Method and system for detecting absolute surface shape of cylindrical mirror by using rotation translation method

Abstract

The invention discloses a method and system for detecting the absolute surface shape of a cylindrical mirror by using a rotation translation method, and the method comprises the steps: carrying out the alignment of a cylindrical CGH and an interferometer host, and carrying out the wavefront matching of the cylindrical CGH and a cylindrical mirror to be detected; initial interference measurement data in the initial alignment state are obtained, and first measurement data are obtained after the cylindrical mirror to be measured is rotated by 180 degrees around the optical axis; based on the first measurement data and the initial interference measurement data, reconstructing a rotation asymmetric component through an iterative algorithm; the cylindrical mirror to be measured is controlled to move by the unit pixel distance in the x-axis direction and the y-axis direction respectively, and after the zero position state is maintained, corresponding second measurement data and third measurement data are collected; deducting a rotational asymmetric component from the first measurement data, the second measurement data and the third measurement data, and solving a rotational symmetric component based on a differential wavefront reconstruction algorithm; and superposing the rotational asymmetric component and the rotational symmetric component to obtain the absolute surface shape error distribution of the cylindrical mirror. According to the invention, the detection precision is obviously improved.

Description

Technical Field

[0001] The present invention relates to the technical field of optical precision measurement, and in particular to a method and system for detecting the absolute surface shape of a cylindrical mirror by using a rotation and translation method. Background Art

[0002] As advanced optical systems accelerate toward ultra-high resolution, lightweight design, and integration, cylindrical optical elements, with their unidirectional curvature, have become core components in high-end optical systems such as LiDAR, medical endoscopes, and synchrotron radiation sources. However, the key bottleneck restricting the machining accuracy of cylindrical elements has shifted from manufacturing processes to measurement technology. The precision limits of traditional measurement methods are directly hindering the performance breakthroughs of cylindrical optical elements.

[0003] Although the zero-position interferometry detection method based on computer-generated holograms (CGHs) is currently the mainstream precision measurement solution, its measurement results still contain systematic errors, including surface errors of the interferometer transmission standard mirror and manufacturing errors of the CGH. In particular, in applications requiring sub-nanometer precision, such as extreme ultraviolet lithography objectives and X-ray reflectors, this type of relative detection method is no longer sufficient. Patent document CN105318843A, published in 2014 by Ma Jun's team, utilizes the conjugate difference method to achieve a new approach to absolute measurement of cylindrical components. However, the pseudo-shearing principle employed by this method is highly susceptible to the influence of cylindrical mirror misalignment aberrations during the detection process, thereby introducing even greater errors.

[0004] Therefore, the existing CGH-based cylindrical surface shape detection process has problems such as low detection accuracy due to the introduction of transmission plane mirror shape errors and CGH manufacturing errors. Summary of the Invention

[0005] The technical problem to be solved by the present invention is that the existing CGH-based cylindrical surface shape detection process has problems such as low detection accuracy due to the introduction of transmission plane mirror surface shape errors and CGH manufacturing errors. The purpose of the present invention is to provide a method and system for detecting the absolute surface shape of a cylindrical mirror using a rotation and translation method. This method is particularly effective in eliminating the transmission plane mirror surface shape errors and CGH manufacturing errors introduced in the CGH-based cylindrical surface shape detection process, significantly improving the detection accuracy. The present invention realizes the measurement of the absolute surface shape error of the cylindrical mirror, provides a feasible technical path for the manufacture of ultra-precision cylindrical components, and has good practical value and broad application prospects.

[0006] The present invention is achieved through the following technical solutions: In a first aspect, the present invention provides a method for detecting the absolute surface shape of a cylindrical mirror using a rotation and translation method, the method comprising: Align the cylindrical CGH with the interferometer host by aligning the holographic area; Using the crosshair mark generated by the cylindrical CGH reference hologram, the cylindrical mirror to be tested is adjusted to the preset position; and the posture of the cylindrical mirror to be tested is adjusted to perform wavefront matching between the cylindrical CGH and the cylindrical mirror to be tested; Get the initial interferometric measurement data W of the initial alignment state rot , rotate the cylindrical mirror to be measured 180° around the optical axis and obtain the first measurement data W1; based on the first measurement data and the initial interferometric measurement data, reconstruct the rotationally asymmetric component W through an iterative algorithm as ; Controlling the orthogonal displacement unit to move the cylindrical mirror to be measured along the x-axis direction and the y-axis direction by a unit pixel distance respectively and maintaining the zero position state, and then collecting the corresponding second measurement data W2 and third measurement data W3; The rotationally asymmetric component W is subtracted from the first measurement data W1, the second measurement data W2 and the third measurement data W3. as , and solve the rotational symmetric component W based on the differential wavefront reconstruction algorithm s ; The rotationally asymmetric component W as With the rotationally symmetric component W s Superposition is performed to obtain the complete absolute surface error distribution of the cylindrical mirror.

[0007] Furthermore, the cylindrical CGH is aligned with the interferometer host by aligning the holographic area, including: The position of the cylindrical CGH is adjusted by the adjustment mechanism until interference fringes are generated in the alignment holographic area and are sparse enough, thereby completing the alignment between the cylindrical CGH and the interferometer host; The posture of the cylindrical surface CGH includes the pitch angle and yaw angle of the cylindrical surface CGH.

