A self-collimation compensation detection method and system for off-axis hyperboloidal reflectors

Abstract

The present application relates to off-axis hyperboloidal mirror detection technical field, especially in kind of off-axis hyperboloidal mirror's self collimation compensation detection method and system, the method includes based on the design parameter of the measured off-axis hyperboloidal mirror, obtains corresponding detection parameter set, the detection parameter set includes theoretical optical axis direction, off-axis amount, equivalent curvature radius and equivalent aspherical surface coefficient;With the theoretical optical axis direction as the detection reference direction, the installation state of the measured off-axis hyperboloidal mirror in the detection device is parameterized with the incident direction of detection beam is associated.The present application establishes initial geometric constraint model, realizes the clear corresponding relationship between mirror geometric parameter, installation deviation and detection light path parameter, makes the detection light path construction under the condition of off-axis structure have clear physical basis, effectively reduces the dependence of traditional off-axis detection on artificial experience and repeated trial.

Description

Technical Field

[0001] This invention relates to the field of off-axis hyperboloid mirror testing technology, specifically to a self-collimation compensation testing method and system for off-axis hyperboloid mirrors. Background Technology

[0002] Off-axis hyperboloid mirrors are widely used in space optics, infrared imaging, and large-aperture reflective optical systems due to their ability to improve system imaging quality, reduce occlusion, and achieve compact optical structures. In practical engineering applications, these mirrors typically require high-precision surface inspection after manufacturing to verify whether their optical performance meets design requirements. Because off-axis hyperboloid mirrors lack rotational symmetry, there is an inherent offset between their theoretical optical axis and the geometric center of the mirror surface. During inspection, the incident direction and reflection path of the light beam are highly sensitive to the mirror's installation position and orientation. Under current inspection conditions, even small installation and adjustment deviations can introduce significant errors into the interferometric measurement results, leading to insufficient stability and repeatability of the test results.

[0003] For convex off-axis hyperboloid secondary mirrors, traditional testing methods usually require the use of high-precision compensators or custom aspherical standard parts to form an effective interferometric testing optical path. This not only makes the testing system complex and costly, but also requires repeated design of compensation schemes for different mirror parameters, making it difficult to meet the needs of multi-specification testing in engineering applications. In addition, existing testing processes mostly rely on manual experience to adjust the optical path, lacking a unified geometric modeling and error analysis mechanism, which limits the accuracy of the testing results. Summary of the Invention

[0004] To address the aforementioned problems, this invention provides a self-collimation compensation detection method for off-axis hyperboloid mirrors.

[0005] This invention employs the following technical solution: a self-collimation compensation detection method for an off-axis hyperboloid mirror, comprising:

[0006] Based on the design parameters of the off-axis hyperboloid mirror under test, a corresponding set of detection parameters is obtained. The set of detection parameters includes the theoretical optical axis direction, off-axis amount, equivalent radius of curvature, and equivalent aspheric coefficient.

[0007] Using the theoretical optical axis direction as the detection reference direction, the installation state of the off-axis hyperboloid mirror under test in the detection device is parametrically correlated with the incident direction of the detection beam to form an initial geometric constraint model characterizing the relationship between the geometric characteristics of the mirror and the detection optical path.

[0008] Based on the initial geometric constraint model, a self-collimating compensation detection optical path that matches the optical characteristics of the off-axis hyperboloid mirror under test is constructed.

[0009] Based on the self-collimating compensation detection optical path, the beam returning to the detection end is subjected to interferometry to obtain interferometry data reflecting the wavefront state of the returning beam. Combined with the initial geometric constraint model, the interferometry data is converted into error information corresponding to the design parameters of the off-axis hyperboloid reflector under test.

[0010] The error information is analyzed by component analysis. Based on the correspondence between the mirror parameters and the detection optical path parameters in the initial geometric constraint model, the error information is divided into error components caused by the mirror surface shape and error components caused by the off-axis adjustment state. The corresponding off-axis deviation, tilt angle deviation and position deviation are further obtained by inversion, forming a set of error parameters for optical path correction.

[0011] Based on the set of error parameters, the incident direction and the position of the auxiliary reference reflector in the self-collimating compensation detection optical path are adjusted.

[0012] As a further description of the above technical solution: the method for obtaining the detection parameter set includes:

[0013] Extract the set of master mirror design parameters from the manufacturing drawings corresponding to the off-axis hyperboloid reflector under test. The set of master mirror design parameters includes the vertex position of the hyperboloid of the master mirror, the direction of the optical axis of the master mirror, and the design surface equation of the hyperboloid of the master mirror.

[0014] Based on the optical axis direction of the parent mirror, and combined with the cutting position parameters of the off-axis hyperboloid mirror under test relative to the parent mirror, the equivalent theoretical optical axis direction of the off-axis hyperboloid mirror under test under ideal optical conditions is determined.

[0015] Based on the design parameters of the off-axis hyperboloid mirror under test, the lateral offset distance of the center point of the off-axis hyperboloid mirror under test relative to the optical axis of the parent mirror is calculated, and the lateral offset distance is defined as the off-axis amount.

[0016] Based on the off-axis amount, and according to the design surface equation of the hyperboloid of the mother mirror, a local curvature analysis is performed on the surface of the mother mirror at the off-axis amount, and the equivalent radius of curvature corresponding to the central region of the measured off-axis hyperboloid mirror is calculated.

[0017] Based on the design surface equation of the hyperboloid of the parent mirror, the off-axis quantity is introduced into the expression of the aspherical term, and the equivalent aspherical coefficient applicable to the detection area of ​​the off-axis hyperboloid reflector is derived.

[0018] The equivalent theoretical optical axis direction, off-axis amount, equivalent radius of curvature, and equivalent aspherical coefficient are uniformly organized into a set of detection parameters.

[0019] As a further description of the above technical solution: the method for forming the initial geometric constraint model includes:

[0020] Obtain the actual installation state parameters of the off-axis hyperboloid mirror under test in the testing device;

[0021] Based on the off-axis amount and combined with the actual installation state parameters, the incident position parameters and incident direction parameters of the detection beam relative to the off-axis hyperboloid reflector under the ideal detection state are determined, so that the detection beam is incident on the designed detection area of ​​the off-axis hyperboloid reflector under the condition of no installation and adjustment error.

[0022] Based on the equivalent radius of curvature and the equivalent aspherical coefficient, the reflection geometry relationship between the detection beam and the measured off-axis hyperboloid mirror is established under the conditions of the incident position and incident direction, which is used to constrain the theoretical propagation path of the detection beam after being reflected by the measured off-axis hyperboloid mirror.

