CN111288933B - Automatic centering method for spherical or rotationally symmetric aspheric optical element - Google Patents

Automatic centering method for spherical or rotationally symmetric aspheric optical element Download PDF

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CN111288933B
CN111288933B CN202010127959.7A CN202010127959A CN111288933B CN 111288933 B CN111288933 B CN 111288933B CN 202010127959 A CN202010127959 A CN 202010127959A CN 111288933 B CN111288933 B CN 111288933B
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laser displacement
optical element
spherical
axis
displacement sensors
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CN111288933A (en
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刘�东
孙焕宇
王狮凌
张健浦
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Zhejiang University ZJU
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01BMEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00Measuring arrangements characterised by the use of optical techniques
    • G01B11/26Measuring arrangements characterised by the use of optical techniques for measuring angles or tapers; for testing the alignment of axes
    • G01B11/27Measuring arrangements characterised by the use of optical techniques for measuring angles or tapers; for testing the alignment of axes for testing the alignment of axes
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01BMEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00Measuring arrangements characterised by the use of optical techniques
    • G01B11/002Measuring arrangements characterised by the use of optical techniques for measuring two or more coordinates
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01MTESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M11/00Testing of optical apparatus; Testing structures by optical methods not otherwise provided for

Abstract

The invention discloses an automatic centering method of a spherical or rotationally symmetric aspheric optical element, which adopts an automatic centering device, wherein the automatic centering device comprises a sample table, a three-dimensional displacement table, three laser displacement sensors, a data acquisition unit, a data analysis processing unit and a control unit for receiving the feedback of the data analysis processing unit and controlling the three-dimensional displacement table to move to the position of an axis of the optical element; when the three laser displacement sensors are used for automatically centering, the relative distances of the three sampling points on the measured optical element are provided by the three laser displacement sensors at the same time, when the relative distances of the three sampling points are 0 or less than an allowable error threshold value, the cross section formed by the three sampling points can be considered as a circular cross section perpendicular to an optical axis, and the circle center is the position of the axis of the optical element. The invention is simple and easy to operate, does not need to rotate the spherical or rotationally symmetric aspheric optical element, reduces the mechanical design and assembly difficulty, and realizes the non-contact, rapid and automatic centering of the optical element.

Description

Automatic centering method for spherical or rotationally symmetric aspheric optical element
Technical Field
The invention belongs to the technical field of optics, and particularly relates to an automatic centering method for a spherical or rotationally symmetric aspheric optical element.
Background
In the field of surface defect detection of optical elements, a microscopic imaging system is mainly adopted to scan and image the surface of a detected sample, so that the appearance and distribution of surface defects are obtained. Spherical optical elements and rotationally symmetric aspherical optical elements play an important role as important means for achieving focusing and dispersion of light beams, but they pose great difficulties in surface defect detection due to their complex surface forms. When detecting spherical and rotationally symmetric aspheric optical elements, element centering needs to be completed first, and scanning path planning is performed by taking the position of an axis line as a reference point.
For example, chinese patent publication No. CN105157617A discloses an automatic centering method for spherical surface defect detection of a spherical optical element, which employs spherical reflection cross-hair imaging, utilizes a self-rotating table to drive a spherical optical element to be detected to rotate, observes position changes of the cross-hair, and fits the center of a circle of a cross-hair motion trajectory, thereby realizing the centering of the spherical optical element. However, the above method has high requirements on mechanical structures, and a self-rotating platform structure needs to be designed to drive the sample to rotate, so that the complexity of design, processing and adjustment is increased; and this method is not suitable for rotationally symmetric aspheric centering. The spherical and rotationally symmetric aspheric or rotationally symmetric aspheric optical elements are usually designed to have a structure with a curved front surface and a rectangular back surface, and the length and width dimensions of the optical elements have been developed to hundreds to thousands of millimeters, and the weight of the optical elements is hundreds of kilograms. Obviously, the self-rotating table structure will greatly increase the mechanical complexity of the centering system, increase the time required for centering, and is not suitable for the centering requirements of the current spherical and rotationally symmetric aspheric optical elements.