[0008] Furthermore, the cylindrical mirror to be tested is adjusted to a preset position using the crosshair mark generated by the cylindrical CGH reference hologram; and the posture of the cylindrical mirror to be tested is adjusted to perform wavefront matching between the cylindrical CGH and the cylindrical mirror to be tested, including: Using the crosshairs generated by the cylindrical CGH reference hologram, the cylindrical mirror to be tested is adjusted to a preset position to achieve alignment between the cylindrical mirror to be tested and the cylindrical CGH; the preset position is the location of the clear crosshairs generated after the test beam passes through the reference holographic area; The position of the cylindrical mirror to be tested is adjusted so that the diffraction wavefront generated by the main holographic area propagates in the opposite direction along the original path after being incident, and interferes with the reference beam to form interference fringes as few as possible; the position of the cylindrical mirror to be tested refers to the degree of freedom of the cylindrical mirror to be tested.

[0009] Furthermore, the initial interferometric measurement data W of the initial alignment state is obtained. rot, rotate the cylindrical mirror to be measured 180° around the optical axis and obtain the first measurement data W1; based on the first measurement data and the initial interferometric measurement data, reconstruct the rotationally asymmetric component W through an iterative algorithm as ,include: The position of the cylindrical mirror to be measured is adjusted by the cylindrical mirror clamping adjustment mechanism, so that the interferometer measurement result does not contain the misalignment aberration as much as possible, and the interferometer host is used for the first measurement to obtain the initial interferometric measurement data W of the initial alignment state. rot ; The cylindrical mirror to be measured is rotated 180° around the optical axis and measured again to obtain the first measurement data W1. The rotational symmetric component is eliminated by subtracting the first measurement data from the initial interferometric measurement data, and the rotational asymmetric component W is reconstructed by an iterative algorithm. as .

[0010] Furthermore, controlling the orthogonal displacement unit to move the cylindrical mirror to be measured along the x-axis direction and the y-axis direction by a unit pixel distance respectively and maintaining the zero position state to collect corresponding second measurement data W2 and third measurement data W3, including: Controlling the orthogonal displacement unit to move the cylindrical mirror to be measured by a unit pixel distance along the x-axis direction, and then collecting the second measurement data W2 after deflecting to a zero position state; the x-axis direction is a horizontal direction orthogonal to the optical axis; The orthogonal displacement unit is controlled to move the cylindrical mirror to be measured by a unit pixel distance along the y-axis direction, and then the third measurement data W3 is collected; the y-axis direction is the vertical direction.

[0011] Furthermore, controlling the orthogonal displacement unit to move the cylindrical mirror to be measured by a unit pixel distance along the x-axis direction, and then collecting the second measurement data W2 after deflecting to a zero position state, includes: The lateral distortion correction coefficient of cylindrical CGH is introduced and converted into image space for calculation to obtain the unit pixel distance; The orthogonal displacement unit is controlled to move the cylindrical mirror to be measured by the unit pixel distance along the x-axis direction, and the interferometer host is reset to a zero position state using the point-to-point mode of the interferometer host to collect the second measurement data W2.

[0012] Furthermore, controlling the orthogonal displacement unit to move the cylindrical mirror to be measured by a unit pixel distance along the y-axis direction and then collecting third measurement data W3 includes: The orthogonal displacement unit is controlled to move the cylindrical mirror to be measured by a unit pixel distance along the y-axis direction, directly convert it into the image space and collect the third measurement data W3.

[0013] Furthermore, the rotationally asymmetric component W is deducted from the first measurement data W1, the second measurement data W2 and the third measurement data W3. as, and solve the rotational symmetric component W based on the differential wavefront reconstruction algorithm s ,include: The rotationally asymmetric component W is subtracted from the first measurement data W1, the second measurement data W2 and the third measurement data W3. as , and perform differential operation to obtain differential wavefront data of the rotationally symmetric component; According to the differential wavefront data, the rotational symmetric component W is reconstructed based on the wavefront restoration algorithm. s ; The wavefront restoration algorithm includes any one of the path integral method, Hudgin slope method, Zernike polynomial fitting reconstruction method and Fourier transform reconstruction method.

