Data processing method for detecting cylindrical mirror based on three-coordinate profile measuring instrument

Abstract

A kind of data processing method for detecting cylindrical mirror based on three-coordinate profile measuring instrument, it is related to optical processing detection technical field, and the method includes the following steps: step S1: cylindrical surface is measured using three-coordinate measuring machine, obtains a group of cylindrical surface three-coordinate values as [x, y, z], wherein x is non-plane direction coordinate value, y is plane direction coordinate value, and z is vector height direction coordinate value;Step S2: using conic section and least square method fitting method, corrects three-coordinate measurement cylindrical original data around z rotation error and in plane direction inclination error, solves the cylindrical vector height z' after correction error;Step S3: remove the high order term part contained in cylindrical surface equation;Step S4: using linear fitting algorithm, fitting cylindrical surface type, solves the cylindrical vector height z'';Step S5: the cylindrical vector height z' solved in step S2 is subtracted from the cylindrical vector height z'' solved in step S4, and the detection surface type residual σ is obtained, and the method improves the accuracy of surface type information when three-coordinate or other profilometer detects cylindrical mirror.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of optical processing detection technology, and can be used for processing and detection of aspherical cylindrical lens and spherical cylindrical lens, and particularly relates to a data processing method for detecting cylindrical lens based on a three-coordinate profile measuring instrument. BACKGROUND

[0002] As an aspherical lens, the intersection of the meridian and sagittal cross sections of the cylindrical lens is a straight line formed by the intersection of two circular arcs and two parallel lines. With the development of science and technology, the cylindrical lens has a wide range of applications in civil products such as photographic equipment, bar codes, medical devices, and plays an important role in military fields such as aerospace and laser emitters. However, the cylindrical lens does not have rotational symmetry, and the processing technology is relatively complex, and the detection is also relatively difficult. The detection of the cylindrical lens mainly includes the sample plate method, the profilometer method, the computer holographic method, and the standard cylindrical lens method. In the early stage of high-precision aspherical cylindrical lens processing, that is, the grinding and rough polishing stage, the lens surface is not bright, and the interference detection cannot be performed. Therefore, the three-coordinate profile measurement technology becomes the main detection means for surface error in the early stage of processing.

[0003] In three-coordinate measurement, the measurement error caused by the machine precision and various unavoidable adjustment errors causes certain difficulties in the detection data analysis of the cylindrical lens, which is a special aspherical lens. In order to improve the early processing precision, accurate detection of surface residual error is used to determine the polishing amount of the lens, which is an effective way to improve the processing efficiency of optical aspherical surface. Therefore, a reliable and high-precision detection data processing method is a key factor for determining the processing efficiency of the cylindrical lens. SUMMARY

[0004] In view of the above problems of the prior art, the present application provides a data processing method for detecting a cylindrical lens based on a three-coordinate profile measuring instrument, which can solve the technical problem that the original data cannot be directly used to guide the processing due to the measurement error in the three-coordinate measurement method.

[0005] In order to achieve the above-mentioned purpose, the present application provides the following technical scheme:

[0006] The data processing method for detecting a cylindrical lens based on a three-coordinate profile measuring instrument comprises the following steps:

[0007] Step S1: measuring the cylindrical lens by using a three-coordinate measuring machine to obtain a group of cylindrical three-coordinate values [x, y, z], wherein x is a non-planar coordinate value, y is a planar coordinate value, and z is a height direction coordinate value;

[0008] Step S2: using the conic curve and the least square method fitting method, correcting the rotation error of the three-coordinate measurement cylinder original data around z and the tilt error in the plane direction, solving the cylinder height z' after the correction error;

[0009] Step S3: removing the high-order term part contained in the cylinder equation;

[0010] Step S4: using the linear fitting algorithm, fitting the cylinder surface, solving the cylinder height z'';

[0011] Step S5: subtracting the cylinder height z' solved in step S2 from the cylinder height z'' solved in step S4, obtaining the detection surface residual σ.

[0012] Preferably, the method only corrects the tilt error in a single plane direction.

