CN102128599A - Contact aspheric surface shape test device - Google Patents

Abstract

The invention relates to a contact-type aspheric surface shape inspection device, which includes a computer and a laser tracker; the computer uses the laser tracker to measure the position coordinates of the feature points on the aspheric surface to be tested and the positions of the corresponding feature points on the CAD model Coordinates, through coordinate transformation, the physical coordinate system of the aspheric surface to be measured at this time and the coordinate system of the CAD model are transferred to the same coordinate system; then the position coordinates of multiple points on the aspheric surface to be measured under the unified coordinate system measured by the laser tracker Perform interpolation calculation to obtain the position coordinates of each point on the aspheric surface to be measured; finally analyze and solve to obtain the deviation between the coordinate values of each point on the aspheric surface to be measured in the unified coordinate system and the corresponding coordinate values of each point on the CAD digital model, and Fit the deviation data to obtain the distribution of the aspheric surface shape to be measured. The invention has simple data processing and mathematical operation, simple and easy experimental operation, low detection cost and short test time, and is suitable for surface shape detection in the whole process of aspheric surface processing.

Description

Contact aspheric surface verifying attachment

Technical field

The present invention relates to a kind of contact surface shape of optical aspheric surface verifying attachment.

Background technology

Current, the method for check non-spherical element has a variety of, mainly is divided into contact type measurement and non-contact measurement.Contact type measurement mainly by contourgraph or three-coordinates measuring machine by optical element is carried out the measurement of a plurality of discrete points, pass through data processing then, match obtains face shape error.Non-contact measurement mainly contains shadowing method, laser scanning method, interferometric method etc.Shadowing method mainly is divided into knife-edge method and Hartmann's method (diaphragm method), and this method is mainly observed the light and shade contrast of the figure and the echo of shade distribution.This method equipment is simple, and it is convenient to measure for some quadric surface, is suitable for field test.But exist subjective, quantitative difficulty, sensitivity to owe high shortcoming.Laser scanning method can divide translation method, rotary process, and the translation rotary process, and this is that a kind of rectilinearity of light of utilizing is carried out the method that face shape is detected, and can calculate aspheric shape parameter by with laser beam tested surface being carried out point-to-point measurement.Its highly versatile can be measured various aspheric surfaces, and is that tested surface is carried out absolute measurement, the precision height, and shortcoming is corresponding data processing more complicated.Interferometric method is a kind of short time to detect aspheric method, because it has advantages such as high-resolution, high precision, high sensitivity, good reproducibility, but when utilizing this commercial measurement aspheric surface, require non-spherical surface that good smooth finish and very high reflection potential are arranged.Therefore, interferometric method generally is applicable to the detection of aspheric surface finishing polish and terminal stage.

Summary of the invention

The technical problem to be solved in the present invention provides a kind of contact aspheric surface verifying attachment that is applicable to the whole process of aspherical mirror machining, this device can directly be realized aspheric measurement, data processing and mathematical operation are simple, experimental implementation is simple, and Measuring Time is short, testing cost is low.

In order to solve the problems of the technologies described above, contact aspheric surface verifying attachment of the present invention comprises computing machine and laser tracker; Described computing machine comprises device, the coordinate transformation device of storing aspheric surface cad model to be measured, finds the solution the device of position coordinates and finds the solution the device that aspheric surface to be measured distributes; Laser tracker is at first measured the position coordinates of unique point on the aspheric surface to be measured and it is transferred to coordinate transformation device, the position coordinates of characteristic of correspondence point on the position coordinates of unique point and the cad model on the aspheric surface of measuring by the coordinate transformation device utilization to be measured, find the solution translational movement and the rotation amount that obtains between aspheric surface to be measured, two coordinate systems of cad model by coordinate transform, physical coordinates system at this moment is unified to the same coordinate system with the coordinate system of cad model with aspheric surface to be measured; Laser tracker is measured under unified coordinate system on the aspheric surface to be measured the position coordinates of multiple spot and it is transferred to the device of finding the solution position coordinates, under the unified coordinate system that records by the device utilization of finding the solution position coordinates on the aspheric surface to be measured the position coordinates of multiple spot carry out the position coordinates that interpolation calculation obtains each point on the aspheric surface to be measured; Find the solution device analysis that aspheric surface to be measured distributes and find the solution the deviation that obtains under the unified coordinate system on the aspheric surface to be measured between the each point coordinate figure corresponding on the coordinate figure of each point and CAD digital-to-analogue, and deviation data is carried out match, obtain aspheric surface distribution to be measured.

