Optical element surface shape detection method, system and equipment

Abstract

The present invention discloses a method, system, and device for detecting the surface shape of an optical element, which relates to the field of optical detection technology and is used to solve the problem in existing surface shape detection methods that wavefront degradation causes instrument transfer function attenuation, thereby affecting surface shape detection. The present invention decomposes the light field of the detected surface of the detected element into multiple microelements, obtains the ideal imaging position of the microelements of the detected surface light field after passing through an interference detection device, and establishes a wavefront degradation model of the microelements of the detected surface light field propagating to the imaging surface after passing through the interference detection device. Based on the wavefront degradation model, an expression is established to describe the relationship between the light field received by the pixel of the imaging surface and the undegraded wavefronts of the multiple microelements of the detected surface light field after passing through the interference detection device. Then, based on the first surface shape result and the expression, the undegraded wavefront is solved, and based on the undegraded wavefronts of the multiple microelements, a second surface shape result of the detected surface is obtained. The present invention can more accurately characterize the surface shape information of the detected element.

Description

Technical Field

[0001] The present invention relates to the field of optical detection technology, and in particular to a method, system and equipment for detecting the surface shape of an optical element. Background Art

[0002] With the gradual development of advanced scientific facilities such as deep space exploration, extreme ultraviolet lithography, and synchrotron radiation, optical system components, the core of advanced scientific equipment, are gradually increasing in size and complexity. This also places higher demands on the surface shape of optical components, requiring not only sub-nanometer manufacturing precision but also high demands for surface features at medium and high spatial frequencies. This poses a significant challenge to optical manufacturing capabilities. As a prerequisite for optical manufacturing, high-precision, wide-band surface shape detection technology has become a key technology that urgently needs breakthroughs.

[0003] Existing technologies use interferometric detection devices to measure the surface shape of optical components. However, as the aperture and asphericity of optical components increase, the detection wavefront degrades during propagation. This wavefront degradation leads to attenuation of the instrument transfer function (ITF), which primarily makes it difficult to detect mid- and high-frequency surface features. This severely restricts the advancement of large-aperture, high-precision optical component manufacturing technology. Summary of the Invention

[0004] The object of the present invention is to provide a method, system and device for detecting the surface shape of an optical element, which can more accurately characterize the surface shape information of the detected element.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] A method for detecting the surface shape of an optical element, using an interference detection device, wherein the interference detection device and the detected element are arranged relative to each other, and the interference detection device is used to obtain a light field of the detected surface of the detected element to obtain a first surface shape result of the detected surface;

[0007] The optical element surface shape detection method comprises:

[0008] Decomposing the detected surface light field of the detected element into a plurality of micro-elements, and obtaining positions of the micro-elements of the detected surface light field in a coordinate system of the detected element;

[0009] Based on the position of the microelement of the light field on the detected surface, obtaining an ideal imaging position of the microelement of the light field on the detected surface after the microelement passes through the interference detection device;

[0010] A wavefront degradation model of the microelement of the light field on the detected surface is established according to the ideal imaging position of the microelement of the light field on the detected surface, wherein the wavefront degradation model describes a wavefront change process of the microelement of the light field on the detected surface propagating from the ideal imaging position to the imaging surface of the interference detection device after the microelement passes through the interference detection device, and the wavefront of the microelement of the light field on the detected surface at the ideal imaging position after passing through the interference detection device is a non-degraded wavefront of the microelement of the light field on the detected surface after passing through the interference detection device;

[0011] Establishing an expression based on the wavefront degradation model of the multiple micro-elements of the light field on the detected surface, wherein the expression describes the relationship between the light field received by the pixel on the imaging surface and the undegraded wavefronts of the multiple micro-elements of the light field on the detected surface after passing through the interference detection device, wherein the light field received by the pixel on the imaging surface is a superposition of the wavefronts propagated from the multiple micro-elements of the light field on the detected surface to the pixel after passing through the interference detection device;

[0012] Based on the first surface shape result and the expression, the undegenerated wavefronts of the multiple elements of the light field of the detected surface after passing through the interference detection device are obtained, and the second surface shape result of the detected surface of the detected element is obtained based on the undegenerated wavefronts of the multiple elements.

[0013] In some embodiments, the number of micro-elements decomposed into the light field of the detection surface is consistent with the number of pixels on the imaging surface of the interference detection device.

[0014] In some embodiments, obtaining, based on the position of the microelement of the light field on the detected surface, an ideal imaging position of the microelement after the light field on the detected surface passes through the interference detection device includes:

[0015] Obtaining, based on theoretical design parameters of the detected element, a curvature radius of a meridional component and a curvature radius of a sagittal component of the microelement of the detected surface light field;

[0016] According to the position of the infinitesimal element of the light field of the detected surface and the theoretical surface shape formula of the detected surface, combined with the fine beam tracing method, the ideal imaging position of the meridional component of the infinitesimal element of the light field of the detected surface after passing through the interference detection device is obtained, and the ideal imaging position of the sagittal component of the infinitesimal element of the light field of the detected surface after passing through the interference detection device is obtained.

[0017] In some embodiments, the wavefront degradation model of the infinitesimal element of the detected surface light field is expressed as:

[0018] ;

[0019] Among them, ui (x, y, z) represents the complex amplitude of the wavefront of the i-th element after it passes through the interference detection device and propagates to the imaging surface, E(z) represents the light field amplitude, Φ AC (z) represents the phase term related to the position along the optical axis, Φ G (z) represents the Gouy phase term, Φ E (x, y, z) represents the phase term related to the distribution perpendicular to the optical axis, Φ0 represents the initial phase, j represents the imaginary unit, wherein the Z axis is parallel to the optical axis of the light propagating from the detected surface to the interference detection device, and an XYZ three-dimensional coordinate system is established, the XY plane is perpendicular to the optical axis, and (x, y, z) represents the position coordinates.

