Optical element surface shape detection method, system and equipment

Abstract

The invention discloses an optical element surface shape detection method, system and equipment, relates to the technical field of optical detection, and is used for solving the problem that the surface shape detection is influenced by instrument transfer function attenuation caused by wavefront degradation in the existing surface shape detection method. A detected surface light field of a detected element is decomposed into a plurality of infinitesimal elements, ideal imaging positions of the infinitesimal elements of the detected surface light field after passing through an interference detection device are obtained, and a wavefront degradation model of the infinitesimal elements of the detected surface light field after passing through the interference detection device and propagating to an imaging surface is established. And according to the wavefront degradation model, establishing an expression for describing the relationship between the light field received by the pixel of the imaging surface and the non-degraded wavefront after the plurality of infinitesimal elements of the light field of the detected surface pass through the interference detection device, and further solving the non-degraded wavefront according to the first surface shape result and the expression. And obtaining a second surface shape result of the detected surface according to the undegraded wavefronts of the plurality of infinitesimal elements. According to the invention, the surface shape information of the detected element can be represented more accurately.

Description

Technical Field

[0001] The present invention relates to the technical field of optical detection, and particularly to a method, a system, and a device 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 of the universe, extreme ultraviolet lithography technology, and synchrotron radiation, as the core of advanced scientific equipment, the components of the optical system are gradually increasing in size and the surface shape is becoming more complex. At the same time, higher requirements are put forward for the surface shape of optical elements. Not only the manufacturing accuracy needs to reach sub-nanometer accuracy, but also there is a high demand for the surface shape characteristics of medium and high spatial frequencies. This poses a great challenge to the optical manufacturing ability. As the prerequisite of optical manufacturing, the surface shape detection technology with high precision and wide frequency domain has become a key technology that urgently needs to break through.

[0003] In the prior art, an interference detection device is used to detect the surface shape of an optical element. However, with the increase in the aperture and asphericity of the optical element, the detected wavefront degenerates during propagation, and the wavefront degeneration will cause the attenuation of the instrument transfer function (ITF), which is mainly manifested as the difficulty in detecting the medium and high frequency surface shape characteristics, seriously restricting the development of the manufacturing technology of large-aperture and high-precision optical elements to a higher level. Summary of the Invention

[0004] The purpose of the present invention is to provide a method, a system, and a 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 purpose, the present invention provides the following technical solutions:

[0006] An optical element surface shape detection method, which applies an interference detection device. The interference detection device and the detected element are arranged opposite to each other. The interference detection device is used to obtain the light field of the detected surface of the detected element to obtain the first surface shape result of the detected surface.

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

[0008] Decompose the light field of the detected surface of the detected element into multiple micro-elements, and obtain the positions of the micro-elements of the light field of the detected surface in the coordinate system of the detected element.

[0009] Based on the positions of the micro-elements of the light field of the detected surface, obtain the ideal imaging positions of the micro-elements of the light field of the detected surface after passing through the interference detection device.

[0010] Based on the ideal imaging position of the microelement of the detected surface light field, a wavefront degradation model of the microelement of the detected surface light field is established. The wavefront degradation model describes the wavefront change process of the microelement of the detected surface light field 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 detected surface light field at the ideal imaging position after passing through the interference detection device is the undegraded wavefront of the microelement of the detected surface light field after passing through the interference detection device;

[0011] An expression is established according to the wavefront degradation models of the multiple microelements of the detected surface light field. The expression describes 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. The light field received by the pixel of the imaging surface is the superposition of the wavefronts propagated from the multiple microelements of the detected surface light field to the pixel after passing through the interference detection device;

[0012] According to 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 interference detection device are obtained by solving, and the second surface shape result of the detected surface of the detected element is obtained according to the undegraded wavefronts of the multiple microelements.

[0013] In some embodiments, the number of microelements into which the detected surface light field is decomposed is the same as the number of pixels of the imaging surface of the interference detection device.

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

[0015] According to the theoretical design parameters of the detected element, the radius of curvature of the meridional direction component and the radius of curvature of the sagittal direction component of the microelement of the detected surface light field are obtained;

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

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

[0018] ;

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

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

[0021] ;

[0022] where x represents the vector of the non-degraded wavefront after the multiple microelements describing the optical field of the detected surface pass through the interference detection device, A represents the parameter matrix, and B represents the vector of the optical field received by each pixel of the imaging plane.

