CN114858091A - Method simultaneously suitable for calibrating return error of plane and spherical surface - Google Patents
Method simultaneously suitable for calibrating return error of plane and spherical surface Download PDFInfo
- Publication number
- CN114858091A CN114858091A CN202210452516.4A CN202210452516A CN114858091A CN 114858091 A CN114858091 A CN 114858091A CN 202210452516 A CN202210452516 A CN 202210452516A CN 114858091 A CN114858091 A CN 114858091A
- Authority
- CN
- China
- Prior art keywords
- coefficient
- return error
- error
- measured
- return
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
Images
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- 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
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
- G01B21/02—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness
- G01B21/04—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness by measuring coordinates of points
- G01B21/042—Calibration or calibration artifacts
Landscapes
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Length Measuring Devices By Optical Means (AREA)
Abstract
The invention discloses a method simultaneously suitable for calibrating return stroke errors of a plane and a spherical surface, belonging to the field of optical detection. The invention firstly measures and obtains the return error size caused by the inclination of the measured mirror relative to the reference mirror along the X direction, the inclination of the Y direction and the defocusing through an actual measurement mode, and performs Zernike polynomial decomposition on the return error one by one. And then establishing a three-dimensional coordinate system by using the inclination coefficient in the X direction, the inclination coefficient in the Y direction and the defocusing coefficient, and obtaining a functional relation between each zernike coefficient in the return error and a three-dimensional coordinate point through data fitting. When the interferometer is used for detecting any measured mirror, the inclination coefficient and the defocusing coefficient are substituted into the function relation obtained before, and the corresponding return error can be calculated and removed.
Description
Technical Field
The invention belongs to the field of optical detection, and particularly relates to a method suitable for calibrating return stroke errors of a plane and a spherical surface simultaneously.
Background
The basic principle of interference detection is that a part of light emitted by a laser is reflected by a reference mirror to form reference light, the other part of the light is reflected by a measured mirror and is called measured light, and the reference light and the measured light are transmitted through an optical system in the interferometer and then are coherently superposed at the position of an observation screen to form interference fringes and are received by a CCD. By processing the interference fringes collected by the camera, the phase information of the detected light relative to the reference light can be obtained.
When the measured light and the reference light transmit the same path in the interferometer, the phase difference between the measured light and the reference light is the surface shape difference between the measured mirror and the reference mirror, and the measured mirror and the reference light can be used for guiding the processing of the measured mirror. If the detected light and the reference light are transmitted in different paths inside the interferometer, additional aberration may be brought, as shown in formula (1), the detection result of the interferometer includes a "return error" trace in addition to the detected surface type T and the reference surface type R.
W＝T-R+retrace, (1)
In order to avoid the influence of the return error on the detection result of the interferometer, the measured mirror is usually adjusted to be in a state of sharing the optical path with the reference mirror as much as possible during detection. However, it is difficult to achieve an absolute common-path state in some cases, for example, when the curvature radius of the measurement lens is small, the non-confocal state of the measured light and the reference light in the micron order causes a non-negligible defocus aberration. While others intentionally require the measured light to deviate from the reference light, such as carrier phase shift, differential de-high order spherical aberration, and dual aperture POWER. In the plane detection, the adjustment error is the tilt in the X direction and the tilt in the Y direction, and in the spherical surface detection, the adjustment error includes not only the tilt error but also the shift in the Z direction, that is, the defocus error. Mathematically, the plane can be regarded as a spherical surface with infinite curvature radius, so that the invention only needs to consider calibrating the return stroke error by using a spherical model.
Disclosure of Invention
The invention aims to obtain a functional relation between adjustment error (X-direction inclination, Y-direction inclination and defocusing) coefficients and return error polynomial coefficients of each order by a real measurement method. During actual measurement, the return error can be calculated only by substituting the adjustment error coefficient into the return error function.
The invention adopts the technical scheme that the method is simultaneously suitable for calibrating return stroke errors of a plane and a spherical surface, and comprises the following steps:
the method comprises the following steps: selecting a reflector with negligible surface shape error as the calibration return error of the measured mirror, adjusting the measured mirror and the reference mirror to a confocal position, namely a 'zero stripe' position, and measuring to obtain the surface shape data W 0 ；
Step two: adjusting the azimuth angle of the measured lens to obtain a new set of surface shapes W i Wherein i is 1,2, … N represents the group number of the measured data, N represents the total group number of the measurement, and the tilt coefficient in X direction, the tilt coefficient in Y direction and the defocus coefficient are a1 , i ,a2 , i ,a3 , i ；
Step three: w i W after removal of tilt and defocus i ', the corresponding return error is WR i ＝W i ’-W 0 The return error is decomposed into WR by zernike i ＝b 4,i *Z4+b 5,i *Z5+…+b 37,i *Z37；
Step four: fitting to obtain each zernike polynomial coefficient and a of return error WR 1 ,a 2 ,a 3 Is respectively expressed as b 4 ＝f 4 (a1,a2,a3)，b 5 ＝f 5 (a1,a2,a3)，…，b 37 ＝f 37 (a1,a2,a3)；
Step five: when the tilt and defocus coefficients (i.e., a1, a2, a3) are determined, the corresponding return error expression is WR-b 4 *Z4+b 5 *Z5+…b 37 Z37; every time a new measured mirror shape is obtained by measurement, the tilt and defocus coefficients are substituted into the function f n The return error can be calculated.