[0020] In some embodiments, the expression is represented by:

[0021] ;

[0022] Wherein, x represents the vector describing the undegraded wavefront after the multiple microelements of the light field of the detected surface pass through the interference detection device, A represents the parameter matrix, and B represents the vector describing the light field received by each pixel of the imaging surface.

[0023] In some embodiments, the reconstructed expression is represented as:

[0024] ;

[0025] Among them, x r The vector representing the real part and the imaginary part of the non-degenerate wavefront after the plurality of microelements describing the light field of the detected surface pass through the interference detection device, that is, x r The first group of elements is the real part of each element of the vector x, and the second group of elements is the imaginary part of each element of the vector x.

[0026] B r Represents the vector describing the real part and imaginary part of the light field received by each pixel on the imaging surface, that is, B r The first group of elements is the real part of each element of the vector B, and the second group of elements is the imaginary part of each element of the vector B;

[0027] A r Represents the parameter matrix, that is, A r It includes a first group of elements and a second group of elements, the first group of elements is the real part of each element of vector A, and the second group of elements is the imaginary part of each element of vector A.

[0028] In some embodiments, solving, based on the first surface shape result and the expression, to obtain the undegenerated wavefronts of the plurality of microelements of the light field of the detected surface after passing through the interference detection device includes:

[0029] An objective function is established based on the expression, and the undegraded wavefronts of the multiple microelements of the light field of the detected surface after passing through the interference detection device that minimize the value of the objective function are obtained by solving the objective function. The objective function describes the difference between the actual measured result of the light field received by the pixel of the imaging surface and the light field received by the pixel of the imaging surface calculated according to the expression.

[0030] In some embodiments, the interference detection device includes:

[0031] an optical component, configured to allow the reference light from the standard element and the reflected light from the detected surface to pass through the optical component and then be incident on the detector;

[0032] a standard element, configured to split a detection beam incident on the standard element into a reference beam, return the reference beam to the detector, emit the remaining detection beam to the detected surface, and allow the reflected light from the detected surface to pass through the standard element and then be incident on the optical component;

[0033] The detector is used to obtain the interference result between the reference light and the reflected light of the detected surface.

[0034] An optical element surface shape detection system, comprising:

[0035] An interference detection device is arranged opposite to the detected element and is used to obtain a light field of the detected surface of the detected element to obtain a first surface shape result of the detected surface of the detected element;

[0036] a decomposition module, configured to decompose the light field of the detected surface of the detected element into a plurality of microelements, and obtain positions of the microelements of the light field of the detected surface in a coordinate system of the detected element;

[0037] an acquisition module, configured to obtain, based on the position of the micro-element of the light field on the detected surface, an ideal imaging position of the micro-element after the micro-element of the light field on the detected surface passes through the interference detection device;

[0038] A first establishing module is configured to establish a wavefront degradation model of the microelement of the light field on the detected surface according to the ideal imaging position of the microelement of the light field on the detected surface, wherein the wavefront degradation model describes a wavefront change process of the microelement of the light field on the detected surface propagating from the ideal imaging position to the imaging surface of the interference detection device after the microelement passes through the interference detection device, and the wavefront of the microelement of the light field on the detected surface at the ideal imaging position after passing through the interference detection device is a non-degraded wavefront of the microelement of the light field on the detected surface after passing through the interference detection device;

[0039] a second establishing module, configured to establish an expression based on the wavefront degradation model of the plurality of microelements of the light field on the detected surface, wherein the expression describes a relationship between the light field received by the pixel on the imaging surface and the undegraded wavefronts of the plurality of microelements of the light field on the detected surface after passing through the interference detection device, wherein the light field received by the pixel on the imaging surface is a superposition of wavefronts propagated from the plurality of microelements of the light field on the detected surface to the pixel after passing through the interference detection device;

[0040] A solution module is used to solve, based on the first surface shape result and the expression, to obtain the undegenerated wavefronts of the multiple infinitesimals of the light field of the detected surface after passing through the interference detection device, and to obtain the second surface shape result of the detected surface of the detected element based on the undegenerated wavefronts of the multiple infinitesimals.

[0041] An optical element surface shape detection device, comprising:

[0042] Memory for storing computer programs;

[0043] A processor is configured to implement the steps of the optical element surface shape detection method as described above when executing the computer program.

[0044] As can be seen from the above technical solutions, the optical element surface shape detection method, system, and device of the present invention decompose the light field of the detected surface of the detected element into multiple microelements, obtain the ideal imaging position of the microelements of the detected surface light field after passing through the interferometric detection device, and establish a wavefront degradation model of the wavefront of the microelements of the detected surface light field propagating to the imaging surface of the interferometric detection device after passing through the interferometric detection device relative to the undegraded wavefront. Based on the wavefront degradation model, an expression is established to describe the relationship between the light field received by the pixel on the imaging surface and the undegraded wavefronts of the multiple microelements of the detected surface light field after passing through the interferometric detection device. Then, based on the first surface shape result and the expression, the undegraded wavefronts of the multiple microelements of the detected surface light field after passing through the interferometric detection device are obtained, and the second surface shape result of the detected surface of the detected element is obtained based on the undegraded wavefronts of the multiple microelements. The beneficial effect of the present invention is that, compared with the prior art, the instrument transfer function of the interferometric detection device is not required, the problem of wavefront degradation causing the instrument transfer function to attenuate and affect the surface shape detection is avoided, and the surface shape information of the detected element can be more accurately characterized. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0046] Figure 1 A flow chart of a method for detecting the surface shape of an optical element provided by one embodiment;

[0047] Figure 2 Schematic diagram of the arrangement of an interference detection device and a detected element in a method for detecting the surface shape of an optical element according to one embodiment;

[0048] Figure 3 FIG. 4 is a flow chart of a method for detecting the surface shape of an optical element according to another embodiment.