[0023] The actual installation state parameters, the incident position parameters, the incident direction parameters, and the reflection geometry are jointly modeled to establish a parameterized correspondence between the changes in installation state and the changes in the propagation state of the detection beam. This allows the installation deviation of the measured off-axis hyperboloid reflector to be mapped to the change in the detection optical path parameters. The parameterized correspondence is then summarized to form an initial geometric constraint model.

[0024] As a further description of the above technical solution: the actual installation state parameters include the spatial position parameters and attitude parameters of the off-axis hyperboloid reflector under test relative to the detection device.

[0025] As a further description of the above technical solution: the method for constructing a self-collimating compensation detection optical path that matches the optical characteristics of the off-axis hyperboloid mirror under test includes:

[0026] By setting an auxiliary reference reflector in the detection optical path, the detection beam is reflected by the off-axis hyperboloid mirror and then incident on the auxiliary reference reflector. After being reflected again, it returns in the opposite direction to the original incident beam, thereby forming a geometrically constrained self-collimating and compensated detection optical path under off-axis conditions.

[0027] As a further description of the above technical solution: the method for obtaining the error information includes:

[0028] Based on the constructed self-collimation compensation detection optical path, the detection beam is made to return to the location of the interferometric measurement unit after passing through the measured off-axis hyperboloid mirror and the auxiliary reference reflection surface in sequence. At the interferometric measurement unit, the returned beam interferes with the reference beam, thereby forming an interference fringe pattern characterizing the wavefront state of the returned beam.

[0029] The interference fringe pattern is acquired and phase-analyzed to obtain wavefront phase distribution data of the returned beam relative to the reference beam.

[0030] The wavefront phase distribution data is introduced into the aforementioned initial geometric constraint model. Based on the detection beam incident conditions, reflection geometry, and theoretical propagation path defined by the initial geometric constraint model, the corresponding theoretical wavefront distribution is calculated, and the theoretical wavefront distribution is used as a comparison benchmark under ideal detection conditions. The detection beam incident conditions include: actual installation state parameters, incident position parameters, and incident direction parameters.

[0031] By comparing and analyzing the actual wavefront phase distribution data with the theoretical wavefront distribution, a wavefront deviation distribution reflecting the deviation of the detection optical path from the ideal state is obtained, and the wavefront deviation distribution is marked as error information.

[0032] As a further description of the above technical solution: the method for obtaining the set of error parameters for optical path correction includes:

[0033] After obtaining the error information corresponding to the design parameters of the off-axis hyperboloid reflector under test, the error information is first introduced into the initial geometric constraint model. Based on the correspondence between the reflector parameters and the detection optical path parameters in the initial geometric constraint model, the type of influence of each error component in the error information on the propagation state of the detection beam is determined.

[0034] Under the constraints of the initial geometric constraint model, the spatial distribution characteristics of the error information are analyzed. Based on the consistency of the change of the error information within the effective detection area of ​​the measured off-axis hyperboloid reflector, the error information is divided into higher-order error components and lower-order error components.

[0035] For the higher-order error components, combined with the equivalent radius of curvature and the equivalent aspherical coefficient parameter set, the correspondence between the higher-order error components and the local normal displacement of the mirror is analyzed, and the higher-order error components are mapped to the local normal displacement of the mirror to obtain surface error information reflecting the local undulations of the mirror.

[0036] For the low-order error components, based on the mapping relationship between the incident position parameters, incident direction parameters, reflection geometry relationship and actual installation state parameters of the reflector in the initial geometric constraint model, the low-order error components are respectively mapped as off-axis deviation, tilt angle deviation and position deviation parameters;

[0037] The surface error information, along with the off-axis deviation, tilt angle deviation, and position deviation parameters, are uniformly organized to form a set of error parameters for self-collimation compensation detection optical path correction.

[0038] As a further description of the above technical solution: the method for distinguishing error information into higher-order error components and lower-order error components includes:

[0039] A matrix is ​​constructed based on the obtained wavefront deviation distribution: in These are the local coordinate points of the mirror surface;

[0040] The effective detection area of ​​the mirror is divided into M×N sampling points to construct a local mirror coordinate system. The origin of the coordinate system is set as the center point of the off-axis mirror;

[0041] Using low-order terms of the Zernike polynomial to process the original error information Perform low-order fitting to obtain low-order error components;

[0042] Calculate the residual between the original error information and the lower-order error components, which is the higher-order error component.

[0043] As a further description of the above technical solution: the method for obtaining surface error information reflecting local undulations of the mirror surface includes:

[0044] For each sampling point The interferometric wavefront error information is converted into the local normal displacement of the mirror surface. ;

[0045] The fitting baseline is obtained by locally fitting a quadratic surface to the designed surface of the detection area using the equivalent radius of curvature.

[0046] The displacement residual is obtained by comparing the local normal displacement of the mirror with the fitted baseline, eliminating the influence of the overall spherical curvature, and then introducing an equivalent aspherical coefficient to correct the displacement residual into a pure local surface deviation.

[0047] The pure local surface deviation is expanded using Zernike polynomials, and the analytical result is the mirror surface error information. The pure local surface deviations of each sampling point are organized into a matrix to form a set of surface error information.

[0048] As a further description of the above technical solution: the method for mapping the low-order error components into off-axis deviation, tilt angle deviation, and position deviation parameters respectively includes:

[0049] Based on the initial geometric constraint model, establish a linear or nonlinear mapping relationship between the reflected beam offset and the mirror adjustment parameters;

[0050] Establish the relationship functions between low-order error components and beam deviation, and the relationship functions between off-axis deviation;

[0051] Discretize the established relational function to sampling points. ;

[0052] Then, construct a matrix equation for all sampling points. ; For sampling points The coefficient matrix formed by the slopes of the sampling points, This is the set of low-order alignment deviation parameters for the off-axis hyperboloid mirror under test relative to its ideal alignment state. These are low-order error components;

[0053] Solve using least squares or optimization methods. This yields a set of low-order alignment deviation parameters of the off-axis hyperboloid mirror relative to the ideal alignment state.

[0054] A self-collimation compensation detection system for an off-axis hyperboloid mirror, used to implement the self-collimation compensation detection method for the off-axis hyperboloid mirror, the system comprising:

[0055] The detection parameter acquisition module acquires a corresponding set of detection parameters based on the design parameters of the off-axis hyperboloid mirror under test. The set of detection parameters includes the theoretical optical axis direction, off-axis amount, equivalent radius of curvature, and equivalent aspherical coefficient.

