An optical plane absolute detection method based on displacement rotation method and second-order partial derivative method

Abstract

An optical plane absolute detection method based on displacement rotation method and second-order partial derivative method, comprising: an interferometer, a computer, an optical platform for placing the interferometer, a five-dimensional adjusting frame, a standard plane mirror and a to-be-measured plane mirror. The second-order partial derivative of the azimuth angle is measured and calculated by rotating the to-be-measured plane mirror, and the second-order partial derivative of the radial direction is measured and calculated by translating the to-be-measured plane mirror. The absolute surface shape of the to-be-measured optical element can be calculated by high-order Zernike fitting. The traditional three-plane absolute detection method needs three plane mirrors, and has strict requirements on the aperture, the size and the direction of the wedge angle of the transmission plane mirror; for large-aperture plane absolute detection, it is not practical to repeatedly replace the reference plane, the absolute detection experimental steps are simplified to two rotations and translations of two plane mirrors, compared with the traditional three-plane mutual detection, the measurement steps are simplified and the measurement time is reduced by nearly two hours. In addition, the wavefront error is expanded to the second order, the influence of environmental noise and interferometer noise can be reduced, and the measurement result has stronger stability.

Description

Technical Field

[0001] The present invention belongs to the field of surface shape detection, and in particular relates to an optical plane absolute detection method based on a displacement rotation method and a second-order partial derivative method. Background Art

[0002] Large-aperture optical components are playing an increasingly important role in numerous engineering and technological fields, such as astronomy, aerospace, and high-tech fields like inertial confinement fusion (ICF). In particular, large-aperture optical components play a crucial role in the design and development of ICF drive systems. Wavefront distortion remains a key concern.

[0003] To achieve the high energy required to trigger nuclear fusion, the laser must undergo multiple stages of amplification. During this amplification process, the laser beam must be amplified to avoid various nonlinear effects, thereby reducing the local energy density of the laser within the optical element. Before the laser is injected into the target chamber, it must be focused to achieve the energy density required for the fusion reaction. Laser wavefront distortion directly affects the focusing characteristics of the beam, resulting in reduced far-field irradiation uniformity at the focal point. This impacts the system's requirements for uniformity in bombarding the target pellet. Therefore, during the design and development process, measures must be taken to correct or minimize wavefront distortion to ensure that the laser beam's focusing and irradiation uniformity meet the requirements.

[0004] In high-power laser systems, optical components are one of the main factors causing wavefront distortion. Large-aperture optical components affect the laser wavefront in two main ways: material uniformity (impurity content, bubbles, etc.) and surface finish (flatness, roughness, etc.).

[0005] LLNL of the United States proposed dividing the laser wavefront distortion caused by the surface shape of NIF system components into the following different spatial frequency ranges:

[0006] (1) Low frequency band: The phase error spatial period L in this frequency band is greater than 33 mm, and the corresponding phase error spatial frequency f is less than 0.03 line / mm. The phase error in this frequency band is usually called "surface shape". In a high-power laser system, its impact on beam quality is mainly concentrated on reducing the brightness and uniformity of the center of the spot, but it does not cause the central bright spot to widen. However, it will affect the focusing properties of the beam.

[0007] (2) Medium frequency band: In this frequency band, the spatial period of the phase error satisfies 0.12 mm < L < 33 mm, and the corresponding spatial frequency of the phase error is 0.03 line / mm < f < 8 line / mm. Generally, the phase error in this frequency band is called "ripple". In a high-power laser system, its main influence on the beam quality is to reduce the brightness of the central bright spot and broaden it. In addition, it is also an important cause of nonlinear self-focusing in a high-power laser system, which poses a great threat to the safe and normal operation of the laser system.

[0008] (3) High frequency band: In this frequency band, the spatial period of the phase error satisfies L < 0.12 mm, and the corresponding spatial frequency of the phase error is f > 8 line / mm. Generally, the phase difference in this frequency band is called "roughness". Its main influence is to greatly reduce the brightness of the central bright spot, but it does not affect the beam quality of the system. However, it will affect the damage threshold of the thin film and increase the scattering loss.

[0009] Traditional optical surface shape inspection methods use relative measurement methods. The result is the deviation between the actual plane and the errors of the interferometer system and the reference plane. When the measurement accuracy requirement is as high as λ / 20, it is necessary to eliminate the influence of the interferometer system error and the reference plane error. Therefore, the concept of absolute plane detection is introduced. The purpose of absolute plane detection is to obtain the absolute surface state of the tested plane (i.e., the deviation of the actual surface relative to the ideal surface) by eliminating the influence of the interferometer system error and the reference plane error on the measurement result.