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

[0024] ;

[0025] where x r represents the vector of the real part and the imaginary part of the non-degraded wavefront after the multiple microelements describing the optical field of the detected surface pass through the interference detection device, that is, x r includes a first set of elements and a second set of elements. The first set of elements is the real part of each element of the vector x, and the second set of elements is the imaginary part of each element of the vector x;

[0026] B r represents the vector of the real part and the imaginary part of the optical field received by each pixel of the imaging plane, that is, B r includes a first set of elements and a second set of elements. The first set of elements is the real part of each element of the vector B, and the second set of elements is the imaginary part of each element of the vector B;

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

[0028] In some embodiments, solving for the non-degraded wavefronts of the plurality of micro-elements of the light field of the surface to be detected after passing through the interference detection device according to the first surface shape result and the expression includes:

[0029] Establishing an objective function according to the expression, and solving for the non-degraded wavefronts of the plurality of micro-elements of the light field of the surface to be detected after passing through the interference detection device that minimize the value of the objective function. The objective function describes the difference between the measured result 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 according to the expression.

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

[0031] An optical component for making the reference light from a standard element and the reflected light of the surface to be detected pass through the optical component and then be incident on a detector;

[0032] A standard element for splitting a reference light from the detection beam incident on the standard element, returning the reference light to the detector, making the remaining detection beam exit to the surface to be detected, and making the reflected light of the surface to be detected pass through the standard element and then be incident on the optical component;

[0033] The detector for obtaining the interference result of the reference light and the reflected light of the surface to be detected.

[0034] An optical element surface shape detection system includes:

[0035] An interference detection device, disposed opposite to the element to be detected, for acquiring the light field of the surface to be detected of the element to be detected to obtain a first surface shape result of the surface to be detected of the element to be detected;

[0036] A decomposition module for decomposing the light field of the surface to be detected of the element to be detected into a plurality of micro-elements, and obtaining the positions of the micro-elements of the light field of the surface to be detected in the coordinate system of the element to be detected;

[0037] An acquisition module for obtaining the ideal imaging positions of the micro-elements of the light field of the surface to be detected after passing through the interference detection device based on the positions of the micro-elements of the light field of the surface to be detected;

[0038] A first establishing module, configured to establish a wavefront degradation model of a micro - element of the detected surface light field according to the ideal imaging position of the micro - element of the detected surface light field. The wavefront degradation model describes the wavefront change process when the micro - element of the detected surface light field propagates 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 micro - element of the detected surface light field at the ideal imaging position after passing through the interference detection device is the non - degraded wavefront of the micro - element of the detected surface light field after passing through the interference detection device;

[0039] A second establishing module, configured to establish an expression according to the wavefront degradation models of the multiple micro - elements of the detected surface light field. The expression describes the relationship between the light field received by the pixel of the imaging surface and the non - degraded wavefronts of the multiple micro - elements of the detected surface light field after passing through the interference detection device. The light field received by the pixel of the imaging surface is the superposition of the wavefronts when the multiple micro - elements of the detected surface light field propagate to the pixel after passing through the interference detection device;

[0040] A solving module, configured to solve and obtain the non - degraded wavefronts of the multiple micro - elements of the detected surface light field after passing through the interference detection device according to the first surface shape result and the expression, and obtain a second surface shape result of the detected surface of the detected element according to the non - degraded wavefronts of the multiple micro - elements.

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

[0042] A memory, configured to store a computer program;

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

[0044] As can be seen from the above technical solutions, in the optical element surface shape detection method, system, and device of the present invention, the light field of the surface to be detected of the element to be detected is decomposed into multiple micro-elements, the ideal imaging positions of the micro-elements of the light field of the surface to be detected after passing through the interference detection device are obtained, and a wavefront degradation model of the wavefront of the micro-elements of the light field of the surface to be detected after passing through the interference detection device and propagating to the imaging surface of the interference detection device relative to the non-degraded wavefront is established. Then, an expression describing the relationship between the light field received by the pixels of the imaging surface and the non-degraded wavefronts of the multiple micro-elements of the light field of the surface to be detected after passing through the interference detection device is established according to the wavefront degradation model. Furthermore, according to the first surface shape result and the expression, the non-degraded wavefronts of the multiple micro-elements of the light field of the surface to be detected after passing through the interference detection device are solved, and the second surface shape result of the surface to be detected of the element to be detected is obtained according to the non-degraded wavefronts of the multiple micro-elements. The beneficial effect of the present invention is that, compared with the prior art, it does not need to use the instrument transfer function of the interference detection device, avoiding the problem that the attenuation of the instrument transfer function caused by wavefront degradation affects the surface shape detection, and can more accurately characterize the surface shape information of the element to be detected. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0046] Figure 1 FIG. is a flowchart of a method for detecting the surface shape of an optical element provided in an embodiment;

[0047] Figure 2 FIG. is a schematic layout diagram of an interference detection device and an element to be detected in a method for detecting the surface shape of an optical element in an embodiment;

[0048] Figure 3 FIG. is a schematic flow diagram of a method for detecting the surface shape of an optical element in another embodiment.

