A correction method for compensating for projection distortion of an optical curved surface shape by CGH detection

Abstract

The application discloses a correction method for compensating for projection distortion of an optical curved surface face shape of a CGH. The method comprises the following steps: setting a center mark point and at least one feature point, marking the center mark point at an arbitrary position of an effective aperture, taking the center mark point as the feature point, and recording coordinates (x i ,y i ) of the feature point on a to-be-detected surface; adjusting an optical path, i.e. adjusting the to-be-detected surface and the CGH so that the center mark point is coincident with a center of a CCD pixel coordinate system in an interferometer, and recording coordinates (x j ,y j ) of the feature point in the CCD pixel coordinate system; solving the feature point to obtain a scaling ratio and a rotation angle of the CCD pixel coordinate and the corresponding CGH ‑2 coordinate, and applying a solving result to a full aperture to obtain a corresponding relationship between the CCD pixel coordinate and the to-be-detected surface coordinate, and completing projection distortion correction. The correction method corrects the projection distortion by using a ray tracing method and a small amount of mark points, and calculates three groups of mapping relationships. The correction method has high correction precision, is simple and convenient to calculate, is easy to program and implement, and is suitable for various surfaces.

Description

Technical Field

[0001] This application belongs to the field of measurement technology in optical surface manufacturing, specifically relating to a method for correcting surface projection distortion when optical surfaces are inspected using computational holography (CGH) interferometry compensation. Background Technology

[0002] With the increasing use of complex optical surfaces in aerospace, military, and civilian fields, the manufacturing of complex optical surfaces has become particularly important. To obtain high-precision optical surfaces, compensation processing is often required. Mirror surface shape detection and feedback are crucial steps in compensation processing, and high-precision mirror surface shape detection can greatly improve the processing efficiency of optical surfaces.

[0003] Interferometer-compensated inspection is a common method for inspecting optical surfaces. For inspecting aspherical or freeform surfaces with large relative diameters or significant deviations, the addition of a CGH or compensator during the interferometer inspection process, along with the inconsistency in the curvature of the surface being measured, leads to a non-linear relationship between the CCD pixel coordinate system (where the interferometer measurement results are located) and the workpiece coordinate system (where the optical surface is located). In other words, a non-linear error, also known as projection distortion, exists. To better utilize the inspection data to guide manufacturing processes, projection distortion needs to be corrected.

[0004] Currently, methods for correcting projection distortion include the marker point method and methods that resolve projection distortion by inversely solving other aberrations.

[0005] The marker point method involves first marking a series of coordinate points on the workpiece, then detecting them to obtain the corresponding marker points in the pixel coordinate system. Projection distortion is then solved by fitting the data, and the accuracy of the projection distortion correction is proportional to the number of marker points. However, the projection distortion correction method mentioned in Chinese patent CN106705888B requires manual marking of light rays, which introduces significant marking errors. Furthermore, the distortion obtained through fitting contains non-negligible calculation errors such as fitting or interpolation, resulting in inaccurate correction results.

[0006] Some studies have introduced defocus by moving the detection platform and used the changes in defocus and spherical aberration in the surface image to solve the distortion in the detection system. However, this method requires precise control of the movement of the detection system and is computationally complex.

[0007] Therefore, it is necessary to improve the current methods for correcting projection distortion. Summary of the Invention

[0008] To address the aforementioned shortcomings, the purpose of this application is to propose a correction method for detecting projection distortion of optical curved surfaces using CGH interferometry. This method eliminates the need for data fitting and complex calculations, making it simple, convenient, and easy to implement.