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

[0050] 1-detected element, 2-computer generated hologram element, 3-standard element, 4-first lens, 5-second lens, 6-detector. DETAILED DESCRIPTION

[0051] In order to enable those skilled in the art to better understand the technical solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0052] This embodiment provides a method for detecting the surface shape of an optical element, using an interference detection device. The interference detection device and the detected element are arranged relative to each other, and the interference detection device is used to obtain the light field of the detected surface of the detected element to obtain a first surface shape result of the detected surface.

[0053] For reference Figure 1 , Figure 1 A flow chart of a method for detecting the surface shape of an optical component is provided in accordance with an embodiment. As shown in the figure, the method for detecting the surface shape of an optical component includes the following steps:

[0054] S11: Decomposing the detected surface light field of the detected element into a plurality of micro-elements, and obtaining positions of the micro-elements of the detected surface light field in a coordinate system of the detected element.

[0055] The method of this embodiment is to detect and obtain the surface shape information of the detected surface of the detected element.

[0056] The light field of the detected surface refers to the light field distribution of the reflected light from the detected surface. The light field of the detected surface contains the surface shape information of the detected surface. The light field of the detected surface is decomposed into multiple microelements, which can also be called sampling microelements.

[0057] S12: Based on the position of the micro-element of the light field on the detected surface, an ideal imaging position of the micro-element of the light field on the detected surface after passing through the interference detection device is obtained.

[0058] Based on the position of the microelement of the detected surface light field in the coordinate system of the detected element and the propagation process of the detected surface light field through the interference detection device, the ideal imaging position of the microelement of the detected surface light field after passing through the interference detection device is obtained.

[0059] S13: Based on the ideal imaging position of the microelement of the light field on the detected surface, a wavefront degradation model of the microelement of the light field on the detected surface is established. The wavefront degradation model describes the wavefront change process of the microelement of the light field on the detected surface propagating from the ideal imaging position to the imaging surface of the interference detection device after passing through the interference detection device. The wavefront of the microelement of the light field on the detected surface at the ideal imaging position after passing through the interference detection device is the non-degraded wavefront of the microelement of the light field on the detected surface after passing through the interference detection device.

[0060] If the imaging surface of the interference detection device deviates from the ideal imaging position, then the wavefront degradation of the micro-element of the light field of the detected surface received by the imaging surface of the interference detection device will occur. When the wavefront of the light field of the detected surface is complex, the ideal imaging positions of the multiple micro-elements of the light field of the detected surface after passing through the interference detection device are not on the same plane, and the imaging surface of the interference detection device is a plane. Therefore, some of the multiple micro-elements of the light field of the detected surface cannot be clearly imaged on the imaging surface of the interference detection device. It is considered that these micro-elements have undergone wavefront degradation when propagating from the ideal imaging position to the imaging surface of the interference detection device. The imaging surface of the interference detection device can be considered as the light receiving surface or light sensing surface of the detector of the interference detection device, which is usually a plane. In this step, a wavefront degradation model of the micro-element of the light field of the detected surface is established. The wavefront degradation model describes the wavefront of the micro-element of the light field of the detected surface after propagating from the ideal imaging position to the imaging surface of the interference detection device after passing through the interference detection device.

[0061] S14: Establish an expression based on the wavefront degradation model of the multiple micro-elements of the light field of the detected surface, wherein the expression describes the relationship between the light field received by the pixel of the imaging surface and the undegraded wavefront after the multiple micro-elements of the light field of the detected surface pass through the interference detection device. The light field received by the pixel of the imaging surface is a superposition of the wavefronts propagated from the multiple micro-elements of the light field of the detected surface to the pixel after passing through the interference detection device.

[0062] The light field received by the pixel on the imaging surface is a superposition of the wavefronts of the multiple microelements of the light field of the detected surface propagated to the pixel after passing through the interference detection device, and the wavefront degradation model of the microelement describes the wavefront change process of the microelement of the light field of the detected surface propagated from the ideal imaging position to the imaging surface of the interference detection device after passing through the interference detection device, that is, it describes the wavefront change process of the microelement of the light field of the detected surface from the non-degraded wavefront to the imaging surface propagated to the interference detection device after passing through the interference detection device. Then, according to the wavefront degradation model of the multiple microelements, an expression can be established, that is, the relationship between the light field received by the pixel on the imaging surface and the wavefronts propagated to the imaging surface after the multiple microelements pass through the interference detection device is established, and further, the relationship between the light field received by the pixel on the imaging surface and the non-degraded wavefronts after the multiple microelements pass through the interference detection device can be established.

[0063] S15: Based on the first surface shape result and the expression, obtain the undegenerated wavefronts of the multiple microelements of the light field of the detected surface after passing through the interference detection device, and obtain the second surface shape result of the detected surface of the detected element based on the undegenerated wavefronts of the multiple microelements.

