according to claim 3, characterized in that, Obtaining the rigid body motion vector of the node includes: based on the initial position of the node, and considering the influence of the rigid body motion of the optical element on the node's motion, using a homogeneous coordinate transformation method in three-dimensional space to obtain the rigid body motion vector of the node, expressed as follows; ； Wherein, in the structural model, the initial position of the i-th node of the optical element is The rigid body motion vector of the i-th node is The rigid body motion vector of the optical element is expressed as: , where i represents the i-th node.

5. The method for evaluating the optical axis stability of an optical system according to claim 3, characterized in that, The rigid body motion vector of the optical element is obtained by using the actual motion vector of the node and the rigid body motion vector of the node. A motion error evaluation function is constructed using the actual motion vector and the rigid body motion vector of the node. The motion error evaluation function describes the sum of the differences between the actual motion vectors and the rigid body motion vectors of the corresponding nodes of the optical element. The motion error evaluation function is used to calculate the partial derivatives of the motion quantities in each degree of freedom direction of the optical element, and the partial derivatives are set to 0. The rigid body motion vector of the optical element is obtained by solving the resulting set of equations.

6. The method for evaluating the optical axis stability of an optical system according to claim 1, characterized in that, Based on the optical axis stability error component coefficients in each degree of freedom direction of the optical element, and the rigid body motion vector of the optical element, the evaluation result of the optical axis stability error of the optical element is obtained, including: Based on the rigid body motion vector of the optical element, the optical axis stability error evaluation result of the optical element is obtained using the optical axis stability error evaluation equation. The optical axis stability error evaluation equation describes that for any motion degree of freedom direction, the optical axis stability error component coefficient of the optical element in the motion degree of freedom direction is multiplied by the motion amount in the motion degree of freedom direction of the rigid body motion vector of the optical element.

7. The method for evaluating the optical axis stability of an optical system according to claim 1, characterized in that, Based on the optical axis stability error component coefficients in each degree of freedom direction of the optical element, and the rigid body motion vector of the optical element, the evaluation result of the optical axis stability error of the optical element is obtained, including: Based on the rigid body motion vector of the optical element, the optical axis stability error evaluation result of the optical element is obtained using the optical axis stability error evaluation equation. 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 each motion degree of freedom direction of the at least one optical element of the optical system. The motion matrix is ​​formed by the rigid body motion vector of the at least one optical element of the optical system.

8. An optical system optical axis stability evaluation system, characterized in that, include: Memory, used to store computer programs; A processor, configured to execute the computer program to implement the steps of the optical system optical axis stability evaluation method as described in any one of claims 1 to 7.

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