[0009] To achieve the above objectives, this application adopts the following technical solution:

[0010] A correction method for CGH compensation detection of optical curved surface projection distortion, characterized in that the method includes the following steps:

[0011] Set a center marker point and at least one feature point. That is, mark a point at any location on the effective aperture, use this as a feature point, and record the coordinates (x, y) of the feature point on the surface to be measured. i ,y i );

[0012] Adjust the optical path, that is, adjust the surface to be measured and the CGH so that the center marker point coincides with the center of the CCD pixel coordinate system in the interferometer, and record the coordinates (x, y) of the feature point in the CCD pixel coordinate system. j ,y j );

[0013] By solving for the feature points, we can obtain the CCD pixel coordinates and the corresponding CGH. -2 The scaling ratio and rotation angle of the coordinates are used to apply the solution to the full aperture to obtain the correspondence between the CCD pixel coordinates and the coordinates of the surface under test, thus completing the projection distortion correction. This correction method addresses the issue that when using CGH compensation to detect aspherical or freeform surfaces with an interferometer, the detection results will produce projection distortion, leading to a non-linear correspondence between the CCD pixel coordinates and the coordinates of the surface under test. The projection distortion is corrected by calculating three sets of mapping relationships.

[0014] In one embodiment, the correction method uses four surface coordinates, including:

[0015] These are the surface to be measured, the first surface of the CGH, the second surface of the CGH (diffraction surface), and the CCD surface of the interferometer. For ease of description, CGH will be used below. -1 CGH -2 These represent the first surface of CGH and the second surface of CGH, respectively.

[0016] The light ray propagates from the surface to be measured. The slope at any point on the surface can be calculated using the equation of the surface. The magnitude of this slope corresponds to the angle at which the light ray strikes the CGH. -1 The tangent of the incident angle α0,

[0017] Given the surface to be measured and CGH -1 The distance d1,

[0018] The relationship between light rays and CGH is obtained from geometric relationships. -1 The location of the intersection;

[0019] Based on the law of refraction and the thickness d of the CGH, the relationship between light and the CGH is obtained. -2 The location of the intersection.

[0020] In one embodiment, solving the coordinate mapping relationship in the correction method includes: solving separately

[0021] S1. The coordinates (x, y) of the surface to be measured and the coordinates of the first surface of CGH. -1 coordinates (x) CGH-1 y CGH-1 The mapping relationship;

[0022] S2.CGH First Surface CGH -1 coordinates (x) CGH-1 y CGH-1 ) and CGH second surface -2 coordinates (x) CGH-2 y CGH-2 The mapping relationship;

[0023] S3.CGH second surface CGH -2 coordinates (x) CGH-2 y CGH-2 The CCD pixel coordinates (x) of the interferometer CCD y CCD The mapping relationship of ).

[0024] In one embodiment, the coordinates (x, y) of the surface to be measured in this correction method are compared with the coordinates of the first surface of the CGH. -1 coordinates (x) CGH-1 y CGH-1 The mapping relationships include:

[0025] Let the vertex of the surface to be measured be connected to CGH. -1 Let d1 be the distance between the two sides, D be the diameter of the surface to be measured, and z(r) be the equation of the surface to be measured.

[0026] Light incident on CGH -1 The angle of incidence is α0.

[0027] The slope at any point can be obtained by solving the equation of the surface to be measured. The magnitude of the slope is the tangent of α0. From geometric relationships, the arrival time of the light ray at CGH can be obtained. -1 Position (x) CGH-1 y CGH-1 ), r CGH-1 For point (x) CGH-1 y CGH-1 ) to CGH -i The distance to the origin of the coordinate system is calculated using the following formula:

[0028]

[0029]

[0030] In one embodiment, the CGH of the first surface of the CGH in this correction method -1 coordinates (x) CGH-1 y CGH-1 ) and CGH second surface -2 coordinates (x) CGH-2 y CGH-2 The mapping relationships include:

[0031] Assume the light passes through CGH -1 Given a back refraction angle of α1, an air refractive index of n0, a CGH material refractive index of n1, and a CGH thickness of d, calculate the refraction angle α1 to determine the light rays passing through the CGH. -1 After arriving at CGH -2 Position (x) CGH-2 y CCH-2 ), r CGH-2 For point (x) CGH-2 y CGH-2 ) to CGH -2 The distance to the origin of the coordinate system is calculated using the following formula:

[0032] n o sinα0=n1sinα1 (3)

[0033] r CGH-2 =r CGH-1 -d×tanα1 (4)

[0034] In one embodiment, in this correction method, the CGH of the second surface of the CGH -2 coordinates (x) CGH-2 y CGH-2 The CCD pixel coordinates (x) of the interferometer CCD y CCD The mapping relationships include:

[0035] First, set the first coordinate (x) i y i Substitute this into step S1, and in step S2 solve for the point corresponding to CGH. -2 coordinates on (x) k y k ),

[0036] According to (x) k y k ) and the coordinates (x) obtained in step S2 j y j CGH can be calculated -2 And the scaling ratio k and rotation angle Δθ of the CCD pixel coordinate system,

[0037] The position (x) of the measured surface on the CCD surface can be calculated based on the scaling ratio and rotation angle. CCD yCCD ),

[0038] r CCD For point (x) CCD y CCD The distance r from the origin of the CCD pixel coordinate system k For point (x) k y k ) to CGH -2 The distance r from the origin of the coordinate system j For point (x) j y j The distance from θ to the origin of the CCD pixel coordinate system; k For r k With CGH -2 The angle between the x-axis and the coordinate system; θ j For r j The angle between the x-axis coordinate and the CCD pixel coordinate system.

[0039] The calculation formula is as follows:

[0040]

[0041]

[0042]

[0043] In the process of solving the scaling ratio k and rotation angle Δθ, multiple feature points can be set in step 1 to reduce random errors. Feature points can also be used to evaluate the correction error of the coordinates of the surface to be measured.

[0044] In one embodiment, the correction method uses a Taylor profilometer to mark a point at the center of the surface to be measured, and uses this point as the center mark.

[0045] Beneficial effects

[0046] Compared with existing technologies, the correction method proposed in this application for calculating the projection distortion of optical curved surfaces in holographic (CGH) compensated detection solves the problem of projection distortion that occurs when aspherical and freeform surfaces are compensated and detected using interferometers and CGH, resulting in a nonlinear relationship between the detection data coordinates and the surface coordinates. The method corrects the projection distortion by calculating three sets of mapping relationships using ray tracing and a small number of marker points. It offers high correction accuracy, simple and convenient calculation, easy programming implementation, and strong applicability, suitable for various surface shapes. Attached Figure Description

[0047] The accompanying drawings are provided to illustrate the technical solutions of this disclosure and form part of the specification. They are used together with the embodiments of this disclosure to explain the technical solutions of this disclosure and do not constitute a limitation on the technical solutions of this disclosure. The shapes and sizes of the components in the drawings do not reflect actual proportions and are only intended to illustrate the content of this application.

[0048] Figure 1 This is a schematic diagram of the optical path structure of the interferometer used for CGH compensation detection in an embodiment of this application;

[0049] Figure 2 This is a simulated optical path diagram of an embodiment of this application;

[0050] Figure 3 In the diagram, a represents the surface to be tested in the light trace image of this application embodiment, and b represents a comparison of the CCD surface of the light trace image, i.e., a schematic diagram of projection distortion.

[0051] In the figure, 1 is the surface to be tested, 2 is the first surface of CGH, 3 is the second surface of CGH, 4 is the interferometer, and 5 is the CCD surface of the interferometer. Detailed Implementation

[0052] The above-described solution will be further illustrated below with reference to specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of this application. The implementation conditions used in the embodiments may be further adjusted according to the conditions of specific manufacturers, and the implementation conditions not specified are generally those in routine experiments.

[0053] The terms "first," "second," and similar terms used in the embodiments of this disclosure do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word covers the element or object listed after the word and its equivalents, without excluding other elements or objects.

[0054] This application proposes a correction method for CGH compensation detection of projection distortion of optical curved surfaces.