[0010] The main influencing factors of the current absolute detection accuracy lie in mechanical errors and algorithm accuracy. Taking the N-bit rotation method as an example, in order to separate the rotationally symmetric component and the non-rotationally symmetric component, an approximation is made to the number of rotations. The accuracy of this method is proportional to the number of rotations. However, increasing the number of measurements will introduce additional uncertainties, mainly composed of interferometer calibration errors and repeatability errors, usually on the order of λ / 60 or 10 nm. In addition, especially for large-aperture planes, their stress deformation cannot be ignored. The slight displacement of the support area after the position change may cause nanoscale deformation of the surface characteristics. Therefore, while ensuring the calculation accuracy, simplifying the measurement process requires a balance between algorithm accuracy and experimental accuracy.

[0011] The principle of absolute plane detection does not introduce the interferometer system error and the reference surface error, and obtains the absolute surface information of the optical plane. This method is particularly useful when the measurement accuracy requirement is very high, and it can provide more accurate surface shape data to meet the requirements for the quality and stability of optical components. Summary of the Invention

[0012] To overcome the shortcomings of the above-mentioned prior art, the present invention proposes an absolute detection method for optical planes based on the displacement-rotation method and the second-order partial derivative method. By combining the displacement-rotation method and the second-order partial derivative method, the present invention utilizes an interferometer, a computer, an optical platform, a five-dimensional adjustment mount, a standard plane mirror A, and a plane mirror B to be measured, thereby achieving accurate measurement of the surface error of the plane mirror B to be measured. Through specific rotation and translation operations, combined with the interference fringes measured by the interferometer, and using a computer to unpack and process the data, the wavefront errors of the standard plane mirror A and the plane mirror to be measured are separated, and the surface error of the plane mirror to be measured is ultimately obtained. This method minimizes the mirror rotation and translation time and reduces measurement errors, providing theoretical support for the measurement of large-aperture optical components.

[0013] The technical solutions of the present invention are as follows:

[0014] An optical plane absolute detection method based on a displacement rotation method and a second-order partial derivative method is characterized in that it includes the following steps:

[0015] Step 1. Construct an inspection optical path: This includes an interferometer, a computer, an optical platform for placing the interferometer, a five-dimensional adjustment mount for placing the plane mirror B to be measured, and a standard plane mirror A. The interferometer is used to split the output light into two beams. One beam is reflected by the rear surface of the standard plane mirror A to become a reference beam. The other beam is transmitted through the standard plane mirror A and then reflected by the front surface of the plane mirror B to be measured to become a measurement beam. The reference beam and the measurement beam return along their original optical paths and eventually overlap to form alternating light and dark interference fringes.

[0016] A computer connected to the interferometer, configured to perform unpacking processing on the interference fringes to obtain the wavefront errors of the standard plane mirror A and the plane mirror to be measured B;

[0017] Step 2. Measurement process:

[0018] Step 2.1: Keeping the standard plane mirror A stationary, rotate the plane mirror B to be measured clockwise by Δθ using the five-dimensional adjustment mount. Perform interferometric measurement and record the measured value W2(ρ,θ). Here, ρ and θ are polar coordinates representing the measured surface error. ρ represents the distance from the pole to the measurement point, and θ represents the angle between the point and the positive x-axis.

[0019] Step 2.2: Return the plane mirror B to its original position, perform interferometry again, and record the measured value W1(ρ,θ);

[0020] Step 2.3: After rotating the plane mirror B counterclockwise by Δθ, perform interferometry and record the measured value W3(ρ,θ).

[0021] Step 2.4 Separate the wavefront errors of the standard plane mirror and the plane mirror to be tested, and obtain the second-order partial derivative wavefront error A of the plane mirror to be tested in the rotation direction. t (ρ,θ), the formula is as follows:

[0022]

[0023] Where W1(ρ,θ)=W reference (ρ,θ)+W test (ρ,θ), W2(ρ,θ)=W reference (ρ,θ)+W test (ρ,θ+Δθ),

[0024] W3(ρ,θ)=W reference (ρ,θ)+W test (ρ,θ-Δθ); where W reference (ρ,θ) is the surface error of the standard plane mirror A, W test (ρ,θ) is the surface error of the plane mirror B to be measured, W test (ρ,θ+Δθ) is the surface error of the plane mirror B to be measured when it rotates clockwise by Δθ, W test (ρ,θ-Δθ) is the surface error of mirror B when it is rotated counterclockwise by Δθ;

[0025] Step 2.5: Adjust the five-dimensional adjustment frame to move the plane mirror B to the right by Δx, perform interferometry, and record the measured value W4(ρ,θ);

[0026] Step 2.6: Return the plane mirror B to its original position and move it to the left by Δx. Perform interferometry and record the measured value W5(ρ,θ).