[0064] The interference detection device emits a detection light beam, which is incident on the detected surface of the detected element and is reflected. The interference detection device obtains the reflected light of the detected surface of the detected element, and can obtain the light field of the detected surface of the detected element, and then obtain the first surface shape result of the detected surface.

[0065] Regarding the expression, the light field received by the pixels on the imaging surface can be obtained based on the first surface shape result. The first surface shape result is the measured surface shape of the detected surface, which is subject to wavefront degradation. The expression can be solved to obtain the undegraded wavefronts of the plurality of microelements of the light field on the detected surface after passing through the interferometric detection device.

[0066] The optical component surface shape detection method of this embodiment decomposes the light field of the detected surface of the detected component into multiple microelements, obtains the ideal imaging position of the microelements of the detected surface light field after passing through an interferometric detection device, establishes a wavefront degradation model for the wavefront of the microelements of the detected surface light field propagating to the imaging surface of the interferometric detection device after passing through the interferometric detection device relative to the undegraded wavefront, and establishes an expression based on the wavefront degradation model to describe the relationship between the light field received by the pixel on the imaging surface and the undegraded wavefronts of the multiple microelements of the detected surface light field after passing through the interferometric detection device. Based on the first surface shape result and the expression, the undegraded wavefronts of the multiple microelements of the detected surface light field after passing through the interferometric detection device are obtained, and a second surface shape result of the detected surface of the detected component is obtained based on the undegraded wavefronts of the multiple microelements. Compared with the prior art, this method does not require the use of the instrument transfer function of the interferometric detection device, avoids the problem of wavefront degradation causing instrument transfer function attenuation and thus affecting surface shape detection, and can more accurately characterize the surface shape information of the detected component.

[0067] In some embodiments, the number of decomposed elements of the light field of the detection surface is consistent with the number of pixels of the imaging surface of the interference detection device. Exemplarily, if the imaging surface of the interference detection device includes M pixels, the light field of the detection surface is decomposed into M elements, where M is a positive integer greater than or equal to 2. The light acquired by the interference detection device is imaged on the imaging surface. In some embodiments, the elements of the light field of the detection surface are represented by elliptical Gaussian elements, and the difference between the beam waist radius of the elliptical Gaussian element and the pixel size of the imaging surface of the interference detection device is less than a preset value, so that the beam waist radius of the elliptical Gaussian element is approximately equal to the pixel size of the imaging surface of the interference detection device.

[0068] In some embodiments, the position of the microelement of the light field of the detected surface in the coordinate system of the detected element can be determined by calibration, and the position coordinate can be expressed as (x s ,y s , z s ).

[0069] In some embodiments, based on the position of the infinitesimal element of the light field of the detected surface, obtaining the ideal imaging position of the infinitesimal element of the light field of the detected surface after passing through the interference detection device includes: obtaining the curvature radius of the meridional component and the curvature radius of the sagittal component of the infinitesimal element of the light field of the detected surface according to the theoretical design parameters of the detected element; according to the position of the infinitesimal element of the light field of the detected surface and the theoretical surface shape formula of the detected surface, combining the fine beam tracing method to obtain the ideal imaging position of the meridional component of the infinitesimal element of the light field of the detected surface after passing through the interference detection device, and obtaining the ideal imaging position of the sagittal component of the infinitesimal element of the light field of the detected surface after passing through the interference detection device.

[0070] According to the theoretical design parameters of the detected element, the normal vector of the infinitesimal element of the detected surface light field is obtained, and the curvature radius of the meridional component and the curvature radius of the sagittal component of the infinitesimal element of the detected surface light field are obtained. According to the position of the infinitesimal element of the detected surface light field and the theoretical surface shape formula of the detected surface, the ideal imaging position of the meridional component of the infinitesimal element of the detected surface light field after passing through the interference detection device is obtained in combination with the fine beam tracing method, and the ideal imaging position of the sagittal component of the infinitesimal element of the detected surface light field after passing through the interference detection device is obtained. The positions of the ideal focal plane of the meridional component and the ideal focal plane of the sagittal component along the axial direction of the optical axis can be expressed as z T 、z S .

[0071] In some embodiments, the wavefront degradation model of the microelement of the detected surface light field is expressed as:

[0072] ; (1)

[0073] Among them, u i (x, y, z) represents the complex amplitude of the wavefront of the i-th element after it passes through the interference detection device and propagates to the imaging surface, E(z) represents the light field amplitude, Φ AC (z) represents the phase term related to the position along the optical axis, Φ G (z) represents the Gouy phase term, Φ E (x, y, z) represents the phase term related to the distribution perpendicular to the optical axis, Φ0 represents the initial phase, j represents the imaginary unit, wherein the Z axis is parallel to the optical axis of the light propagating from the detected surface to the interference detection device, and an XYZ three-dimensional coordinate system is established, the XY plane is perpendicular to the optical axis, and (x, y, z) represents the position coordinate. Φ AC (z), Φ G (z) and Φ E (x, y, z) is related to the defocus of the imaging surface relative to the ideal imaging position after the i-th element passes through the interference detection device.

[0074] The lateral distribution of the wavefront corresponding to each microelement of the light field on the detected surface propagating from the ideal imaging position to the imaging surface is expressed according to formula (1). Based on formula (1), a wavefront degradation model expressed in the form of convolution is established.