[0056] The model building module uses the theoretical optical axis direction as the detection reference direction to parametrically correlate the installation state of the off-axis hyperboloid mirror under test in the detection device with the incident direction of the detection beam, forming an initial geometric constraint model that characterizes the relationship between the geometric characteristics of the mirror and the detection optical path.

[0057] The detection optical path construction module, based on the initial geometric constraint model, constructs a self-collimating and compensated detection optical path that matches the optical characteristics of the off-axis hyperboloid mirror under test;

[0058] The error information acquisition module, based on the self-collimating compensation detection optical path, performs interferometry on the beam returning to the detection end, acquires interferometry data reflecting the wavefront state of the returning beam, and, in conjunction with the initial geometric constraint model, converts the interferometry data into error information corresponding to the design parameters of the off-axis hyperboloid reflector under test.

[0059] The parameter inversion module performs component analysis on the error information. Based on the correspondence between the mirror parameters and the detection optical path parameters in the initial geometric constraint model, the error information is divided into error components caused by the mirror surface shape and error components caused by the off-axis adjustment state. The corresponding off-axis deviation, tilt deviation and position deviation are further inverted to form a set of error parameters for optical path correction.

[0060] The compensation module adjusts the incident direction and the position of the auxiliary reference reflector in the autocollimation compensation detection optical path based on the set of error parameters.

[0061] The beneficial effects of this invention are:

[0062] This invention constructs an equivalent theoretical optical axis, equivalent radius of curvature, and equivalent aspherical coefficient based on the design parameters of the parent mirror and the off-axis cutting parameters of the off-axis hyperboloid mirror under test. This forms a set of detection parameters that are consistent with the actual optical characteristics of the off-axis hyperboloid mirror under test, so that the detection process is directly based on the real design of the mirror. This avoids detection deviations caused by relying on general assumptions or simplified models, and improves the accuracy and consistency of off-axis hyperboloid mirror detection modeling.

[0063] Secondly, by using the theoretical optical axis as the detection reference direction, the actual installation state of the reflector is parametrically correlated with the incident position parameters and incident direction parameters of the detection beam, and an initial geometric constraint model is established. This realizes a clear correspondence between the geometric parameters of the reflector, the installation deviation and the detection optical path parameters, so that the construction of the detection optical path under off-axis structure conditions has a clear physical basis, effectively reducing the dependence of traditional off-axis detection on manual experience and repeated trial and error. Attached Figure Description

[0064] The present invention will be further explained below with reference to the accompanying drawings and embodiments:

[0065] Figure 1 This is a flowchart of a self-collimation compensation detection method for an off-axis hyperboloid mirror provided in Embodiment 1 of the present invention;

[0066] Figure 2 This is a flowchart of a method for obtaining a set of detection parameters provided in Embodiment 1 of the present invention;

[0067] Figure 3 This is a flowchart of the method for forming the initial geometric constraint model provided in Embodiment 1 of the present invention;

[0068] Figure 4 This is a module connection diagram of a self-collimation compensation detection system for an off-axis hyperboloid mirror provided in Embodiment 2 of the present invention. Detailed Implementation

[0069] To make the technical means, creative features, objectives, and effects of this invention readily understandable, the invention is further described below with reference to specific illustrations. It should be noted that, unless otherwise specified, the embodiments and features described in these embodiments can be combined with each other.

[0070] Example 1

[0071] Please see Figures 1-3 This invention provides a technical solution: a self-collimation compensation detection method for an off-axis hyperboloid mirror, comprising:

[0072] Based on the design parameters of the off-axis hyperboloid reflector under test, a corresponding set of detection parameters is obtained. The set of detection parameters includes the theoretical optical axis direction, off-axis amount, equivalent radius of curvature, and equivalent aspheric coefficient.

[0073] Methods for obtaining the corresponding detection parameter set include:

[0074] The design parameter information of the hyperboloid of the parent mirror is read from the manufacturing drawing corresponding to the off-axis hyperboloid reflector under test, and the set of parent mirror design parameters used to describe the overall optical morphology of the parent mirror is extracted. The set of parent mirror design parameters includes the vertex position of the parent mirror hyperboloid, the direction of the parent mirror optical axis, and the design surface equation of the parent mirror hyperboloid, which is used to characterize the theoretical optical structure features of the parent mirror.

[0075] Based on the optical axis direction of the parent mirror, and combined with the cutting position parameters of the off-axis hyperboloid mirror relative to the parent mirror, the equivalent theoretical optical axis direction of the off-axis hyperboloid mirror under ideal optical conditions is determined. The equivalent theoretical optical axis direction is derived from the optical axis of the parent mirror based on the off-axis cutting relationship and is used to characterize the optical axis pointing characteristics of the off-axis mirror. Preferably, the equivalent theoretical optical axis direction is defined as: the direction passing through the center point of the off-axis hyperboloid mirror under test and consistent with the normal of the surface designed by the parent mirror at the cutting position, or the principal ray direction determined according to the ray tracing results of the parent mirror design.

[0076] Based on the design parameters of the off-axis hyperboloid mirror, the lateral offset distance of the center point of the off-axis hyperboloid mirror under test relative to the optical axis of the parent mirror is calculated, and the lateral offset distance is defined as the off-axis amount, which is used to quantitatively describe the spatial offset relationship of the off-axis hyperboloid mirror under test relative to the axis of symmetry of the parent mirror.

[0077] The lateral offset distance of the center point of the measured off-axis hyperboloid mirror relative to the optical axis of the parent mirror can be understood as the lateral projection of the radius of curvature of the parent mirror along the off-axis tangent direction.

[0078] Based on the determined off-axis amount, and according to the design surface equation of the hyperboloid of the parent mirror, a local curvature analysis is performed on the parent mirror surface at the off-axis amount. The equivalent radius of curvature corresponding to the central region of the measured off-axis hyperboloid mirror is calculated, which is used to characterize the local surface bending characteristics of the off-axis mirror in the detection area. The equivalent radius of curvature is: the equivalent radius of curvature obtained by performing local quadratic surface least squares fitting on the parent mirror surface at the off-axis amount, with the center point of the mirror as the reference.

[0079] Based on the design surface equation of the hyperboloid of the mother mirror:

[0080]

[0081] in, The height of the mother mirror surface at radius r, in mm, is the radial distance centered on the optical axis of the mother mirror, in mm. =-1.0 is the hyperbolic coefficient. , For aspherical higher-order coefficients, with the off-axis quantity Δx as the center point, a local quadratic least-squares fit is performed on the parent mirror surface in this region to obtain the local equivalent radius of curvature. .

[0082] Specifically, the method involves first taking the first derivative of the equation of the mother mirror surface. and second derivative Calculate, then substitute into the local curvature formula: The result was obtained through calculation.