Therefore, there is a need for a simple and efficient apparatus and method for self-centering spherical and rotationally symmetric aspheric optical elements.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides an automatic centering method for a spherical or rotationally symmetric aspheric optical element, which realizes non-contact, rapid and automatic centering of the spherical and rotationally symmetric aspheric optical element.
The technical scheme of the invention is as follows:
an automatic centering method for a spherical or rotationally symmetric aspheric optical element adopts an automatic centering device, wherein the automatic centering device comprises a sample table, a three-dimensional displacement table, three laser displacement sensors arranged on the three-dimensional displacement table, a data acquisition unit electrically connected with the laser displacement sensors, a data analysis processing unit electrically connected with the data acquisition unit, and a control unit for receiving feedback of the data analysis processing unit and controlling the three-dimensional displacement table to move to the position of an axis of the optical element;
the method specifically comprises the following steps:
(1) calibrating the initial positions of the three laser displacement sensors;
(2) fixing a spherical or rotationally symmetric aspheric optical element to be centered on a sample table by adopting a vertical placing posture;
(3) moving X, Y two shafts of the three-dimensional displacement table to enable three sampling points of the three laser displacement sensors to be located on the surface of the spherical optical element; wherein the X, Y axis of the three-dimensional displacement table is perpendicular to the optical axis of the optical element;
(4) moving the Z axis of the three-dimensional displacement table to enable all three laser displacement sensors to be located within the working distance, and obtaining the relative distance d between the three sampling points on the spherical or rotationally symmetrical aspheric optical element and the corresponding laser displacement sensors through the data acquisition unit1、d2、d3(ii) a Wherein the Z axis of the three-dimensional displacement table is parallel to the optical axis of the optical element;
(5) the control unit controls the three-dimensional displacement table to move along the Y axis until | d is satisfied1-d2| is less than Δ d, and Δ d is an allowable error threshold;
(6) the control unit controls the three-dimensional displacement table to move along the X axis until | d is satisfied2-d3| is less than Δ d, and Δ d is an allowable error threshold;
(7) if | d1-d2If | is more than delta d, repeating the step (5) to the step (6), feeding back the relative distance of the three sampling points in real time by the data analysis processing unit, and correcting the movement amount of the sample adjusting platform until | d is satisfied simultaneously1-d2|<Δd、|d2-d3If the | is less than the Δ d, the three laser displacement sensors form the outer center position of a triangle, namely the axial lead position of the optical element, so that the automatic centering of the spherical or rotationally symmetrical aspheric optical element is completed.
In the automatic centering device, an X, Y axis of the three-dimensional displacement table is vertical to an optical axis of the optical element, and can bear the laser displacement sensor to perform two-dimensional translation; the Z axis is parallel to the optical axis of the optical element and can bear the axial translation of the laser displacement sensor. The measuring directions of the three laser displacement sensors are parallel to the Z axis, and the relative distances from three sampling points on the optical element to the laser displacement sensors are provided.
The three laser displacement sensors are arranged on the three-dimensional displacement platform in a triangular shape.
Preferably, the three laser displacement sensors are arranged on the three-dimensional displacement table in a right triangle shape, and the connecting line of the mounting positions of the first laser displacement sensor and the second laser displacement sensor is parallel to the Y axis; and the connecting line of the mounting positions of the second laser displacement sensor and the third laser displacement sensor is parallel to the X axis.
The spherical or rotationally symmetrical aspheric optical element is fixed on the sample stage through a clamping mechanism.
Before centering, the initial positions of the three laser displacement sensors are firstly calibrated. The three sampling points form a section on the surface of the optical element, and any section perpendicular to the optical axis is circular according to the characteristics of the spherical surface and the rotation symmetry aspheric surface optical element. Therefore, when the relative distance between the three sampling points is 0 or less than the allowable error threshold, the cross section is considered to be a circular cross section perpendicular to the optical axis, the triangle formed by the three sampling points is an inscribed triangle of the circular cross section, and the center of the circle (the outer center of the triangle) is the axial lead of the optical element. During automatic centering, the data acquisition unit is connected with the three laser displacement sensors, receives the relative distance of the three sampling points in real time and transmits the relative distance to the data analysis processing unit. And after analysis and processing, feeding back to the displacement table control unit to control the three-dimensional displacement table to the position of the axis of the optical element so as to finish automatic centering. And in the centering process, the relative distance of the three sampling points is fed back in real time, the movement amount of the three-dimensional displacement table is corrected, and closed-loop control is realized.