[0075] In some embodiments, the expression can be expressed as:

[0076] ; (2)

[0077] Wherein, x represents the vector describing the undegraded wavefront after the multiple microelements of the light field of the detected surface pass through the interference detection device, A represents the parameter matrix, and B represents the vector describing the light field received by each pixel of the imaging surface.

[0078] x includes the amplitude and phase information of the undegraded wavefront of the microelement of the light field on the detected surface, and B includes the amplitude and phase information of the light field received by the pixel on the imaging surface. In formula (2), A, x, and B are all in the complex domain.

[0079] The mathematical representation of the entire wavefront of the light field of the detected surface propagating from the clear imaging position (i.e., the ideal imaging position) to the imaging surface can be expressed in the form of convolution. In this embodiment, the convolution expression is further converted into a matrix expression, and the convolution model is converted into a matrix multiplication operation to facilitate numerical calculation.

[0080] If the light field of the detected surface is decomposed into M microelements and the number of pixels actually acquired on the imaging surface is N, then x is an M-dimensional vector, A is an N×M (i.e., N rows and M columns) parameter matrix, and B is an N-dimensional vector.

[0081] In some implementations, the complex elements of A, x, and B may be decomposed into real and imaginary parts, and the reconstructed expressions may be expressed as follows:

[0082] ; (3)

[0083] Among them, x r The vector representing the real part and the imaginary part of the non-degenerate wavefront after the plurality of microelements describing the light field of the detected surface pass through the interference detection device, that is, x r including a first set of elements and a second set of elements, the first set of elements including the real parts of the elements of the vector x, and the second set of elements including the imaginary parts of the elements of the vector x;

[0084] B r Represents the vector describing the real part and imaginary part of the light field received by each pixel on the imaging surface, that is, B r including a first group of elements and a second group of elements, the first group of elements including the real parts of the elements of the vector B, and the second group of elements including the imaginary parts of the elements of the vector B;

[0085] A r Represents the parameter matrix, that is, A r It includes a first group of elements and a second group of elements, the first group of elements is the real part of each element of vector A, and the second group of elements is the imaginary part of each element of vector A.

[0086] Then x r is a 2M-dimensional vector, A r is a parameter matrix of 2N×2M (i.e. 2N rows and 2M columns), B r is a 2N-dimensional vector.

[0087] In some embodiments, solving the problem of obtaining the undegraded wavefronts of the plurality of microelements of the light field of the detected surface after passing through the interferometric detection device based on the first surface shape result and the expression includes: establishing an objective function based on the expression, and solving the problem of obtaining the undegraded wavefronts of the plurality of microelements of the light field of the detected surface after passing through the interferometric detection device that minimizes the value of the objective function, wherein the objective function describes the difference between the actual measured results of the light field received by the pixels of the imaging surface and the light field received by the pixels of the imaging surface calculated based on the expression. The actual measured results of the light field received by the pixels of the imaging surface are obtained based on the first surface shape result obtained by the interferometric detection device.

[0088] In this embodiment, the method for solving the first surface shape result and the expression to obtain the undegenerated wavefronts of the plurality of microelements of the light field of the detected surface after passing through the interferometric detection device is not limited. In some embodiments, the solution may be obtained using, but not limited to, the gradient descent method or the conjugate gradient method, or other optimization algorithms.

[0089] In some embodiments, the objective function is expressed as:

[0090] , ; (4)

[0091] Where x represents the vector of the non-degenerate wavefront after the plurality of microelements describing the light field of the detected surface pass through the interference detection device, A represents the parameter matrix, Ax represents the light field received by the pixel of the imaging surface calculated according to the expression, and B represents the measured result of the light field received by each pixel of the imaging surface. The optimization problem described by formula (4) can be calculated using, but not limited to, the complex conjugate gradient method and other optimization algorithms applicable to the complex domain. .

[0092] In some embodiments, the objective function can be expressed as:

[0093] , ; (5)

[0094] Among them, x r The vector representing the real part and the imaginary part of the non-degenerate wavefront after the plurality of microelements describing the light field of the detected surface pass through the interference detection device, that is, x r including a first set of elements and a second set of elements, the first set of elements including the real parts of the elements of the vector x, and the second set of elements including the imaginary parts of the elements of the vector x;

[0095] A r Represents the parameter matrix, that is, A r The first group of elements is the real part of each element of the vector A, and the second group of elements is the imaginary part of each element of the vector A;

[0096] B r Represents the vector of the real and imaginary parts of the light field measurement results received by each pixel on the imaging surface, that is, B r The first group of elements includes the real parts of the elements of the vector B representing the measured results of the light field received by each pixel of the imaging surface, and the second group of elements includes the imaginary parts of the elements of the vector B representing the measured results of the light field received by each pixel of the imaging surface.

[0097] The optimization problem described by formula (5) is to solve x because all variables are in the real number domain. r Optimization algorithms such as, but not limited to, gradient descent or conjugate gradient methods can be used. Formula (4) and Formula (5) are equivalent, and their corresponding optimal solutions are the same. The optimal solution of either formula can obtain the complex amplitude distribution of the undegraded wavefront.

[0098] For example, you can refer to Figure 3 , Figure 3 This is a flow chart of another embodiment of a method for detecting the surface shape of an optical component. A mathematical model for recovering wavefront degradation is constructed. Based on the wavefront degradation model of the multiple elements of the light field on the surface being detected, an expression is established to describe the relationship between the light field received by the pixels on the imaging surface and the undegraded wavefront after the multiple elements of the light field on the surface being detected pass through the interferometric detection device. Furthermore, an objective function is established. The undegraded wavefront is then determined based on the actual surface shape measurement results.