[0014] In a second aspect, the present invention provides a system for detecting the absolute surface shape of a cylindrical mirror using a rotation-translation method, the system comprising: an interferometric measurement cavity module, a cylindrical computer-generated holographic module, a cylindrical mirror module to be measured, and a computer processing module; Interferometer measurement cavity module, including interferometer host and transmission standard mirror; Cylindrical computer-generated holography module, including cylindrical CGH and CGH clamping and adjustment mechanism; The cylindrical mirror module to be tested includes the cylindrical mirror to be tested, a cylindrical mirror clamping and adjustment mechanism, and an orthogonal displacement unit, wherein the orthogonal displacement unit is used to control the movement of the cylindrical mirror to be tested in two directions orthogonal to the optical axis; A computer processing module includes an integrated displacement control unit and a data analysis and processing unit. The data analysis and processing unit is used to analyze and process the data results of the interferometer host measuring the cylindrical mirror to be measured at different positions to obtain the absolute surface error distribution of the cylindrical mirror to be measured; The interferometer host generates a parallel light beam and is divided into two beams. One beam is reflected by the transmission standard mirror to form a reference beam; the other beam is transmitted through the transmission standard mirror to form a test beam and is incident on the cylindrical computer-generated holographic module fixed by the CGH clamping adjustment mechanism. After diffraction, it is incident on the cylindrical mirror to be tested fixed by the cylindrical mirror clamping adjustment mechanism; then the beam returns to the interferometer host along the original path, meets the reference beam inside the interferometer host and interferes, generating an interference pattern; the interference pattern is processed by the computer processing module to obtain the initial interference measurement data W rot ; Based on the initial interferometric measurement data, the surface shape distribution of the cylindrical mirror is divided into rotationally asymmetric components and rotationally symmetric components through the rotation-translation method, and the measurements are performed separately to obtain the absolute surface shape error of the cylindrical mirror to be measured.

[0015] Furthermore, based on the initial interferometric measurement data, the surface shape distribution of the cylindrical mirror is divided into rotationally asymmetric components and rotationally symmetric components through the rotation-translation method, and the measurements are solved separately, including: Obtain initial interference measurement data in the initial state, rotate the cylindrical mirror to be measured 180° around the optical axis, and then complete data processing through a computer processing module to obtain first measurement data W1; The rotational symmetric component is eliminated by subtracting the first measurement data W1 from the initial interferometric measurement data Wrot, and the rotational asymmetric component W is reconstructed by an iterative algorithm. as ; Control the orthogonal displacement unit to move the cylindrical mirror to be measured along the x-axis direction and the y-axis direction respectively by a unit pixel distance and maintain the zero position state, and then collect the corresponding second measurement data W2 and third measurement data W3, The rotationally asymmetric component W is subtracted from the first measurement data W1, the second measurement data W2 and the third measurement data W3. as , and solve the rotational symmetric component W based on the differential wavefront reconstruction algorithm s ; The rotationally asymmetric component W as With the rotationally symmetric component W s Superposition is performed to obtain the complete distribution of absolute cylindrical surface error.

[0016] Compared with the prior art, the present invention has the following advantages and beneficial effects: The present invention discloses a method and system for detecting the absolute surface shape of a cylindrical mirror using a rotational translation method. By dividing the cylindrical surface shape into a rotationally asymmetric component and a rotationally symmetric component, the rotational method and the translational difference method are applied to solve the problems, respectively, ultimately accurately reconstructing the absolute surface shape error distribution of the cylindrical optical element. The method of the present invention is particularly effective in eliminating the surface shape errors of the transmission plane mirror introduced during the cylindrical surface shape detection process based on CGH, as well as the CGH manufacturing errors, significantly improving detection accuracy. The present invention enables the measurement of the absolute surface shape error of a cylindrical mirror, provides a feasible technical path for the manufacture of ultra-precision cylindrical components, and has excellent practical value and broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] The drawings described herein are used to provide a further understanding of the embodiments of the present invention, constitute a part of this application, and do not constitute a limitation of the embodiments of the present invention. In the drawings: Figure 1 This is a measurement optical path diagram of a system for detecting the absolute surface shape of a cylindrical mirror using a rotation and translation method according to the present invention; Figure 2 This is a diagram showing the measurement results of a method for detecting the absolute surface shape of a cylindrical mirror using a rotation and translation method according to the present invention; Figure 3 This is a flow chart of a method for detecting the absolute surface shape of a cylindrical mirror using a rotation and translation method according to the present invention.

[0018] Reference numerals and corresponding component names: 1-Interferometer host, 2-Transmission standard mirror, 3-CGH clamping and adjustment mechanism, 4-Cylindrical CGH, 5-Cylindrical mirror clamping and adjustment mechanism, 6-Cylindrical mirror to be measured, 7-Computer processing module. DETAILED DESCRIPTION

[0019] Hereinafter, the terms "include" or "may include" used in various embodiments of the present invention indicate the presence of the invented function, operation or element, and do not limit the addition of one or more functions, operations or elements. In addition, as used in various embodiments of the present invention, the terms "include", "have" and their cognates are intended only to indicate specific features, numbers, steps, operations, elements, components or combinations of the foregoing, and should not be understood as excluding the presence of one or more other features, numbers, steps, operations, elements, components or combinations of the foregoing or the possibility of adding one or more features, numbers, steps, operations, elements, components or combinations of the foregoing.

[0020] In various embodiments of the present invention, the expression "or" or "at least one of A or / and B" includes any or all combinations of the words listed simultaneously. For example, the expression "A or B" or "at least one of A or / and B" may include A, may include B, or may include both A and B.

[0021] The expressions (such as "first", "second", etc.) used in the various embodiments of the present invention may modify the various constituent elements in the various embodiments, but may not limit the corresponding constituent elements. For example, the above expressions do not limit the order and / or importance of the elements. The above expressions are only used to distinguish one element from other elements. For example, a first user device and a second user device indicate different user devices, although both are user devices. For example, without departing from the scope of the various embodiments of the present invention, a first element may be referred to as a second element, and similarly, a second element may also be referred to as a first element.