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

[0050] 1 - Element to be detected, 2 - Computer-generated hologram element, 3 - Standard element, 4 - First lens, 5 - Second lens, 6 - Detector. DETAILED DESCRIPTION OF THE EMBODIMENTS

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

[0052] This embodiment provides an optical element surface shape detection method, which is applied to an interference detection device. The interference detection device and the element to be detected are arranged opposite to each other. The interference detection device is used to obtain the light field of the surface to be detected of the element to be detected to obtain the first surface shape result of the surface to be detected.

[0053] Reference can be made to Figure 1 , Figure 1 For a flowchart of an optical element surface shape detection method provided by an embodiment, as shown in the figure, the optical element surface shape detection method includes the following steps:

[0054] S11: Decompose the light field of the surface to be detected of the element to be detected into multiple micro-elements, and obtain the positions of the micro-elements of the light field of the surface to be detected in the coordinate system of the element to be detected.

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

[0056] The light field of the surface to be detected refers to the light field distribution of the reflected light of the surface to be detected. The light field of the surface to be detected contains the surface shape information of the surface to be detected. Decompose the light field of the surface to be detected into multiple micro-elements, and the micro-elements can also be called sampling micro-elements.

[0057] S12: Based on the positions of the micro-elements of the light field of the surface to be detected, obtain the ideal imaging positions of the micro-elements of the light field of the surface to be detected after passing through the interference detection device.

[0058] Based on the positions of the micro-elements of the light field of the surface to be detected in the coordinate system of the element to be detected, according to the propagation process of the light field of the surface to be detected passing through the interference detection device, obtain the ideal imaging positions of the micro-elements of the light field of the surface to be detected after passing through the interference detection device.

[0059] S13: Establish a wavefront degradation model for the micro - element of the detected surface light field according to the ideal imaging position of the micro - element of the detected surface light field. The wavefront degradation model describes the wavefront change process when the micro - element of the detected surface light field propagates 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 micro - element of the detected surface light field at the ideal imaging position after passing through the interference detection device is the non - degraded wavefront of the micro - element of the detected surface light field after passing through the interference detection device.

[0060] If there is a deviation between the imaging surface of the interference detection device and the ideal imaging position, then the wavefront of the micro - element of the detected surface light field received by the imaging surface of the interference detection device has degraded. When the wavefront of the detected surface light field is complex, the ideal imaging positions of the multiple micro - elements of the detected surface light field after passing through the interference detection device are not in the same plane, while the imaging surface of the interference detection device is a plane. Therefore, some of the multiple micro - elements of the detected surface light field cannot be clearly imaged on the imaging surface of the interference detection device, and it is considered that the wavefront of these micro - elements has degraded during the propagation 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 the light - sensing surface of the detector of the interference detection device, and is usually a plane. In this step, a wavefront degradation model for the micro - element of the detected surface light field is established, and the wavefront degradation model describes the wavefront after the micro - element of the detected surface light field passes through the interference detection device and propagates from the ideal imaging position to the imaging surface of the interference detection device.

[0061] S14: Establish an expression according to the wavefront degradation models of the multiple micro - elements of the detected surface light field. The expression describes the relationship between the light field received by the pixel of the imaging surface and the non - degraded wavefronts of the multiple micro - elements of the detected surface light field after passing through the interference detection device. The light field received by the pixel of the imaging surface is the superposition of the wavefronts propagated from the multiple micro - elements of the detected surface light field to the pixel after passing through the interference detection device.

[0062] The light field received by the pixels on the imaging surface is the superposition of the wavefronts propagated to the pixels after the multiple micro-elements of the light field on the detected surface pass through the interference detection device. The wavefront degradation model of the micro-elements describes the wavefront change process of the micro-elements of the light field on the detected surface 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 micro-elements of the light field on the detected surface from the non-degraded wavefront to the wavefront propagated to the imaging surface of the interference detection device after passing through the interference detection device. Then, an expression can be established according to the wavefront degradation models of the multiple micro-elements, that is, the relationship between the light field received by the pixels on the imaging surface and the wavefronts propagated to the imaging surface after the multiple micro-elements pass through the interference detection device can be established. Further, the relationship between the light field received by the pixels on the imaging surface and the non-degraded wavefronts of the multiple micro-elements after passing through the interference detection device can be established.

[0063] S15: According to the first surface shape result and the expression, solve to obtain the non-degraded wavefronts of the multiple micro-elements of the light field on the detected surface after passing through the interference detection device, and obtain the second surface shape result of the detected surface of the detected component according to the non-degraded wavefronts of the multiple micro-elements.

