CN108362225B - Measuring device and measuring method for conical mirror cylindrical surface shape - Google Patents
Measuring device and measuring method for conical mirror cylindrical surface shape Download PDFInfo
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- CN108362225B CN108362225B CN201810140014.1A CN201810140014A CN108362225B CN 108362225 B CN108362225 B CN 108362225B CN 201810140014 A CN201810140014 A CN 201810140014A CN 108362225 B CN108362225 B CN 108362225B
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- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/24—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures
- G01B11/2441—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures using interferometry
Abstract
A measuring device and a measuring method for the surface shape of a cylindrical mirror of a conical mirror are provided, the measuring device comprises a wave surface measuring interferometer, an interferometer bracket, a precise rotating platform and a rotating platform real-time measuring system, and the wave surface measuring interferometer is arranged on the interferometer bracket; the real-time measuring system of the rotary table comprises an auxiliary measuring cylinder and 5 precise displacement measuring sensors. The invention has the characteristics of high precision, low cost, high universality, capability of simultaneously measuring the surface shape information of the element to be measured and the rotation error of the main shaft of the precision rotating platform and simultaneously removing synchronous errors and asynchronous errors.
Description
Technical Field
The invention relates to the field of interference measurement, in particular to a device and a method for measuring the surface shapes of a conical mirror and a cylindrical mirror.
Background
The cone mirror is a special rotation symmetry aspheric surface, a point light source on the axis of the cone mirror forms a series of image points along the axis of the cone mirror, and the cone mirror can convert a collimated light beam into an annular light beam, and the characteristics are applied to aspects of high-resolution optical coherence tomography, cold atom capture, photoetching machine annular illumination generation and the like. The cylindrical mirror is also a rotationally symmetric aspheric surface, and can focus the collimated light beam into a line. However, the deterministic optical processing of conical and cylindrical mirrors is always limited by their surface shape detection techniques, which affects their application range and cost. The conical mirror is different from the cylindrical mirror in that a generatrix of the conical mirror has a certain included angle with a rotational symmetry axis thereof, and the generatrix of the cylindrical mirror is parallel to the rotational symmetry axis thereof, namely the included angle is 0.
Prior art [1](Jun Ma, Christof Pruss, Rihong Zhu, Zhishan Gao, Caojin Yuan, and Wolfgang Osten, "An absolute test for axicon surfaces," opt. Lett.36,2005-2007(2011)), and prior art 2(Jun Ma, Christof Pruss, Matthias)Rihong Zhu,Zhishan Gao,Caojin Yuan,Wolfgang Osten,"Axicon metrology usiThe high linear computer-generated algorithms, "Proc. SPIE 8082, Optical measurement systems for Industrial Inspection VII,80821I (2011)) all adopt a calculation hologram as a compensation mirror, and detect the surface shape of the conical mirror; the method has higher measurement precision, but needs to manufacture a compensating mirror element for each measured conical mirror, increases the measurement cost and the measurement period, and has poorer universality. In addition, when a large-caliber conical mirror is measured, a larger-caliber compensating mirror element and an interferometer are needed, and the measurement cost and the manufacturing difficulty of the compensating mirror are increased.
The prior art [2] (Yuan Qiao, Zeng's army, Zhanghua, Huang Huijie, detection method of axicon surface shape and cone angle, Chinese invention patent 201310180723.X) discloses a method for measuring conical mirror surface shape. The method actually measures the transmission wavefront of the conical mirror, a test light path passes through different test areas of the conical mirror in the test process, although the measurement result can evaluate the surface shape quality of the conical mirror to be tested, the measurement result cannot be used as the basis of feedback processing; and this method cannot be used to measure concave mirror shapes.
In the prior art [3] (schjiajun, jiaxin, xufuji, chenginen, a convex cone mirror online detection processing device and method, chinese patent 201510351236.4) a laser displacement sensor is used to detect the shape of a cone mirror surface by means of point scanning, which puts high requirements on the precision of the displacement sensor and a rotating system and increases the system cost; and this method cannot be used to measure the concave conical mirror profile.
In the prior art [4] (cone lens surface shape measuring device and measuring method, Chinese invention patent), a wave surface measuring interferometer is adopted to output collimated light beams to vertically irradiate a bus of an optical element to be measured, so that the surface shape information of the bus is measured. The method depends on the precision of the precision rotating platform, the main shaft rotation error of the precision rotating platform needs to be calibrated in advance, and only the synchronous error can be removed.