[0022] It should be noted that when a component is described as being “connected” to another component, the first component may be directly connected to the second component, and a third component may be “connected” between the first and second components. Conversely, when a component is described as being “directly connected” to another component, it can be understood that there is no third component between the first and second components.

[0023] The terms used in various embodiments of the present invention are only used to describe the purpose of specific embodiments and are not intended to limit the various embodiments of the present invention. As used herein, the singular form is intended to also include the plural form, unless the context clearly indicates otherwise. Unless otherwise limited, all terms used here (including technical terms and scientific terms) have the same meaning as those of ordinary skill in the art generally understood by the various embodiments of the present invention. The terms (such as those defined in generally used dictionaries) will be interpreted as having the same meaning as the contextual meaning in the relevant technical field and will not be interpreted as having idealized meaning or too formal meaning, unless clearly defined in various embodiments of the present invention.

[0024] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with examples and drawings. The exemplary embodiments of the present invention and their descriptions are only used to explain the present invention and are not intended to limit the present invention.

[0025] In order to solve the problems of low detection accuracy caused by the introduction of transmitted plane mirror shape errors and CGH manufacturing errors in the existing CGH-based cylindrical surface shape detection process, the present invention breaks through the geometric property that the non-curvature direction of cylindrical optical elements can be regarded as a plane, and innovatively proposes a method for detecting the absolute surface shape of a cylindrical mirror using the rotation and translation method.

[0026] The innovative design of the present invention lies in that the absolute surface error distribution of the cylindrical optical element is accurately reconstructed by dividing the cylindrical surface shape into a rotationally asymmetric component and a rotationally symmetric component, and applying the rotation method and the translation difference method to solve them respectively.

[0027] Specifically, the present invention takes into account the characteristic that a cylindrical mirror has curvature in only one direction, and divides the surface shape distribution of the cylindrical mirror into a rotationally asymmetric component and a rotationally symmetric component through a rotational translation method, and solves them separately. First, a 180° rotational symmetry measurement method is adopted, and the rotationally asymmetric component is solved by comparing the surface shape difference distribution before and after rotation using an iterative optimization algorithm. Subsequently, an x ​​and y direction translation shear detection is implemented, and the rotationally symmetric component is obtained on the basis of eliminating the known rotationally asymmetric error. Finally, the absolute surface shape distribution of the cylindrical mirror is obtained by summing the two results. The method of the present invention realizes the measurement of the absolute surface shape error of the cylindrical mirror, provides a feasible technical path for the manufacture of ultra-precision cylindrical components, and has good practical value and broad application prospects.

[0028] Example 1 like Figure 1 As shown, the present invention provides a system for detecting the absolute surface shape of a cylindrical mirror using a rotation and translation method, the system comprising: an interferometric measurement cavity module, a cylindrical computer-generated holographic module, a cylindrical mirror module to be measured, and a computer processing module; An interferometer measurement cavity module includes an interferometer host 1 and a transmission standard mirror 2; A cylindrical computer-generated holographic module, comprising a cylindrical CGH 4 and a CGH clamping and adjusting mechanism 3; The cylindrical mirror module to be tested comprises a cylindrical mirror to be tested 6, a cylindrical mirror clamping and adjusting mechanism 5 and an orthogonal displacement unit, wherein the orthogonal displacement unit is used to control the movement of the cylindrical mirror to be tested in two directions orthogonal to the optical axis; The computer processing module 7 includes an integrated displacement control unit and a data analysis and processing unit. The data analysis and processing unit is used to analyze and process the data results of the interferometer host 1 measured at different positions of the cylindrical mirror to be measured to obtain the absolute surface error distribution of the cylindrical mirror to be measured; The interferometer host 1 generates a parallel light beam and is divided into two beams. One beam is reflected by the rear surface of the transmission standard mirror 2 to form a reference beam. The other beam is transmitted through the transmission standard mirror 2 to form a test beam and is incident on the cylindrical computer-generated hologram module fixed by the CGH clamping adjustment mechanism 3. After diffraction, it is incident on the cylindrical mirror to be tested 6 fixed by the cylindrical mirror clamping adjustment mechanism 5. The beam then returns to the interferometer host 1 along the original path and meets and interferes with the reference beam inside the interferometer host 1 to generate an interference pattern. The interference pattern is processed by the computer processing module 7 to obtain the initial interference measurement data W. rot ; Based on the initial interferometric measurement data, the surface shape distribution of the cylindrical mirror is divided into rotationally asymmetric components and rotationally symmetric components through the rotation-translation method, and the measurements are performed separately to obtain the absolute surface shape error of the cylindrical mirror to be measured.