Three points of described unique point for setting on aspheric surface to be measured are as the lightweight circular hole at side or back, the center of circle of taper hole or tri-angle-holed center etc.

The present invention is by expanding the existing capability of laser tracker, utilize the target ball of laser tracker that non-spherical surface is carried out the multiple spot contact measurement, and the result that will measure and data model are analyzed contrast, processing and computing, obtain aspheric shape distributed intelligence, need not other auxiliary optical component and just can realize detection accurately aperture aspherical face shape.Data processing of the present invention and mathematical operation are simple, and experimental implementation is simple, and it is very low to detect cost, and the test duration is short, are applicable to that the face shape of the whole process of aspherical mirror machining is detected.

Description of drawings

Below in conjunction with the drawings and specific embodiments the present invention is described in further detail.

Fig. 1 is a contact aspheric surface verifying attachment structural representation of the present invention.

Fig. 2 is a computer measurement software function module synoptic diagram.

Fig. 3 is a non-spherical structure synoptic diagram to be measured.

Fig. 4 is the process flow diagram that utilizes the present invention that aspheric surface is tested.

Embodiment

As shown in Figure 1, contact aspheric surface verifying attachment of the present invention comprises computing machine 1 and laser tracker 2; Described laser tracker 2 and computing machine 1 are connected by data line.

Laser tracker 2 is a kind of high precision, jumbo portable three coordinate measurment instruments, and this laser tracker uses two rotary angle encoders and a laser distance measuring system, with the position of tracking and measurement target drone ball 3.Target ball 3 is made up of hollow corner cube mirror, and this catoptron accurately is fixed in the processing spheroid.Outer surface of spheroid is to the distance at center known (being radius of sphericity), and the laser tracker Survey Software utilizes radius of sphericity to measure skew or compensating measure.Laser tracker emission also receives the red He-Ne Lasers that returns from the target ball, and two rotary angle encoders and Range Measurement System feedack that the direction of laser tracker mechanical axis can receive according to the location sensitive detector of its inside are constantly adjusted.Laser tracker is determined the coordinate of target by measuring two angles and distance.These angles are measured by the scrambler that is installed on angle, summit axle and the azimuth axis.Radial distance is to be measured by fringe count micrometer or a kind of phase deviation absolute distance measurement system (XtremeADM).Laser tracker generally is used for the relative position relation between the Measuring Object, and can the Direct Test plane and the face shape of sphere object, but but can not realize Direct Test for the face shape of non-spherical element.

As shown in Figure 2, the Survey Software of described computing machine 1 comprises device 11, the coordinate transformation device 12 of storing aspheric surface cad model to be measured, finds the solution the device 13 of position coordinates and finds the solution the device 14 that aspheric surface to be measured distributes.

Described coordinate transformation device 12 is searched aspheric cad model to be measured, extracts the unique point p that measures with laser tracker 2 ₁(x ₁, y ₁, z ₁), p ₂(x ₂, y ₂, z ₂) and p ₃(x ₃, y ₃, z ₃) the position coordinates P of unique point on the corresponding cad model ₁(X ₁, Y ₁, Z ₁), P ₂(X ₂, Y ₂, Z ₂) and P ₃(X ₃, Y ₃, Z ₃), as shown in Figure 3; By the Nonlinear System of Equations of solution by iterative method formula (1) and formula (5) simultaneous, the translational movement d of coordinate system on x direction, y direction, z direction that to obtain aspheric physical coordinates to be measured be relative cad model _x, d _yAnd d _zAnd the aspheric physical coordinates to be measured coordinate system that is relative cad model is around angle of rotation tolerance α, the β and the γ of x axle, y axle, z axle, and then two coordinate systems are unified to the same coordinate system;

$\left\{\begin{array}{c}(x_1,y_1,z_1,1)=(X_1,Y_1,Z_1,1)\&CenterDot;V\\ (x_2,y_2{,z}_2,1)=(X_2,Y_2,Z_2,1)\&CenterDot;V\\ (x_3,y_3,z_3,1)=(X_3,{\mathrm{<figure-callout\; id="3"\; label="Y"\; filenames="HDA0000040780800000011.png"\; state="\{\{state\}\}">Y</figure-callout>}}_3,Z_3,1)\&CenterDot;V\end{array}\right.---\left(1\right)$