The surface shape testing method of the cylindrical mirror is similar to the surface shape testing method of the conical mirror, the computing hologram compensating mirror is adopted for measurement by Diffraction International company, Arizona Optical Metrology LLC and the like, and different compensating mirrors are needed for different F numbers and calibers.
At present, no universal device and method for measuring the surface shape of the conical mirror with high precision and low cost exist.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a device and a method for measuring the surface shapes of a conical mirror and a cylindrical mirror, wherein the device has universality, can measure the surface shapes of a convex conical mirror and a concave conical mirror with different calibers and different vertex angles, can also measure cylindrical mirrors with different diameters and different rotation angle ranges, has a simple measuring system and lower cost, can measure the rotation error of a main shaft of a precision rotating table while measuring the surface shape information of a component to be measured, simultaneously removes synchronous errors and asynchronous errors, and has higher measuring precision.
The technical solution of the invention is as follows:
a measuring device for the surface shapes of a conical mirror and a cylindrical mirror is characterized by comprising a wave surface measuring interferometer, an interferometer bracket, a precise rotating platform and a rotating platform real-time measuring system; the wave surface measuring interferometer is arranged on the interferometer bracket; the real-time measuring system of the rotary table comprises an auxiliary measuring cylinder and 5 precise displacement measuring sensors,
the auxiliary measuring cylinder is arranged on the precision rotating platform, and the central shaft of the auxiliary measuring cylinder is coaxial with the rotating shaft of the precision rotating platform; the 5 precision displacement measuring sensors are respectively a precision displacement measuring sensor for Z-channel displacement in the Z-axis direction, the X-axis direction and the Y-axis direction outside the auxiliary measuring cylinder, a precision displacement measuring sensor for X-channel displacement of an upper section, a precision displacement measuring sensor for X-channel displacement of a lower section, a precision displacement measuring sensor for Y-channel displacement of an upper section and a precision displacement measuring sensor for Y-channel displacement of a lower section, the upper section and the lower section are two horizontal planes with a certain distance, and the vertical distance is marked as l; and the upper surface of the auxiliary measuring cylinder is used for placing a conical mirror or a cylindrical mirror of the optical element to be measured.
The conical lens is a convex conical lens or a concave conical lens with the vertex angle more than or equal to 90 degrees;
the wave surface measuring interferometer is a Fizeau interferometer with a plane standard mirror, or a Tyman Green interferometer, or a Mach Zehnder interferometer, or a point diffraction interferometer outputting plane light waves, or a single-amplitude interference pattern measuring interferometer, or a dynamic measuring interferometer, or a high-speed dynamic measuring interferometer.
The interferometer support is a multi-dimensional adjusting support.
The measuring method using the conical mirror and cylindrical mirror surface shape measuring device comprises the following steps:
establishing a coordinate system of a detection system, taking the direction of a rotating shaft of a precision rotating table as a Z direction, taking two radial orthogonal directions of the precision rotating table as an X direction and a Y direction respectively, recording an included angle between a bus of a measured optical element and a rotational symmetry axis of the measured optical element as alpha, and superposing the projection of the bus perpendicular to emergent light of a wave surface measuring interferometer on an XY plane with the X axis; the range of the rotation angle of the precision rotary table is the same as the range of the rotation angle of the measured optical element; the rotation angle range N of the precision rotary table is equally divided and recorded as thetaiWhere i is 1,2,3, …, N is a positive integer, θ1The starting angle is corresponding to the starting position of the measured surface of the measured optical element;
calibrating roundness error h (theta) of auxiliary measuring surface of auxiliary measuring cylinderi) And a deviation z of flatness0(θi)；
Adjusting the measuring device to enable the wave surface measuring interferometer to observe a linear interference pattern corresponding to one bus of the measured optical element, wherein the number of interference fringes is minimum, the interference fringes are widest, the bus of the measured optical element is measured in the central position of the interference fringe area, and the central position of the interference fringe area is vertical to emergent light of the wave surface measuring interferometer;
rotating the rotation angle theta of the precision rotating platform to theta1I.e. the starting angular position;