[0029] In this embodiment, based on the initial interferometric measurement data, the surface shape distribution of the cylindrical mirror is divided into a rotationally asymmetric component and a rotationally symmetric component by a rotation-translation method, and the measurements are performed separately, including: Initial interference measurement data Wrot is obtained in the initial state, and the cylindrical mirror 6 to be measured is rotated 180° around the optical axis and then the computer processing module 7 completes data processing to obtain first measurement data W1; By combining the first measurement data W1 with the initial interferometric measurement data W rot Subtract to eliminate the rotational symmetric component and reconstruct the rotational asymmetric component W through an iterative algorithm as ; Control the orthogonal displacement unit to move the cylindrical mirror 6 to be measured along the x-axis direction and the y-axis direction respectively by a unit pixel distance and maintain the zero position state, and then collect the corresponding second measurement data W2 and third measurement data W3, The rotationally asymmetric component W is subtracted from the first measurement data W1, the second measurement data W2 and the third measurement data W3. as , and solve the rotational symmetric component W based on the differential wavefront reconstruction algorithm s ; The rotationally asymmetric component Was With the rotationally symmetric component W s Superposition is performed to obtain the complete distribution of absolute cylindrical surface error.

[0030] In this embodiment, controlling the orthogonal displacement unit to move the cylindrical mirror 6 to be measured by a unit pixel distance along the x-axis direction and the y-axis direction respectively and maintaining the zero position state, and then collecting the corresponding second measurement data W2 and third measurement data W3, includes: (1) Controlling the orthogonal displacement unit to move the cylindrical mirror 6 to be measured by a unit pixel distance along the x-axis direction, then using the cylindrical mirror clamping adjustment mechanism 5 to rotate the cylindrical mirror 6 to be measured back to the zero position state, and completing data processing through the computer processing module 7 to obtain second measurement data W2; the x-axis direction is the horizontal direction orthogonal to the optical axis; (2) Control the orthogonal displacement unit to move the cylindrical mirror to be measured by a unit pixel distance along the y-axis direction, and complete data processing through the computer processing module 7 to obtain the third measurement data W3; the y-axis direction is the vertical direction.

[0031] After obtaining the above four sets of measurement results, the absolute surface error of the cylindrical mirror to be measured can be obtained by applying the iterative optimization algorithm and the pseudo-shear reconstruction algorithm.

[0032] The interferometer host 1 of the present invention generates a parallel light beam and is divided into two beams, one of which is reflected by the rear surface of the transmission standard mirror 2 to form a reference beam; the other beam serves as a test wavefront. The test wavefront first passes through the main holographic area of ​​the cylindrical CGH. During this process, a specific phase function is added by diffraction to form a diffraction wavefront, which transforms the plane wavefront into a wavefront that matches the theoretical surface shape of the cylindrical mirror to be measured. Subsequently, the wavefront is incident and reflected in the normal direction of the cylindrical mirror to be measured, and passes through the cylindrical CGH again along the original path. At this time, the cylindrical CGH superimposes an opposite phase function on the wavefront. This process converts the wavefront carrying the surface shape information of the cylindrical mirror to be measured into a plane wavefront. Finally, this plane wavefront returns to the interferometer host and interferes with the reference wavefront, thereby achieving accurate measurement of the cylindrical mirror.

[0033] Example 2 like Figure 2 and Figure 3 As shown, the difference between this embodiment and embodiment 1 is that this embodiment provides a method for detecting the absolute surface shape of a cylindrical mirror using a rotation and translation method. This method is based on the cylindrical zero position interferometry measurement system constructed in embodiment 1. The method includes: Step 1, aligning the cylindrical CGH with the interferometer host by aligning the holographic area; In this embodiment, step 1 specifically includes: The position of the cylindrical CGH is adjusted by the adjustment mechanism until interference fringes are generated in the alignment holographic area and are sparse enough, thereby completing the alignment between the cylindrical CGH and the interferometer host; The posture of the cylindrical surface CGH includes the pitch angle and yaw angle of the cylindrical surface CGH.

[0034] Step 2: Using the crosshair mark generated by the cylindrical CGH reference hologram, adjust the cylindrical mirror to a preset position; and adjust the posture of the cylindrical mirror to be tested to perform wavefront matching between the cylindrical CGH and the cylindrical mirror to be tested; In this embodiment, step 2 specifically includes: Using the crosshairs generated by the cylindrical CGH reference hologram, the cylindrical mirror to be tested is adjusted to a preset position to achieve alignment between the cylindrical mirror to be tested and the cylindrical CGH; the preset position is the location of the clear crosshairs generated after the test beam passes through the reference holographic area; The position of the cylindrical mirror to be tested is adjusted so that the diffraction wavefront generated by the main holographic area propagates in the opposite direction along the original path after being incident, and interferes with the reference beam to form interference fringes with as few interference fringes as possible, thereby completing the wavefront matching between the cylindrical CGH and the cylindrical mirror to be tested; the position of the cylindrical mirror to be tested refers to the degree of freedom of the cylindrical mirror to be tested.

[0035] Step 3: Obtain the initial interferometric measurement data W of the initial alignment state rot , rotate the cylindrical mirror to be measured 180° around the optical axis and obtain the first measurement data W1; based on the first measurement data and the initial interferometric measurement data, reconstruct the rotationally asymmetric component W through an iterative algorithm as ; In this embodiment, step 3 specifically includes: Step 31: Adjust the position of the cylindrical mirror to be measured by the cylindrical mirror clamping adjustment mechanism so that the interferometer measurement result does not contain the misalignment aberration as much as possible, and then use the interferometer host to perform the first measurement to obtain the initial interferometric measurement data of the initial alignment state. ; (1) Among them, W SE (x, y) is the system error, including the transmission standard mirror shape error and CGH manufacturing error, etc., W TS (x, y) is the surface error of the cylindrical mirror to be measured, [·] π Indicates a 180° rotation around the optical axis.