$V=\left[\begin{array}{cccc}\cos \mathrm{\&beta;}\cos \mathrm{\&gamma;}& \cos \mathrm{\&beta;}\sin \mathrm{\&gamma;}& -\sin \mathrm{\&beta;}& 0\\ \sin \mathrm{\&alpha;}\sin \mathrm{\&beta;}\cos \mathrm{\&gamma;}-\cos \mathrm{\&alpha;}\sin \mathrm{\&gamma;}& \sin \mathrm{\&alpha;}\sin \mathrm{\&beta;}\sin \mathrm{\&gamma;}+\cos \mathrm{\&alpha;}\cos \mathrm{\&gamma;}& \sin \mathrm{\&alpha;}\cos \mathrm{\&beta;}& 0\\ \cos \mathrm{\&alpha;}\sin \mathrm{\&beta;}\cos \mathrm{\&gamma;}+\sin \mathrm{\&alpha;}\sin \mathrm{\&gamma;}& \cos \mathrm{\&alpha;}\sin \mathrm{\&beta;}\sin \mathrm{\&gamma;}-\sin \mathrm{\&alpha;}\cos \mathrm{\&gamma;}& \cos \mathrm{\&alpha;}\cos \mathrm{\&beta;}& 0\\ d_x& d_y& d_z& 1\end{array}\right]---\left(5\right)$

(x wherein ₁, y ₁, z ₁, 1) and be p ₁(x ₁, y ₁, z ₁) the coordinate row matrix of point in aspheric physical coordinates to be measured is, (X ₁, Y ₁, Z ₁, 1) be and p ₁(x ₁, y ₁, z ₁) put corresponding P ₁(X ₁, Y ₁, Z ₁) the coordinate row matrix of point in the cad model coordinate system; (x ₂, y ₂, z ₂, 1) and be p ₂(x ₂, y ₂, z ₂) the coordinate row matrix of point in aspheric physical coordinates to be measured is, (X ₂, Y ₂, Z ₂, 1) be and p ₂(x ₂, y ₂, z ₂) put corresponding P ₂(X ₂, Y ₂, Z ₂) the coordinate row matrix of point in the cad model coordinate system; (x ₃, y ₃, z ₃, 1) and be p ₃(x ₃, y ₃, z ₃) the coordinate row matrix of point in aspheric physical coordinates to be measured is, (X ₃, Y ₃, Z ₃, 1) be and p ₃(x ₃, y ₃, z ₃) put corresponding P ₃(X ₃, Y ₃, Z ₃) the coordinate row matrix of point in the cad model coordinate system; d _x, d _yAnd d _zBeing respectively aspheric physical coordinates to be measured is the translational movement of relative cad model coordinate system on x direction, y direction, z direction, and it is the angle of rotation tolerance of relative cad model coordinate system around x axle, y axle, z axle that α, β are respectively aspheric physical coordinates to be measured with γ.

Described unique point p ₁(x ₁, y ₁, z ₁), p ₂(x ₂, y ₂, z ₂) and p ₃(x ₃, y ₃, z ₃) be the lightweight circular hole at aspheric surface to be measured side or back, the center of circle of taper hole or tri-angle-holed center.Can measure the coordinate of any three points on circular hole or the taper hole edge by elder generation, and then calculate its central coordinate of circle; The coordinate at tri-angle-holed center can utilize the coordinate on an Atria summit by calculating.

Described device 13 of finding the solution position coordinates utilizes the position coordinates of multiple spot on the aspheric surface that measures, and calculates by cubic spline interpolation or Newton interpolation method and finds the solution the position coordinates that obtains each point on the aspheric surface.

As shown in Figure 4, the step of utilizing the present invention that aspheric surface is tested is as follows:

1) at first, sets up aspheric cad model to be measured, and this cad model is imported in the Survey Software of computing machine 1;

2) utilize laser tracker 2 to measure three unique point p at aspheric surface to be measured side or back ₁, p ₂And p ₃Position coordinates p ₁(x ₁, y ₁, z ₁), p ₂(x ₂, y ₂, z ₂) and p ₃(x ₃, y ₃, z ₃);

3) search aspheric cad model, extract and the unique point p that measures ₁(x ₁, y ₁, z ₁), p ₂(x ₂, y ₂, z ₂) and p ₃(x ₃, y ₃, z ₃) the position coordinates P of unique point on the corresponding CAD digital-to-analogue ₁(X ₁, Y ₁, Z ₁), P ₂(X ₂, Y ₂, Z ₂) and P ₃(X ₃, Y ₃, Z ₃);