[0099] In some embodiments, the interference detection device includes: an optical component for allowing the reference light from the standard element 3 and the reflected light from the detected surface to pass through the optical component and then be incident on the detector 6; the standard element 3 for separating a reference light from the detection beam incident on the standard element 3, returning the reference light to the detector 6, allowing the remaining detection beam to be emitted to the detected surface, and allowing the reflected light from the detected surface to pass through the standard element 3 and then be incident on the optical component; the detector 6 for obtaining the interference result of the reference light and the reflected light from the detected surface. For example, reference can be made to Figure 2 , Figure 2 The figure is a schematic diagram of the arrangement of the interference detection device and the detected element of the optical element surface detection method according to one embodiment. The interference detection device includes a detector 6, an optical component and a standard element 3. The optical component represents the equivalent optical path inside the interference detection device. Figure 2 The description is simplified with the first lens 4 and the second lens 5. It will be understood that in other embodiments, the optical assembly may include other numbers of lenses and lenses arranged in other forms, which are also within the scope of protection of the present invention. The optical element surface shape detection method can be applied to an interference detection process without a compensator, and can also be applied to an interference detection process using a compensator. In some embodiments, a computational hologram element 2 is also included, and the detected element 1 and the interference detection device are arranged relative to each other, and the computational hologram element 2 is arranged between the detected element 1 and the interference detection device. The computer hologram (CGH) element can also be replaced by any other type of compensator for interference compensation detection. In this embodiment, there is no restriction on the type of interference detection device, including but not limited to a Fizeau interferometer or a Twyman-Green interferometer.

[0100] There are two methods for improving ITF in hardware in the existing technology: the first method is to use the fusion of different detection methods with different spatial frequency domain response capabilities to improve the frequency domain detection capability of the interferometer. However, due to the different detection principles, different detection technologies have different error generation mechanisms in detection, making direct data fusion difficult to achieve; the second method is to use larger-sized CGHs in the detection of large-aperture optical components to improve detection capabilities, but larger-sized CGHs increase the difficulty of production and increase costs.

[0101] This optical component surface shape detection method, based on complex beam tracing and the elliptical Gaussian element model, establishes an analytical model to characterize the wavefront degradation caused by interferometer imaging aberrations. This algorithm then restores the true, undegraded surface shape information, thereby recovering the instrument transfer function of the interferometric detection system. This method is simple and efficient; simply inputting the parameters of the various components of the detection optical path allows for the recovery of the degraded wavefront in a computer. This method eliminates the need for fabricating a larger CGH or employing multiple detection techniques for data fusion, making it suitable for the detection of various complex aspheric mirrors, including those without rotational symmetry.

[0102] This embodiment further provides an optical element surface shape detection system, comprising:

[0103] An interference detection device is arranged opposite to the detected element and is used to obtain a light field of the detected surface of the detected element to obtain a first surface shape result of the detected surface of the detected element;

[0104] a decomposition module, configured to decompose the light field of the detected surface of the detected element into a plurality of microelements, and obtain positions of the microelements of the light field of the detected surface in a coordinate system of the detected element;

[0105] an acquisition module, configured to obtain, based on the position of the micro-element of the light field on the detected surface, an ideal imaging position of the micro-element after the micro-element of the light field on the detected surface passes through the interference detection device;

[0106] A first establishing module is configured to establish a wavefront degradation model of the microelement of the light field on the detected surface according to the ideal imaging position of the microelement of the light field on the detected surface, wherein the wavefront degradation model describes a wavefront change process of the microelement of the light field on the detected surface propagating from the ideal imaging position to the imaging surface of the interference detection device after the microelement passes through the interference detection device, and the wavefront of the microelement of the light field on the detected surface at the ideal imaging position after passing through the interference detection device is a non-degraded wavefront of the microelement of the light field on the detected surface after passing through the interference detection device;

[0107] a second establishing module, configured to establish an expression based on the wavefront degradation model of the plurality of microelements of the light field on the detected surface, wherein the expression describes a relationship between the light field received by the pixel on the imaging surface and the undegraded wavefronts of the plurality of microelements of the light field on the detected surface after passing through the interference detection device, wherein the light field received by the pixel on the imaging surface is a superposition of wavefronts propagated from the plurality of microelements of the light field on the detected surface to the pixel after passing through the interference detection device;

[0108] A solution module is used to solve, based on the first surface shape result and the expression, to obtain the undegenerated wavefronts of the multiple infinitesimals of the light field of the detected surface after passing through the interference detection device, and to obtain the second surface shape result of the detected surface of the detected element based on the undegenerated wavefronts of the multiple infinitesimals.

[0109] The optical component surface shape detection system of this embodiment decomposes the light field of the detected surface of the detected component into multiple microelements, obtains the ideal imaging position of the microelements of the detected surface light field after passing through an interferometer detection device, establishes a wavefront degradation model for the wavefront of the microelements of the detected surface light field propagating to the imaging surface of the interferometer detection device after passing through the interferometer detection device relative to the undegraded wavefront, and establishes an expression based on the wavefront degradation model to describe the relationship between the light field received by the pixel on the imaging surface and the undegraded wavefronts of the multiple microelements of the detected surface light field after passing through the interferometer detection device. Based on the first surface shape result and the expression, the undegraded wavefronts of the multiple microelements of the detected surface light field after passing through the interferometer detection device are obtained, and a second surface shape result of the detected surface of the detected component is obtained based on the undegraded wavefronts of the multiple microelements. Compared with the prior art, the present system does not require the instrument transfer function of the interferometer detection device, thus avoiding the problem of wavefront degradation causing instrument transfer function attenuation and thus affecting surface shape detection, and can more accurately characterize the surface shape information of the detected component.