[0064] The interference detection device emits a detection light beam, makes the detection light beam incident on the detected surface of the detected component and be reflected, and the interference detection device acquires the reflected light of the detected surface of the detected component, then the light field of the detected surface of the detected component can be acquired, and further the first surface shape result of the detected surface can be obtained.

[0065] For the expression, the light field received by the pixels on the imaging surface can be obtained according to the first surface shape result. The first surface shape result is the measured surface shape of the detected surface, and there is wavefront degradation. The non-degraded wavefronts of the multiple micro-elements of the light field on the detected surface after passing through the interference detection device can be solved according to the expression.

[0066] In the optical element surface shape detection method of this embodiment, the light field of the detected surface of the detected component is decomposed into multiple micro-elements, the ideal imaging positions of the micro-elements of the light field of the detected surface after passing through the interference detection device are obtained, and a wavefront degradation model of the wavefront relative to the non-degraded wavefront of the micro-elements of the light field of the detected surface after passing through the interference detection device and propagating to the imaging surface of the interference detection device is established. And an expression describing the relationship between the light field received by the pixels on the imaging surface and the non-degraded wavefronts of the multiple micro-elements of the light field of the detected surface after passing through the interference detection device is established according to the wavefront degradation model. Further, according to the first surface shape result and the expression, solve to obtain the non-degraded wavefronts of the multiple micro-elements of the light field on the detected surface after passing through the interference detection device, and obtain the second surface shape result of the detected surface of the detected component according to the non-degraded wavefronts of the multiple micro-elements. Compared with the prior art, this method does not need to use the instrument transfer function of the interference detection device, avoids the problem that the attenuation of the instrument transfer function caused by wavefront degradation affects the surface shape detection, and can more accurately characterize the surface shape information of the detected component.

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

[0068] In some embodiments, calibration can be used to determine the position of the micro - elements of the light field on the detected surface in the coordinate system of the detected element, and the position coordinates can be expressed as (x s , y s , z s ).

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

[0070] According to the theoretical design parameters of the detected element, obtain the normal vector of the micro - elements of the light field on the detected surface, and obtain the radius of curvature of the meridional direction component and the radius of curvature of the sagittal direction component of the micro - elements of the light field on the detected surface. According to the position of the micro - elements of the light field on the detected surface and the theoretical surface shape formula of the detected surface, combine the thin - beam tracing method to obtain the ideal imaging position of the meridional direction component of the micro - elements of the light field on the detected surface after passing through the interference detection device, and obtain the ideal imaging position of the sagittal direction component of the micro - elements of the light field on the detected surface after passing through the interference detection device. The positions of the ideal focal planes of the meridional component and the sagittal component along the optical axis can be expressed as z T , z S .

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

[0072] ; (1)

[0073] where u i (x, y, z) represents the complex amplitude of the wavefront that propagates to the imaging plane after the i-th microelement passes through the interference detection device, E(z) represents the optical field amplitude, and Φ AC (z) represents the phase term related to the position along the optical axis direction, and Φ G (z) represents the Gouy phase term, and Φ E (x, y, z) represents the phase term related to the distribution perpendicular to the optical axis direction, Φ0 represents the initial phase, j represents the imaginary unit, where the Z-axis is parallel to the optical axis of the light propagating from the detected surface to the interference detection device, 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. Φ AC (z), Φ G (z) and Φ E (x, y, z) are related to the defocus amount of the imaging plane relative to the ideal imaging position after the i-th microelement passes through the interference detection device.

[0074] The transverse distribution of the wavefront corresponding to each microelement of the optical field of the detected surface propagating from the ideal imaging position to the imaging plane is represented according to formula (1). A wavefront degradation model represented in a convolution form is established according to formula (1).

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

[0076] ; (2)

[0077] where x represents the vector of the non-degraded wavefront of the multiple microelements describing the optical field of the detected surface after passing through the interference detection device, A represents the parameter matrix, and B represents the vector describing the optical field received by each pixel of the imaging plane.

[0078] x includes the amplitude information and phase information of the non-degraded wavefront of the microelements of the optical field of the detected surface, and B includes the amplitude information and phase information of the optical field received by the pixels of the imaging plane. A, x, and B in formula (2) are all in the complex domain.

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

[0080] If the optical field of the detected surface is decomposed into M microelements and the number of pixels of the actual acquired image on the imaging plane 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 embodiments, the complex elements of A, x, and B can be decomposed into real and imaginary parts, and the reconstructed expression is represented as:

[0082] ; (3)

[0083] where x r represents a vector of the real part and the imaginary part of the non-degraded wavefront of the multiple micro-elements describing the light field of the detected surface after passing through the interference detection device, that is, x r includes a first set of elements and a second set of elements. The first set of elements includes the real parts of the respective elements of the vector x, and the second set of elements includes the imaginary parts of the respective elements of the vector x;

[0084] B r represents a vector of the real part and the imaginary part of the light field received by each pixel of the imaging surface, that is, B r includes a first set of elements and a second set of elements. The first set of elements includes the real parts of the respective elements of the vector B, and the second set of elements includes the imaginary parts of the respective elements of the vector B;

[0085] A r represents a parameter matrix, that is, A r includes a first set of elements and a second set of elements. The first set of elements is the real parts of the respective elements of the vector A, and the second set of elements is the imaginary parts of the respective elements of the vector A.