[0083] Based on the design surface equation of the hyperboloid of the master mirror, the off-axis quantity is introduced into the expression of the aspherical term, and the equivalent aspherical coefficient applicable to the detection area of ​​the off-axis hyperboloid mirror is derived. The equivalent aspherical coefficient can reflect the actual deviation of the mirror shape from the ideal sphere in the off-axis area. The equivalent aspherical coefficient is the coefficient obtained by equivalent fitting of the higher-order aspherical term after expanding the design surface of the master mirror into a standard aspherical expression in the off-axis detection area.

[0084] The equivalent theoretical optical axis direction, off-axis amount, equivalent radius of curvature, and equivalent aspherical coefficient are uniformly organized into a detection parameter set, which serves as the basic input parameters for subsequent detection optical path construction, self-collimation compensation condition setting, and error inversion analysis.

[0085] In this embodiment, based on the design parameters of the parent mirror and the off-axis cutting parameters of the off-axis hyperboloid reflector under test, an equivalent theoretical optical axis, equivalent radius of curvature, and equivalent aspherical coefficient are constructed to form a set of detection parameters consistent with the actual optical characteristics of the off-axis hyperboloid reflector under test. This allows the detection process to be directly based on the actual design of the reflector, avoiding detection deviations caused by relying on general assumptions or simplified models, and improving the accuracy and consistency of the off-axis hyperboloid reflector detection modeling.

[0086] Using the theoretical optical axis direction as the detection reference direction, the installation state of the off-axis hyperboloid mirror under test in the detection device is parametrically correlated with the incident direction of the detection beam to form an initial geometric constraint model characterizing the relationship between the geometric characteristics of the mirror and the detection optical path.

[0087] The method for forming the initial geometric constraint model includes:

[0088] The actual installation state parameters of the off-axis hyperboloid mirror under test in the testing device are obtained. The actual installation state parameters include the spatial position parameters and attitude parameters of the off-axis hyperboloid mirror under test relative to the testing device. The actual installation state parameters are decomposed relative to the equivalent theoretical optical axis to obtain the axial offset parameters along the equivalent theoretical optical axis and the lateral offset parameters perpendicular to the equivalent theoretical optical axis.

[0089] It should be noted that the spatial position parameters are used to describe the translational state of the off-axis hyperboloid mirror under test relative to the detection device, including:

[0090] The axial offset parameter is used to characterize the installation position offset of the off-axis hyperboloid mirror under test along the reference propagation direction of the detection beam. This axial position parameter reflects the change in the axial distance between the off-axis hyperboloid mirror under test and the detection light source or auxiliary reference reflecting surface.

[0091] The lateral offset parameter is used to characterize the translational offset of the off-axis hyperboloid mirror under test perpendicular to the propagation direction of the detection beam reference. The lateral position parameter reflects the installation offset characteristics of the off-axis hyperboloid mirror under test in the off-axis direction.

[0092] The attitude parameters are used to describe the angular installation state of the off-axis hyperboloid mirror under test relative to the detection device, and include: a first rotation angle parameter about a direction perpendicular to the detection reference direction, used to characterize the tilt state of the off-axis hyperboloid mirror under test in the pitch direction; a second rotation angle parameter about a direction perpendicular to the detection reference direction, used to characterize the tilt state of the off-axis hyperboloid mirror under test in the azimuth direction; and a rotation angle parameter about the detection reference direction, used to characterize the rotation state of the off-axis hyperboloid mirror under test about its own normal direction.

[0093] Based on the off-axis amount and combined with the actual installation state parameters, the incident position parameters and incident direction parameters of the detection beam relative to the off-axis hyperboloid reflector under ideal detection conditions are determined, so that the detection beam is incident on the designed detection area of ​​the off-axis hyperboloid reflector under no installation or adjustment errors.

[0094] Based on the equivalent radius of curvature and the equivalent aspherical coefficient, the reflection geometry between the detection beam and the measured off-axis hyperboloid mirror is established under the conditions of the incident position and incident direction, which is used to constrain the theoretical propagation path of the detection beam after reflection by the measured off-axis hyperboloid mirror.

[0095] The actual installation state parameters, the incident position parameters, the incident direction parameters, and the reflection geometry are jointly modeled to establish a parameterized correspondence between the changes in installation state and the changes in the propagation state of the detection beam. This allows the installation deviation of the measured off-axis hyperboloid reflector to be mapped to the change in the detection optical path parameters. The above parameterized correspondence is then summarized to form an initial geometric constraint model.

[0096] The initial geometric constraint model is used to uniformly describe the intrinsic relationship between the geometric characteristics, installation state and detection optical path of the measured off-axis hyperboloid mirror, and serves as the basic constraint condition for subsequent self-collimation compensation detection optical path construction, interference data analysis and error separation inversion.

[0097] It should be noted that the initial geometric constraint model is preferably established under conditions of small angular deviation and small displacement deviation, ignoring the second-order influence of higher-order aberrations on optical path propagation, in order to meet the detection accuracy requirements.

[0098] In this embodiment, by using the theoretical optical axis as the detection reference direction, the actual installation state of the reflector is parameterized and associated with the incident position parameters and incident direction parameters of the detection beam, and an initial geometric constraint model is established. This realizes a clear correspondence between the geometric parameters of the reflector, the installation deviation, and the detection optical path parameters, so that the construction of the detection optical path under off-axis structure conditions has a clear physical basis, effectively reducing the dependence of traditional off-axis detection on manual experience and repeated trial and error.

[0099] Based on the initial geometric constraint model, a self-collimating compensation detection optical path that matches the optical characteristics of the off-axis hyperboloid mirror under test is constructed.

[0100] The method for constructing a self-collimating compensation detection optical path that matches the optical characteristics of the off-axis hyperboloid mirror under test includes:

[0101] By setting an auxiliary reference reflector in the detection optical path, the detection beam is reflected by the off-axis hyperboloid mirror and then incident on the auxiliary reference reflector. After being reflected again, it returns in the opposite direction to the original incident beam, thereby forming a geometrically constrained self-collimating detection optical path under off-axis conditions.

[0102] In this embodiment, by introducing an auxiliary reference reflector to construct a self-collimating compensation detection optical path, the detection beam can still return to the interferometric measurement unit along a controlled path under off-axis conditions. This enables the convex off-axis hyperboloid reflector to perform interferometric detection without a high-precision custom compensator, significantly reducing the manufacturing cost and usage threshold of the detection system, shortening the detection preparation cycle, and improving engineering applicability.