The vertical placement posture means that the optical axis of the spherical or rotationally symmetric aspheric optical element is placed parallel to the horizontal plane.
The laser displacement sensor is a non-contact measuring sensor, and the linear distance between an object to be measured and the sensor is obtained by applying the laser triangular reflection principle.
The measuring direction of the laser displacement sensor is the emergent laser direction of the laser displacement sensor, namely the direction of the linear distance between the object to be measured and the sensor.
In the step (1), the specific steps of calibrating the initial positions of the three laser displacement sensors are as follows:
(1-1) adopting a vertical placing posture, and fixing a spherical or rotationally symmetric aspheric optical element for calibration on a sample table through a clamping mechanism;
(1-2) moving X, Y two shafts of the three-dimensional displacement platform to enable three sampling points of the three laser displacement sensors to be located on the surface of the optical element;
(1-3) moving the Z axis of the three-dimensional displacement table to enable all three laser displacement sensors to be located within the working distance of the three laser displacement sensors, and obtaining the relative distance between three sampling points on the spherical or rotationally symmetrical non-spherical optical element and the laser displacement sensors;
(1-4) using a three-dimensional displacement platform to bear a first laser displacement sensor, scanning two section lines of the spherical surface or the rotationally symmetric aspheric optical element along the direction X, Y respectively, and recording the coordinate position of the three-dimensional displacement platform and the relative distance d acquired by the first laser displacement sensor in real time1(ii) a In the X direction, d1When the minimum value is obtained, the corresponding X-axis coordinate of the three-dimensional displacement table is recorded as X1(ii) a In the Y direction, d1When the minimum value is obtained, the Y-axis coordinate of the corresponding three-dimensional displacement table is recorded as Y1;(X1,Y1) The calibration position of the first laser displacement sensor is obtained;
(1-5) repeating the method in step (4) to obtain the calibration position (X) of the second laser displacement sensor2,Y2) And the calibration position (X) of the third laser displacement sensor3,Y3);
(1-6) calculating coordinates (X)1,Y1)、(X2,Y2) And (X)3,Y3) The outscenters (a, b) of the triangle formed by the three points move the XY axes of the three-dimensional displacement table to the coordinate positions (a, b);
(1-7) relative distance d acquired by three laser displacement sensors1、d2、d3And setting the initial position of the three laser displacement sensors to be 0, and finishing the calibration of the initial positions of the three laser displacement sensors.
The purpose of calibrating the initial positions of the three laser displacement sensors is as follows: when the system is installed, three laser displacement sensors cannot be strictly ensured to be positioned in the same plane; therefore, before automatic centering, the initial relative distances of the three laser displacement sensors need to be calibrated to obtain the relative position information of the three laser displacement sensors. If the relative positions of the three laser displacement sensors are not changed, calibration work is only needed to be carried out when the system is used for the first time.
In the step (1-6), the coordinate positions (a, b) are calculated as follows:
Figure BDA0002394965110000051
Figure BDA0002394965110000052
in the steps (5) and (6), the allowable error threshold Δ d may be determined according to the measurement accuracy of the laser displacement sensor, and the threshold is generally set to be greater than the measurement accuracy of the laser displacement sensor.
Compared with the prior art, the invention has the following beneficial effects:
the invention provides a new device and a new method for the automatic centering of the spherical or rotationally symmetric aspheric optical element, and for the spherical and rotationally symmetric aspheric optical element, only the laser displacement sensor needs to be carried for three-dimensional movement, and a sample spinning platform structure is not needed, so that the mechanical design and the assembly and adjustment difficulty are greatly reduced; three laser displacement sensors are adopted for real-time closed-loop adjustment, full-aperture scanning of a sample is not needed, and centering speed and precision are greatly improved. The centering method has the advantages of simple operation, few steps, high speed, high efficiency and great engineering application value, and lays a foundation for the surface defect detection of the spherical and rotationally symmetric aspheric optical elements with high efficiency, high speed and high precision.
