Calibration method for testing distortion of interferometer

Abstract

The invention belongs to the technical field of optical detection, and relates to an interferometer test distortion calibration method, which comprises the following steps of: constructing a whole ray tracing simulation model of an interferometer test element; creating a tracing point and # imgabs0 #, and converting the # imgabs0 # into a tracing point and a tracing ray vector in a world coordinate system; calculating a tracing point coordinate of the test element, calculating a tracing point coordinate of the reference spherical surface, and obtaining an element normalization normal vector, an incident ray normalization vector and an emergent ray normalization vector at the tracing point of the test element; determining a spatial position mapping relation of the coordinates of the test element; establishing a test light path and testing by using an interferometer to obtain a wavefront test result # imgabs1 # of the test element; calculating an error distribution relation after the distortion correction of the # imgabs2 #; surface wavefront test results of the test elements are converted into element surface shape errors, and distortion calibration is carried out according to the errors. The beneficial effects are that the calibration mode is simple, the test precision is high, and a surface shape error result suitable for optical processing can be rapidly obtained.

Description

Technical Field

[0001] The invention relates to the technical field of optical detection, and in particular to a calibration method for interferometer distortion testing. Background Art

[0002] The surface shape detection of optical components generally uses an interferometer to test the wavefront error of the component and the reference surface. The surface shape error of the optical component is calculated based on the surface shape error of the reference surface. The Fizeau interferometer is generally used for testing. Since there is no proportional correspondence between the phase information recorded by the CCD on the interferometer and the projection coordinate system of the test component during the test, it is impossible to obtain the surface shape error distribution on the test component through simple component calibration. At present, there are two distortion correction methods in the actual optical processing process. The first is to use the ray tracing theory to calculate. Since this method requires accurate calibration of the CCD size, it is cumbersome to apply it to the actual optical processing process, and the calibration error of the CCD will be introduced into the calculation, thereby affecting the actual processing process; the second is to use the experimental calibration method. First, the three coordinates are used on the component to calibrate the surface. During the interferometer test, the specific positions of the pixels corresponding to all the three-coordinate calibration points are found, and then the distortion of the interferometer test results is calibrated by interpolation. The above method requires the use of three coordinates to calibrate the entire surface of the processing component, and at the same time, the coordinates of each calibration point on the test result are determined. For the distortion calibration of off-axis aspheric and free-form surface components, the above process is extremely cumbersome. At the same time, since there is no component information outside the calibration points during the test process, data point interpolation is generally required in the distortion calibration. This method will lose the correction accuracy of the distortion outside the calibration points. Summary of the invention

[0003] Technical issues to be solved In view of the above-mentioned shortcomings and deficiencies of the prior art, the present invention provides a calibration method for interferometer distortion testing, which solves the technical problems that the existing distortion calibration method has a complicated process and the accuracy needs to be further improved.

[0004] Technical Solution In order to achieve the above object, the main technical solutions adopted by the present invention include: The present invention provides a calibration method for interferometer test distortion, comprising: Construct the ray tracing simulation model of the interferometer test element as a whole, and establish the transformation matrix from each tracing surface coordinate system to the world coordinate system and the inverse matrix ,in , is the number of tracing surfaces; Based on the transformation matrix and the inverse matrix Complete the tracing of all faces; Calculate the coordinates of the tracking points of the test component and , calculate the coordinates of the tracking point on the reference sphere and , and simultaneously obtain the normalized normal vector of the component at the tracing point of the test component, the normalized vector of the incident light ray, and the normalized vector of the outgoing light ray; based on , , and The spatial position mapping relationship of the test element coordinates is determined by interpolating discrete points: On the test component, mark a point to determine the position , and calibrate any other test points on the test element ; Build a test optical path and use an interferometer to test and obtain the wavefront test results of the test component ; , calculate and determine the marking point on the test element and The corresponding reference spherical marker coordinates and ; Based on the test results, calibration The corresponding pixel coordinate position; Calculate pixel spacing , and based on ,Sure for ,in is the coordinates of the tracking point on the reference sphere in the tracking model; ,calculate Error distribution relationship after distortion correction ; The surface wavefront test results of the test components are respectively Convert it into component surface error so as to perform distortion calibration based on the error.

[0005] Optionally, based on the transformation matrix and the inverse matrix Complete the tracing of all faces, including: Use the reference sphere as the starting surface for tracing and create tracing points based on the world coordinate system. ; Using the inverse matrix of the next tracing surface Will and Convert to the incident point and incident light vector of the next tracing surface; The Newton iteration method is used to calculate the incident point, incident ray vector, intersection point of the tracing surface and outgoing ray vector; Transform the intersection point of the tracing surface and the coordinates of the outgoing light vector into the tracing point and tracing light vector in the world coordinate system; Repeat the above steps until all faces are traced.