measuring with a wavefront measuring interferometer, and storing the surface shape measurement result S (theta) of central line pixel of effective region of interferogramiW); the real-time measuring system of the rotary table measures each rotating position of the precision rotary tableAxial runout error δ z (θ)i) Radial run-out error δ x (θ)i) X direction rotation error Tx(θi) (ii) a W is a generatrix coordinate, W is 0,1,2, …, W-1, W is a positive integer and represents a pixel coordinate along the length direction of the generatrix of the measured optical element;
sixthly, rotating the precision rotating platform to thetaiRepeating the fifth step at the next rotation angle position of the rotation angle until the measurement of all N rotation angle positions is completed; respectively with S (theta) of different w1W) is a starting point, W is 0,1,2, …, W-1, and W sets of surface shape measurement data S (θ) are measurediW) (i is 1,2,3, …, N) and the phase unwrapping is performed on the corresponding phase, so that the W sets of surface profile measurement data S (θ)iW) are continuous data;
from S (theta) according to the following formula (1)iW) removing the rotary axial runout error delta z (theta) of the calibrated precision rotary tablei) Rotation radial runout error δ x (θ)i) Error of rotation tilt Tx(θi) The effect on the result of the measurement is,
F`(θi,w)＝S(θi,w)-δz(θi)·sin(α)-δx(θi)·cos(α)-Tx(θi)·w·PW， (1)
PW is the width of each coordinate pixel corresponding to the bus coordinates;
from F' (theta)iAnd w), taking K groups with different bus coordinates w at will to remove the surface shape measurement data F' (theta) after errorsi,wk) Wherein i is 1,2,3, …, N, K is 1,2,3, …, K, F' (θ) caused by the mounting eccentricity error when the measured optical element is mounted on the precision rotary table is separated therefrom according to the rotating clamping eccentricity error separating methodi,wk) Detection error E (theta)i,wk) (ii) a K group E (θ)i,wk) Average value of E (θ)i) Comprises the following steps:
E(θi)＝(E(θi,w1)+E(θi,w2)+…+E(θi,wK))/K,
from F' (θ)iW) is removed from the detected error E (theta) caused by the installation eccentricity of the optical element to be detectedi) To obtainTo the surface shape detection result F (theta) of the detected optical elementi,w)，
F(θi,w)＝F`(θi,w)-E(θi)。
The roundness deviation h (theta) of the auxiliary measuring surface of the calibration auxiliary measuring cylinderi) The method of (1) adopts a multi-step method, a multipoint method or a reverse method.
The flatness deviation z of the auxiliary measuring surface of the calibration auxiliary measuring cylinder0(θi) The method of (1) adopts a laser planimetry method, a level meter method or a three-coordinate measurement method.
The rotation inclination error T of the calibration precision rotating platformx(θi)，Ty(θi) The method adopts a main shaft rotation error separation method of multi-channel data acquisition; inclination error Tx(θi)，Ty(θi) Calculated by the following formula:
y1(θi) The roundness error h of the auxiliary measuring surface of the auxiliary measuring cylinder of the upper section is subtracted from the displacement measured by the precision displacement measuring sensor of the Y channel in the upper section1(θi) The result of (1); y is2(θi) The roundness error h of the auxiliary measuring surface of the auxiliary measuring cylinder of the lower section is subtracted from the displacement measured by the precision displacement measuring sensor of the Y channel in the lower section2(θi) The result of (1).
The rotation axial runout error delta z (theta) of the calibration precision rotating platformi) The method adopts the displacement Z (theta) measured by the precise displacement measuring sensor of the Z channeli) Subtracting the flatness deviation z of the auxiliary measuring surface of the auxiliary measuring cylinder0(θi) (ii) a Rotational radial runout error δ x (θ)i) The method adopts multi-channel data acquisitionThe least squares circle centers of the upper channel and the lower channel are O respectively1(a1,b1) And O2(a2,b2) Rotation radial runout error δ x (θ)i) Calculated by the following formula:
δx(θi)＝-l·Ty(θi)+(a2-a1)·cos(θ)+(b2-b1)·sin(θ)
the rotating clamping eccentricity error separation method is an optimal sine curve fitting method or a frequency domain Fourier transform filtering method.
The principle of the invention is that only the surface shape of one bus on the surface of the measured optical element is measured each time, and different buses are measured by scanning of the precision rotating platform; and eliminating errors caused by axial and radial runout, inclination and rotation eccentricity of the precision turntable from the measurement results of different buses, and obtaining the surface shape measurement result of the measured optical element.
The measuring system has the advantages that the measuring system has universality, can measure the surface shapes of the convex conical mirror and the concave conical mirror with different calibers and different vertex angles, can also measure cylindrical mirrors with different diameters and different rotation angle ranges, is simple and low in cost, can measure the rotation error of the main shaft of the precision rotating table while measuring the surface shape information of the element to be measured, simultaneously removes synchronous errors and asynchronous errors, and has higher measuring precision.