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

[0087] In some embodiments, according to the first surface shape result and the expression, solving for the non-degraded wavefront of the multiple micro-elements of the light field of the detected surface after passing through the interference detection device includes: establishing an objective function according to the expression, and solving for the non-degraded wavefront of the multiple micro-elements of the light field of the detected surface that minimizes the value of the objective function. The objective function describes the difference between the measured result 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 according to the expression. The measured result of the light field received by the pixels of the imaging surface is obtained according to the first surface shape result obtained by the interference detection device.

[0088] In this embodiment, the method for solving for the non-degraded wavefront of the multiple micro-elements of the light field of the detected surface after passing through the interference detection device according to the first surface shape result and the expression is not limited. In some embodiments, it can be solved by, but not limited to, the gradient descent method or the conjugate gradient method, or other optimization algorithms can also be used for solving.

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

[0090] , ; (4)

[0091] where x represents a vector of the non-degraded wavefronts of the multiple micro-elements describing the light field of the surface to be detected after passing through the interference detection device, A represents a parameter matrix, Ax represents the light field received by the pixels of the imaging surface calculated according to the expression, and B represents the measured results of the light fields received by the respective pixels of the imaging surface. The optimization problem described by Equation (4) can be calculated using, but not limited to, optimization algorithms applicable to the complex domain such as the complex conjugate gradient method .

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

[0093] , ; (5)

[0094] where x r represents a vector of the real part and the imaginary part of the non-degraded wavefronts of the multiple micro-elements describing the light field of the surface to be detected after passing through the interference detection device, that is, x r includes a first set of elements and a second set of elements. The first set of elements includes the real parts of the respective elements of vector x, and the second set of elements includes the imaginary parts of the respective elements of vector x;

[0095] A r represents a parameter matrix, that is, A r includes a first set of elements and a second set of elements. The first set of elements is the real part of each element of vector A, and the second set of elements is the imaginary part of each element of vector A;

[0096] B r represents a vector of the real part and the imaginary part of the measured results of the light fields received by the respective pixels of the imaging surface, that is, B r includes a first set of elements and a second set of elements. The first set of elements includes the real parts of the respective elements of vector B representing the measured results of the light fields received by the respective pixels of the imaging surface, and the second set of elements includes the imaginary parts of the respective elements of vector B representing the measured results of the light fields received by the respective pixels of the imaging surface.

[0097] Since all variables of the optimization problem described by Equation (5) are in the real number domain, to solve for x r optimization algorithms such as, but not limited to, the gradient descent method or the conjugate gradient method can be used. Equation (4) and Equation (5) are equivalent, with the same corresponding optimal solution, and the optimal solution of either of them can obtain the complex amplitude distribution of the non-degraded wavefront.

[0098] Exemplarily, reference can be made toFigure 3 , Figure 3 is a schematic flowchart of an optical element surface shape detection method according to another embodiment. A mathematical model for restoring wavefront degradation is constructed, that is, according to the wavefront degradation models of the multiple micro-elements of the light field of the surface to be detected, an expression is established to describe the relationship between the light field received by the pixels of the imaging surface and the non-degraded wavefront of the multiple micro-elements of the light field of the surface to be detected after passing through the interference detection device, and an objective function is established. Furthermore, the non-degraded wavefront is solved according to the actual measurement result of the surface shape.

[0099] In some embodiments, the interference detection device includes: an optical component for making the reference light from the standard element 3 and the reflected light of the surface to be detected enter the detector 6 after passing through the optical component; a standard element 3 for splitting a path of reference light from the detection beam incident on the standard element 3, returning the reference light to the detector 6, making the remaining detection beam exit to the surface to be detected, and making the reflected light of the surface to be detected enter the optical component after passing through the standard element 3; a detector 6 for obtaining the interference result of the reference light and the reflected light of the surface to be detected. Exemplarily, reference can be made to Figure 2 , Figure 2 is a schematic layout diagram of the interference detection device and the element to be detected of an optical element surface shape detection method according to an 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. In Figure 2 it is simply described by the first lens 4 and the second lens 5. It can be understood that in other embodiments, the optical component may include other numbers of lenses and other arrangement forms of lenses, which are all within the protection scope of the present invention. This optical element surface shape detection method can be applied to the interference detection process without a compensator, and can also be applied to the interference detection process using a compensator. In some embodiments, it further includes a computer-generated hologram element 2. The element to be detected 1 and the interference detection device are arranged oppositely, and the computer-generated hologram element 2 is arranged between the element to be detected 1 and the interference detection device. The computer-generated hologram (CGH) can also be replaced by any other type of compensator for interference compensation detection. In this embodiment, there is no limitation on the type of the interference detection device, including but not limited to a Fizeau interferometer or a Twyman-Green interferometer.