Drawings
FIG. 1 is a schematic view of the self-centering device of the present invention;
FIG. 2 is a schematic diagram of the calibration of the initial position of the laser displacement sensor according to the present invention;
FIG. 3 is a calibration curve diagram of the initial position of the laser displacement sensor according to the present invention;
FIG. 4 is a Y-axis centering process diagram of the three-dimensional displacement table;
FIG. 5 is a process diagram of X-axis centering of the three-dimensional translation stage;
FIG. 6 is a flowchart of a method for automatically centering a spherical or rotationally symmetric aspheric optical element according to the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings, in which the following embodiments are provided to facilitate understanding of the present invention and are not intended to limit the present invention in any way.
The method of the invention adopts an automatic centering device, as shown in figure 1, the optical element 7 is a plano-convex spherical optical element with the length of 800mm, the width of 600mm and the curvature radius of 2000mm, and is fixed on the sample platform in a vertical placement posture. The three laser displacement sensors are of the same type, the working distance is 90 +/-20 mm, the linear precision is +/-12 microns, and the allowable error threshold delta d is set to be 12 microns. The three laser displacement sensors are respectively as follows: the displacement sensor comprises a first laser displacement sensor 1, a second laser displacement sensor 2 and a third laser displacement sensor 3. The three-dimensional displacement table is a large-stroke high-precision three-dimensional displacement table, and the positioning precision of the three-dimensional displacement table is +/-10 mu m. Three laser displacement sensors are placed on the three-dimensional displacement table and are about 90mm away from the sample.
The X, Y axis of the three-dimensional displacement platform is perpendicular to the optical axis of the optical element 7, and can bear the laser displacement sensor to perform two-dimensional translation; the Z axis is parallel to the optical axis of the spherical optical element and can bear the axial translation of the laser displacement sensor; the origin 0 is located at the mechanical starting point of the XY axes of the three-dimensional displacement table.
The three laser displacement sensors are arranged in an XY plane, and connecting lines of the arrangement positions of the three laser displacement sensors form a triangle. The connecting line of the positions where the first laser displacement sensor 1 and the second laser displacement sensor 2 are placed is parallel to the Y axis, and the distance is 300 mm; the connecting line of the positions where the second laser displacement sensor 2 and the third laser displacement sensor 3 are placed is parallel to the X axis and is 300mm away. The measuring directions of the three laser displacement sensors are parallel to the Z axis, and the relative distances from three sampling points on the spherical optical element to the laser displacement sensors are provided. The first laser displacement sensor 1 corresponds to a sampling point 4, the second laser displacement sensor 2 corresponds to a sampling point 5, and the third laser displacement sensor 3 corresponds to a sampling point 6.
Referring to fig. 2, the calibration method for the initial positions of three laser displacement sensors is as follows:
step 1, adopting a vertical placement posture, and fixing a spherical or rotationally symmetric aspheric optical element 7 on a sample table through a clamping mechanism;
step 2, moving X, Y two shafts of the three-dimensional displacement table to enable three sampling points of the three laser displacement sensors to be located on the surface of the optical element 7;
step 3, moving the Z axis of the three-dimensional displacement table to enable all three laser displacement sensors to be located within the working distance, and obtaining the relative distance between three sampling points on the optical element 7 and the laser displacement sensors;
step 4, using the three-dimensional displacement table to bear the first laser displacement sensor 1, scanning two section lines (dotted lines) of the optical element 7 along the X, Y direction, recording the coordinate position of the three-dimensional displacement table in real time and the relative distance d acquired by the first laser displacement sensor 11. As shown in FIG. 3 (a), d is the X-axis1Plotting the curve for the ordinate, d1When the minimum value is obtained, the corresponding X-axis coordinate of the three-dimensional displacement table is recorded as X1(ii) a As shown in FIG. 3 (b), d is the abscissa of the Y-axis1Plotting the curve for the ordinate, d1When the minimum value is obtained, the Y-axis coordinate of the corresponding three-dimensional displacement table is recorded as Y1。(X1,Y1) Is the calibration position of the first laser displacement sensor 1;
and 5, repeating the method in the step 4 to obtain the calibration position (X) of the second laser displacement sensor 22,Y2) The calibration position (X) of the third laser displacement sensor 33,Y3). The initial position calibration results of the three laser displacement sensors are shown in table 1.