[0027] Step 2.7 Separate the wavefront errors of the standard plane mirror A and the plane mirror to be measured B, and obtain the second-order partial derivative wavefront error A of the plane mirror to be measured B in the radial direction. r (x,y), the formula is as follows:

[0028]

[0029] In the formula, W4(x,y)=W reference (x,y)+W test (x+Δx,y), W5(x,y)=W reference (x,y)+W test (x-Δx,y); where W test (x+Δx,y) is the surface error of mirror B when it moves right by Δx, W test (x-Δx,y) is the surface error of mirror B when it is shifted to the left by Δx;

[0030] Step 2.8: Expand the wavefront error using Zernike polynomials. By taking the derivative of the Zernike polynomials, the Zernike polynomial coefficients corresponding to the second-order partial derivative wavefront error in the rotational and radial directions are obtained.

[0031] In step 2.9, the Zernike polynomial coefficients in the rotational direction and the Zernike polynomial coefficients in the radial direction are combined and added together to fit and calculate the surface shape error of the optical element of the plane mirror B to be measured.

[0032] Furthermore, in step 2.8, the wavefront error is expanded using Zernike polynomials, and the formula is as follows:

[0033]

[0034] Where W(ρ,θ) is the wavefront error, Z l (ρ,θ) is the Zernike term, a l is the coefficient.

[0035] Furthermore, in step 2.8, by deriving the Zernike polynomial, we obtain:

[0036]

[0037] Here, m and n are the number of terms in the Zernike polynomial.

[0038] Furthermore, the coefficient a in step 2.8 is l According to formula (5), we can get:

[0039]

[0040] Where A t (ρ,θ) is the second-order partial derivative wavefront error in the rotation direction, Q l is the second-order partial derivative of the Zernike polynomial with respect to θ.

[0041] Compared with the prior art, the present invention has the following advantages:

[0042] 1. Compared with the traditional three-side absolute detection method, the present invention simplifies the experimental procedure, only requires two plane mirrors, and the measurement only includes two rotations and two translations.

[0043] 2. The present invention extends the wavefront error to the second order, which can reduce the influence of environmental interference and make the measurement more stable. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 This is a schematic diagram of the optical path of the optical element detection device of the present invention;

[0045] Figure 2 This is a schematic diagram of the optical element detection principle of the present invention;

[0046] Figure 3 Simulation results: (a) theoretical surface shape of the mirror to be tested; (b) calculated surface shape of the mirror to be tested; (c) surface shape residual diagram; (d) comparison of Zernike polynomial coefficients of the original surface shape and the calculated results. DETAILED DESCRIPTION

[0047] The present invention will be further described below with reference to the accompanying drawings and embodiments, but the scope of protection of the present invention should not be limited thereto.

[0048] Figure 1 The figure is a schematic diagram of the optical path of absolute detection of optical plane based on the displacement rotation method and the second-order partial derivative method of the present invention. Figure 1 Shown, including:

[0049] Interferometer: Used to generate two coherent beams of light, one as a reference beam and the other as a measurement beam. After reflecting off a standard plane mirror A and a plane mirror B to be measured, the two beams meet again to form interference fringes.

[0050] Computer: connected to the interferometer and electrical control system through a data line, used to control the interferometer's measurement process, collect interference fringe data, and perform data processing.

[0051] Optical platform: provides a stable working environment for the interferometer.

[0052] Five-dimensional adjustment stand: used to precisely adjust the position and angle of the standard plane mirror A and the plane mirror to be measured B.

[0053] Standard plane mirror A: As a reference plane, its surface error is known or negligible.

[0054] Plane mirror B to be measured: The optical element whose surface error needs to be measured.

[0055] The interference fringes generated by the interferometer can be used to measure the wavefront error of the combination of standard plane mirror A and test mirror B. However, the goal is to obtain the surface error of the test mirror B alone. To achieve this, the displacement rotation method and the second-order partial derivative method are used.

[0056] Measurement steps:

[0057] Rotational measurement: By rotating the plane mirror B clockwise and counterclockwise, three sets of interference fringe data at different angles can be obtained. This data contains the combined wavefront error of the standard plane mirror A and the plane mirror B under test at different angles.