[0013] Compared with the prior art, the beneficial effects of the present application are:

[0014] (1) The method of the present application uses the conic curve equation and the least square method to correct the rotation error and the tilt error in the plane direction of the measurement data, avoiding the inaccurate fitting caused by the 45° astigmatism of the rotation error on the surface fitting;

[0015] (2) The previous data processing method adopts the method of correcting the tilt error of the entire surface, but since the cylinder fitting surface will correct the translation in the non-plane direction, this method will cause the coma to occur in the subsequent surface fitting in the non-plane direction, therefore, the method of the present application only corrects the tilt error in a single plane direction, which can avoid the occurrence of the coma;

[0016] (3) The method of the present application uses the linear fitting algorithm to fit the cylinder surface, realizes the rapid calculation, and improves the accuracy of the fitted surface.

[0017] (4) The application discloses a data processing method for detecting a cylindrical lens based on a three-coordinate profile measuring instrument, and the implementation process of the method comprises the following steps: S1: a three-coordinate measuring machine is used to measure the cylindrical lens, and a group of three-coordinate values of the cylindrical lens, namely [x, y, z], are obtained, wherein x is a non-planar direction coordinate value, y is a planar direction coordinate value, and z is a height direction coordinate value; S2: a conic curve and a least square method fitting method are used to correct the rotation error of the three-coordinate measurement cylindrical original data around z and the tilt error in the planar direction, and the cylindrical height z' after the correction error is solved; S3: the high-order term part contained in the cylindrical equation is removed; S4: a linear fitting algorithm is used to fit the cylindrical surface type, and the cylindrical height z'' is solved; and S5: the cylindrical height z' solved in the step S2 is subtracted from the cylindrical height z'' solved in the step S4, and the detection surface type residual σ is obtained. The conic curve formula and the least square method fitting are used to correct the tilt and rotation error, the linear fitting algorithm is used to fit the surface type, the detection surface type residual σ is calculated, the accuracy of the surface type information when the three-coordinate or other profile instrument detects the cylindrical lens is improved, and the method can be applied to the fields of optical processing and detection of aspherical cylindrical lenses and spherical cylindrical lenses. BRIEF DESCRIPTION OF DRAWINGS

[0018] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments. Obviously, the drawings described in the following description are only some embodiments of the present application, and other drawings can also be obtained by those skilled in the art according to these drawings.

[0019] Figure 1 is a flowchart of the present application;

[0020] Figure 2 is a group of cylindrical lens three-coordinate measurement example diagrams;

[0021] Figure 3 is a 45° astigmatism error example diagram caused by the z rotation error of the present application;

[0022] Figure 4 is a surface shape residual example diagram after the three-coordinate detection cylindrical lens data processing. DETAILED DESCRIPTION

[0023] The content of the present application will be described in detail in the form of examples in combination with the drawings of the specification. Obviously, the described embodiments are only some embodiments of the present application, not all embodiments.

[0024] The data processing method for detecting the cylindrical lens based on the three-coordinate profile measuring instrument, as shown in Figure 1 , comprises the following steps:

[0025] Step S1: measuring the cylindrical surface by using a three-coordinate or other profilometer to obtain a set of three-coordinate values of the cylindrical surface as [x, y, z], wherein x is a non-planar coordinate value, y is a planar coordinate value, and z is a height direction coordinate value, as shown in the following figure: Figure 2

[0026] The step S1 is specifically: measuring the cylindrical surface by using a three-coordinate measuring machine to obtain a set of three-coordinate values of the cylindrical surface as [x, y, z], and a general cylindrical surface equation is:

[0027]

[0028] wherein c is a curvature, k is a conic coefficient, and A1 and A2 are high-order coefficients.