[0006] Optionally, the spatial position mapping relationship of the test element coordinates is determined by referring to the spherical coordinates as follows: , .

[0007] Optionally, the pixel spacing is calculated based on the following formula : .

[0008] Optionally, the surface wavefront test results of the test element are respectively Converted into component surface error, including: If the test component surface is a reflective surface, the test error ; If the test element is a transmission surface, the test error , , ; in, The normalized normal vector of the component at the tracing point of the test component; is the normalized vector of the incident ray; Normalized vector of the outgoing ray.

[0009] Beneficial Effects The beneficial effects of the present invention are as follows: an interferometer test distortion calibration method of the present invention is applicable to the optical processing of aspheric surfaces and free-form surfaces, and is used for the distortion calibration of interferometer test results corresponding to components, and the corresponding relationship between the interference test results and the components can be obtained. The calibration method is simple, the test accuracy is high, and the surface error results suitable for optical processing can be quickly obtained. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figure 1 A schematic diagram of an off-axis parabolic reflector test optical path provided in an embodiment of the present invention; Figure 2 A schematic diagram of the test optical path modeling of an off-axis polished reflector provided in an embodiment of the present invention; Figure 3 A comparison diagram of face errors before and after distortion correction provided by an embodiment of the present invention.

[0011] Description of Reference Numerals 1-interferometer; 2-spherical standard lens; 3-focus of spherical standard mirror; 4-optical axis; 5-off-axis parabolic reflector; 6-test light; 7-standard plane reflector; 8-reference sphere and relative coordinate system; 9-world coordinate system; 10-off-axis parabolic reflector and relative coordinate system; 11-standard plane reflector and relative coordinate system. DETAILED DESCRIPTION

[0012] In order to better explain the present invention and facilitate understanding, the present invention is described in detail below in conjunction with the accompanying drawings through specific embodiments. Although exemplary embodiments of the present invention are shown in the accompanying drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided in order to enable a clearer and more thorough understanding of the present invention and to be able to fully convey the scope of the present invention to those skilled in the art.

[0013] Reference Figure 1 This embodiment provides a calibration method for interferometer test distortion, including: S1, build the ray tracing simulation model of the interferometer test element as a whole, replace the system composed of the interferometer and the standard mirror with a reference sphere with the same curvature radius as the focal length of the standard mirror, where the center of the reference sphere coincides with the focus of the standard mirror, and establish the transformation matrix from each tracing surface coordinate system to the world coordinate system and the inverse matrix ,in , is the number of tracing surfaces.

[0014] Start modeling from the interferometer. Based on the interferometer, the test light can be divided into plane waves and spherical waves. If the test light is a plane wave, the test light position matrix is ​​established based on the relative position relationship between the plane standard mirror and the test element. , based on the emission direction of the interferometer test light, establish the test light vector matrix If the test light is a spherical wave, the test light position matrix is ​​established based on the focal position of the spherical standard mirror. , based on the emission direction at the focus of the spherical mirror and the spherical standard mirror , establish the test light vector matrix .

[0015] Construct the ray tracing simulation model of the interferometer test element as a whole. Starting from the interferometer, the surfaces passed during the test are modeled one by one. The model number is , is the total number of test surfaces passed during the test.

[0016] For the test surface Based on the design equations and parameters of the component surface, the vector height equation in the local rectangular coordinate system is established ,in are the coordinate parameters of the component surface in the rectangular coordinate system; For the test surface , based on whether the transmission process is transmission or reflection, set the refractive index .

[0017] For the test surface , based on the surface phase distribution, set .

[0018] For the test surface , based on the coordinate transformation law with the world coordinate system, establish the coordinate transformation matrix .

[0019] S2, using the reference sphere as the starting surface for tracing, creates tracing points based on the world coordinate system ,in, , is the number of tracking points.

[0020] S3, using the inverse matrix of the next tracing surface Will and Convert to the incident point of the next tracing surface and the incident light vector .

[0021] S4, calculate the incident point using Newton iteration method , the incident light vector , the intersection of the tracing surfaces and the outgoing ray vector .

[0022] S5, the intersection of the tracing surface and the outgoing ray vector Coordinate transformation to the tracking point in the world coordinate system and the traced ray vector .