[0058] Translation measurement: By translating the plane mirror B to be measured left and right, three sets of interference fringe data can be obtained at different positions. These data contain the combined wavefront errors of the standard plane mirror A and the plane mirror B to be measured at different positions.

[0059] Data processing:

[0060] Wavefront error separation: The wavefront errors of the standard plane mirror A and the plane mirror to be measured B are separated by the difference between the three groups of combined wavefronts.

[0061] Second-order partial derivative calculation: Based on the separated wavefront error of the plane mirror B to be measured, its second-order partial derivative wavefront error in the rotation direction and radial direction is calculated.

[0062] Zernike polynomial fitting: The wavefront error is expanded using Zernike polynomials and the coefficients of each order polynomial are obtained by differentiation. These coefficients can be used to describe the surface error of the plane mirror B to be measured.

[0063] Implementation Cases:

[0064] It consists of a 100mm interferometer, a computer, an optical platform for placing the interferometer, a five-dimensional adjustment frame, a standard plane mirror A, and a plane mirror B to be measured.

[0065] The operation process is as follows:

[0066] 1) Keep mirror A stationary and rotate mirror B 5° clockwise. Mirrors A and B interfere with each other and the measured value is W2(ρ,θ)=W reference (ρ,θ)+W test (ρ,θ+5°), where W test (ρ,θ+5°) is the surface error of mirror B when it is rotated 5° clockwise, W reference (ρ,θ) is the surface error of mirror A;

[0067] 2) Keep mirror A stationary and rotate mirror B back to its original position. Mirrors A and B interfere with each other and the measured value is W1(ρ,θ)=W reference (ρ,θ)+W test (ρ,0), where W reference (ρ,θ) is the surface error of mirror A, W test (ρ,0) is the surface error of mirror B;

[0068] 3) Keep mirror A stationary and rotate mirror B 5° counterclockwise. The interference between mirrors A and B is obtained, and the measured value is W3(ρ,θ)=W reference (ρ,θ)+W test (ρ,θ-5°), where W test (ρ,θ-5°) is the surface error of mirror B when it is rotated 5° counterclockwise;

[0069] 4) According to step 1), step 2), and step 3), the wavefront errors of the standard plane mirror and the plane mirror to be measured are separated by the difference between the three sets of combined wavefronts, and the second-order partial derivative wavefront error of the plane mirror to be measured in the rotation direction is obtained:

[0070]

[0071] 5) Keeping mirror A stationary, move mirror B 0.1mm to the right. Mirrors A and B interfere with each other, and the measured value is W4(x,y)=W reference (x,y)+W test (x+0.1,y), where W test (x+0.1,y) is the surface error of mirror B when it is shifted 0.1mm to the right;

[0072] 6) Keeping mirror A stationary, mirror B returns to its original position and then moves 0.1 mm to the left, mirrors A and B interfere with each other, and the measured value is W5(x, y) = W reference (x,y)+W test (x-0.1,y), where W test (x-0.1,y) is the surface error of mirror B when it is shifted 0.1mm to the left;

[0073] 7) According to step 2), step 5), and step 6), the wavefront errors of the standard plane mirror and the plane mirror to be tested are separated by the difference between the three sets of combined wavefronts to obtain the second-order partial derivative wavefront error of the plane mirror to be tested in the radial direction:

[0074]

[0075] Step h: The wavefront error can be expanded using Zernike polynomials:

[0076]

[0077] In the absolute surface shape detection method, the wavefront error can be expanded using the Zernike polynomial:

[0078]

[0079] where m and n are the number of terms in the Zernike polynomial.

[0080] Finally, the coefficient a l It can be obtained by formula (5):

[0081]

[0082] In the absolute surface shape detection method, the plane mirror to be measured is rotated counterclockwise from 5° to -5° to obtain three sets of data. A is obtained from these three sets of data. t(ρ,θ), the Zernike polynomial coefficients of the rotation direction can be obtained from equations (4) and (5); the plane mirror to be measured is translated from 0.1mm to -0.1mm to obtain three sets of data, and A is obtained from these three sets of data r (x, y), the Zernike polynomial coefficients in the radial direction can be obtained in the same way; by combining and accumulating the Zernike polynomial coefficients in the rotational direction and the Zernike polynomial coefficients in the radial direction, the surface fitting of the optical element can be calculated.

[0083] like Figure 3 (b) shows that Figure 3 Compared with (a), the residual error of the PV of the plane mirror to be measured is 2.1×10 -2 nm, the RMS residual is 8×10 -3 nm by Figure 3 (c) shown.