[0103] Based on the self-collimating compensation detection optical path, the beam returning to the detection end is subjected to interferometry to obtain interferometry data reflecting the wavefront state of the returning beam. Combined with the initial geometric constraint model, the interferometry data is converted into error information corresponding to the design parameters of the off-axis hyperboloid reflector under test, so that the detection results can characterize the comprehensive influence of the mirror surface shape and assembly state on the optical path.

[0104] The method for obtaining the error information includes:

[0105] Under the aforementioned self-collimation compensation detection optical path, the detection beam is made to return to the location of the interferometric measurement unit after passing through the measured off-axis hyperboloid mirror and the auxiliary reference reflection surface in sequence. The returned beam is then made to interfere with the reference beam at the interferometric measurement unit, thereby forming an interference fringe pattern that characterizes the wavefront state of the returned beam.

[0106] It should be noted that the reference beam is generated by the reference optical path inside the interferometric measurement unit. Specifically, it is obtained by splitting a light source of the same origin as the detection beam through a beam splitter. The reference beam does not pass through the measured off-axis hyperboloid mirror and the auxiliary reference reflector. After propagating along the preset reference optical path inside the interferometric measurement unit, the reference beam directly enters the interference region.

[0107] The interference fringe pattern is acquired and phase-analyzed to obtain wavefront phase distribution data of the returned beam relative to the reference beam. The wavefront phase distribution data reflects the change in optical path difference caused by the influence of the surface characteristics and installation state of the measured off-axis hyperboloid reflecting mirror during the propagation of the detection beam.

[0108] The wavefront phase distribution data is introduced into the aforementioned initial geometric constraint model. Based on the detection beam incident conditions, reflection geometry, and theoretical propagation path defined by the initial geometric constraint model, the corresponding theoretical wavefront distribution is calculated, and the theoretical wavefront distribution is used as a comparison benchmark under ideal detection conditions. The detection beam incident conditions include: actual installation state parameters, incident position parameters, and incident direction parameters.

[0109] By comparing and analyzing the actual wavefront phase distribution data with the theoretical wavefront distribution, a wavefront deviation distribution reflecting the deviation of the detection optical path from the ideal state is obtained. The wavefront deviation distribution is marked as error information, which can comprehensively characterize the influence of mirror surface error and off-axis assembly deviation on the detection results.

[0110] The process of obtaining the wavefront phase distribution through phase analysis is as follows:

[0111] Using an interferometry unit, such as a Fizeau interferometer or a phase-shift interferometer, images of the interference fringes of the returning beam are acquired. The images are then subjected to grayscale correction and background noise filtering to ensure clear fringes.

[0112] Phase demodulation algorithms, such as the four-step phase shift method, are used to analyze the fringe intensity distribution. ( ) converted to phase distribution ; The sampling point is located at the local coordinates of the mirror surface;

[0113] Example of the four-step phase shift method formula: In the formula, , , and These are the grayscale values ​​of the stripes collected in four steps.

[0114] The process of calculating the theoretical wavefront distribution is as follows:

[0115] Based on the initial geometric constraint model, the position and direction of the ideal incident beam are determined, and the incident beam parameters, including wavelength λ, beam diameter, and beam propagation direction vector, are obtained.

[0116] Using a geometric optics model, the light beam is propagated sequentially onto the surface of the mirror, taking into account the curvature and normal direction of the reflecting surface, and the direction and path length after reflection are calculated for each sampled light beam.

[0117] Based on the length of the light propagation path Calculate the theoretical wavefront distribution using a reference optical path. :in, In the formula, λ is the wavelength.

[0118] The sampling point matrix of the entire effective detection area is calculated to obtain the theoretical wavefront distribution matrix;

[0119] The method for generating error information through comparative analysis is as follows:

[0120] Calculate wavefront deviation: ;

[0121] Will Converting the error to mirror normal displacement or local wavefront error, such as Zernike expansion, yields higher-order surface error information and lower-order assembly error information, which is the error information mentioned above.

[0122] In this embodiment, after acquiring the interference data, based on the initial geometric constraint model, the wavefront deviation distribution of the returned beam is converted into error information that directly corresponds to the design parameters of the off-axis hyperboloid reflector under test. This allows the detection results to not only reflect changes in the optical wavefront, but also to quantitatively characterize the combined influence of the mirror surface shape error and the off-axis assembly state on the detection optical path, thereby improving the physical interpretability of the detection results.

[0123] The error information is analyzed by component analysis. Based on the correspondence between the mirror parameters and the detection optical path parameters in the initial geometric constraint model, the error information is divided into error components caused by the mirror surface shape and error components caused by the off-axis adjustment state. The corresponding off-axis deviation, tilt deviation and position deviation are further obtained by inversion, forming a set of error parameters for optical path correction.

[0124] The method for obtaining the set of error parameters used for optical path correction includes:

[0125] After obtaining the error information corresponding to the design parameters of the off-axis hyperboloid reflector under test, the error information is first introduced into the initial geometric constraint model. Based on the correspondence between the reflector parameters and the detection optical path parameters in the initial geometric constraint model, the influence type of each error component in the error information on the propagation state of the detection beam is determined, providing a physical constraint basis for subsequent error analysis.

[0126] It should be noted that the types of influence include angular influence, positional influence, and shape influence, which correspond one-to-one with the influence on the beam propagation direction, the influence on the beam propagation position, and the influence on the beam wavefront shape.

[0127] Specifically, changes in the overall tilt angle of the reflector act on the reflection direction of the detection beam through the law of reflection, causing the returned beam to deflect overall, thus affecting the propagation direction of the detection beam; the overall translation or off-axis deviation of the reflector relative to the detection optical path changes the incident and return positions of the detection beam on the reflector surface, thereby causing an overall positional shift of the returned beam on the detection plane; local surface shape errors of the reflector surface change the local optical path distribution of the reflected beam, causing local undulations or distortions in the wavefront of the returned beam, thus affecting the wavefront shape of the detection beam.

[0128] Through the above analysis, the error components that affect the propagation direction of the detection beam, the error components that affect the propagation position of the detection beam, and the error components that affect the wavefront shape of the detection beam are physically distinguished, providing a clear physical constraint basis for subsequent error component analysis and parameter inversion.

[0129] Under the constraints of the initial geometric constraint model, the spatial distribution characteristics of the error information are analyzed. Based on the consistency of the error information changes within the effective detection area of ​​the measured off-axis hyperboloid reflector, the error information is divided into higher-order error components and lower-order error components. The higher-order error components correspond to the mirror surface shape error components caused by changes in the local morphology of the mirror, and the lower-order error components correspond to the off-axis assembly and adjustment error components caused by changes in the overall assembly and adjustment state of the reflector.