4), can find the solution and obtain two translational movement and rotation amounts between the coordinate system, thereby make that aspheric surface to be measured physical coordinates system at this moment is consistent with the coordinate system of cad model by coordinate transform;

The specific algorithm step is as follows:

Set p ₁The coordinate representation of point in aspheric physical coordinates to be measured is is row matrix (x ₁, y ₁, z ₁, 1), with p ₁Corresponding P ₁The coordinate representation of point in the cad model coordinate system is row matrix (X ₁, Y ₁, Z ₁, 1); Suppose that the translational movement of coordinate system on x direction, y direction, z direction that aspheric physical coordinates to be measured is relative cad model is respectively d _x, d _yAnd d _zThe coordinate system that aspheric physical coordinates to be measured is relative cad model is respectively α, β and γ around the angle of rotation tolerance of x axle, y axle, z axle, then according to the coordinate transform theory, the position coordinates of character pair has following relation on feature locations coordinate that aspheric physical coordinates to be measured is fastened and the cad model:

$\left\{\begin{array}{c}(x_1,y_1,z_1,1)=(X_1,Y_1,Z_1,1)\&CenterDot;V\\ (x_2,y_2{,z}_2,1)=(X_2,Y_2,Z_2,1)\&CenterDot;V\\ (x_3,y_3,z_3,1)=(X_3,{\mathrm{<figure-callout\; id="3"\; label="Y"\; filenames="HDA0000040780800000011.png"\; state="\{\{state\}\}">Y</figure-callout>}}_3,Z_3,1)\&CenterDot;V\end{array}\right.---\left(1\right)$

Wherein V is two transformation matrixs between the coordinate system, and it is the product between translation transformation matrix T and the rotational transform matrix R, that is:

V＝T·R (2)

$T=T_x.T_y{.T}_z=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& 1& 0\\ d_x& 0& 0& 1\end{array}\right]\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& 1& 0\\ d_y& 0& 0& 1\end{array}\right]\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& 1& 0\\ d_z& 0& 0& 1\end{array}\right]=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& 1& 0\\ d_x& d_y& d_z& 1\end{array}\right]---\left(3\right)$

T wherein _x, T _yAnd T _zBe respectively the translation matrix of two row matrixs on x direction, y direction and z direction.

$R=R_x{\&CenterDot;R}_y\&CenterDot;R_z=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& \cos \mathrm{\&alpha;}& \sin \mathrm{\&alpha;}& 0\\ 0& -\sin \mathrm{\&alpha;}& \cos \mathrm{\&alpha;}& 0\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{cccc}\cos \mathrm{\&beta;}& 0& -\sin \mathrm{\&beta;}& 0\\ 0& 1& 0& 0\\ \sin \mathrm{\&beta;}& 0& \cos \mathrm{\&beta;}& 0\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{cccc}\cos \mathrm{\&gamma;}& \sin \mathrm{\&gamma;}& 0& 0\\ -\sin \mathrm{\&gamma;}& \cos \mathrm{\&gamma;}& 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& 1\end{array}\right]---\left(4\right)$

$=\left[\begin{array}{cccc}\cos \mathrm{\&beta;}\cos \mathrm{\&gamma;}& \cos \mathrm{\&beta;}\sin \mathrm{\&gamma;}& -\sin \mathrm{\&beta;}& 0\\ \sin \mathrm{\&alpha;}\sin \mathrm{\&beta;}\cos \mathrm{\&gamma;}-\cos \mathrm{\&alpha;}\sin \mathrm{\&gamma;}& \sin \mathrm{\&alpha;}\sin \mathrm{\&beta;}\sin \mathrm{\&gamma;}+\cos \mathrm{\&alpha;}\cos \mathrm{\&gamma;}& \sin \mathrm{\&alpha;}\cos \mathrm{\&beta;}& 0\\ \cos \mathrm{\&alpha;}\sin \mathrm{\&beta;}\cos \mathrm{\&gamma;}+\sin \mathrm{\&alpha;}\sin \mathrm{\&gamma;}& \cos \mathrm{\&alpha;}\sin \mathrm{\&beta;}\sin \mathrm{\&gamma;}-\sin \mathrm{\&alpha;}\cos \mathrm{\&gamma;}& \cos \mathrm{\&alpha;}\cos \mathrm{\&beta;}& 0\\ 0& 0& 0& 1\end{array}\right]$

R wherein _x, R _yAnd R _zBe respectively the rotation matrix of two row matrixs on x direction, y direction and z direction.

