阅读说明：本技术 光学面形补偿干涉测量中的投影畸变校正方法、系统及介质 (Projection distortion correction method, system and medium in optical surface shape compensation interferometry ) 是由 陈善勇 戴一帆 胡皓 关朝亮 翟德德 熊玉朋 薛帅 于 2020-12-01 设计创作，主要内容包括：本发明公开了一种光学面形补偿干涉测量中的投影畸变校正方法、系统及介质,本发明的投影畸变校正方法包括：建立测量系统光学模型,在与点光源共焦位置插入一个虚拟参考球面；进行光线追迹,分别获得入瞳坐标网格光线对应的被测镜面上交点的横坐标{(x_m,y_m)}和虚拟参考球面上交点的横坐标{(x_r,y_r)}；标定干涉仪像面上的像素坐标(u,v)对应虚拟参考球面上横坐标(x_(rt),y_(rt))的线性比例因子,将干涉仪测得面形误差分布的像素坐标转换为虚拟参考球面上的横坐标(x_(rt),y_(rt))；进行畸变校正得到结果。本发明不需使用实物标记点序列,不需对畸变进行函数拟合,具有计算方法简单、效率高和精度高的优点。(The invention discloses a projection distortion correction method, a system and a medium in optical surface shape compensation interferometry, wherein the projection distortion correction method comprises the following steps: establishing an optical model of the measuring system, and inserting a virtual reference spherical surface at a confocal position with the point light source; performing ray tracing to respectively obtain the abscissa (x) of the intersection point on the measured lens surface corresponding to the entrance pupil coordinate grid ray m ,y m ) X and the abscissa of the intersection on the virtual reference sphere r ,y r ) }; calibrating pixel coordinates (u, v) on the image surface of the interferometer to correspond to the horizontal coordinates (x) on the virtual reference sphere rt ,y rt ) The linear scale factor of (2) converts the pixel coordinates of the surface shape error distribution measured by the interferometer into the abscissa (x) on the virtual reference sphere rt ,y rt ) (ii) a And carrying out distortion correction to obtain a result. The method does not need to use a real object mark point sequence, does not need to perform function fitting on distortion, and has the advantages of simple calculation method, high efficiency and high precision.)

1. A method for correcting projection distortion in optical surface shape compensation interferometry is characterized by comprising the following steps:

1) inputting a profile error distribution (u, v, w) of the compensation interferometry;

2) establishing an optical model of the measuring system, and inserting a virtual reference spherical surface at a confocal position with the point light source;

3) performing ray tracing based on an optical model of a measuring system, and respectively obtaining an abscissa { (x) of an intersection point on the measured mirror surface corresponding to an entrance pupil coordinate grid ray_m,y_m) X and the abscissa of the intersection on the virtual reference sphere_r,y_r)}；

4) Calibrating pixel coordinates (u, v) on the image surface of the interferometer to correspond to the horizontal coordinates (x) on the virtual reference sphere_rt,y_rt) The linear scale factor of (2) converts the pixel coordinates of the surface shape error distribution measured by the interferometer into the abscissa (x) on the virtual reference sphere_rt,y_rt,w)；

5) Using the abscissa { (x)_m,y_m) And abscissa { (x)_r,y_r) Interpolating to obtain the horizontal coordinate (x) of the virtual reference sphere_rt,y_rt) Corresponding abscissa (x) on the measured mirror surface_mt,y_mt) Outputting the surface shape error distribution (x) corresponding to the abscissa on the measured mirror surface_mt,y_mt,w)。

2. The method of claim 1, wherein the optical model of the measurement system created in step 2) is an imaging system with an aperture of a point source comprising a point source and a compensator, and the step of inserting a virtual reference sphere at a position confocal with the point source comprises: a dummy element is inserted between the point light source and the compensator and serves as a virtual reference spherical surface, the spherical center of the virtual reference spherical surface is coincided with the point light source, and the connecting line of the point light source and the top point of the virtual reference spherical surface is parallel to the optical axis of the compensator.