[0055] The method includes:

[0056] Marking involves setting a central marker point and at least one feature point. Specifically, a marker point is placed at any location on the effective aperture, serving as the feature point. The coordinates (x, y) of this feature point on the surface to be measured are recorded. i y i );

[0057] Adjust the optical path, that is, adjust the surface to be measured and the CGH so that the center marker point coincides with the center of the CCD pixel coordinate system in the interferometer, and record the coordinates (x, y) of the feature point in the CCD pixel coordinate system. j y j );

[0058] Solving the coordinate mapping relationship involves finding the CCD pixel coordinates and their corresponding CGH coordinates through feature point calculations. -2 The scaling ratio and rotation angle of the coordinates.

[0059] The solution is applied to the full aperture to obtain the correspondence between CCD pixel coordinates and the coordinates of the surface under test, thus completing the projection distortion correction. This correction method uses ray tracing and a small number of marker points to calculate three sets of mapping relationships (the coordinates of the surface under test (x, y) and the coordinates of CGH). -1 coordinates (x) CGH-1 y CCH-1 The mapping relationship between CGH and CGH. -1 coordinates (x) CGH-1 y CGH-1 ) and CGH -2 coordinates (x) CGH-2 y CGH-2 The mapping relationship between CGH and CGH. -2 coordinates (x) CGH-2 y CGH-2 The CCD pixel coordinates (x) of the interferometer CCD y CCD This method corrects projection distortion using a mapping relationship, achieving high accuracy and simple, convenient calculation. It eliminates the need for data fitting and complex calculations, making it easy to implement in programming. It is highly applicable to various surface shapes without requiring re-derivation, calculation, or reprogramming. It solves the problem of projection distortion in the detection results of aspherical or freeform surfaces using CGH compensation in interferometers, leading to a non-linear relationship between CCD pixel coordinates and the coordinates of the measured surface.

[0060] Next, we will combine the appendix Figures 1-3 This describes the correction method proposed in this application.

[0061] In one embodiment, taking the use of an interferometer with CGH compensation to detect a quadratic surface as an example, the schematic diagram of the optical path structure during detection is shown below. Figure 1 Table 1 shows the simulation parameters of the surface to be tested and the detection system.

[0062] Table 1. Simulation parameters of the surface to be tested and the detection system

[0063] Serial Number item index 1 Conic coefficient -1 2 radius of curvature 500mm 3 caliber 220mm 4 <![CDATA[d1]]> 425mm 5 d 1.5mm 6 <![CDATA[d2]]> 85mm 7 Interferometer focal length 100mm 8 Pixel coordinate diameter 44.56mm

[0064] The simulated optical path diagram of the data in the above table in the optical design software is as follows: Figure 2 As shown, a correction method for surface projection distortion of the surface under test is used for CGH compensation detection.

[0065] Includes the following steps:

[0066] 1. Marking: Use a Taylor profilometer to find the center position (0,0) of the surface to be measured and mark it as the center mark point; set the point with coordinates (77,77) as the feature point (there can be multiple feature points);

[0067] 2. Adjust the optical path: After setting up the detection optical path, adjust the test surface and CGH so that the center mark point of the test surface coincides with the center of the CCD pixel coordinate system in the interferometer, and record the coordinates of the feature point in the CCD pixel coordinate system as (-15.552, -15.552).

[0068] 3. Solve for the coordinate mapping relationship:

[0069] This step mainly uses three sets of mapping relationships, namely the coordinates (x, y) of the surface to be measured and CGH. -1 coordinates (x) CGH-1 ,y CGH-1 The mapping relationship between CGH and CGH. -1 coordinates (x) CGH-1 ,y CGH-1 ) and CGH -2 coordinates (x) CGH-2 ,y CGH-2 The mapping relationship between CGH and CGH. -2 coordinates (x) CGH-2 ,y CGH-2) The CCD pixel coordinates (x) of the interferometer CCS ,y CCS The mapping relationship of ).

[0070] 3.1 Surface to be tested - CGH -1 Given the distance from the vertex of the surface to be measured to CGH -1 The distance is d1, the diameter of the surface to be measured is D, and the equation of the surface to be measured is z(r).