[0110] This embodiment further provides an optical element surface shape detection device, comprising:

[0111] Memory for storing computer programs;

[0112] A processor is configured to implement the steps of the optical element surface shape detection method as described above when executing the computer program.

[0113] The optical element surface shape detection apparatus of this embodiment decomposes the light field of the detected surface of the detected element into multiple microelements, obtains the ideal imaging position of the microelements of the detected surface light field after passing through an interferometric detection device, establishes a wavefront degradation model of the wavefront propagated from the microelements of the detected surface light field to the imaging surface of the interferometric detection device after passing through the interferometric detection device relative to the undegraded wavefront, and establishes an expression based on the wavefront degradation model to describe the relationship between the light field received by the pixel on the imaging surface and the undegraded wavefronts of the multiple microelements of the detected surface light field after passing through the interferometric detection device. Based on the first surface shape result and the expression, the undegraded wavefronts of the multiple microelements of the detected surface light field after passing through the interferometric detection device are obtained, and a second surface shape result of the detected surface of the detected element is obtained based on the undegraded wavefronts of the multiple microelements. Compared with the prior art, the instrument transfer function of the interferometric detection device is not required, thus avoiding the problem of wavefront degradation causing instrument transfer function attenuation and affecting surface shape detection, and can more accurately characterize the surface shape information of the detected element.

[0114] According to the differential geometric characteristics of the optical surface, the present invention decomposes the surface wavefront into corresponding elliptical Gaussian elements, and calculates the ideal imaging position of the elements after propagating through the compensator, standard elements and the internal optical system of the interference detection device itself through beam tracing. Subsequently, the wavefront change process of the elements propagating from the ideal imaging position to the detector is expressed in the form of convolution, and the elliptical Gaussian elements are the convolution kernels. The present invention expresses the convolution operation in a matrix and constructs an objective function, and uses an optimization algorithm to solve the optimal solution that satisfies the minimum objective function. The optimal solution can achieve the decoupling of the interference imaging aberration and solve the non-degraded wavefront, and finally solve the problem of being unable to accurately characterize the surface shape information of the detected element due to the decrease in ITF. The present invention can improve the attenuation of the instrument transfer function of the interference detection system caused by wavefront degradation, avoid the influence of different error sources of various detection methods on the detection accuracy, avoid the production of larger-sized computer holographic elements, and save costs.

[0115] The above is a detailed introduction to the optical element surface shape detection method, system and equipment provided by the present invention. Specific examples are used herein to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method and core ideas of the present invention. It should be pointed out that for ordinary technicians in this technical field, without departing from the principles of the present invention, the present invention can also be improved and modified, and these improvements and modifications also fall within the scope of protection of the present invention.

Claims

1. A method for detecting the surface shape of an optical element, characterized in that: An interference detection device is used, wherein the interference detection device and the detected element are arranged opposite to each other, and the interference detection device is used to obtain the light field of the detected surface of the detected element to obtain a first surface shape result of the detected surface; The optical element surface shape detection method comprises: Decomposing the detected surface light field of the detected element into a plurality of micro-elements, and obtaining positions of the micro-elements of the detected surface light field in a coordinate system of the detected element; Based on the position of the microelement of the light field on the detected surface, obtaining an ideal imaging position of the microelement of the light field on the detected surface after the microelement passes through the interference detection device; A wavefront degradation model of the microelement of the light field on the detected surface is established according to the ideal imaging position of the microelement of the light field on the detected surface, wherein the wavefront degradation model describes a wavefront change process of the microelement of the light field on the detected surface propagating from the ideal imaging position to the imaging surface of the interference detection device after the microelement passes through the interference detection device, and the wavefront of the microelement of the light field on the detected surface at the ideal imaging position after passing through the interference detection device is a non-degraded wavefront of the microelement of the light field on the detected surface after passing through the interference detection device; Establishing an expression based on the wavefront degradation model of the multiple micro-elements of the light field on the detected surface, wherein the expression describes the relationship between the light field received by the pixel on the imaging surface and the undegraded wavefronts of the multiple micro-elements of the light field on the detected surface after passing through the interference detection device, wherein the light field received by the pixel on the imaging surface is a superposition of the wavefronts propagated from the multiple micro-elements of the light field on the detected surface to the pixel after passing through the interference detection device; Based on the first surface shape result and the expression, the undegenerated wavefronts of the multiple elements of the light field of the detected surface after passing through the interference detection device are obtained, and the second surface shape result of the detected surface of the detected element is obtained based on the undegenerated wavefronts of the multiple elements.

2. The optical element surface shape detection method according to claim 1, characterized in that: The number of micro-elements decomposed from the light field of the detected surface is consistent with the number of picture elements on the imaging surface of the interference detection device.

3. The optical element surface shape detection method according to claim 1, characterized in that: Obtaining, based on the position of the microelement of the light field on the detected surface, an ideal imaging position of the microelement of the light field on the detected surface after passing through the interference detection device includes: Obtaining, based on theoretical design parameters of the detected element, a curvature radius of a meridional component and a curvature radius of a sagittal component of the microelement of the detected surface light field; According to the position of the infinitesimal element of the light field of the detected surface and the theoretical surface shape formula of the detected surface, combined with the fine beam tracing method, the ideal imaging position of the meridional component of the infinitesimal element of the light field of the detected surface after passing through the interference detection device is obtained, and the ideal imaging position of the sagittal component of the infinitesimal element of the light field of the detected surface after passing through the interference detection device is obtained.