[0029] Step S2: correcting the 45° astigmatism error caused by the z rotation error of the three-coordinate measurement cylindrical original data and the tilt error in the planar direction by using a conic curve and a least square fitting method, the method only corrects a single planar tilt error, and the cylindrical height z' after the correction error is solved, as shown in the following figure: Figure 3

[0030] The step S2 is specifically: correcting the 45° astigmatism error caused by the z rotation error of the three-coordinate measurement cylindrical original data and the tilt error in the planar direction by using a conic curve and a least square fitting method. The conic curve equation is: z=ax 2 +by 2 +cxy+dx+ey+f, and the related coefficients are solved by using a least square method:

[0031] Let F(x, y, z)=(ax 2 +by 2 +cxy+dx+ey+f-z) 2

[0032]

[0033]

[0034]

[0035]

[0036]

[0037]

[0038] ​​After solving the six-element linear equation, a, b, c, d, e, and f are obtained. According to the geometric properties of the conic curve equation, c is the rotation parameter of the three-dimensional data, d is the inclination parameter in the x direction, and e is the inclination parameter in the y direction. The y direction is the plane direction, so the corrected error of the height z' is:

[0039] z' = z - (cxy + ey + f)

[0040] Step S3: remove the high-order term part contained in the cylindrical surface equation;

[0041] The step S3 is specifically: if the cylindrical surface is a high-order term-containing aspherical cylindrical surface, the linear fitting surface type cannot be directly used, and the high-order term part needs to be removed, that is:

[0042] z = z' - (A1x 2 +A2x 4 +...)

[0043] Step S4: use a linear fitting algorithm to fit the cylindrical surface type and solve the cylindrical surface height z'';

[0044] The step S4 is specifically: using a linear fitting algorithm to fit the cylindrical surface type, and based on the cylindrical surface model:

[0045] (x-b x ) 2 = 2r(z'-b z )-(1+k)(z'-b z ) 2

[0046] Where b x is the x-direction eccentricity, and b z is the z-direction eccentricity.

[0047] The above formula is converted to:

[0048] x 2 +z' 2 = 2[r+b z (1+k)]z'-kz' 2 -2rb z -(1+k)b z 2 +2xb x

[0049] Let

[0050] A = x 2 +z' 2 ,

[0051] a1 = r + b z (1+k),

[0052] a2=k,

[0053] a3=2rb z +(1+k)b z 2 ,

[0054] a4=bx,

[0055] E=[2z',-z' 2 ,-1,2x]

[0056] The above formula is:

[0057]

[0058]

[0059] Obtained:

[0060]

[0061] The sag of the cylindrical surface is:

[0062]

[0063] Step S5: subtract the cylindrical surface sag z' solved in step S2 from the cylindrical surface sag z'' solved in step S4 to obtain the detection surface shape residual σ, as shown in the formula: Figure 4

[0064] The step S5 is specifically: subtract the cylindrical surface sag z' solved in step S2 from the cylindrical surface sag z'' solved in step S4 to obtain the detection surface shape residual σ.

[0065] σ=z'-z"

[0066] The application can be applied to guide the optical processing of the cylindrical mirror. Since there is an original measurement error, the data processing method provided by the application can accurately calculate the detection surface shape residual to determine the polishing amount of the mirror surface, thereby effectively improving the optical processing precision and efficiency of the cylindrical mirror.

[0067] The above is only the preferred specific embodiment of the application, but the protection scope of the application is not limited to this. Any person skilled in the art can make equivalent replacement or change according to the technical solution and application concept of the application within the technical range disclosed by the application, which should be covered in the protection scope of the application.​

Claims

1. A data processing method for detecting cylindrical mirrors based on a coordinate measuring machine, characterized in that, This method corrects tilt errors in a single plane direction only, and includes the following steps: Step S1: Measure the cylindrical surface using a coordinate measuring machine to obtain a set of cylindrical surface coordinate values. , where x is the coordinate value in the non-planar direction, y is the coordinate value in the planar direction, and z is the coordinate value in the sag direction; Step S2: Using conic sections and the least squares fitting method, correct the rotation error around the z-axis and the tilt error in the plane direction of the original coordinate measuring machine cylinder data, and solve for the cylinder sagitta after error correction. ; Step S3: Remove the higher-order terms contained in the cylindrical equation; Step S4: Use a linear fitting algorithm to fit the cylindrical surface shape and solve for the cylindrical sag. ; Step S5: Obtain the cylindrical sagitta from step S2. The cylindrical sagitta obtained in step S4 By subtracting, the residual of the detected surface shape is obtained. .

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