[0071] First, the slope at any point can be obtained by solving the equation of the surface to be measured. The magnitude of the slope corresponds to the incident light ray at CGH. -1 The tangent of the incident angle α0 can be obtained from geometric relationships to determine the distance the ray reaches CGH. -1 position r CGH-1 The formula is as follows:

[0072]

[0073]

[0074] 3.2 CGH -1 -CGH -2 This step mainly considers the refraction effect, assuming the light passes through CGH. -1Given that the refractive index of air is n0, the refractive index of CGH material is n1, and the thickness of CGH is d, calculate the refractive angle α1 to determine the light rays passing through CGH. -1 After arriving at CGH -2 position r CGH-2 The formula is as follows:

[0075] n0sinα0=n1sinα1 (3)

[0076] r CGH-2 =r CGH-1 -d×tanα1 (4)

[0077] 3.3 CGH -2 -CCD: First, substitute the feature point (77, 77) marked in step 1 into steps 3.1 and 3.2 to solve, and obtain the corresponding coordinates of this point in CGH. -2 The coordinates on the graph are (13.219, 13.219). Based on the coordinates (-15.552, -15.552) obtained in step 2, CGH can be calculated. -2 Given the scaling ratio k and rotation angle Δθ of the CCD surface coordinate system, the corresponding CCD surface pixel coordinates (x, y, y) of the measured surface can be calculated based on the scaling ratio and rotation angle. CCD y CCD The formula is as follows:

[0078]

[0079] The calculation yields k = 1.1765 and Δθ = 3.1416;

[0080]

[0081]

[0082] Applying this method to the full aperture allows us to determine the correspondence between the interferometer CCD pixel coordinates and the coordinates of the surface under test, thus correcting the projection distortion. Taking a series of feature points in step 1 allows us to calculate the correction accuracy. The results are shown in Table 2.

[0083] Table 2. Calibration Accuracy (Unit: mm)

[0084]

[0085] Table 2 shows that the maximum correction error of the selected feature points calculated using this method is 0.016. The correction errors listed in the table indicate that this distortion correction method solves the distortion problems that occur when the surface under test is tested using CGH interferometric compensation. Figure 3 The projection distortion shown (a is the surface to be measured in the light trace image, b is the CCD surface in the light trace image) demonstrates that the correction accuracy of this application is high; the calculation is simple and convenient, and it has strong applicability and can be used for various surface shapes.

[0086] In one embodiment, multiple feature points can be set to reduce random errors.

[0087] The above embodiments are only for illustrating the technical concept and features of this application, and are intended to enable those skilled in the art to understand the content of this application and implement it accordingly. They should not be construed as limiting the scope of protection of this application. All equivalent changes or modifications made in accordance with the spirit and essence of this application should be included within the scope of protection of this application.