[0100] In the prior art, two types of methods for improving ITF in terms of hardware include: The first type of method is to fuse different detection methods with various spatial frequency domain response capabilities to improve the frequency domain detection ability of the interferometer. However, due to different detection principles of different detection techniques, the error generation mechanisms in their detections are different, and it is difficult to achieve direct data fusion; the second type of method is to use a larger-sized CGH in the detection of large-aperture optical elements to improve the detection ability. However, the larger-sized CGH increases the manufacturing difficulty and raises the cost.

[0101] This optical element surface shape detection method is based on the complex beam tracing method and the elliptical Gaussian microelement model, establishes an analytical model for characterizing the wavefront degradation caused by the imaging aberration of the interferometer, and uses an algorithm to restore the real non-degraded surface shape information to realize the recovery of the instrument transfer function of the interference detection system. The method is simple and efficient. Only by inputting the parameters of each component of the detection optical path can the recovery of the degraded wavefront be realized in a computer, without making a larger-sized CGH and without using multiple detection techniques for data fusion. It is applicable to the detection of various complex aspherical mirrors including non-rotationally symmetric mirrors.

[0102] This embodiment also provides an optical element surface shape detection system, including:

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

[0104] A decomposition module, which is used to decompose the light field of the detected surface of the element to be detected into multiple microelements, and obtain the positions of the microelements of the light field of the detected surface in the coordinate system of the element to be detected;

[0105] An acquisition module, which is used to obtain the ideal imaging position of the microelement of the light field of the detected surface after passing through the interference detection device based on the position of the microelement of the light field of the detected surface;

[0106] A first establishment module, which is used to establish a wavefront degradation model of the microelement of the light field of the detected surface according to the ideal imaging position of the microelement of the light field of the detected surface. The wavefront degradation model describes the wavefront change process of the microelement of the light field of the detected surface 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 of 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 of the detected surface after passing through the interference detection device;

[0107] A second establishment module, which is used to establish an expression according to the wavefront degradation models of the multiple microelements of the light field of the detected surface. The expression describes the relationship between the light field received by the pixel of the imaging surface and the non-degraded wavefronts of the multiple microelements of the light field of the detected surface after passing through the interference detection device. The light field received by the pixel of the imaging surface is the superposition of the wavefronts of the multiple microelements of the light field of the detected surface after passing through the interference detection device and propagating to the pixel;

[0108] A solution module, configured to solve, according to the first surface shape result and the expression, for the non-degraded wavefronts of the multiple micro-elements of the detected surface optical field after passing through the interference detection device, and obtain a second surface shape result of the detected surface of the detected element according to the non-degraded wavefronts of the multiple micro-elements.

[0109] In the optical element surface shape detection system of this embodiment, the detected surface optical field of the detected element is decomposed into multiple micro-elements, the ideal imaging positions of the micro-elements of the detected surface optical field after passing through the interference detection device are obtained, a wavefront degradation model of the wavefront of the micro-elements of the detected surface optical field after passing through the interference detection device and propagating to the imaging surface of the interference detection device with respect to the non-degraded wavefront is established, and an expression describing the relationship between the optical field received by the pixels of the imaging surface and the non-degraded wavefronts of the multiple micro-elements of the detected surface optical field after passing through the interference detection device is established according to the wavefront degradation model. Then, according to the first surface shape result and the expression, the non-degraded wavefronts of the multiple micro-elements of the detected surface optical field after passing through the interference detection device are solved, and a second surface shape result of the detected surface of the detected element is obtained according to the non-degraded wavefronts of the multiple micro-elements. Compared with the prior art, this system does not need to use the instrument transfer function of the interference detection device, avoids the problem that the wavefront degradation causes the attenuation of the instrument transfer function and affects the surface shape detection, and can more accurately characterize the surface shape information of the detected element.