[0130] Specifically, methods for distinguishing error information into higher-order error components and lower-order error components include:

[0131] A matrix is ​​constructed based on the obtained wavefront deviation distribution: ,in These are the local coordinate points of the mirror surface;

[0132] The effective detection area of ​​the mirror is divided into M×N sampling points to construct a local mirror coordinate system. The origin of the coordinate system is set as the center point of the off-axis mirror;

[0133] Using low-order terms of the Zernike polynomial to process the original error information By performing a low-order fit, the low-order error components are obtained, and their expressions are as follows: In the formula, These are basis functions of low-order Zernike polynomials. These are the fitting coefficients. These are low-order error components, reflecting deviations in the overall alignment or tilt and translation of the mirror surface;

[0134] Calculate the residual between the original error information and the lower-order error components; the calculation formula is: ; The residual between the original error information and the lower-order error components, i.e. the higher-order error components, reflects the local undulations of the mirror surface and the deviation of the aspherical surface.

[0135] For the higher-order error components, combined with the equivalent radius of curvature and the equivalent aspherical coefficient parameter set, the correspondence between the higher-order error components and the local normal displacement of the mirror surface is analyzed. The higher-order error components are mapped to the local normal displacement of the mirror surface to obtain surface error information reflecting the local undulations of the mirror surface, which is used to characterize the actual deviation of the measured off-axis hyperboloid reflector from the design surface.

[0136] Specifically, methods for obtaining surface shape error information reflecting local undulations of the mirror surface include:

[0137] For each sampling point The interferometric wavefront error information is converted into the local normal displacement of the mirror surface. The conversion formula is: In the formula, For the phase data corresponding to higher-order error components, For the wavelength of the interference light, The coordinates of the point are Local normal displacement of the mirror surface;

[0138] The fitting baseline is obtained by locally fitting a quadratic surface to the designed surface of the detection area using the equivalent radius of curvature.

[0139] The formula for fitting the local quadratic surface is as follows: In the formula, To fit the baseline, The equivalent radius of curvature, These are the coordinates in the local coordinate system of the mirror surface.

[0140] The displacement residual is obtained by comparing the local normal displacement with the fitted baseline, eliminating the influence of the overall spherical curvature, and then introducing an equivalent aspherical coefficient to correct the displacement residual into a pure local surface deviation.

[0141] The formula for calculating the residual is as follows: In the formula, This represents the displacement residual.

[0142] The expression for correcting displacement residuals to pure local surface deviation is: In the formula, For displacement residuals, For equivalent aspherical coefficients, To design the expression for higher-order aspherical terms of the surface, This is a purely local surface shape deviation.

[0143] The pure local surface deviation is expanded using Zernike polynomials, and the analytical result is the mirror surface error information. The pure local surface deviations of each sampling point are organized into a matrix to form a set of surface error information.

[0144] Zernike polynomial expansion formula: In the formula, The coefficients are the Zernike polynomial expansion coefficients. For Zernike polynomial functions, For order, This refers to the direction number.

[0145] For the low-order error components, based on the mapping relationship between the incident position parameters, incident direction parameters, reflection geometry and actual installation state parameters of the detection beam in the initial geometric constraint model, the low-order error components are mapped to off-axis deviation, tilt angle deviation and position deviation parameters, respectively, to characterize the degree of deviation of the measured off-axis hyperboloid reflector from the ideal installation state.

[0146] The methods for mapping the low-order error components to off-axis deviation, tilt deviation, and position deviation parameters include:

[0147] Based on the initial geometric constraint model, establish a linear or nonlinear mapping relationship between the reflected beam offset and the mirror adjustment parameters;

[0148] Optionally, the mapping relationship is as follows: In the formula, , To return the deflection angle of the beam around the X and Y axes, i.e., the tilt angle deviation, , and To return the overall positional deviation of the beam, To determine the off-axis deviation of the returned beam; , The function is obtained through calculations using the law of reflection and optical path geometry;

[0149] Establish the relationship functions between low-order error components and beam deviation, and the relationship functions between off-axis deviation:

[0150] The relational function is:

[0151] + In the formula, To translate the entire optical axis, , To tilt the whole around the X and Y axes, , Local mirror coordinates; , The slope of the mirror-designed curved surface at local sampling points maps the lateral translation to the normal displacement. and This represents the global translation of the mirror surface along the X and Y directions of the local coordinate system.

[0152] Discretize the established relational function to sampling points. ;

[0153] The expression is:

[0154]

[0155] Then, construct a matrix equation for all sampling points. ;

[0156]

[0157]

[0158]

[0159] in, For sampling points The coefficient matrix formed by the slopes of the sampling points, This is the set of low-order alignment deviation parameters of the off-axis hyperboloid mirror under test relative to the ideal alignment state;

[0160] This refers to the off-axis deviation of the returned beam along the equivalent optical axis. The lateral translation of the return beam in the X direction, i.e., the positional deviation, The lateral translation of the return beam in the Y direction, i.e., the positional deviation, , To return the tilt angle deviation of the beam around the X and Y axes.

[0161] Solve using least squares or optimization methods. This yields a set of low-order alignment deviation parameters of the off-axis hyperboloid mirror relative to the ideal alignment state.

[0162] The mirror surface shape error information, along with the off-axis deviation, tilt angle deviation, and position deviation parameters, are uniformly organized to form a set of error parameters for self-collimation compensation detection optical path correction.

[0163] In this embodiment, by performing component analysis on the error information, the error is clearly distinguished into a higher-order error component caused by the local surface shape of the mirror and a lower-order error component caused by the off-axis assembly state. Furthermore, the off-axis deviation, tilt angle deviation and position deviation parameters are obtained by inversion, which effectively decouples the surface shape error and the assembly error, avoiding the problem of the two types of errors superimposed and difficult to distinguish in traditional detection.

[0164] Based on the set of error parameters, the incident direction and the position of the auxiliary reference reflector in the self-collimating compensation detection optical path are adjusted.

[0165] Example 2

[0166] Please see Figure 4 This invention provides a technical solution: a self-collimation compensation detection system for an off-axis hyperboloid mirror, used to implement the self-collimation compensation detection method for the off-axis hyperboloid mirror, the system comprising:

[0167] The detection parameter acquisition module acquires a corresponding set of detection parameters based on the design parameters of the off-axis hyperboloid mirror under test. The set of detection parameters includes the theoretical optical axis direction, off-axis amount, equivalent radius of curvature, and equivalent aspherical coefficient.