Claims

1. An optical plane absolute detection method based on displacement rotation method and second-order partial derivative method, characterized in that: The following steps are involved: Step 1. Construct an inspection optical path: This includes an interferometer, a computer, an optical platform for placing the interferometer, a five-dimensional adjustment mount for placing the plane mirror B to be measured, and a standard plane mirror A. The interferometer is used to split the output light into two beams. One beam is reflected by the rear surface of the standard plane mirror A to become a reference beam. The other beam is transmitted through the standard plane mirror A and then reflected by the front surface of the plane mirror B to be measured to become a measurement beam. The reference beam and the measurement beam return along their original optical paths and eventually overlap to form alternating light and dark interference fringes. A computer connected to the interferometer, configured to perform unpacking processing on the interference fringes to obtain the wavefront errors of the standard plane mirror A and the plane mirror to be measured B; Step 2. Measurement process: Step 2.1: Keeping the standard plane mirror A stationary, rotate the plane mirror B to be measured clockwise by Δθ using the five-dimensional adjustment mount. Perform interferometric measurement and record the measured value W2(ρ,θ). Here, ρ and θ are polar coordinates representing the measured surface error. ρ represents the distance from the pole to the measurement point, and θ represents the angle between the point and the positive x-axis. Step 2.2: Return the plane mirror B to its original position, perform interferometry again, and record the measured value W1(ρ,θ); Step 2.3: After rotating the plane mirror B counterclockwise by Δθ, perform interferometry and record the measured value W3(ρ,θ). Step 2.4 Separate the wavefront errors of the standard plane mirror and the plane mirror to be tested, and obtain the second-order partial derivative wavefront error A of the plane mirror to be tested in the rotation direction. t (ρ,θ), the formula is as follows: where \(W_1(\rho,\theta)=W\) reference \((\rho,\theta)+W\) test \((\rho,\theta)\), \(W_2(\rho,\theta)=W\) reference \((\rho,\theta)+W\) test \((\rho,\theta + \Delta\theta)\) W3(ρ,θ)=W reference (ρ,θ)+W test (ρ,θ-Δθ); where W reference (ρ,θ) is the surface error of the standard plane mirror A, W test (ρ,θ) is the surface error of the plane mirror B to be measured, W test (ρ,θ+Δθ) is the surface error of the plane mirror B to be measured when it rotates clockwise by Δθ, W test (ρ,θ-Δθ) is the surface error of mirror B when it is rotated counterclockwise by Δθ; Step 2.5: Adjust the five-dimensional adjustment frame to move the plane mirror B to the right by Δx, perform interferometry, and record the measured value W4(ρ,θ); Step 2.6: Return the plane mirror B to its original position and move it to the left by Δx. Perform interferometry and record the measured value W5(ρ,θ). Step 2.7 Separate the wavefront errors of the standard plane mirror A and the plane mirror to be measured B, and obtain the second-order partial derivative wavefront error A of the plane mirror to be measured B in the radial direction. r (x,y), the formula is as follows: In the formula, W4(x,y)=W reference (x,y)+W test (x+Δx,y), W5(x,y)=W reference (x,y)+W test (x-Δx,y); where W test (x+Δx,y) is the surface error of mirror B when it moves right by Δx, W test (x-Δx,y) is the surface error of mirror B when it is shifted to the left by Δx; Step 2.8: Expand the wavefront error using Zernike polynomials. By taking the derivative of the Zernike polynomials, the Zernike polynomial coefficients corresponding to the second-order partial derivative wavefront error in the rotational and radial directions are obtained. In step 2.9, the Zernike polynomial coefficients in the rotational direction and the Zernike polynomial coefficients in the radial direction are combined and added together to fit and calculate the surface shape error of the optical element of the plane mirror B to be measured.

2. The optical plane absolute detection method based on the displacement rotation method and the second-order partial derivative method according to claim 1 is characterized in that: In step 2.8, the wavefront error is expanded using Zernike polynomials, and the formula is as follows: Where W(ρ,θ) is the wavefront error, Z l (ρ,θ) is the Zernike term, a l is the coefficient.

3. The optical plane absolute detection method based on the displacement rotation method and the second-order partial derivative method according to claim 2 is characterized in that: In step 2.8, by deriving the Zernike polynomial, we obtain: Here, m and n are the number of terms in the Zernike polynomial.

4. The optical plane absolute detection method based on the displacement rotation method and the second-order partial derivative method according to claim 2 is characterized in that: The coefficient a in step 2.8 l According to formula (5), we can get: Where A t (ρ,θ) is the second-order partial derivative wavefront error in the rotation direction, Q l is the second-order partial derivative of the Zernike polynomial with respect to θ.

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