[0023] S6, repeat S2 to S5 until all faces are traced.

[0024] S7, calculate the tracking point coordinates of the test element and , calculate the coordinates of the tracking point on the reference sphere and , and at the same time obtain the normalized normal vector of the component at the tracking point of the test component , the normalized vector of the incident light And the normalized vector of the outgoing ray is .

[0025] S8, based on , , and The spatial position mapping relationship of the test element coordinates is established by interpolating discrete points: , .

[0026] S9, mark a point on the test element to determine the position , generally the midpoint of the test element is used, and any other test points are calibrated on the test element .

[0027] S10, build the test optical path and use the interferometer to test and obtain the wavefront test results of the test component ,in, and is the pixel coordinate on the CCD.

[0028] S11, using , calculate and determine the marking point on the test element and The corresponding reference spherical marker coordinates and .

[0029] S12, based on test results , calibration and The corresponding pixel coordinate position and .

[0030] S13, calculate pixel interval , and based on ,Sure for ,in is the coordinate of the tracking point on the reference sphere in the tracking model.

[0031] S14, using ,calculate Error distribution relationship after distortion correction .

[0032] S15, respectively test the surface wavefront test results of the test element Convert it into component surface error so as to perform distortion calibration based on the error.

[0033] Optionally, the pixel spacing is calculated based on the following formula : .

[0034] Optionally, the surface wavefront test results of the test element are respectively Converted into component surface error, including: If the test component surface is a reflective surface, the test error .

[0035] If the test element is a transmission surface, the test error , , .

[0036] The interferometer test distortion calibration method of this embodiment can compensate for any optical element test surface during the optical processing process with high compensation accuracy and a small number of marking points during the test process, thereby shortening the overall processing cycle.

[0037] The following is a further introduction to a method for calibrating distortion of an interferometer test in the present application in conjunction with a specific embodiment: See also Figure 1 , which is a general optical path for testing the surface error of an off-axis parabolic reflector using zero-position detection, including an interferometer 1, a spherical standard lens 2, an off-axis parabolic reflector 5, and a standard plane reflector 7.

[0038] See also Figure 2 , establish the interferometer test element ray tracing simulation model, based on the focal length of the spherical standard lens 2 A reference sphere and relative coordinate system 8 are established in the simulation model for the radius of curvature, a simulation model is established based on the focus 3 of the spherical standard mirror, an off-axis parabolic reflector and a relative coordinate system 10 are established in the simulation model based on the off-axis parabolic reflector 5, and a standard plane reflector and a relative coordinate system 11 are established in the simulation model based on the standard plane reflector.

[0039] See also Figure 2 , respectively establish the reference sphere and relative coordinate system 8, the spherical standard mirror focus 3, the off-axis parabolic reflector and relative coordinate system 10, the standard plane reflector and relative coordinate system 11 on the coordinate point conversion matrix to the world coordinate system 9 , , , , and calculate the inverse matrix , , , .

[0040] See also Figure 2 , reference sphere and relative coordinate system 8, matrix of tracking points on reference sphere 8 , , is the number of tracking points.

[0041] See also Figure 2 , start tracing from the reference sphere, and calculate the initial tracing point matrix in the world coordinate system 9 as ,pass and Calculate the initial tracing ray vector .

[0042] See also Figure 2 ,use and , calculate and transform the next tracking surface, that is, the off-axis parabolic reflector and the incident tracking point under the relative coordinate system 10 and the incident light vector .

[0043] See also Figure 2 , the incident tracing point after coordinate transformation , the incident light vector after coordinate transformation and the geometric parameters of the off-axis parabolic reflector 5, and the intersection point with the off-axis parabolic reflector and the relative coordinate system 10 is calculated by using the Newton iteration method. and the outgoing ray vector .

[0044] See also Figure 2 , calculate the tracking point matrix in the world coordinate system 9 as , calculate the tracing ray vector .

[0045] See also Figure 2 ,use and , calculate and transform the next tracking surface, that is, the standard plane reflector and the incident tracking point under the relative coordinate system 11 and the incident light vector .

[0046] See also Figure 2 , incident tracking point , the incident light vector and the geometrical parameters of the standard plane reflector 7.

[0047] See also Figure 2 Based on the results of the tracking point matrix, calculate the coordinates of the tracking points of the off-axis parabolic reflector and the relative coordinate system 10 , and the coordinates of the tracking point under the reference sphere and relative coordinate system 8 , , calculate the intersection point The normalized normal vector of the element at , the normalized incident light vector And the normalized vector of the outgoing ray is .