[0168] The model building module uses the theoretical optical axis direction as the detection reference direction to parametrically correlate the installation state of the off-axis hyperboloid mirror under test in the detection device with the incident direction of the detection beam, forming an initial geometric constraint model that characterizes the relationship between the geometric characteristics of the mirror and the detection optical path.

[0169] The detection optical path construction module, based on the initial geometric constraint model, constructs a self-collimating and compensated detection optical path that matches the optical characteristics of the off-axis hyperboloid mirror under test;

[0170] The error information acquisition module, based on the self-collimating compensation detection optical path, performs interferometry on the beam returning to the detection end, acquires interferometry data reflecting the wavefront state of the returning beam, and, in conjunction with the initial geometric constraint model, converts the interferometry data into error information corresponding to the design parameters of the off-axis hyperboloid reflector under test.

[0171] The parameter inversion module performs component analysis on the error information. Based on the correspondence between the mirror parameters and the detection optical path parameters in the initial geometric constraint model, the error information is divided into error components caused by the mirror surface shape and error components caused by the off-axis adjustment state. The corresponding off-axis deviation, tilt deviation and position deviation are further inverted to form a set of error parameters for optical path correction.

[0172] The compensation module adjusts the incident direction and the position of the auxiliary reference reflector in the autocollimation compensation detection optical path based on the set of error parameters.

[0173] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A self-collimation compensation detection method for an off-axis hyperboloid mirror, characterized in that, include: Based on the design parameters of the off-axis hyperboloid mirror under test, a corresponding set of detection parameters is obtained. The set of detection parameters includes the theoretical optical axis direction, off-axis amount, equivalent radius of curvature, and equivalent aspheric coefficient. Using the theoretical optical axis direction as the detection reference direction, the installation state of the off-axis hyperboloid mirror under test in the detection device is parametrically correlated with the incident direction of the detection beam to form an initial geometric constraint model characterizing the relationship between the geometric characteristics of the mirror and the detection optical path. Based on the initial geometric constraint model, a self-collimating compensation detection optical path that matches the optical characteristics of the off-axis hyperboloid mirror under test is constructed. Based on the self-collimating compensation detection optical path, the beam returning to the detection end is subjected to interferometry to obtain interferometry data reflecting the wavefront state of the returning beam. Combined with the initial geometric constraint model, the interferometry data is converted into error information corresponding to the design parameters of the off-axis hyperboloid reflector under test. The error information is analyzed by component analysis. Based on the correspondence between the mirror parameters and the detection optical path parameters in the initial geometric constraint model, the error information is divided into error components caused by the mirror surface shape and error components caused by the off-axis adjustment state. The corresponding off-axis deviation, tilt deviation and position deviation are further obtained by inversion, forming a set of error parameters for optical path correction. Based on the set of error parameters, the incident direction and the position of the auxiliary reference reflector in the self-collimating compensation detection optical path are adjusted.

2. The self-collimation compensation detection method for an off-axis hyperboloid mirror according to claim 1, characterized in that, The method for obtaining the detection parameter set includes: Extract the set of master mirror design parameters from the manufacturing drawings corresponding to the off-axis hyperboloid reflector under test. The set of master mirror design parameters includes the vertex position of the hyperboloid of the master mirror, the direction of the optical axis of the master mirror, and the design surface equation of the hyperboloid of the master mirror. Based on the optical axis direction of the parent mirror, and combined with the cutting position parameters of the off-axis hyperboloid mirror under test relative to the parent mirror, the equivalent theoretical optical axis direction of the off-axis hyperboloid mirror under test under ideal optical conditions is determined. Based on the design parameters of the off-axis hyperboloid mirror under test, the lateral offset distance of the center point of the off-axis hyperboloid mirror under test relative to the optical axis of the parent mirror is calculated, and the lateral offset distance is defined as the off-axis amount. Based on the off-axis amount, and according to the design surface equation of the hyperboloid of the mother mirror, a local curvature analysis is performed on the surface of the mother mirror at the off-axis amount, and the equivalent radius of curvature corresponding to the central region of the measured off-axis hyperboloid mirror is calculated. Based on the design surface equation of the hyperboloid of the parent mirror, the off-axis quantity is introduced into the expression of the aspherical term, and the equivalent aspherical coefficient applicable to the detection area of ​​the off-axis hyperboloid reflector is derived. The equivalent theoretical optical axis direction, off-axis amount, equivalent radius of curvature, and equivalent aspherical coefficient are uniformly organized into a set of detection parameters.

3. The self-collimation compensation detection method for an off-axis hyperboloid mirror according to claim 1, characterized in that, The method for forming the initial geometric constraint model includes: Obtain the actual installation state parameters of the off-axis hyperboloid mirror under test in the testing device; Based on the off-axis amount and combined with the actual installation state parameters, the incident position parameters and incident direction parameters of the detection beam relative to the off-axis hyperboloid reflector under the ideal detection state are determined, so that the detection beam is incident on the designed detection area of ​​the off-axis hyperboloid reflector under the condition of no installation and adjustment error. Based on the equivalent radius of curvature and the equivalent aspherical coefficient, the reflection geometry relationship between the detection beam and the measured off-axis hyperboloid mirror is established under the conditions of the incident position and incident direction, which is used to constrain the theoretical propagation path of the detection beam after being reflected by the measured off-axis hyperboloid mirror. The actual installation state parameters, incident position parameters, incident direction parameters, and reflection geometry are jointly modeled to establish a parameterized correspondence between changes in installation state and changes in the propagation state of the detection beam. This allows the installation deviation of the measured off-axis hyperboloid reflector to be mapped to changes in the detection optical path parameters. The above parameterized correspondence is then summarized to form an initial geometric constraint model.

4. The self-collimation compensation detection method for an off-axis hyperboloid mirror according to claim 3, characterized in that, The actual installation status parameters include the spatial position parameters and attitude parameters of the off-axis hyperboloid reflector under test relative to the testing device.

5. The self-collimation compensation detection method for an off-axis hyperboloid mirror according to claim 1, characterized in that, The method for constructing a self-collimating compensation detection optical path that matches the optical characteristics of the off-axis hyperboloid mirror under test includes: By setting an auxiliary reference reflector in the detection optical path, the detection beam is reflected by the off-axis hyperboloid mirror and then incident on the auxiliary reference reflector. After being reflected again, it returns in the opposite direction to the original incident beam, thereby forming a geometrically constrained self-collimating and compensated detection optical path under off-axis conditions.