Then can being derived by (3)-(4), to obtain two transformation matrix V between the coordinate system be formula (5),

$V=\left[\begin{array}{cccc}\cos \mathrm{\&beta;}\cos \mathrm{\&gamma;}& \cos \mathrm{\&beta;}\sin \mathrm{\&gamma;}& -\sin \mathrm{\&beta;}& 0\\ \sin \mathrm{\&alpha;}\sin \mathrm{\&beta;}\cos \mathrm{\&gamma;}-\cos \mathrm{\&alpha;}\sin \mathrm{\&gamma;}& \sin \mathrm{\&alpha;}\sin \mathrm{\&beta;}\sin \mathrm{\&gamma;}+\cos \mathrm{\&alpha;}\cos \mathrm{\&gamma;}& \sin \mathrm{\&alpha;}\cos \mathrm{\&beta;}& 0\\ \cos \mathrm{\&alpha;}\sin \mathrm{\&beta;}\cos \mathrm{\&gamma;}+\sin \mathrm{\&alpha;}\sin \mathrm{\&gamma;}& \cos \mathrm{\&alpha;}\sin \mathrm{\&beta;}\sin \mathrm{\&gamma;}-\sin \mathrm{\&alpha;}\cos \mathrm{\&gamma;}& \cos \mathrm{\&alpha;}\cos \mathrm{\&beta;}& 0\\ d_x& d_y& d_z& 1\end{array}\right]---\left(5\right)$

Because three unique points coordinate figure in two coordinate systems respectively are known, by the Nonlinear System of Equations of solution by iterative method formula (1) and formula (5) simultaneous, the translational movement d of coordinate system on x direction, y direction, z direction that can to obtain aspheric physical coordinates to be measured be relative cad model _x, d _yAnd d _zAnd the aspheric physical coordinates to be measured coordinate system that is relative cad model is around angle of rotation tolerance α, the β and the γ of x axle, y axle, z axle, thereby two coordinate systems can be come together;

5) after two coordinate system unanimities, utilize laser tracker 1 to measure under unified coordinate system the position coordinates of multiple spot on the aspheric surface to be measured;

6) utilize the position coordinates of multiple spot on the aspheric surface to be measured measure, calculate by cubic spline interpolation and find the solution the position coordinates that obtains each point on the aspheric surface to be measured;

7) analysis and solution obtains under the unified coordinate system on the aspheric surface to be measured the deviation of each point coordinate figure on the coordinate figure of each point and corresponding cad model, and deviation data is carried out match, is aspheric shape to be measured and distributes.

Claims (3)

1. a contact aspheric surface verifying attachment is characterized in that comprising computing machine (1) and laser tracker (2); The device that described computing machine (1) comprises device (11), the coordinate transformation device (12) of storing aspheric surface cad model to be measured, find the solution position coordinates (13 and find the solution the device (14 that aspheric surface to be measured distributes; Laser tracker (2) is at first measured the position coordinates of unique point on the aspheric surface to be measured and it is transferred to coordinate transformation device (12), by the coordinate transformation device (position coordinates of characteristic of correspondence point on the position coordinates of unique point and the cad model on 12 aspheric surfaces of utilize measuring to be measured, find the solution translational movement and the rotation amount that obtains between aspheric surface to be measured, two coordinate systems of cad model by coordinate transform, physical coordinates system at this moment is unified to the same coordinate system with the coordinate system of cad model with aspheric surface to be measured; Laser tracker (2) is measured under unified coordinate system on the aspheric surface to be measured the position coordinates of multiple spot and it is transferred to the device (13) of finding the solution position coordinates, under the unified coordinate system that records by the device of finding the solution position coordinates (13) utilization on the aspheric surface to be measured the position coordinates of multiple spot carry out the position coordinates that interpolation calculation obtains each point on the aspheric surface to be measured; Find the solution device (14) analysis and solution that aspheric surface to be measured distributes and obtain under the unified coordinate system on the aspheric surface to be measured deviation between the each point coordinate figure corresponding on the coordinate figure of each point and CAD digital-to-analogue, and deviation data carried out match, obtain aspheric surface to be measured and distribute.