TABLE 1
Figure BDA0002394965110000071
Figure BDA0002394965110000081
Step 6, moving the three-dimensional displacement table to three laser displacement sensors to form triangular outsoles (a, b), wherein in the XY plane, the spherical surface is superposed with the axial lead and the outsoles of the rotationally symmetric aspheric optical element; the method for calculating the outer centers (a and b) of the triangles is as follows:
Figure BDA0002394965110000082
Figure BDA0002394965110000083
substitution of (X)1,Y1)、(X2,Y2)、(X3,Y3) The calculation results are a-411.2896 and b-320.8210.
Step 7, acquiring relative distances d of the three laser displacement sensors1、d2、d3And setting the initial position of the three laser displacement sensors to be 0, and finishing the calibration of the initial positions of the three laser displacement sensors.
As shown in fig. 6, the method for automatically centering an optical element of a spherical surface or a rotationally symmetric aspherical surface is as follows:
s01, adopting a vertical placement posture, and fixing the spherical or rotationally symmetric aspheric optical element 7 on the sample stage through a clamping mechanism.
And S02, moving two shafts X, Y of the three-dimensional displacement table to enable all three sampling points of the three laser displacement sensors to be located on the surface of the optical element 7.
S03, moving the Z axis of the three-dimensional displacement table to make the three laser displacement sensors all located within the working distance, and obtaining the relative distance d between the three sampling points on the optical element 7 and the laser displacement sensors1、d2、d3
S04, when the three-dimensional displacement table deviates from the axis position in the Y direction, | d1-d2I > Δ d, as shown in fig. 4 (a); the three-dimensional displacement table moves along the Y axis until | d is satisfied1-d2< Δ d, as shown in (b) of FIG. 4.
S05, when the three-dimensional displacement table deviates from the axis position in the X direction, | d2-d3I > Δ d Δ d, as shown in fig. 5 (a); the three-dimensional displacement table moves along the X axis until | d is satisfied2-d3< Δ d, as shown in (b) of FIG. 5.
S06, if so, | d1-d2If | is more than delta d, repeating the steps S04-S05, feeding back the relative distance of the three sampling points in real time, and correcting the movement amount of the three-dimensional displacement table until | d is satisfied simultaneously1-d2|<Δd、|d2-d3If the | is less than the Δ d, the three laser displacement sensors form the outer center of a triangle, namely the axial lead position of the optical element, and the automatic centering of the spherical and rotationally symmetrical aspheric optical element is completed.
The above description is only exemplary of the preferred embodiments of the present invention, and is not intended to limit the present invention, and any modifications, equivalents, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (7)

1. The automatic centering method of the spherical or rotationally symmetric aspheric optical element is characterized in that an automatic centering device is adopted, and the automatic centering device comprises a sample table, a three-dimensional displacement table, three laser displacement sensors arranged on the three-dimensional displacement table, a data acquisition unit electrically connected with the laser displacement sensors, a data analysis processing unit electrically connected with the data acquisition unit, and a control unit for receiving feedback of the data analysis processing unit and controlling the three-dimensional displacement table to move to the position of the axis of the optical element;
the method specifically comprises the following steps:
(1) calibrating the initial positions of the three laser displacement sensors;
(2) fixing a spherical or rotationally symmetric aspheric optical element to be centered on a sample table by adopting a vertical placing posture;
(3) moving X, Y two shafts of the three-dimensional displacement table to enable three sampling points of the three laser displacement sensors to be located on the surface of the spherical surface or the rotationally symmetric aspheric optical element; wherein the X, Y axis of the three-dimensional displacement table is perpendicular to the optical axis of the optical element;
(4) moving the Z axis of the three-dimensional displacement table to enable all three laser displacement sensors to be located within the working distance, and obtaining the relative distance d between the three sampling points on the spherical or rotationally symmetrical aspheric optical element and the corresponding laser displacement sensors through the data acquisition unit1、d2、d3(ii) a Wherein the Z axis of the three-dimensional displacement table is parallel to the axis line of the optical element;
(5) the control unit controls the three-dimensional displacement table to move along the Y axis until | d is satisfied1-d2| is less than Δ d, and Δ d is an allowable error threshold;
(6) the control unit controls the three-dimensional displacement table to move along the X axis until | d is satisfied2-d3| is less than Δ d, and Δ d is an allowable error threshold;
(7) if | d1-d2If | is more than delta d, repeating the step (5) to the step (6), feeding back the relative distance of the three sampling points in real time by the data analysis processing unit, and correcting the movement amount of the sample stage until | d is satisfied simultaneously1-d2|<Δd、|d2-d3If the | is less than the Δ d, the three laser displacement sensors form the outer center position of a triangle, namely the axial lead position of the optical element, so that the automatic centering of the spherical or rotationally symmetrical aspheric optical element is completed.