[0048] Based on the coordinates of the tracking points on the mirror , and the coordinates of the tracking point on the reference sphere , The spatial position mapping relationship of the test element coordinates is determined by interpolating discrete points: , .

[0049] Using a three-coordinate measuring machine, mark a point on the off-axis parabolic reflector 5 to determine the position. , generally the midpoint of the test element is used, and any other test points are calibrated on the test element .

[0050] See also Figure 1 , build a test optical path, use interferometer 1 to test, and obtain the wavefront test results of off-axis parabolic reflector 5 ,in, and is the pixel coordinate on the CCD.

[0051] use , calculate and determine the marking point on the off-axis parabolic reflector 5 and The corresponding reference spherical marker coordinates and ; Based on the test results , calibration and The corresponding pixel coordinate position and .

[0052] refer to Figure 2 , use the following formula to calculate the pixel spacing , , based on ,Sure for ,in are the coordinates of the tracking point on the reference sphere in the reference sphere and relative coordinate system 8.

[0053] use ,calculate Error distribution after distortion correction .

[0054] 19) Depending on whether the test element surface is a reflective surface or a transmissive surface, the wavefront test results can be Converted into component surface error, if the test component surface is a reflective surface, the test error , If the test element is a transmission surface, the test error , The incident angle and the exit angle The calculation relationship is shown in the following formula: , .

[0055] refer to Figure 3 , based on the result a before distortion correction, the shape error result b after distortion correction is obtained.

[0056] Experiments show that the present application utilizes ray tracing and calibration processing, and the distortion error of the calculated result is smaller than the pixel resolution on the test element, thus realizing a calibration method for interferometer test distortion.

[0057] Obviously, those skilled in the art can make various modifications and variations to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention should also include these modifications and variations.

[0058] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations of the present invention. A person skilled in the art may alter, modify, replace and modify the above embodiments within the scope of the present invention.

Claims

1. A method for calibrating interferometer distortion testing, characterized in that: include: Construct the ray tracing simulation model of the interferometer test element as a whole, and establish the transformation matrix from each tracing surface coordinate system to the world coordinate system and the inverse matrix ,in , is the number of tracing surfaces; Based on the transformation matrix and the inverse matrix Complete the tracing of all faces; Calculate the coordinates of the tracking points of the test component and , calculate the coordinates of the tracking point on the reference sphere and , and simultaneously obtain the normalized normal vector of the component at the tracing point of the test component, the normalized vector of the incident light ray, and the normalized vector of the outgoing light ray; based on , , and The spatial position mapping relationship of the test element coordinates is determined by interpolating discrete points: On the test component, mark a point to determine the position , and calibrate any other test points on the test element ; Build a test optical path and use an interferometer to test and obtain the wavefront test results of the test component ; , calculate and determine the marking point on the test element and The corresponding reference spherical marker coordinates and ; Based on the test results, calibration The corresponding pixel coordinate position; Calculate pixel spacing , and based on ,Sure for ,in is the coordinates of the tracking point on the reference sphere in the tracking model; ,calculate Error distribution relationship after distortion correction ; The surface wavefront test results of the test components are respectively Convert it into component surface error so as to perform distortion calibration based on the error.

2. The method for calibrating the distortion of an interferometer according to claim 1, characterized in that: Based on the transformation matrix and the inverse matrix Complete the tracing of all faces, including: Use the reference sphere as the starting surface for tracing and create tracing points based on the world coordinate system. ; Using the inverse matrix of the next tracing surface Will and Convert to the incident point and incident light vector of the next tracing surface; The Newton iteration method is used to calculate the incident point, incident ray vector, intersection point of the tracing surface and outgoing ray vector; Transform the intersection point of the tracing surface and the coordinates of the outgoing light vector into the tracing point and tracing light vector in the world coordinate system; Repeat the above steps until all faces are traced.

3. The method for calibrating interferometer distortion testing according to claim 1, characterized in that: The spatial position mapping relationship of the test component coordinates determined by reference spherical coordinates is as follows: ， 。 4. The method for calibrating the distortion of an interferometer according to claim 1, characterized in that: The pixel spacing is calculated based on the following formula : 。 5. The method for calibrating interferometer distortion testing according to claim 1, characterized in that: The surface wavefront test results of the test components are respectively Converted into component surface error, including: If the test component surface is a reflective surface, the test error ; If the test element is a transmission surface, the test error , , ; in, The normalized normal vector of the component at the tracing point of the test component; is the normalized vector of the incident ray; Normalized vector of the outgoing ray.

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