Drawings
FIG. 1 is a schematic structural diagram of an improved measuring device for the surface shape of a cylindrical mirror of a conical mirror according to the present invention;
FIG. 2 is a schematic diagram of the coordinate relationship and the position relationship of a precision displacement measuring sensor during the measurement process of the present invention;
FIG. 3 is a schematic structural diagram of an embodiment of an improved apparatus for measuring the surface shape of a cylindrical mirror of a conical mirror according to the present invention;
FIG. 4 is a schematic structural diagram of an embodiment of an improved apparatus for measuring the surface shape of a cylindrical mirror of a conical mirror according to the present invention;
Detailed Description
The invention is further illustrated by the following examples in conjunction with the drawings, without limiting the scope of the invention.
Fig. 1 is a schematic structural diagram of an improved measuring device for the surface shape of a cylindrical mirror of a conical mirror of the present invention, and it can be seen from the figure that the measuring device for the surface shape of the conical mirror and the cylindrical mirror of the present invention comprises a wavefront measuring interferometer 1, an interferometer support 2, a precision rotary table 12 and a rotary table real-time measuring system; the wave surface measuring interferometer 1 is arranged on the interferometer bracket 2; the real-time measuring system of the rotary table comprises an auxiliary measuring cylinder 3 and 5 precise displacement measuring sensors,
the auxiliary measuring cylinder 3 is arranged on the precision rotary table 12, and the central axis of the auxiliary measuring cylinder 3 is coaxial with the rotating shaft of the precision rotary table 12; the 5 precision displacement measuring sensors are respectively a precision displacement measuring sensor 5 for Z-channel displacement in the Z-axis direction, the X-axis direction and the Y-axis direction outside the auxiliary measuring cylinder 3, a precision displacement measuring sensor 6 for X-channel displacement of an upper section, a precision displacement measuring sensor 8 for X-channel displacement of a lower section, a precision displacement measuring sensor 7 for Y-channel displacement of an upper section and a precision displacement measuring sensor 9 for Y-channel displacement of a lower section, the upper section 10 and the lower section 11 are two horizontal planes with a certain distance, and the vertical distance is marked as l; the upper surface of the auxiliary measuring cylinder 3 is used for placing a conical mirror or a cylindrical mirror of the optical element 4 to be measured.
FIG. 1 is a schematic structural diagram of a convex cone lens measuring device of the present invention, which includes a wavefront measuring interferometer 1, an interferometer holder 2, an auxiliary measuring cylinder 3, and a precision rotary table 12, wherein the real-time measuring system of the rotary table includes a Z-channel precision displacement measuring sensor 5, an X-channel precision displacement measuring sensor 6 of an upper section 10, a Y-channel precision displacement measuring sensor 7 of an upper section 10, an X-channel precision displacement measuring sensor 8 of a lower section 11, a Y-channel precision displacement measuring sensor 9 of a lower section 11, and an auxiliary measuring cylinder 3; the wave surface measuring interferometer 1 is arranged on the interferometer bracket 2; the wave surface measuring interferometer 1 outputs collimated light beams and is provided with a plane reference light path; the measured optical element 4 is a convex cone lens; the emergent light of the wave surface measuring interferometer 1 is incident to the surface of the measured optical element 4, and the emergent light of the wave surface measuring interferometer 1 is vertical to a bus of the measured optical element 4, so that the light incident to the bus returns along the original path, and the light is received by the wave surface measuring interferometer 1 and generates an interference signal with the reference light; the measured optical element 4 is arranged on the precision rotary table 12, and the rotation symmetry axis of the measured optical element 4 is aligned with the rotation axis of the precision rotary table 12; the X-channel precise displacement measuring sensor 6 of the upper section 10, the X-channel precise displacement measuring sensor 8 of the lower section 11 and the Y-channel precise displacement measuring sensor 7 of the upper section 10, the Y-channel precise displacement measuring sensor 9 of the lower section 11 are respectively arranged in the same vertical plane, the two planes are vertical to each other, the X-channel precise displacement measuring sensor 6 of the upper section 10, the Y-channel precise displacement measuring sensor 7 of the upper section 10 and the X-channel precise displacement measuring sensor 8 of the lower section 11, the Y-channel precise displacement measuring sensor 9 of the lower section 11 are respectively arranged in the same horizontal plane, and the detection direction of the precise displacement measuring sensor 5 is vertical to the precise rotating table 12;