[0036] Step 32: Rotate the cylindrical mirror to be measured 180° around the optical axis and measure again to obtain the first measurement data. ; (2) Step 33, eliminate the rotational symmetric component by subtracting the first measurement data from the initial interferometric measurement data, i.e., performing the operation ΔW(x,y)= W1-W rot Eliminate the rotationally symmetric component and reconstruct the rotationally asymmetric component W through an iterative algorithm as .

[0037] (3) Among them, W as (x, y) is the rotational asymmetric component of the cylindrical surface error, W s (x, y) is a rotationally symmetric component that satisfies W s (x, y)=[W s (x, y)] π , so the difference before and after rotation effectively eliminates the contribution of the rotational symmetric component to the measurement result, so that ΔW(x, y) only retains the information of the rotational asymmetric component. A nonlinear least squares iterative optimization algorithm can be used to recover W as (x, y), the algorithms include trust region reflective algorithm, Levenberg-Marquardt algorithm, etc.

[0038] Step 4: Control the orthogonal displacement unit to move the cylindrical mirror to be measured by a unit pixel distance along the x-axis direction and the y-axis direction respectively, and collect the corresponding second measurement data W2(x, y) and third measurement data W3(x, y) after maintaining the zero position state; In this embodiment, step 4 specifically includes: Step 41: Control the orthogonal displacement unit to move the cylindrical mirror to be measured by a unit pixel distance along the x-axis direction, and then collect second measurement data W2(x, y) after deflecting to a zero position state; the x-axis direction is a horizontal direction orthogonal to the optical axis; specifically: The lateral distortion correction coefficient of cylindrical CGH is introduced and converted into image space for calculation to obtain the unit pixel distance; The orthogonal displacement unit is controlled to move the cylindrical mirror to be measured by the unit pixel distance along the x-axis direction, and the interferometer host is reset to the zero position state using the point-to-point mode of the interferometer host to collect the second measurement data W2 (x, y).

[0039] Step 42: Control the orthogonal displacement unit to move the cylindrical mirror to be measured by a unit pixel distance along the y-axis direction to collect third measurement data W3 (x, y); the y-axis direction is the vertical direction. Specifically: The orthogonal displacement unit is controlled to move the cylindrical mirror to be measured by a unit pixel distance along the y-axis direction, directly convert it into the image space and collect the third measurement data (x, y).

[0040] Among them, W2(x, y) and W3(x, y) are expressed as: (4) Step 5: deduct the rotationally asymmetric component W from the first measurement data W1, the second measurement data W2 and the third measurement data W3. as , and solve the rotational symmetric component W based on the differential wavefront reconstruction algorithm s ; In this embodiment, step 5 specifically includes: The rotationally asymmetric component W is subtracted from the first measurement data W1, the second measurement data W2 and the third measurement data W3. as , and perform differential operation to obtain differential wavefront data of the rotationally symmetric component; According to the differential wavefront data, the rotational symmetric component W is reconstructed based on the wavefront restoration algorithm. s .

[0041] In the above technical solution, step 5 is to deduct the rotationally asymmetric component from the three measurement results, and then perform a differential operation to obtain the differential wavefronts ΔWs x and ΔWs y of the rotationally symmetric components. The calculation process is: (5) Where Was(x+Δx, y) and Was(x+Δx, y+Δy) represent the rotationally symmetric components after translation along the x-axis and y-axis, respectively. Based on the differential wavefront data, the rotationally symmetric component Ws(x, y) can be reconstructed using a wavefront restoration algorithm, such as the path integral method, the Hudgin slope method, the Zernike polynomial fitting reconstruction method, and the Fourier transform reconstruction method.

[0042] Step 6: The rotationally asymmetric component W obtained by the rotation method as (x, y) and the rotational symmetric component W obtained by the pseudo-shearing method s (x, y) are superimposed to obtain the complete absolute surface error distribution W of the cylindrical mirror TS (x, y)=W as (x, y)+W s (x, y).