[0110] This embodiment also provides an optical element surface shape detection device, including:

[0111] A memory, configured to store a computer program;

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

[0113] In the optical element surface shape detection device of this embodiment, the detected surface optical field of the detected element is decomposed into multiple micro-elements, the ideal imaging positions of the micro-elements of the detected surface optical field after passing through the interference detection device are obtained, a wavefront degradation model of the wavefront of the micro-elements of the detected surface optical field after passing through the interference detection device and propagating to the imaging surface of the interference detection device with respect to the non-degraded wavefront is established, and an expression describing the relationship between the optical field received by the pixels of the imaging surface and the non-degraded wavefronts of the multiple micro-elements of the detected surface optical field after passing through the interference detection device is established according to the wavefront degradation model. Then, according to the first surface shape result and the expression, the non-degraded wavefronts of the multiple micro-elements of the detected surface optical field after passing through the interference detection device are solved, and a second surface shape result of the detected surface of the detected element is obtained according to the non-degraded wavefronts of the multiple micro-elements. Compared with the prior art, it does not need to use the instrument transfer function of the interference detection device, avoids the problem that the wavefront degradation causes the attenuation of the instrument transfer function and affects the 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 positions of the elements after propagation through the compensator, standard element and the internal optical system of the interference detection device by beam tracing. Subsequently, the wavefront change process of the element from the ideal imaging position to the detector is expressed in the form of convolution, and the elliptical Gaussian element is the convolution kernel. The present invention formulates the convolution operation in matrix form and constructs an objective function, and uses an optimization algorithm to solve the optimal solution under the condition that the objective function is minimized. Obtaining the optimal solution can decouple the interference imaging aberration and solve the non-degraded wavefront, and finally solve the problem that the surface shape information of the detected element cannot be accurately characterized due to the decrease of ITF. The present invention can improve the attenuation of the instrument transfer function of the interference detection system caused by wavefront degradation, can avoid the influence of different error sources of various detection methods on the detection accuracy, can avoid manufacturing a computational holographic element with a larger size, and save costs.

[0115] The above has introduced in detail the method, system and device for detecting the surface shape of an optical element provided by the present invention. Specific examples are used in this article to elaborate on the principle and implementation manner of the present invention. The description of the above embodiments is only used to help understand the method and its core idea of the present invention. It should be pointed out that for those of ordinary skill in the art in this technical field, without departing from the principle of the present invention, several improvements and modifications can be made to the present invention, and these improvements and modifications also fall within the protection scope of the present invention.

Claims

1. An optical element surface shape detection method, characterized in that An interference detection device is applied. The interference detection device and the element to be detected are arranged opposite to each other. The interference detection device is used to acquire the light field of the surface to be detected of the element to be detected to obtain the first surface shape result of the surface to be detected; The method for detecting the surface shape of the optical element includes: Decompose the light field of the surface to be detected of the element to be detected into a plurality of micro-elements, and obtain the positions of the micro-elements of the light field of the surface to be detected in the coordinate system of the element to be detected; Based on the positions of the micro-elements of the light field of the surface to be detected, obtain the ideal imaging positions of the micro-elements of the light field of the surface to be detected after passing through the interference detection device; According to the ideal imaging positions of the micro-elements of the light field of the surface to be detected, establish a wavefront degradation model for the micro-elements of the light field of the surface to be detected. The wavefront degradation model describes the wavefront change process when the micro-elements of the light field of the surface to be detected pass through the interference detection device and propagate from the ideal imaging position to the imaging surface of the interference detection device. The wavefront of the micro-elements of the light field of the surface to be detected at the ideal imaging position after passing through the interference detection device is the non-degraded wavefront of the micro-elements of the light field of the surface to be detected after passing through the interference detection device; Establish an expression according to the wavefront degradation models of the plurality of micro-elements of the light field of the surface to be detected. The expression describes the relationship between the light field received by the pixels of the imaging surface and the non-degraded wavefronts of the plurality of micro-elements of the light field of the surface to be detected after passing through the interference detection device. The light field received by the pixels of the imaging surface is the superposition of the wavefronts propagated from the plurality of micro-elements of the light field of the surface to be detected after passing through the interference detection device to the pixels; According to the first surface shape result and the expression, solve to obtain the non-degraded wavefronts of the plurality of micro-elements of the light field of the surface to be detected after passing through the interference detection device, and obtain the second surface shape result of the surface to be detected of the element to be detected according to the non-degraded wavefronts of the plurality of micro-elements.

2. The method for detecting the surface shape of an optical element according to claim 1, wherein The number of micro-elements obtained by decomposing the light field of the surface to be detected is consistent with the number of pixels of the imaging surface of the interference detection device.