3. The method of claim 1, wherein step 3) comprises: the point light source is used as an object point to emit light rays, and the coordinate of the light rays on the entrance pupil surface is in a value range of [ -1,1]Then calculating to obtain the abscissa of the intersection point on the measured mirror surface corresponding to the grid ray { (x)_m,y_m) X and the abscissa of the intersection on the virtual reference sphere_r,y_r)}。

4. The method of claim 1, wherein step 4) comprises:

4.1) selecting the pixel coordinates (u) of two characteristic points in an effective data area on an image surface of the interferometer to measure the surface shape error distribution₁,v₁)、(u₂,v₂) Finding out the coordinate (x) corresponding to the feature point on the measured mirror surface by using the real-time interferogram_m1,y_m1)、(x_m2,y_m2) Determining coordinates (x) of feature points corresponding to the virtual reference sphere by ray tracing_r1,y_r1)、(x_r2,y_r2) Then based on the pixel coordinates (u) of the two feature points₁,v₁)、(u₂,v₂) And its coordinates (x) corresponding to the virtual reference sphere_r1,y_r1)、(x_r2,y_r2) Calculating a linear scale factor alpha;

4.2) according to x_rt＝α(u-u₁)+x_r1，y_rt＝α(v-v₁)+y_r1Converting the pixel coordinates of the surface shape error distribution measured by the interferometer into the abscissa on the virtual reference spherical surface to obtain the surface shape error distribution (x) corresponding to the abscissa on the virtual reference spherical surface_rt,y_rt,w)。

5. The method of claim 4, wherein the function of calculating the linear scale factor α in step 4.1) is expressed by the following formula:

in the above formula, (u)₁,v₁)、(u₂,v₂) Measuring the pixel coordinates of two characteristic points in the effective data area on the image surface of the surface shape error distribution for the interferometer, (x)_r1,y_r1)、(x_r2,y_r2) The pixel coordinates for the two feature points correspond to the coordinates on the virtual reference sphere.

6. The method of claim 1, wherein the step 5) utilizes the abscissa { (x)_m,y_m) And abscissa { (x)_r,y_r) Interpolating to obtain the horizontal coordinate (x) of the virtual reference sphere_rt,y_rt) Corresponding abscissa (x) on the measured mirror surface_mt,y_mt) Comprises the following steps: calculating the abscissa { (x)_r,y_r) Delaunay triangulation of the virtual reference sphere, finding the horizontal coordinates (x) of the virtual reference sphere_rt,y_rt) Corresponding triangle vertex (x)_ra,y_ra)、(x_rb,y_rb)、(x_rc,y_rc) And its corresponding abscissa (x) on the measured mirror surface_ma,y_ma)、(x_mb,y_mb)、(x_mc,y_mc) Calculating to obtain a virtual reference sphere by a linear weighted average methodTransverse plane coordinate (x)_rt,y_rt) Corresponding to the abscissa (x) of the measured mirror surface_mt,y_mt)。

7. The method of claim 6, wherein the calculating of the horizontal coordinate (x) on the virtual reference sphere by the linear weighted average method is used to correct the projection distortion in the optical profile compensated interferometry_rt,y_rt) Corresponding to the abscissa (x) of the measured mirror surface_mt,y_mt) The function expression of (a) is as follows:

x_mt＝(1-β-γ)x_ma+βx_mb+γx_mc,y_mt＝(1-β-γ)y_ma+βy_mb+γy_mc

in the above formula, (x)_mt,y_mt) For a virtual reference sphere abscissa (x)_rt,y_rt) Corresponding to the abscissa (x) of the measured mirror surface_mt,y_mt) Beta and gamma are weight factors, (x)_ma,y_ma)、(x_mb,y_mb)、(x_mc,y_mc) Respectively representing the horizontal coordinate (x) of the virtual reference sphere_rt,y_rt) Corresponding triangle vertex (x)_ra,y_ra)、(x_rb,y_rb)、(x_rc,y_rc) And the horizontal coordinate on the corresponding measured mirror surface.

8. A system for correcting projection distortion in optical surface shape compensation interferometry, comprising a microprocessor and a memory connected to each other, wherein the microprocessor is programmed or configured to perform the steps of the method for correcting projection distortion in optical surface shape compensation interferometry according to any of claims 1-7.

9. A system for correcting projection distortion in optical surface shape compensation interferometry, comprising a microprocessor and a memory connected to each other, wherein the memory stores a computer program programmed or configured to perform a method for correcting projection distortion in optical surface shape compensation interferometry according to any of claims 1-7.