[0043] In the specific implementation, the method of the present invention is used to simulate the measurement of a cylindrical mirror based on CGH. The measurement diameter of the cylindrical mirror is 20mm×20mm, the wavelength λ of the interferometer is 632.8nm, and the imaging resolution is 100pixel×100pixel. The simulated surface of the cylindrical mirror is as follows: Figure 3 As shown in (a), the system error simulation including the transmission standard mirror shape error and CGH manufacturing error is as follows Figure 3 (b) shows the first measurement result (i.e., initial interferometric measurement data) W rot(x, y) Figure 3 As shown in (c), after the cylindrical mirror is rotated 180°, the second measurement result (i.e. the first measurement data) W1(x, y) is as follows Figure 3 As shown in (d), after the cylindrical mirror is moved unit pixel along the x-axis and rotated back to the zero position, the third measurement result (i.e., the second measurement data) W2(x, y) is as follows Figure 3 As shown in (e), after the cylindrical mirror is moved unit pixel along the y-axis direction, the fourth measurement result (i.e. the third measurement data) W3(x,y) is as follows Figure 3 (f) The difference between the first and second results is obtained, and the rotational asymmetric error component W is obtained using an iterative optimization algorithm. as (x, y), such as Figure 3 (g) The second, third, and fourth measurement results are subtracted from each other to obtain the differential wavefront in the x and y directions, and the rotational symmetric component W is restored using the wave surface integral restoration algorithm. s (x, y), such as Figure 3 Finally, the absolute surface error can be obtained by summing the two components, as shown in (h). Figure 3 As shown in (i), and compared with the cylindrical mirror simulation surface shape, its measurement error PV value is only 6.71×10 -13 The RMS value of λ is only 1.56×10 -13 λ, can realize the absolute surface measurement of cylindrical mirror.

[0044] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present application may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0045] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0046] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0047] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0048] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for detecting the absolute surface shape of a cylindrical mirror using a rotation and translation method, characterized in that: The method includes: Align the cylindrical CGH with the interferometer host by aligning the holographic area; Using the crosshair mark generated by the cylindrical CGH reference hologram, the cylindrical mirror to be tested is adjusted to the preset position; and the posture of the cylindrical mirror to be tested is adjusted to perform wavefront matching between the cylindrical CGH and the cylindrical mirror to be tested; Acquire initial interferometric measurement data of an initial alignment state, rotate the cylindrical mirror to be measured 180° around the optical axis, and then acquire first measurement data; reconstruct the rotationally asymmetric component through an iterative algorithm based on the first measurement data and the initial interferometric measurement data; Controlling the orthogonal displacement unit to move the cylindrical mirror to be measured by a unit pixel distance along the x-axis direction and the y-axis direction respectively and maintaining the zero position state, and then collecting corresponding second measurement data and third measurement data; Deducting the rotationally asymmetric component from the first measurement data, the second measurement data, and the third measurement data, and solving the rotationally symmetric component based on a differential wavefront reconstruction algorithm; The rotationally asymmetric component and the rotationally symmetric component are superimposed to obtain the absolute surface error distribution of the cylindrical mirror.

2. The method for detecting the absolute surface shape of a cylindrical mirror using a rotation and translation method according to claim 1, wherein: Alignment of the cylindrical CGH with the interferometer host is performed by aligning the holographic area, including: The position of the cylindrical CGH is adjusted by the adjustment mechanism until interference fringes are generated in the alignment holographic area and are sparse enough, thereby completing the alignment between the cylindrical CGH and the interferometer host; The posture of the cylindrical surface CGH includes the pitch angle and yaw angle of the cylindrical surface CGH.

3. The method for detecting the absolute surface shape of a cylindrical mirror using a rotation and translation method according to claim 1, wherein: Use the crosshairs mark generated by the cylindrical CGH reference hologram to adjust the cylindrical mirror to the preset position; And adjust the posture of the cylindrical mirror to be tested, and perform wavefront matching between the cylindrical CGH and the cylindrical mirror to be tested, including: Using the crosshairs generated by the cylindrical CGH reference hologram, the cylindrical mirror to be tested is adjusted to a preset position to achieve alignment between the cylindrical mirror to be tested and the cylindrical CGH; the preset position is the location of the crosshairs generated after the test beam passes through the reference holographic area; The position of the cylindrical mirror to be tested is adjusted so that the diffraction wavefront generated by the main holographic area propagates in the opposite direction along the original path after being incident, and interferes with the reference beam to form interference fringes; the position of the cylindrical mirror to be tested refers to the degree of freedom of the cylindrical mirror to be tested.

4. The method for detecting the absolute surface shape of a cylindrical mirror using a rotation and translation method according to claim 1, wherein: Acquire initial interferometric measurement data of an initial alignment state, rotate the cylindrical mirror to be measured 180 degrees around the optical axis, and then acquire first measurement data; reconstruct the rotationally asymmetric component based on the first measurement data and the initial interferometric measurement data through an iterative algorithm, including: The position of the cylindrical mirror to be measured is adjusted by the cylindrical mirror clamping adjustment mechanism so that the interferometer measurement result does not include the misalignment aberration, and the interferometer host is used to perform the first measurement to obtain the initial interferometric measurement data of the initial alignment state; Rotate the cylindrical mirror to be measured 180° around the optical axis and measure it again to obtain the first measurement data. The rotationally symmetric component is eliminated by subtracting the first measurement data from the initial interferometric measurement data, and the rotationally asymmetric component is reconstructed by an iterative algorithm.

5. The method for detecting the absolute surface shape of a cylindrical mirror using a rotation and translation method according to claim 1, wherein: Controlling the orthogonal displacement unit to move the cylindrical mirror to be measured by a unit pixel distance along the x-axis direction and the y-axis direction respectively and maintaining the zero position state to collect corresponding second measurement data and third measurement data, including: Controlling the orthogonal displacement unit to move the cylindrical mirror to be measured by a unit pixel distance along the x-axis direction, and then collecting second measurement data after deflecting to a zero position state; the x-axis direction is a horizontal direction orthogonal to the optical axis; The orthogonal displacement unit is controlled to move the cylindrical mirror to be measured by a unit pixel distance along the y-axis direction, and then the third measurement data is collected; the y-axis direction is the vertical direction.