the wave surface measuring interferometer 1 is a Fizeau interferometer with a plane standard mirror, or a Tyman Green interferometer, or a Mach Zehnder interferometer, or a point diffraction interferometer outputting plane light waves;
the wave surface measuring interferometer 1 is a phase shift measuring interferometer, a single-amplitude interference pattern measuring interferometer, a dynamic measuring interferometer or a high-speed dynamic measuring interferometer;
the real-time measuring system of the rotary table comprises an auxiliary measuring cylinder 3 and 5 precise displacement measuring sensors, wherein the auxiliary measuring cylinder 3 is arranged on the precise rotary table 12, and the central axis of the auxiliary measuring cylinder is aligned with the rotating shaft of the precise rotary table; the 5 precise displacement measuring sensors comprise a precise displacement measuring sensor for detecting Z-channel displacement, two precise displacement measuring sensors for detecting X-channel displacement, two precise displacement measuring sensors for detecting Y-channel displacement, two X-channel precise displacement measuring sensors and two Y-channel precise displacement measuring sensors which are respectively arranged in an upper section and a lower section; the distance between the upper section and the lower section is recorded as l;
the interferometer bracket 2 can adjust the installation direction of the wave surface measuring interferometer, thereby adjusting the emergent direction of the collimated light beam of the wave surface measuring interferometer;
the interferometer bracket 2 can drive the wave surface measuring interferometer 1 to perform translational motion along the direction parallel to the rotating shaft of the precision rotating platform 12, so as to measure different areas of the surface of the measured optical element;
the measuring method of the improved measuring device for the surface shape of the conical mirror cylinder is characterized by comprising the following steps:
firstly, establishing a coordinate system of a detection system, and FIG. 2 is a schematic diagram of a coordinate relationship in a measurement process of the invention, wherein a detection direction of a precise displacement measurement sensor 5 is along a Z-axis direction, precise displacement measurement sensors 6 and 8 are arranged along an X-axis direction, and precise displacement measurement sensors 7 and 9 are arranged along a Y-axis direction; the rotation axis direction of the precise rotating platform 12 is taken as the Z direction, two radial orthogonal directions of the precise rotating platform 12 are respectively the X direction and the Y direction, an included angle between a bus of the measured optical element 4 and a rotation symmetry axis of the measured optical element 4 is taken as alpha, and the projection of the bus perpendicular to the emergent light of the wave surface measuring interferometer 1 on an XY plane is superposed with the X axis; the range of the rotation angle of the precision rotation stage 12 is the same as the range of the rotation angle of the optical element 4 to be measured; the rotation angle range N of the precision rotation table 12 is equally divided into θiWhere i is 1,2,3, …, N is a positive integer, θ1The initial angle is corresponding to the initial position of the measured surface of the measured optical element 4;
calibrating roundness deviation h (theta) of auxiliary measuring surface of auxiliary measuring cylinder 3i) And a deviation z of flatness0(θi)；
Adjusting the measuring device, observing a linear interference pattern corresponding to one bus of the measured optical element by the wave surface measuring interferometer, so that the number of interference fringes is minimum and the interference fringes are widest, measuring the central position of the interference fringe area by the bus of the measured optical element, and at the moment, the central position of the interference fringe area is vertical to the emergent light of the wave surface measuring interferometer;
rotating the rotation angle theta of the precision rotation table 12 to theta1I.e. the starting angular positionPlacing;
measuring by using the wave surface measuring interferometer 1, and storing the surface shape measuring result S (theta) of central line pixel of the effective area of the interference patterniW); the real-time measuring system of the rotary table measures the axial runout error delta z (theta) of each rotary position of the precision rotary tablei) Radial run-out error δ x (θ)i) X direction rotation error Tx(θi) (ii) a W is a generatrix coordinate, W is 0,1,2, …, and W-1, W is a positive integer, and represents a pixel coordinate along the generatrix length direction of the measured optical element 4;
