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

Abstract

The invention discloses an optical plane absolute detection method based on a displacement rotation method and a second-order partial derivative method. An interferometer, a computer, an optical platform for placing the interferometer, a five-dimensional adjusting frame, a standard plane mirror and a to-be-detected plane mirror are included. The second-order partial derivative of the azimuth angle is measured and calculated by rotating the to-be-measured plane mirror, and the radial second-order partial derivative is measured and calculated by translating the to-be-measured plane mirror. The absolute surface shape of the optical element to be measured can be calculated through high-order Zernike fitting. A traditional three-plane absolute detection method needs three plane mirrors, and has strict requirements on the aperture of the transmission plane mirror and the size and direction of a wedge angle; for absolute detection of a large-aperture plane, repeated replacement of a reference plane is not practical, the absolute detection experimental step is simplified to twice rotation translation of the two plane mirrors, and compared with traditional three-plane mutual detection, measurement steps are simplified, and measurement time is shortened by about two hours. Besides, the wavefront error is expanded to the second order, so that the influence of environmental noise and interferometer noise can be reduced, and the measurement result has higher stability.

Description

Technical Field

[0001] The 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 many engineering and technical fields, such as astronomy, aerospace, and inertial confinement fusion (ICF) and other high-tech fields. In particular, large-aperture optical components play a pivotal role in the design and development of ICF drive systems. Among them, wavefront distortion has always been a focus issue that has attracted much attention.

[0003] In order to obtain the required high energy to detonate nuclear fusion, the laser must undergo multiple stages of amplification in the system. In this amplification process, in order to avoid the generation of various nonlinear effects, the laser beam needs to be amplified to reduce the energy density of the laser in the local optical element. Before the laser is injected into the target chamber, it needs to be focused to obtain an energy density that meets the requirements of the fusion reaction. Laser wavefront distortion will directly affect the focusing characteristics of the beam, resulting in a decrease in the far-field irradiation uniformity of the focus point. This will affect the system's uniformity requirements for bombarding the target pellet. Therefore, during the design and development process, measures need to be taken to correct or minimize the wavefront distortion to ensure that the focusing effect and irradiation uniformity of the laser beam can meet the requirements.

[0004] In high-power laser systems, optical components are one of the main factors that cause wavefront distortion. Large-aperture optical components have two main effects on laser wavefronts: one is the material uniformity of the optical components (impurity content, bubbles, etc.), and the other is the surface processing quality of the optical components (flatness and roughness of the surface, 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 the beam quality is mainly concentrated on reducing the brightness and uniformity of the center of the spot, but it will not cause the widening of the central bright spot, but 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. Usually, the phase error in this frequency band is called "ripple". In a high-power laser system, its influence on the beam quality is mainly 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 is L < 0.12 mm, and the corresponding spatial frequency of the phase error is f > 8 line / mm. Usually, the phase difference in this frequency band is called "roughness". Its influence is mainly 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 factors affecting the current absolute detection accuracy are 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 trade-off 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] In order to overcome the deficiencies of the above-mentioned prior art, the present invention proposes an optical plane absolute detection method based on a displacement rotation method and a second-order partial derivative method, which combines the displacement rotation method and the second-order partial derivative method, and uses interferometers, computers, optical platforms, five-dimensional adjustment frames, standard plane mirrors A, and plane mirrors B to be measured and other measuring devices to achieve accurate measurement of the surface shape error of the plane mirror B to be measured. Through specific rotation and translation operations, combined with the interference fringes measured by the interferometer, the computer is used to unpack and process the data, so as to separate the wavefront errors of the standard plane mirror A and the plane mirror B to be measured, and finally obtain the surface shape error of the plane mirror B to be measured, thereby minimizing the mirror rotation and translation time, and reducing the measurement error, providing theoretical support for the measurement of large-aperture optical components.

[0013] The technical solution of the present invention is 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 comprises the following steps:

[0015] Step 1. Construct an inspection optical path: including an interferometer, a computer, an optical platform for placing the interferometer, a five-dimensional adjustment frame for placing the plane mirror B to be measured, and a standard plane mirror A; use the interferometer to split the emitted light into two beams, one beam of light is reflected by the rear surface of the standard plane mirror A to become a reference beam, and the other beam of light is transmitted through the standard plane mirror A and 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 the original optical path, and finally overlap to form light and dark interference fringes;

[0016] A computer connected to the interferometer, used for unpacking 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 Keep the standard plane mirror A still, rotate the plane mirror B to be measured clockwise by Δθ through the five-dimensional adjustment frame, perform interference measurement, and record the measured value W 2 (ρ,θ), where ρ and θ are polar coordinates used to represent the measured surface error, i.e., 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 interference measurement again, and record the measured value W. 1 (ρ,θ);

[0020] Step 2.3 After rotating the plane mirror B counterclockwise by Δθ, perform interference measurement and record the measured value W. 3 (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 W 1 (ρ,θ)=W reference (ρ,θ)+W test (ρ,θ),W 2 (ρ,θ)=W reference (ρ,θ)+W test (ρ,θ+Δθ),

[0024] W 3 (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 interference measurement, and record the measured value W. 4 (ρ,θ);

[0026] Step 2.6 Return the plane mirror B to its original position, move it to the left by Δx, perform interference measurement, and record the measured value W. 5 (ρ,θ);