10. A computer-readable storage medium having stored thereon a computer program programmed or configured to perform the method of projection distortion correction in optical surface shape compensation interferometry according to any of claims 1-7.

Technical Field

The invention relates to an optical surface shape interferometry, in particular to a projection distortion correction method, a system and a medium in optical surface shape compensation interferometry.

Background

Because the optical surface shapes of the aspheric surface, the off-axis aspheric surface, the free-form surface and the like deviate from the ideal spherical shape, when the wave surface interferometer is used for interference measurement, a compensator is required to be used for aberration compensation, namely, standard spherical waves emitted by the interferometer are converted into aspheric waves matched with the measured mirror surface, so that complex nonlinear mapping exists between pixel coordinates of surface shape error distribution measured by the interferometer and abscissa on the measured mirror surface. The abscissa on the measured mirror surface can not be calibrated by the linear scale factor like a measuring plane any more, and the nonlinear mapping causes the abscissa on the measured mirror surface to deviate from the position corresponding to the linear mapping, namely projection distortion.

Modern deterministic optical machining is compensation machining based on measured surface shape errors, residence time distribution of a polishing tool on a mirror surface is controlled, and accurate removal of corresponding materials at high points of errors is achieved. Therefore, the projection distortion must be corrected to determine the surface shape error measured by the interferometer corresponding to the abscissa position on the measured mirror surface, so that the deterministic processing can be performed on the correct position on the mirror surface.

The common distortion correction method is to make a series of mark points on the measured mirror surface, the abscissa of the mark points on the measured mirror surface is calibrated, and find the corresponding pixel coordinates of each mark point in the interferogram, so as to establish the corresponding relation between the pixel coordinates on the image surface of the interferometer and the abscissa of the measured mirror surface. However, due to the limitations of cost and efficiency, the number of marked points is generally not large, and therefore a polynomial function is often used to fit such a non-linear mapping. For a complex off-axis aspheric surface or free-form surface, when distortion is serious, hundreds of marking points in a two-dimensional array are needed to accurately reflect the distortion characteristic, so that the method has poor actual operability.

The other method is to trace the light of the measuring system, but only trace the corresponding relationship between the measured mirror surface and the abscissa of the optical surface of the compensator. In fact, the abscissa on the optical surface of the compensator to the pixel coordinate on the image surface of the interferometer is still not a linear mapping, resulting in distortion correction errors or poor results.

Disclosure of Invention

The technical problems to be solved by the invention are as follows: aiming at the problems in the prior art, the invention provides a projection distortion correction method, a system and a medium in optical surface shape compensation interferometry.

In order to solve the technical problems, the invention adopts the technical scheme that:

a method of projection distortion correction in optical profile compensation interferometry, comprising:

1) inputting a profile error distribution (u, v, w) of the compensation interferometry;

2) establishing an optical model of the measuring system, and inserting a virtual reference spherical surface at a confocal position with the point light source;

3) performing ray tracing based on an optical model of a measuring system, and respectively obtaining an abscissa { (x) of an intersection point on the measured mirror surface corresponding to an entrance pupil coordinate grid ray_m,y_m) X and the abscissa of the intersection on the virtual reference sphere_r,y_r)}；

4) Calibrating pixel coordinates (u, v) on the image surface of the interferometer to correspond to the horizontal coordinates (x) on the virtual reference sphere_rt,y_rt) The linear scale factor of (2) converts the pixel coordinates of the surface shape error distribution measured by the interferometer into the abscissa (x) on the virtual reference sphere_rt,y_rt,w)；

5) Using the abscissa { (x)_m,y_m) And abscissa { (x)_r,y_r) Interpolating to obtain the horizontal coordinate (x) of the virtual reference sphere_rt,y_rt) Corresponding transverse direction on the measured mirror surfaceCoordinate (x)_mt,y_mt) Outputting the surface shape error distribution (x) corresponding to the abscissa on the measured mirror surface_mt,y_mt,w)。

Optionally, the optical model of the measurement system established in step 2) is an imaging system comprising a point light source and a compensator and using the point light source as an aperture, and the step of inserting a virtual reference sphere at a position confocal with the point light source comprises: a dummy element is inserted between the point light source and the compensator and serves as a virtual reference spherical surface, the spherical center of the virtual reference spherical surface is coincided with the point light source, and the connecting line of the point light source and the top point of the virtual reference spherical surface is parallel to the optical axis of the compensator.