sixthly, the precision rotating platform 12 is rotated to thetaiRepeating the fifth step until the measurement of all N rotation angle positions is completed; respectively with S (theta) of different w1W) is a starting point, W is 0,1,2, …, W-1, and W sets of surface shape measurement data S (θ) are measurediW) (i is 1,2,3, …, N) and the phase unwrapping is performed on the corresponding phase, so that the W sets of surface profile measurement data S (θ)iW) are continuous data;
from S (theta) according to formula (1)iW) is removed from the calibrated rotational axial runout error deltaz (theta) of the precision rotary table 12i) Rotation radial runout error δ x (θ)i) Error of rotation tilt Tx(θi) Influence on the measurement F ` ([ theta ])i,w)＝S(θi,w)-δz(θi)·sin(α)-δx(θi)·cos(α)-Tx(θi)·w·PW-h(θi)， (1)
PW is the width of each coordinate pixel corresponding to the bus coordinates;
from F' (theta)iAnd w), taking K groups with different bus coordinates w at will to remove the surface shape measurement data F' (theta) after errorsi,wk) Wherein i is 1,2,3, …, N, K is 1,2,3, …, K, F' (θ) caused by the mounting eccentricity error when the optical element 4 to be measured is mounted on the precision rotary table 12 is separated therefrom according to the rotating clamping eccentricity error separating methodi,wk) Detection error E (theta)i,wk) (ii) a K group E (θ)i,wk) Average value of E (θ)i) Is composed of
E(θi)＝(E(θi,w1)+E(θi,w2)+…+E(θi,wK))/K,
From F' (θ)iW) is removed from the detected error E (theta) caused by the installation eccentricity of the optical element to be detectedi) Obtaining the surface shape detection result F (theta) of the measured optical element 4i,w)，
F(θi,w)＝F`(θi,w)-E(θi)；
The roundness deviation h (theta) of the auxiliary measuring surface of the calibration auxiliary measuring cylinder 3i) The method adopts a multi-step method (see the prior art 5, leaf Beijing, Guqitai, Octopus-Yanshen. theory, the measurement precision of the multi-step method error separation technology [ J)]Metrology report, 1990,11(2):119-]Mechanical engineering journal, 2002,38(6):56-60.), or the reverse Method (see Prior Art 7, Donaldson R R.A Simple Method for Separating free axle Error from Test ballRoundness Error [ J].CIRP Annals-Manufacturing Technology,1971，21.)；
The flatness deviation z of the auxiliary measuring surface of the calibration auxiliary measuring cylinder 30(θi) The method adopts a laser planimetry method (http:// www.hamarlaser.com /), or a three-coordinate measuring method (see the prior art 8, the freehand incident structured light measures the mechanical grinding surface flatness technology research [ D]The institute of optoelectronics and technology, academy of sciences of china);
the rotation inclination error T of the calibration precision rotating platform 12x(θi)，Ty(θi) The method adopts a main shaft rotation error separation method of multi-channel data acquisition; synchronous tilt error Tx(θi)，Ty(θi) Calculated by the following formula:
y1(θi) The roundness error h of the auxiliary measuring surface of the auxiliary measuring cylinder of the upper section is subtracted from the displacement measured by the precision displacement measuring sensor of the Y channel in the upper section1(θi) The result of (1); y is2(θi) The roundness error h of the auxiliary measuring surface of the auxiliary measuring cylinder of the lower section is subtracted from the displacement measured by the precision displacement measuring sensor of the Y channel in the lower section2(θi) The result of (1).
The rotation axial runout error delta z (theta) of the calibration precision rotating platform 12i) The method adopts the displacement Z (theta) measured by the precise displacement measuring sensor of the Z channeli) Subtracting the flatness deviation z of the auxiliary measuring surface of the auxiliary measuring cylinder0(θi) (ii) a The calibrated rotation radial run-out error delta x (theta)i) The method adopts a main shaft rotation error separation method of multi-channel data acquisition, and the least square circle centers of an upper section channel and a lower section channel are O respectively1(a1,b1) And O2(a2,b2) Rotation synchronous radial runout error δ x (θ)i) Calculated by the following formula:
δx(θi)＝-l·Ty(θi)+(a2-a1)·cos(θ)+(b2-b1)·sin(θ)
the separation method of the rotating clamping eccentric errors is an optimal sinusoidal curve fitting method (see the prior art 10, Zhou Zu Wang, Zhangrong, Ling Ming, Zhang Yi. high-precision machine tool spindle rotation error online test system [ J ]. Chinese test, 2016,42(07):64-67.), or a frequency domain Fourier transform filtering method (see the prior art 11, Jamalian, A. (2010), A new method for machining radial error motion: a two-dimensional point of view (T). University of British Columbia.).
Fig. 3 is a schematic structural diagram of another embodiment of the improved measuring device for the surface shape of the conical mirror cylinder of the present invention, which is different from the embodiment of fig. 1 in that the measured optical element 4 is a concave conical mirror, and the vertex angle of the concave conical mirror is greater than or equal to 90 degrees.