2. The method of claim 1, wherein three laser displacement sensors are mounted on the three-dimensional displacement stage in a triangular configuration.
3. The method for automatically centering a spherical or rotationally symmetric aspherical optical element as defined in claim 2, wherein three laser displacement sensors are mounted on the three-dimensional displacement stage in the form of a right triangle, and the line connecting the mounting positions of the first laser displacement sensor and the second laser displacement sensor is parallel to the Y-axis; and the connecting line of the mounting positions of the second laser displacement sensor and the third laser displacement sensor is parallel to the X axis.
4. The method of claim 1, wherein the spherical or rotationally symmetric aspheric optical element is fixed on the sample stage by a clamping mechanism.
5. The method for automatically centering a spherical or rotationally symmetric aspheric optical element as claimed in claim 1, wherein the step (1) comprises the following steps:
(1-1) adopting a vertical placing posture, and fixing a spherical or rotationally symmetric aspheric optical element for calibration on a sample table through a clamping mechanism;
(1-2) moving X, Y two shafts of the three-dimensional displacement platform to enable three sampling points of the three laser displacement sensors to be located on the surface of the optical element;
(1-3) moving the Z axis of the three-dimensional displacement table to enable all three laser displacement sensors to be located within the working distance of the three laser displacement sensors, and obtaining the relative distance between three sampling points on the spherical or rotationally symmetrical non-spherical optical element and the laser displacement sensors;
(1-4) using a three-dimensional displacement platform to bear a first laser displacement sensor, scanning two section lines of the spherical surface or the rotationally symmetric aspheric optical element along the direction X, Y respectively, and recording the coordinate position of the three-dimensional displacement platform and the relative distance d acquired by the first laser displacement sensor in real time1(ii) a In the X direction, d1When the minimum value is obtained, the corresponding X-axis coordinate of the three-dimensional displacement table is recorded as X1(ii) a In the Y direction, d1When the minimum value is obtained, the Y-axis coordinate of the corresponding three-dimensional displacement table is recorded as Y1;(X1,Y1) The calibration position of the first laser displacement sensor is obtained;
(1-5) repeating the method in step (4) to obtain the calibration position (X) of the second laser displacement sensor2,Y2) And the calibration position (X) of the third laser displacement sensor3,Y3);
(1-6) calculating coordinates (X)1,Y1)、(X2,Y2) And (X)3,Y3) Three-point structureForming the outer centers (a, b) of the triangles, and moving the XY axes of the three-dimensional displacement table to the coordinate positions (a, b);
(1-7) relative distance d acquired by three laser displacement sensors1、d2、d3And setting the initial position of the three laser displacement sensors to be 0, and finishing the calibration of the initial positions of the three laser displacement sensors.
6. The method for automatically centering a spherical or rotationally symmetric aspherical optical element as defined in claim 5, wherein in the steps (1-6), the coordinate positions (a, b) are calculated as follows:
Figure FDA0002984893240000031
Figure FDA0002984893240000032
7. the method for automatically centering a spherical or rotationally symmetric aspherical optical element as defined in claim 1, wherein the allowable error threshold Δ d in the steps (5) and (6) is determined based on the measurement accuracy of the laser displacement sensor, and the threshold is set to be greater than the measurement accuracy of the laser displacement sensor.
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