Optionally, step 3) comprises: the point light source is used as an object point to emit light rays, and the coordinate of the light rays on the entrance pupil surface is in a value range of [ -1,1]Then calculating to obtain the abscissa of the intersection point on the measured mirror surface corresponding to the grid ray { (x)_m,y_m) X and the abscissa of the intersection on the virtual reference sphere_r,y_r)}。

Optionally, step 4) comprises:

4.1) selecting the pixel coordinates (u) of two characteristic points in an effective data area on an image surface of the interferometer to measure the surface shape error distribution₁,v₁)、(u₂,v₂) Finding out the coordinate (x) corresponding to the feature point on the measured mirror surface by using the real-time interferogram_m1,y_m1)、(x_m2,y_m2) Determining coordinates (x) of feature points corresponding to the virtual reference sphere by ray tracing_r1,y_r1)、(x_r2,y_r2) Then based on the pixel coordinates (u) of the two feature points₁,v₁)、(u₂,v₂) And its coordinates (x) corresponding to the virtual reference sphere_r1,y_r1)、(x_r2,y_r2) Calculating a linear scale factor alpha;

4.2) according to x_rt＝α(u-u₁)+x_r1，y_rt＝α(v-v₁)+y_r1Converting the pixel coordinates of the surface shape error distribution measured by the interferometer into the abscissa on the virtual reference spherical surface to obtain the surface shape error corresponding to the abscissa on the virtual reference spherical surfaceDifference distribution (x)_rt,y_rt,w)。

Optionally, the functional expression for calculating the linear scale factor α in step 4.1) is as follows:

in the above formula, (u)₁,v₁)、(u₂,v₂) Measuring the pixel coordinates of two characteristic points in the effective data area on the image surface of the surface shape error distribution for the interferometer, (x)_r1,y_r1)、(x_r2,y_r2) The pixel coordinates for the two feature points correspond to the coordinates on the virtual reference sphere.

Optionally, step 5) utilizes the abscissa { (x)_m,y_m) And abscissa { (x)_r,y_r) Interpolating to obtain the horizontal coordinate (x) of the virtual reference sphere_rt,y_rt) Corresponding abscissa (x) on the measured mirror surface_mt,y_mt) Comprises the following steps: calculating the abscissa { (x)_r,y_r) Delaunay triangulation of the virtual reference sphere, finding the horizontal coordinates (x) of the virtual reference sphere_rt,y_rt) Corresponding triangle vertex (x)_ra,y_ra)、(x_rb,y_rb)、(x_rc,y_rc) And its corresponding abscissa (x) on the measured mirror surface_ma,y_ma)、(x_mb,y_mb)、(x_mc,y_mc) Calculating the horizontal coordinate (x) of the virtual reference sphere by a linear weighted average method_rt,y_rt) Corresponding to the abscissa (x) of the measured mirror surface_mt,y_mt)。

Optionally, the horizontal coordinate (x) on the virtual reference sphere is calculated by a linear weighted average method_rt,y_rt) Corresponding to the abscissa (x) of the measured mirror surface_mt,y_mt) The function expression of (a) is as follows:

x_mt＝(1-β-γ)x_ma+βx_mb+γx_mc,y_mt＝(1-β-γ)y_ma+βy_mb+γy_mc

in the above formula, (x)_mt,y_mt) For a virtual reference sphere abscissa (x)_rt,y_rt) Corresponding to the abscissa (x) of the measured mirror surface_mt,y_mt) Beta and gamma are weight factors, (x)_ma,y_ma)、(x_mb,y_mb)、(x_mc,y_mc) Respectively representing the horizontal coordinate (x) of the virtual reference sphere_rt,y_rt) Corresponding triangle vertex (x)_ra,y_ra)、(x_rb,y_rb)、(x_rc,y_rc) And the horizontal coordinate on the corresponding measured mirror surface.