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

[0028]

[0029] Where W 4 (x,y)=W reference (x,y)+W test (x+Δx,y),W 5 (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, and obtain the Zernike polynomial coefficients corresponding to the second-order partial derivative wavefront errors in the rotation direction and radial direction by taking the derivative of the Zernike polynomials;

[0031] Step 2.9 combines and accumulates the Zernike polynomial coefficients in the rotation direction and the Zernike polynomial coefficients in the radial direction, and fits and calculates 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 a Zernike polynomial, 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 taking the derivative of the Zernike polynomial, we obtain:

[0036]

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

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

[0039]

[0040] In the formula, 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 advantages of:

[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 expands 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 It is a schematic diagram of the optical path of the optical element detection device in the present invention;

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

[0046] Figure 3 The simulation results are as follows: (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 between the Zernike polynomial coefficients of the original surface shape and the calculated results. DETAILED DESCRIPTION

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

[0048] Figure 1 FIG. 1 is a schematic diagram of an optical path for absolute detection of an optical plane based on the displacement rotation method and the second-order partial derivative method of the present invention. Figure 1 As 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 the two beams of light are reflected on the standard plane mirror A and the plane mirror to be measured B, they meet again to form interference fringes.

[0050] Computer: connected to the interferometer and electrical control system through data lines, used to control the measurement process of the interferometer, 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 accurately adjust the position and angle of the standard plane mirror A and the plane mirror B to be measured.

[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 measure the wavefront error of the combination of the standard plane mirror A and the plane mirror to be measured B. However, the goal is to obtain the surface error of the plane mirror to be measured B. To achieve this, the displacement rotation method and the second-order partial derivative method are used.

[0056] Measurement steps:

[0057] Rotation measurement: By rotating the plane mirror B to be tested clockwise and counterclockwise, three sets of interference fringe data at different angles can be obtained. These data contain the combined wavefront errors of the standard plane mirror A and the plane mirror B to be tested at different angles.

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

[0059] Data processing:

[0060] Wavefront error separation: The wavefront errors of the standard plane mirror A and the plane mirror B to be tested 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: Expand the wavefront error with Zernike polynomials and obtain the coefficients of each order polynomial 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 still and rotate mirror B 5° clockwise. Mirror A and mirror B interfere with each other and the measured value is W 2 (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 still and turn mirror B back to its original position. Mirror A and mirror B interfere with each other and the measured value is W 1 (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 still and rotate mirror B 5° counterclockwise. Mirror A and mirror B interfere with each other and the measured value is W 3 (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 of the three groups 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) Keep mirror A still and move mirror B to the right by 0.1 mm. Mirror A and mirror B interfere with each other and the measured value is W. 4 (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) Keep mirror A still, turn mirror B back to its original position, and then move 0.1mm to the left. Mirror A and mirror B interfere with each other, and the measured value is W 5 (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 of the three groups of combined wavefronts, and the second-order partial derivative wavefront error of the plane mirror to be tested in the radial direction is obtained:

[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, and 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; the surface fitting of the optical element can be calculated by combining and accumulating the Zernike polynomial coefficients in the rotation direction with the Zernike polynomial coefficients in the radial direction.

[0083] like Figure 3 (b) shows that Figure 3 Compared with (a), the residual error of the plane mirror PV to be measured is 2.1×10 -2 nm, the RMS residual is 8×10 -3 nm Figure 3 (c) as 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: including an interferometer, a computer, an optical platform for placing the interferometer, a five-dimensional adjustment frame for placing the plane mirror B to be measured, and a standard plane mirror A; use the interferometer to split the emitted light into two beams, one beam of light is reflected by the rear surface of the standard plane mirror A to become a reference beam, and the other beam of light is transmitted through the standard plane mirror A and 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 the original optical path, and finally overlap to form light and dark interference fringes; A computer connected to the interferometer, used for unpacking 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 Keep the standard plane mirror A stationary, rotate the plane mirror B to be measured clockwise by Δθ through the five-dimensional adjustment frame, perform interferometric measurement, and record the measured value W2(ρ,θ), where ρ and θ are polar coordinate forms used to represent the measured surface error, that is, ρ represents the distance from the pole to the measuring point, and θ represents the angle between the point and the positive x-axis; Step 2.2: Rotate the plane mirror B to be measured back to its original position, perform interference measurement again, and record the measured value W1(ρ,θ); Step 2.3 After rotating the plane mirror B to be measured counterclockwise by Δθ, perform interference measurement 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 W1(ρ,θ) = W reference (ρ,θ) + W test (ρ,θ), W2(ρ,θ) = W reference (ρ,θ) + W test (ρ,θ + Δθ), 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 interference measurement, and record the measured value W4(ρ,θ); Step 2.6: Return the plane mirror B to its original position, move it to the left by Δx, perform interference measurement, 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 tested B, and obtain the radial second-order partial derivative wavefront error A of the plane mirror to be tested B. 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, and obtain the Zernike polynomial coefficients corresponding to the second-order partial derivative wavefront errors in the rotation direction and radial direction by taking the derivative of the Zernike polynomials; Step 2.9 combines and accumulates the Zernike polynomial coefficients in the rotation direction and the Zernike polynomial coefficients in the radial direction, and fits and calculates 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: Where 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 Through formula (5), we get: In the formula, 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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