Claims

1. A correction method for CGH compensation detection of projection distortion of optical curved surfaces, characterized in that, The method includes the following steps: The optical path structure of the CGH compensation detection includes: a surface to be detected, a first surface CGH -1 of the CGH, a second surface CGH -2 of the CGH, and an interferometer CCD surface. Set a center marker point and at least one feature point. That is, mark a point at any location on the effective aperture, use this as a feature point, and record the coordinates (x, y) of the feature point on the surface to be measured. i ,y i ); Adjusting the light path, that is, adjusting the surface to be measured and the CGH so that the center mark point coincides with the center of the CCD pixel coordinate system in the interferometer, recording the coordinates (x j ,y j ) of the feature points in the CCD pixel coordinate system; The light ray propagates from the surface to be measured, and the slope of any point on the surface to be measured can be solved according to the equation of the surface to be measured, and the numerical value corresponds to the tangent value of the incident angle α0 of the light ray incident to the CGH -1 . the distance d1 of the surface to be measured from the CGH -1 is known, The intersection position of the light and the CGH is obtained from the geometric relationship. -1 The intersection position of the light and the CGH is obtained from the geometric relationship. According to the refraction law and the CGH thickness d, the intersection position of the light ray and the CGH is obtained. -2 ​ Solve separately: S1. mapping relationship between the coordinate (x, y) of the surface to be measured and the CGH coordinate (x, y) of the first surface of the CGH -1 CGH-1 CGH-1 ) of the first surface of the CGH​​ Through the calculation formula: Obtain the coordinates (x, y) of the surface to be measured and the CGH of the first surface of CGH. -1 coordinates (x) CGH-1 ,y CGH-1 The mapping relationship is given by the formula, where d1 is the distance from the vertex of the surface to be measured to CGH. -1 The distance, D is the aperture of the surface to be measured, z(r) is the equation of the surface to be measured, and α0 is the distance of the light ray incident on CGH. -1 The angle of incidence can be used to solve for the slope at any point using the equation of the surface to be measured. The magnitude of the slope is the tangent of α0. From geometric relationships, the arrival time of the light ray at CGH can be determined. -1 Position (x) CGH-1 ,y CGH-1 ), r CGH-1 For point (x) CGH-1 ,y CGH-1 ) to CGH -1 Distance from the origin of the coordinate system; S2.CGH First Surface CGH -1 coordinates (x) CGH-1 ,y CGH-1 ) and CGH second surface -2 coordinates (x) CGH-2 ,y CGH-2 The mapping relationship; Assume the light passes through CGH -1 Given a back refraction angle of α1, an air refractive index of n0, a CGH material refractive index of n1, and a CGH thickness of d, calculate the refraction angle α1 to determine the light rays passing through the CGH. -1 After arriving at CGH -2 Position (x) CGH-2 ,y CGH-2 ), r CGH-2 For point (x) CGH-2 ,y CGH-2 ) to CGH -2 The distance to the origin of the coordinate system is calculated using the following formula: n0sinα0=n1sinα1 r CGH-2 =r CGH-1 -d×tanα1 The CGH of the first surface of the CGH is obtained -1 coordinates (x) CGH-1 ,y CGH-1 ) and CGH second surface -2 coordinates (x) CGH-2 ,y CGH-2 The mapping relationship; S3.CGH second surface CGH -2 coordinates (x) CGH-2 ,y CGH-2 The CCD pixel coordinates (x) of the interferometer CCD ,y CCD The mapping relationship; Through the calculation formula: The CGH of the second surface of CGH is obtained. -2 coordinates (x) CGH-2 ,y CGH-2 The CCD pixel coordinates (x) of the interferometer CCD ,y CCD The mapping relationship of r, where r is... CCD For point (x) CCD ,y CCD The distance r from the origin of the CCD pixel coordinate system k For point (x) k ,y k ) to CGH -2 The distance r from the origin of the coordinate system j For point (x) j ,y j The distance from θ to the origin of the CCD pixel coordinate system; k For r k With CGH -2 The angle between the x-axis and the coordinate system; θ j For r j The angle between the x-axis and the CCD pixel coordinate system; By solving for the feature points, we can obtain the CCD pixel coordinates and the corresponding CGH. -2 The scaling ratio and rotation angle of the coordinates are used to apply the solution to the full aperture to obtain the correspondence between the CCD pixel coordinates and the coordinates of the surface to be measured, thus completing the projection distortion correction.

2. The correction method for CGH compensation detection of optical curved surface projection distortion as described in claim 1, characterized in that, Also includes: Set the first coordinate (x) i ,y i Substitute this into step S1, and in step S2 solve for the point corresponding to CGH. -2 coordinates on (x) k ,y k ), According to (x) k ,y k ) and the coordinates (x) obtained in step S2 j ,y j CGH can be calculated -2 And the scaling ratio k and rotation angle Δθ of the CCD pixel coordinate system, The position (x) of the measured surface on the CCD surface can be calculated based on the scaling ratio and rotation angle. CCD ,y CCD ).

3. The correction method for CGH compensation detection of optical curved surface projection distortion as described in claim 1, characterized in that, Mark a point at the center of the surface to be measured using a Taylor profilometer, and use this point as the center marker.

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