3. The method for detecting the surface shape of an optical element according to claim 1, characterized in that, Based on the positions of the micro-elements of the light field of the surface to be detected, obtaining the ideal imaging positions of the micro-elements of the light field of the surface to be detected after passing through the interference detection device includes: According to the theoretical design parameters of the element to be detected, obtain the radius of curvature of the meridional direction component and the radius of curvature of the sagittal direction component of the micro-elements of the light field of the surface to be detected; According to the positions of the micro-elements of the light field of the surface to be detected and the theoretical surface shape formula of the surface to be detected, combine the thin beam tracing method to obtain the ideal imaging positions of the meridional direction components of the micro-elements of the light field of the surface to be detected after passing through the interference detection device, and obtain the ideal imaging positions of the sagittal direction components of the micro-elements of the light field of the surface to be detected after passing through the interference detection device.

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

5. The method for detecting the surface shape of an optical element according to claim 1, characterized in that, The expression is expressed as: ； Where, x represents the vector describing the non-degraded wavefronts of the plurality of micro-elements of the light field of the surface to be detected after passing 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 method for detecting the surface shape of an optical element according to claim 5, wherein After reconstruction, the expression is represented as: ； where x r represents a vector of the real part of the non-degraded wavefront and the imaginary part of the non-degraded wavefront of the plurality of micro-elements describing the light field of the surface to be detected after passing through the interference detection device, that is, x r includes a first set of elements and a second set of elements, the first set of elements includes the real parts of the respective elements of the vector x, and the second set of elements includes the imaginary parts of the respective elements of the vector x; B r A vector representing the real part and the imaginary part of the light field received by each pixel of the imaging surface, i.e., B r It includes a first group of elements and a second group of elements. The first group of elements includes the real parts of the respective elements of vector B, and the second group of elements includes the imaginary parts of the respective elements of vector B; A r represents a parameter matrix, i.e., A r includes a first set of elements and a second set of elements. The first set of elements includes the real parts of the respective elements of vector A, and the second set of elements includes the imaginary parts of the respective elements of vector A.

7. The method for detecting the surface shape of an optical element according to claim 1, wherein Based on the first surface shape result and the expression, solving to obtain the non-degraded wavefronts of the multiple micro-elements of the light field of the surface to be detected after passing through the interference detection device includes: Based on the expression, a target function is established, and the non-degraded wavefronts of the multiple micro-elements of the light field of the surface to be detected after passing through the interference detection device that minimize the value of the target function are obtained. The target function describes the difference between the measured result 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 according to the expression.

8. The method for detecting the surface shape of an optical element according to any one of claims 1 to 7, characterized in that, The interference detection device includes: An optical component for making the reference light from the standard element and the reflected light of the surface to be detected pass through the optical component and then be incident on the detector; A standard element for splitting a reference light from the detection beam incident on the standard element, making the reference light return to the detector, making the remaining detection beam exit to the surface to be detected, and making the reflected light of the surface to be detected pass through the standard element and then be incident on the optical component; The detector for obtaining the interference result of the reference light and the reflected light of the surface to be detected.

9. An optical element surface shape detection system, characterized in that It includes: An interference detection device, which is arranged opposite to the element to be detected, and is used to obtain the light field of the surface to be detected of the element to be detected to obtain the first surface shape result of the surface to be detected of the element to be detected; A decomposition module for decomposing the light field of the surface to be detected of the element to be detected into multiple micro-elements, and obtaining the positions of the micro-elements of the light field of the surface to be detected in the coordinate system of the element to be detected; An acquisition module for obtaining the ideal imaging positions of the micro-elements of the light field of the surface to be detected after passing through the interference detection device based on the positions of the micro-elements of the light field of the surface to be detected; A first establishment module for establishing a wavefront degradation model of the micro-elements of the light field of the surface to be detected according to the ideal imaging positions of the micro-elements of the light field of the surface to be detected. The wavefront degradation model describes the wavefront change process of the micro-elements of the light field of the surface to be detected 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 micro-elements of the light field of the surface to be detected at the ideal imaging position after passing through the interference detection device is the non-degraded wavefront of the micro-elements of the light field of the surface to be detected after passing through the interference detection device; A second establishment module for establishing an expression according to the wavefront degradation models of the multiple micro-elements of the light field of the surface to be detected. The expression describes the relationship between the light field received by the pixels of the imaging surface and the non-degraded wavefronts of the multiple micro-elements of the light field of the surface to be detected after passing through the interference detection device. The light field received by the pixels of the imaging surface is the superposition of the wavefronts of the multiple micro-elements of the light field of the surface to be detected after passing through the interference detection device and propagating to the pixels; A solution module for solving to obtain the non-degraded wavefronts of the multiple micro-elements of the light field of the surface to be detected after passing through the interference detection device according to the first surface shape result and the expression, and obtaining the second surface shape result of the surface to be detected of the element to be detected according to the non-degraded wavefronts of the multiple micro-elements.

10. An optical element surface shape detection device, characterized in that, It includes: A memory for storing a computer program; A processor for implementing 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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