Fig. 4 is a schematic structural diagram of another embodiment of the improved measuring device for the surface shape of the conical mirror cylindrical mirror of the present invention, which is different from the embodiment of fig. 1 in that the measured optical element 4 is a cylindrical mirror, an included angle α between a bus of the cylindrical mirror and a rotational symmetry axis is 0 °, and a value of a rotation angle of the cylindrical mirror ranges from 0 ° to 360 °.
The measuring system has the advantages that the measuring system has universality, can measure the surface shapes of the convex conical mirror and the concave conical mirror with different calibers and different vertex angles, can also measure cylindrical mirrors with different diameters and different rotation angle ranges, and is simple and low in cost. The surface shape information of the element to be measured and the rotation error of the main shaft of the precision rotating platform can be measured simultaneously, synchronous errors and asynchronous errors are removed simultaneously, and the measurement precision is higher.
Claims (9)
1. A measuring device for the surface shape of a cylindrical mirror of a conical mirror is characterized by comprising a wave surface measuring interferometer (1), an interferometer bracket (2), a precise rotating platform (12) and a real-time rotating platform measuring system; the wave surface measuring interferometer (1) is arranged on the interferometer bracket (2); the real-time measuring system of the rotary table comprises an auxiliary measuring cylinder (3) and 5 precise displacement measuring sensors;
the auxiliary measuring cylinder (3) is arranged on the precision rotary table (12), and the central shaft of the auxiliary measuring cylinder (3) is coaxial with the rotating shaft of the precision rotary table (12); the 5 precise displacement measurement sensors are respectively a precise displacement measurement sensor (5) for Z-channel displacement in the Z-axis direction, the X-axis direction and the Y-axis direction outside the auxiliary measurement cylinder (3), a precise displacement measurement sensor (6) for X-channel displacement of an upper section and a precise displacement measurement sensor (8) for X-channel displacement of a lower section, a precise displacement measurement sensor (7) for Y-channel displacement of an upper section and a precise displacement measurement sensor (9) for Y-channel displacement of a lower section, the upper section (10) and the lower section (11) are two horizontal planes with a certain distance, the vertical distance is marked as l, and the upper surface of the auxiliary measurement cylinder (3) is used for placing a conical mirror or a cylindrical mirror of an optical element (4) to be measured.
2. The device for measuring the surface shapes of a conical mirror and a cylindrical mirror according to claim 1, wherein the conical mirror is a convex conical mirror or a concave conical mirror with an apex angle of 90 degrees or more;
3. the apparatus for measuring the surface shapes of a conical mirror and a cylindrical mirror according to claim 1, wherein the wavefront measuring interferometer is a Fizeau interferometer with a plane standard mirror, or a tmann green interferometer, or a mach zehnder interferometer, or a point diffraction interferometer that outputs a plane light wave, or a single-amplitude interferogram measuring interferometer, or a dynamic measuring interferometer, or a high-speed dynamic measuring interferometer.
4. The apparatus according to claim 1, wherein the interferometer holder is a multi-dimensional adjustable holder.
5. A measuring method using the conical mirror and cylindrical mirror surface shape measuring apparatus according to claim 1, characterized in that the method comprises the steps of:
establishing a coordinate system of a detection system, taking the direction of a rotating shaft of a precise rotating platform (12) as a Z direction, taking two radial orthogonal directions of the precise rotating platform as an X direction and a Y direction respectively, recording an included angle between a bus of a measured optical element (4) and a rotational symmetry axis of the measured optical element as alpha, and superposing the projection of the bus perpendicular to the emergent light of the wave surface measuring interferometer on an XY plane with the X axis; the range of the rotation angle of the precision rotary table is the same as the range of the rotation angle of the measured optical element; the rotation angle range N of the precision rotary table is equally divided and recorded as thetaiWhere i is 1,2,3, …, N is a positive integer, θ1The starting angle is corresponding to the starting position of the measured surface of the measured optical element;
calibrating roundness error h (theta) of auxiliary measuring surface of auxiliary measuring cylinder (3)i) And a deviation z of flatness0(θi)；