6. The self-collimation compensation detection method for an off-axis hyperboloid mirror according to claim 1, characterized in that, The method for obtaining the error information includes: Based on the constructed self-collimation compensation detection optical path, the detection beam is made to return to the location of the interferometric measurement unit after passing through the measured off-axis hyperboloid mirror and the auxiliary reference reflection surface in sequence. At the interferometric measurement unit, the returned beam interferes with the reference beam, thereby forming an interference fringe pattern characterizing the wavefront state of the returned beam. The interference fringe pattern is acquired and phase-analyzed to obtain wavefront phase distribution data of the returned beam relative to the reference beam. The wavefront phase distribution data is introduced into the aforementioned initial geometric constraint model. Based on the detection beam incident conditions, reflection geometry, and theoretical propagation path defined by the initial geometric constraint model, the corresponding theoretical wavefront distribution is calculated, and the theoretical wavefront distribution is used as a comparison benchmark under ideal detection conditions. The detection beam incident conditions include: actual installation state parameters, incident position parameters, and incident direction parameters. By comparing and analyzing the actual wavefront phase distribution data with the theoretical wavefront distribution, a wavefront deviation distribution reflecting the deviation of the detection optical path from the ideal state is obtained, and the wavefront deviation distribution is marked as error information.

7. The self-collimation compensation detection method for an off-axis hyperboloid mirror according to claim 1, characterized in that, The method for obtaining the set of error parameters used for optical path correction includes: After obtaining the error information corresponding to the design parameters of the off-axis hyperboloid reflector under test, the error information is first introduced into the initial geometric constraint model. Based on the correspondence between the reflector parameters and the detection optical path parameters in the initial geometric constraint model, the type of influence of each error component in the error information on the propagation state of the detection beam is determined. Under the constraints of the initial geometric constraint model, the spatial distribution characteristics of the error information are analyzed. Based on the consistency of the change of the error information within the effective detection area of ​​the measured off-axis hyperboloid reflector, the error information is divided into higher-order error components and lower-order error components. For the higher-order error components, combined with the equivalent radius of curvature and the equivalent aspherical coefficient parameter set, the correspondence between the higher-order error components and the local normal displacement of the mirror is analyzed, and the higher-order error components are mapped to the local normal displacement of the mirror to obtain surface error information reflecting the local undulations of the mirror. For the low-order error components, based on the mapping relationship between the incident position parameters, incident direction parameters, reflection geometry relationship and actual installation state parameters of the reflector in the initial geometric constraint model, the low-order error components are respectively mapped as off-axis deviation, tilt angle deviation and position deviation parameters; The surface error information, along with the off-axis deviation, tilt angle deviation, and position deviation parameters, are uniformly organized to form a set of error parameters for self-collimation compensation detection optical path correction.

8. The self-collimation compensation detection method for an off-axis hyperboloid mirror according to claim 7, characterized in that, The method for distinguishing error information into higher-order error components and lower-order error components includes: A matrix is ​​constructed based on the obtained wavefront deviation distribution: ,in These are the local coordinate points of the mirror surface; The effective detection area of ​​the mirror is divided into M×N sampling points to construct a local mirror coordinate system. The origin of the coordinate system is set as the center point of the off-axis mirror; Using low-order terms of the Zernike polynomial to process the original error information Perform low-order fitting to obtain low-order error components; Calculate the residual between the original error information and the lower-order error components, which is the higher-order error component.

9. The self-collimation compensation detection method for an off-axis hyperboloid mirror according to claim 7, characterized in that, The method for obtaining surface shape error information reflecting local undulations of the mirror surface includes: For each sampling point The interferometric wavefront error information is converted into the local normal displacement of the mirror surface. ; The fitting baseline is obtained by locally fitting a quadratic surface to the designed surface of the detection area using the equivalent radius of curvature. The displacement residual is obtained by comparing the local normal displacement of the mirror with the fitted baseline, eliminating the influence of the overall spherical curvature, and then introducing an equivalent aspherical coefficient to correct the displacement residual into a pure local surface deviation. The pure local surface deviation is expanded using Zernike polynomials, and the analytical result is the mirror surface error information. The pure local surface deviations of each sampling point are organized into a matrix to form a set of surface error information.

10. The self-collimation compensation detection method for an off-axis hyperboloid mirror according to claim 8, characterized in that, The methods for mapping the low-order error components to off-axis deviation, tilt deviation, and position deviation parameters include: Based on the initial geometric constraint model, establish a linear or nonlinear mapping relationship between the reflected beam offset and the mirror adjustment parameters; Establish the relationship functions between low-order error components and beam deviation, and the relationship functions between off-axis deviation; Discretize the established relational function to sampling points. ; Then, construct a matrix equation for all sampling points. ; For sampling points The coefficient matrix formed by the slopes of the sampling points, This is the set of low-order alignment deviation parameters for the off-axis hyperboloid mirror under test relative to its ideal alignment state. These are low-order error components; Solve using least squares or optimization methods. This yields a set of low-order alignment deviation parameters of the off-axis hyperboloid mirror relative to the ideal alignment state.

11. A self-collimation compensation detection system for an off-axis hyperboloid mirror, used to implement the self-collimation compensation detection method for an off-axis hyperboloid mirror as described in any one of claims 1-10, characterized in that, The system includes: The detection parameter acquisition module acquires a corresponding set of detection parameters based on the design parameters of the off-axis hyperboloid mirror under test. The set of detection parameters includes the theoretical optical axis direction, off-axis amount, equivalent radius of curvature, and equivalent aspherical coefficient. The model building module uses the theoretical optical axis direction as the detection reference direction to parametrically correlate the installation state of the off-axis hyperboloid mirror under test in the detection device with the incident direction of the detection beam, forming an initial geometric constraint model that characterizes the relationship between the geometric characteristics of the mirror and the detection optical path. The detection optical path construction module, based on the initial geometric constraint model, constructs a self-collimating and compensated detection optical path that matches the optical characteristics of the off-axis hyperboloid mirror under test; The error information acquisition module, based on the self-collimating compensation detection optical path, performs interferometry on the beam returning to the detection end, acquires interferometry data reflecting the wavefront state of the returning beam, and, in conjunction with the initial geometric constraint model, converts the interferometry data into error information corresponding to the design parameters of the off-axis hyperboloid reflector under test. The parameter inversion module performs component analysis on the error information. Based on the correspondence between the mirror parameters and the detection optical path parameters in the initial geometric constraint model, the error information is divided into error components caused by the mirror surface shape and error components caused by the off-axis adjustment state. The corresponding off-axis deviation, tilt deviation and position deviation are further inverted to form a set of error parameters for optical path correction. The compensation module adjusts the incident direction and the position of the auxiliary reference reflector in the autocollimation compensation detection optical path based on the set of error parameters.

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