6. The method for detecting the absolute surface shape of a cylindrical mirror using a rotation and translation method according to claim 5, characterized in that: Controlling the orthogonal displacement unit to move the cylindrical mirror to be measured by a unit pixel distance along the x-axis direction, and then collecting second measurement data after deflecting to a zero position state, including: The lateral distortion correction coefficient of cylindrical CGH is introduced and converted into image space for calculation to obtain the unit pixel distance; The orthogonal displacement unit is controlled to move the cylindrical mirror to be measured by the unit pixel distance along the x-axis direction, and the interferometer host is reset to a zero position state using the point-to-point mode of the interferometer host to collect second measurement data.

7. The method for detecting the absolute surface shape of a cylindrical mirror using a rotation and translation method according to claim 1, wherein: Controlling the orthogonal displacement unit to move the cylindrical mirror to be measured by a unit pixel distance along the y-axis direction and then collecting third measurement data, including: The orthogonal displacement unit is controlled to move the cylindrical mirror to be measured by a unit pixel distance along the y-axis direction, directly convert it into the image space and collect the third measurement data.

8. The method for detecting the absolute surface shape of a cylindrical mirror using a rotation and translation method according to claim 1, wherein: Subtracting the rotationally asymmetric component from the first measurement data, the second measurement data, and the third measurement data, and solving the rotationally symmetric component based on a differential wavefront reconstruction algorithm, comprising: Deducting the rotationally asymmetric component from the first measurement data, the second measurement data, and the third measurement data, and performing a differential operation to obtain differential wavefront data of the rotationally symmetric component; According to the differential wavefront data, the rotationally symmetric component is reconstructed based on a wavefront restoration algorithm; the wavefront restoration algorithm includes any one of a path integral method, a Hudgin slope method, a Zernike polynomial fitting reconstruction method, and a Fourier transform reconstruction method.

9. A system for detecting the absolute surface shape of a cylindrical mirror using a rotation-translation method, characterized in that: The system includes: An interferometer measurement cavity module, comprising an interferometer host (1) and a transmission standard mirror (2); A cylindrical computer-generated holographic module, comprising a cylindrical CGH (4) and a CGH clamping and adjusting mechanism (3); The cylindrical mirror module to be tested comprises a cylindrical mirror to be tested (6), a cylindrical mirror clamping and adjusting mechanism (5), and an orthogonal displacement unit, wherein the orthogonal displacement unit is used to control the movement of the cylindrical mirror to be tested in two directions orthogonal to the optical axis; A computer processing module (7) includes an integrated displacement control unit and a data analysis and processing unit, wherein the data analysis and processing unit is used to analyze and process the data results of the interferometer host (1) measured at different positions of the cylindrical mirror to be measured, so as to obtain the absolute surface error distribution of the cylindrical mirror to be measured; The interferometer host (1) generates a parallel light beam and is divided into two beams, one of which is reflected by the transmission standard mirror (2) to form a reference beam; the other beam is transmitted through the transmission standard mirror (2) to form a test beam and is incident on the cylindrical computer holographic module, and is incident on the cylindrical mirror to be measured (6) after diffraction; the light beam then returns to the interferometer host (1) along the original path, and meets and interferes with the reference beam inside the interferometer host (1), generating an interference pattern; the interference pattern is processed by the computer processing module (7) to obtain initial interference measurement data; and based on the initial interference measurement data, the surface shape distribution of the cylindrical mirror is divided into a rotationally asymmetric component and a rotationally symmetric component by the rotation-translation method, and the measurement is performed separately to obtain the absolute surface shape error of the cylindrical mirror to be measured.

10. The system for detecting the absolute surface shape of a cylindrical mirror using a rotation and translation method according to claim 9, characterized in that: Based on the initial interferometric measurement data, the surface shape distribution of the cylindrical mirror is divided into rotationally asymmetric components and rotationally symmetric components through the rotation-translation method, and the measurements are performed separately, including: Initial interference measurement data is obtained in the initial state, and the cylindrical mirror (6) to be measured is rotated 180 degrees around the optical axis, and then the data is processed by a computer processing module (7) to obtain first measurement data; Eliminating the rotationally symmetric component by subtracting the first measurement data from the initial interferometric measurement data, and reconstructing the rotationally asymmetric component by an iterative algorithm; Controlling the orthogonal displacement unit to move the cylindrical mirror (6) to be measured along the x-axis direction and the y-axis direction by a unit pixel distance respectively and maintaining the zero position state, and then collecting the corresponding second measurement data and third measurement data, Deducting the rotationally asymmetric component from the first measurement data, the second measurement data, and the third measurement data, and solving the rotationally symmetric component based on a differential wavefront reconstruction algorithm; The rotationally asymmetric component and the rotationally symmetric component are superimposed to obtain the absolute surface error distribution of the cylindrical surface.

Images