Adjusting the measuring device to enable the wave surface measuring interferometer (1) to observe a linear interference pattern corresponding to one bus of the measured optical element (4), wherein the number of interference fringes is minimum, the interference fringes are widest, the bus of the measured optical element is measured in the central position of the interference fringe area, and the central position of the interference fringe area is vertical to the emergent light of the wave surface measuring interferometer;
rotating the rotation angle theta of the precision rotating table (12) to theta1I.e. the starting angular position;
measuring by using a wavefront measuring interferometer (1), and storing the surface shape measurement result S (theta) of the central line pixel of the effective area of the interference patterniW); the real-time measuring system of the rotary table measures the axial runout error delta z (theta) of each rotary position of the precision rotary tablei) Radial run-out error δ x (θ)i) X direction rotation error Tx(θi) (ii) a W is a generatrix coordinate, W is 0,1,2, …, W-1, W is a positive integer and represents a pixel coordinate along the length direction of the generatrix of the measured optical element;
sixthly, rotating the precision rotating platform (12) to thetaiRepeating the fifth step at the next rotation angle position of the rotation angle until the measurement of all N rotation angle positions is completed; respectively with S (theta) of different w1W) is a starting point, W is 0,1,2, …, W-1, and W sets of surface shape measurement data S (θ) are measurediW) (i is 1,2,3, …, N) and the phase unwrapping is performed on the corresponding phase, so that the W sets of surface profile measurement data S (θ)iW) are continuous data;
from S (theta) according to the following formula (1)iW) removing the rotary axial runout error delta z (theta) of the calibrated precision rotary tablei) Rotation radial runout error δ x (θ)i) Error of rotation tilt Tx(θi) The effect on the result of the measurement is,
F`(θi,w)＝S(θi,w)-δz(θi)·sin(α)-δx(θi)·cos(α)-Tx(θi)·w·PW， (1)
PW is the width of each coordinate pixel corresponding to the bus coordinates;
from F' (theta)iAnd w), taking K groups with different bus coordinates w at will to remove the surface shape measurement data F' (theta) after errorsi,wk) Wherein i is 1,2,3, …, N, K is 1,2,3, …, K, according to the rotating clamping eccentricity error separation method, separating the measured optical element from the measured optical element when the measured optical element is mounted on the precise rotating tableF' (theta) due to mounting eccentricity errori,wk) Detection error E (theta)i,wk) (ii) a K group E (θ)i,wk) Average value of E (θ)i) Comprises the following steps:
E(θi)＝(E(θi,w1)+E(θi,w2)+…+E(θi,wK))/K,
from F' (θ)iW) is removed from the detected error E (theta) caused by the installation eccentricity of the optical element to be detectedi) Obtaining the surface shape detection result F (theta) of the optical element to be detectedi,w)，
F(θi,w)＝F`(θi,w)-E(θi)。
6. The measuring method according to claim 5, wherein the roundness deviation h (θ) of the auxiliary measuring surface of the calibration auxiliary measuring cylinderi) The method of (1) adopts a multi-step method, a multipoint method or a reverse method.
7. The measuring method as claimed in claim 5, wherein the flatness deviation z of the auxiliary measuring surface of the calibration auxiliary measuring cylinder0(θi) The method of (1) adopts a laser planimetry method, a level meter method or a three-coordinate measurement method.
8. Measuring method according to claim 5, characterized in that said calibration precision rotation stage has a rotation tilt error Tx(θi)，Ty(θi) The method adopts a main shaft rotation error separation method of multi-channel data acquisition; inclination error Tx(θi)，Ty(θi) Calculated by the following formula:
y1(θi) The roundness error h of the auxiliary measuring surface of the auxiliary measuring cylinder of the upper section is subtracted from the displacement measured by the precision displacement measuring sensor of the Y channel in the upper section1(θi) The result of (1); y is2(θi) The roundness error h of the auxiliary measuring surface of the auxiliary measuring cylinder of the lower section is subtracted from the displacement measured by the precision displacement measuring sensor of the Y channel in the lower section2(θi) The result of (1).
9. A method according to any one of claims 5 to 8, wherein the precision rotary table is calibrated for a rotational axial runout error δ z (θ)i) The method adopts the displacement Z (theta) measured by the precise displacement measuring sensor of the Z channeli) Subtracting the flatness deviation z of the auxiliary measuring surface of the auxiliary measuring cylinder0(θi) (ii) a Rotational radial runout error δ x (θ)i) The method adopts a main shaft rotation error separation method of multi-channel data acquisition, and the least square circle centers of an upper channel and a lower channel are O respectively1(a1,b1) And O2(a2,b2) Rotation radial runout error δ x (θ)i) Calculated by the following formula:
δx(θi)＝-l·Ty(θi)+(a2-a1)·cos(θ)+(b2-b1)·sin(θ)
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