2. contact aspheric surface verifying attachment according to claim 1 is characterized in that described coordinate transformation device (12) searches aspheric cad model to be measured, extracts the unique point p that measures with laser tracker (2) ₁(x ₁, y ₁, z ₁), p ₂(x ₂, y ₂, z ₂) and p ₃(x ₃, y ₃, z ₃) the position coordinates P of unique point on the corresponding cad model ₁(X ₁, Y ₁, Z ₁), P ₂(X ₂, Y ₂, Z ₂) and P ₃(X ₃, Y ₃, Z ₃); By the Nonlinear System of Equations of solution by iterative method formula (1) and formula (5) simultaneous, the translational movement d of coordinate system on x direction, y direction, z direction that to obtain aspheric physical coordinates to be measured be relative cad model _x, d _yAnd d _zAnd the aspheric physical coordinates to be measured coordinate system that is relative cad model is around angle of rotation tolerance α, the β and the γ of x axle, y axle, z axle, and then two coordinate systems are unified to the same coordinate system;

$\left\{\begin{array}{c}(x_1,y_1,z_1,1)=(X_1,Y_1,Z_1,1)\&CenterDot;V\\ (x_2,y_2{,z}_2,1)=(X_2,Y_2,Z_2,1)\&CenterDot;V\\ (x_3,y_3,z_3,1)=(X_3,Y_3,Z_3,1)\&CenterDot;V\end{array}\right.---\left(1\right)$

$V=\left[\begin{array}{cccc}\cos \mathrm{\&beta;}\cos \mathrm{\&gamma;}& \cos \mathrm{\&beta;}\sin \mathrm{\&gamma;}& -\sin \mathrm{\&beta;}& 0\\ \sin \mathrm{\&alpha;}\sin \mathrm{\&beta;}\cos \mathrm{\&gamma;}-\cos \mathrm{\&alpha;}\sin \mathrm{\&gamma;}& \sin \mathrm{\&alpha;}\sin \mathrm{\&beta;}\sin \mathrm{\&gamma;}+\cos \mathrm{\&alpha;}\cos \mathrm{\&gamma;}& \sin \mathrm{\&alpha;}\cos \mathrm{\&beta;}& 0\\ \cos \mathrm{\&alpha;}\sin \mathrm{\&beta;}\cos \mathrm{\&gamma;}+\sin \mathrm{\&alpha;}\sin \mathrm{\&gamma;}& \cos \mathrm{\&alpha;}\sin \mathrm{\&beta;}\sin \mathrm{\&gamma;}-\sin \mathrm{\&alpha;}\cos \mathrm{\&gamma;}& \cos \mathrm{\&alpha;}\cos \mathrm{\&beta;}& 0\\ d_x& d_y& d_z& 1\end{array}\right]---\left(5\right)$

(x wherein ₁, y ₁, z ₁, 1) and be p ₁(x ₁, y ₁, z ₁) the coordinate row matrix of point in aspheric physical coordinates to be measured is, (X ₁, Y ₁, Z ₁, 1) be and p ₁(x ₁, y ₁, z ₁) put corresponding P ₁(X ₁, Y ₁, Z ₁) the coordinate row matrix of point in the cad model coordinate system; (x ₂, y ₂, z ₂, 1) and be p ₂(x ₂, y ₂, z ₂) the coordinate row matrix of point in aspheric physical coordinates to be measured is, (X ₂, Y ₂, Z ₂, 1) be and p ₂(x ₂, y ₂, z ₂) put corresponding P ₂(X ₂, Y ₂, Z ₂) the coordinate row matrix of point in the cad model coordinate system; (x ₃, y ₃, z ₃, 1) and be p ₃(x ₃, y ₃, z ₃) the coordinate row matrix of point in aspheric physical coordinates to be measured is, (X ₃, Y ₃, Z ₃, 1) be and p ₃(x ₃, y ₃, z ₃) put corresponding P ₃(X ₃, Y ₃, Z ₃) the coordinate row matrix of point in the cad model coordinate system; d _x, d _yAnd d _zBeing respectively aspheric physical coordinates to be measured is the translational movement of relative cad model coordinate system on x direction, y direction, z direction, and it is the angle of rotation tolerance of relative cad model coordinate system around x axle, y axle, z axle that α, β are respectively aspheric physical coordinates to be measured with γ.

3. contact aspheric surface verifying attachment according to claim 1, the position coordinates that it is characterized in that multiple spot on the aspheric surface that the described device (13) of finding the solution position coordinates utilization measures calculates by cubic spline interpolation or Newton interpolation and to find the solution the position coordinates that obtains each point on the aspheric surface.

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