4. The optical element surface shape detection method according to claim 1, wherein: The wavefront degradation model of the microelement of the detected surface light field is expressed as: ； Among them, u i (x, y, z) represents the complex amplitude of the wavefront of the i-th element after it passes through the interference detection device and propagates to the imaging surface, E(z) represents the light field amplitude, Φ AC (z) represents the phase term related to the position along the optical axis, Φ G (z) represents the Gouy phase term, Φ E (x, y, z) represents the phase term related to the distribution perpendicular to the optical axis, Φ0 represents the initial phase, j represents the imaginary unit, wherein the Z axis is parallel to the optical axis of the light propagating from the detected surface to the interference detection device, and an XYZ three-dimensional coordinate system is established, the XY plane is perpendicular to the optical axis, and (x, y, z) represents the position coordinates.

5. The optical element surface shape detection method according to claim 1, characterized in that: The expression is expressed as: ； Wherein, x represents the vector describing the undegraded wavefront after the multiple microelements of the light field of the detected surface pass through the interference detection device, A represents the parameter matrix, and B represents the vector describing the light field received by each pixel of the imaging surface.

6. The optical element surface shape detection method according to claim 5, characterized in that: After reconstruction, the expression is expressed as: ； Among them, x r The vector representing the real part and the imaginary part of the non-degenerate wavefront after the plurality of microelements describing the light field of the detected surface pass through the interference detection device, that is, x r including a first set of elements and a second set of elements, the first set of elements including the real parts of the elements of the vector x, and the second set of elements including the imaginary parts of the elements of the vector x; B r Represents the vector describing the real part and imaginary part of the light field received by each pixel on the imaging surface, that is, B r including a first group of elements and a second group of elements, the first group of elements including the real parts of the elements of the vector B, and the second group of elements including the imaginary parts of the elements of the vector B; A r Represents the parameter matrix, that is, A r The first group of elements includes the real parts of the elements of vector A, and the second group of elements includes the imaginary parts of the elements of vector A.

7. The optical element surface shape detection method according to claim 1, characterized in that: Solving, based on the first surface shape result and the expression, to obtain the undegenerated wavefronts of the plurality of microelements of the light field of the detected surface after passing through the interference detection device comprises: An objective function is established based on the expression, and the undegraded wavefronts of the multiple microelements of the light field of the detected surface after passing through the interference detection device that minimize the value of the objective function are obtained by solving the objective function. The objective function describes the difference between the actual measured result of the light field received by the pixel of the imaging surface and the light field received by the pixel of the imaging surface calculated according to the expression.

8. The optical element surface shape detection method according to any one of claims 1 to 7, characterized in that: The interference detection device comprises: an optical component, configured to allow the reference light from the standard element and the reflected light from the detected surface to pass through the optical component and then be incident on the detector; a standard element, configured to split a detection beam incident on the standard element into a reference beam, return the reference beam to the detector, emit the remaining detection beam to the detected surface, and allow the reflected light from the detected surface to pass through the standard element and then be incident on the optical component; The detector is used to obtain the interference result between the reference light and the reflected light of the detected surface.

9. An optical element surface shape detection system, characterized in that: include: An interference detection device is arranged opposite to the detected element and is used to obtain a light field of the detected surface of the detected element to obtain a first surface shape result of the detected surface of the detected element; a decomposition module, configured to decompose the light field of the detected surface of the detected element into a plurality of microelements, and obtain positions of the microelements of the light field of the detected surface in a coordinate system of the detected element; an acquisition module, configured to obtain, based on the position of the micro-element of the light field on the detected surface, an ideal imaging position of the micro-element after the micro-element of the light field on the detected surface passes through the interference detection device; A first establishing module is configured to establish a wavefront degradation model of the microelement of the light field on the detected surface according to the ideal imaging position of the microelement of the light field on the detected surface, wherein the wavefront degradation model describes a wavefront change process of the microelement of the light field on the detected surface propagating from the ideal imaging position to the imaging surface of the interference detection device after the microelement passes through the interference detection device, and the wavefront of the microelement of the light field on the detected surface at the ideal imaging position after passing through the interference detection device is a non-degraded wavefront of the microelement of the light field on the detected surface after passing through the interference detection device; a second establishing module, configured to establish an expression based on the wavefront degradation model of the plurality of microelements of the light field on the detected surface, wherein the expression describes a relationship between the light field received by the pixel on the imaging surface and the undegraded wavefronts of the plurality of microelements of the light field on the detected surface after passing through the interference detection device, wherein the light field received by the pixel on the imaging surface is a superposition of wavefronts propagated from the plurality of microelements of the light field on the detected surface to the pixel after passing through the interference detection device; A solution module is used to solve, based on the first surface shape result and the expression, to obtain the undegenerated wavefronts of the multiple infinitesimals of the light field of the detected surface after passing through the interference detection device, and to obtain the second surface shape result of the detected surface of the detected element based on the undegenerated wavefronts of the multiple infinitesimals.

10. An optical element surface shape detection device, characterized in that: include: Memory for storing computer programs; A processor, configured to implement the steps of the optical element surface shape detection method according to any one of claims 1 to 8 when executing the computer program.

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