In addition, the invention also provides a projection distortion correction system in the optical surface shape compensation interferometry, which comprises a microprocessor and a memory which are connected with each other, wherein the microprocessor is programmed or configured to execute the steps of the projection distortion correction method in the optical surface shape compensation interferometry.

In addition, the invention also provides a projection distortion correction system in the optical surface shape compensation interferometry, which comprises a microprocessor and a memory which are connected with each other, wherein the memory stores a computer program which is programmed or configured to execute the projection distortion correction method in the optical surface shape compensation interferometry.

Furthermore, the present invention also provides a computer-readable storage medium having stored therein a computer program programmed or configured to execute the method for projection distortion correction in optical surface shape compensation interferometry.

Compared with the prior art, the invention has the following advantages:

1. the invention introduces the virtual reference spherical surface and performs ray tracing to obtain the accurate corresponding relation between the transverse coordinate of the measured lens surface and the transverse coordinate of the virtual reference spherical surface, and then the accurate corresponding relation between the transverse coordinate of the measured lens surface and the pixel coordinate of the image surface of the interferometer can be determined through linear mapping calibration, thereby realizing distortion correction.

2. The method does not need to use a real object mark point sequence or perform function fitting on distortion, can select the light ray tracing dot matrix density according to the severity of the distortion, needs manual intervention except for calibrating the linear scale factor in the step 5), and completes distortion correction by a computer program.

3. The invention can be used for the compensation interference measurement data processing of aspheric surfaces, off-axis aspheric surfaces, free-form surfaces and the like, is suitable for the compensation measurement of a traditional lens type compensator, a reflection type compensator, a refraction and reflection type compensator or a Computer Generated Hologram (CGH) compensator, and obtains the accurate horizontal coordinate of the measured surface shape error distribution of the interferometer corresponding to the measured mirror surface.

Drawings

FIG. 1 is a schematic view of an aspherical CGH compensating interferometry system in accordance with an embodiment of the present invention.

FIG. 2 is a basic flow diagram of a method according to an embodiment of the present invention.

FIG. 3 is an optical model of a measurement system in an embodiment of the invention.

Fig. 4 is a corresponding relationship between pixel coordinates and abscissa on the measured mirror surface and the virtual reference spherical surface in the embodiment of the present invention.

FIG. 5 is a diagram illustrating a grid interpolation method according to an embodiment of the present invention.

Illustration of the drawings: 21. a point light source; 22. a virtual reference sphere; 23. a compensator; 24. a measured mirror surface; 25. an interferometer optical axis; 31. an interferometer image plane; 32. an interferometer; 33. an interferometer exit pupil; 34. a spherical lens; 35. spherical lens reference surface.

Detailed Description

The following describes the projection distortion correction method, system and medium in the optical surface shape compensation interferometry in further detail by using an example of CGH compensation interferometry of an aspheric surface. The measured surface is an ellipsoid with the apex curvature radius of 691.1mm and the quadratic constant k being-0.9911, the caliber is phi 470mm, and the diameter of the central blocking hole is 100 mm.

As shown in fig. 1, the compensated interferometry of the ellipsoidal mirror surface shape is performed using a spherical wave interferometer 32 equipped with a spherical lens 34 and a compensator 23(CGH compensator), and the measurement result is a surface shape error distribution corresponding to the pixel coordinates on the interferometer image plane 31. The pixel coordinates are linearly mapped to the abscissa of the last surface of the spherical lens 34, i.e., the spherical lens reference surface 35, but are non-linearly mapped to the abscissa of the measured mirror surface 24. In fig. 1, reference numeral 33 denotes the interferometer exit pupil, reference numeral 21 denotes a point light source, and reference numeral 24 denotes a measured mirror surface.

As shown in fig. 2, the method for correcting projection distortion in the optical profile compensation interferometry of the present embodiment includes:

1) inputting a profile error distribution (u, v, w) of compensation interferometry, wherein w is a profile error value measured at a pixel coordinate (u, v) on an image surface of a corresponding interferometer;

2) establishing an optical model of the measuring system, and inserting a virtual reference spherical surface at a confocal position with the point light source;

3) performing ray tracing based on an optical model of a measuring system, and respectively obtaining an abscissa { (x) of an intersection point on the measured mirror surface corresponding to an entrance pupil coordinate grid ray_m,y_m) X and the abscissa of the intersection on the virtual reference sphere_r,y_r)}；

4) Calibrating pixel coordinates (u, v) on the image surface of the interferometer to correspond to the horizontal coordinates (x) on the virtual reference sphere_rt,y_rt) The linear scale factor of (2) converts the pixel coordinates of the surface shape error distribution measured by the interferometer into the abscissa (x) on the virtual reference sphere_rt,y_rt,w)；

5) Using the abscissa { (x)_m,y_m) And abscissa { (x)_r,y_r) Interpolating to obtain the horizontal coordinate (x) of the virtual reference sphere_rt,y_rt) Corresponding abscissa (x) on the measured mirror surface_mt,y_mt) Outputting the surface shape error distribution (x) corresponding to the abscissa on the measured mirror surface_mt,y_mt,w)。

As shown in fig. 3, the optical model of the measurement system established in step 2) is an imaging system including a point light source 21 and a compensator 23 and having the point light source 21 as an aperture, and the step of inserting a virtual reference sphere at a position confocal with the point light source includes: a dummy is inserted between the point light source 21 and the compensator 23 as a virtual reference sphere 22, the sphere center of the virtual reference sphere 22 coincides with the point light source 21, and the line connecting the point light source 21 and the vertex of the virtual reference sphere 22 is parallel to the optical axis of the compensator, so that the virtual reference sphere 24 and the spherical lens reference surface 35 are conjugate.

The optical model of the measuring system established in step 2) omits the internal optical system of the interferometer 32 and the spherical lens 34, and simplifies the model into an imaging system with the point light source 21 as an aperture.

In this embodiment, step 3) includes: the point light source is used as an object point to emit light rays, and the coordinate of the light rays on the entrance pupil surface is in a value range of [ -1,1]Then calculating to obtain the abscissa of the intersection point on the measured mirror surface corresponding to the grid ray (x { (x)_m,y_m) X and the abscissa of the intersection on the virtual reference sphere_r,y_r)}。

Fig. 4 is a corresponding relationship between the pixel coordinates and the abscissa on the measured mirror surface and the virtual reference spherical surface in the present embodiment, wherein reference numeral 41 denotes an entrance pupil coordinate grid of the tracking light; reference numeral 42 denotes an intersection point of the tracing ray on the measured mirror surface; reference numeral 43 denotes an intersection point of the trace ray on the virtual reference spherical surface; reference numeral 44 denotes the interferometer-measured profile error distribution; reference numeral 45 denotes a surface shape error distribution corresponding to the abscissa on the measured mirror surface after the distortion correction. As shown in fig. 4, step 4) includes:

4.1) selecting the pixel coordinates (u) of two characteristic points in an effective data area on an image surface of the interferometer to measure the surface shape error distribution₁,v₁)、(u₂,v₂) Finding out the coordinate (x) corresponding to the feature point on the measured mirror surface by using the real-time interferogram_m1,y_m1)、(x_m2,y_m2) Determining coordinates (x) of feature points corresponding to the virtual reference sphere by ray tracing_r1,y_r1)、(x_r2,y_r2) Then based on the pixel coordinates (u) of the two feature points₁,v₁)、(u₂,v₂) And its coordinates (x) corresponding to the virtual reference sphere_r1,y_r1)、(x_r2,y_r2) Calculating a linear scale factor alpha;

4.2) according to x_rt＝α(u-u₁)+x_r1，y_rt＝α(v-v₁)+y_r1Will dryThe pixel coordinates of the surface shape error distribution measured by the interferometer are converted into the abscissa on the virtual reference spherical surface, and the surface shape error distribution (x) corresponding to the abscissa on the virtual reference spherical surface is obtained_rt,y_rt,w)。

The functional expression for calculating the linear scale factor α in step 4.1) of this embodiment is shown as follows:

in the above formula, (u)₁,v₁)、(u₂,v₂) Measuring the pixel coordinates of two characteristic points in the effective data area on the image surface of the surface shape error distribution for the interferometer, (x)_r1,y_r1)、(x_r2,y_r2) The pixel coordinates for the two feature points correspond to the coordinates on the virtual reference sphere.

As an alternative implementation manner, in step 5) of this embodiment, the abscissa { (x) is used_m,y_m) And abscissa { (x)_r,y_r) The interpolation is carried out in a grid interpolation mode: in the step 5), the abscissa (x) is utilized_m,y_m) And abscissa { (x)_r,y_r) Interpolating to obtain the horizontal coordinate (x) of the virtual reference sphere_rt,y_rt) Corresponding abscissa (x) on the measured mirror surface_mt,y_mt) Comprises the following steps: calculating the abscissa { (x)_r,y_r) Delaunay triangulation of (x) }, as shown in FIG. 5, find the horizontal coordinates (x) of the virtual reference sphere_rt,y_rt) Corresponding triangle vertex (x)_ra,y_ra)、(x_rb,y_rb)、(x_rc,y_rc) And its corresponding abscissa (x) on the measured mirror surface_ma,y_ma)、(x_mb,y_mb)、(x_mc,y_mc) Calculating the horizontal coordinate (x) of the virtual reference sphere by a linear weighted average method_rt,y_rt) Corresponding to the abscissa (x) of the measured mirror surface_mt,y_mt)。

In this embodiment, the virtual reference spherical upper cross is calculated by a linear weighted average methodCoordinate (x)_rt,y_rt) Corresponding to the abscissa (x) of the measured mirror surface_mt,y_mt) The function expression of (a) is as follows:

x_mt＝(1-β-γ)x_ma+βx_mb+γx_mc,y_mt＝(1-β-γ)y_ma+βy_mb+γy_mc

in the above formula, (x)_mt,y_mt) For a virtual reference sphere abscissa (x)_rt,y_rt) Corresponding to the abscissa (x) of the measured mirror surface_mt,y_mt) Beta and gamma are weight factors, (x)_ma,y_ma)、(x_mb,y_mb)、(x_mc,y_mc) Respectively representing the horizontal coordinate (x) of the virtual reference sphere_rt,y_rt) Corresponding triangle vertex (x)_ra,y_ra)、(x_rb,y_rb)、(x_rc,y_rc) And the horizontal coordinate on the corresponding measured mirror surface.

In this embodiment, the weighting factors β ≧ 0, γ ≧ 0, β + γ ≦ 1, represented by the abscissa (x)_rt,y_rt) To triangle vertex (x)_ra,y_ra)、(x_rb,y_rb)、(x_rc,y_rc) Determining the reciprocal of the distance of (a); referring to FIG. 5, the virtual reference sphere is referenced to the horizontal coordinate (x)_rt,y_rt) The corresponding triangle specifically means: the abscissa is (x)_rt,y_rt) At the vertex coordinate of (x)_ra,y_ra)、(x_rb,y_rb)、(x_rc,y_rc) Within the triangular convex hull.

In this embodiment, the abscissa { (x) is used in step 5)_m,y_m) And abscissa { (x)_r,y_r) The manner of interpolating into grid interpolation is only an example of two-dimensional point set data interpolation, and in this start, a person skilled in the art may use other two-dimensional interpolation methods to calculate the coordinate values as needed, for example, bilinear interpolation method, bicubic interpolation method, and the like.

In addition, the present embodiment also provides a projection distortion correction system in optical profile compensation interferometry, which includes a microprocessor and a memory connected to each other, wherein the microprocessor is programmed or configured to execute the steps of the projection distortion correction method in optical profile compensation interferometry.

In addition, the present embodiment also provides a projection distortion correction system in optical profile compensation interferometry, which includes a microprocessor and a memory connected to each other, wherein the memory stores therein a computer program programmed or configured to execute the projection distortion correction method in optical profile compensation interferometry.

Furthermore, the present embodiment also provides a computer-readable storage medium having stored therein a computer program programmed or configured to execute the aforementioned projection distortion correction method in optical surface shape compensation interferometry.

As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-readable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein. The present application is directed to methods, apparatus (systems), and computer program products according to embodiments of the application wherein instructions, which execute via a flowchart and/or a processor of the computer program product, create means for implementing functions specified in the flowchart and/or block diagram block or blocks. These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks. These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.

The above description is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above embodiments, and all technical solutions belonging to the idea of the present invention belong to the protection scope of the present invention. It should be noted that modifications and embellishments within the scope of the invention may occur to those skilled in the art without departing from the principle of the invention, and are considered to be within the scope of the invention.