The principle of the invention is as follows: the method is suitable for calibrating return stroke errors of a plane and a spherical surface at the same time, and the plane can be regarded as the spherical surface with infinite curvature radius in practice, so that the calibration of the return stroke errors can be realized by the spherical surface no matter plane detection or spherical surface detection is carried out. The method comprises the following steps: the method comprises the following steps: actually measuring N groups of surface types to obtain the return error surface types WR corresponding to the inclination in the X direction, the inclination in the Y direction and the defocusing in different sizes i (i ═ 1,2, … N); step two: decomposing the return error surface type by using a Zernike polynomial to obtain various Zernike polynomial coefficients b n (n-4, 5, … 37); step three: fitting the functional relation f between each zernike polynomial coefficient and the inclination coefficient in the X direction, the inclination coefficient in the Y direction and the defocusing coefficient n (a1, a2, a3) (n is 4,5, … 37), and the return error expression is WR is f 4 Z4+f 5 Z5+…+f 37 Z37; step four: each time a new measured surface shape is obtained by measurement, the inclination and defocus coefficients are substituted into the function f n The return error can be calculated. Because the plane can be regarded as a spherical surface with infinite curvature radius in practice, the calibration of the return error can be realized by the spherical surface no matter plane detection or spherical surface detection is carried out.
Compared with the prior art, the invention has the advantages that:
(1) the invention calibrates the return error by an actual measurement mode, and avoids the condition that the calculated return error of the simulation software does not accord with the actual situation.
(2) The invention measures return errors of three dimensions of inclination and defocusing, and can be simultaneously used for plane detection and spherical detection.
Drawings
Fig. 1 shows that a coordinate point in a three-dimensional coordinate system corresponds to only one two-dimensional return stroke error surface type.
Fig. 2 is a theoretical ratio and actual ratio curve of spherical aberration coefficient and defocusing coefficient in a differential surface type when defocusing errors exist in large NA spherical surface detection.
FIG. 3 is a curve showing the ratio of spherical aberration coefficient to defocus coefficient in the difference surface after the return error is eliminated by the method of the present invention.
Detailed Description
The invention is described in detail below with reference to the figures and the detailed description.
The invention relates to a method for calibrating return stroke errors simultaneously suitable for planes and spheres, and a schematic diagram of the principle of the invention is shown in figure 1. The three axes on the left side of the graph represent the X-direction tilt coefficient, the Y-direction tilt coefficient and the defocus coefficient, respectively, and the combination of the three coefficient values corresponds to a unique coordinate point in space, which in turn corresponds to a unique profile of the return error as shown on the right side of fig. 1. Since the measured tilt coefficient cannot traverse every point in space in real time, a polynomial fit is needed to approximate the functional relationship between the return error and the tilt and defocus coefficients. The more data measured, the higher the accuracy of the fit.
The method comprises the following steps: choosing a surface type error that is negligible (RMS)<0.5nm) small NA spherical mirror (NA)<0.15) the reflector is used as a measured mirror to calibrate return stroke errors, the measured mirror and the reference mirror are adjusted to be at a confocal position, namely a 'zero stripe' position, and the surface type data W at the moment is obtained through measurement 0 ；
Step two: adjusting the azimuth angle of the measured lens to obtain a new set of surface shapes W i Wherein i is 1,2, … N represents the number of groups of measured data, N represents the total number of measurements, and the tilt coefficient in X direction, the tilt coefficient in Y direction and the defocus coefficient are respectively a1 , i ,a2 , i ,a3 , i 。
Step three: w i W after tilting and defocusing i ', corresponding return error is WR i ＝W i ’-W 0 The return error is decomposed into WR by zernike i ＝b 4,i *Z4+b 5,i *Z5+…+b 37,i *Z37；
Step four: fitting to obtain each zernike polynomial coefficient and a of return error WR 1 ,a 2 ,a 3 Is respectively expressed as b 4 ＝f 4 (a1,a2,a3)，b 5 ＝f 5 (a1,a2,a3)，…，b 37 ＝f 37 (a1,a2,a3)。
Step five: when the tilt and defocus coefficients, i.e., a1, a2, a3, are determined, the corresponding return error expression is WR-b 4 *Z4+b 5 *Z5+…b 37 *Z37。
When the large NA spherical reflector is detected, the slight defocusing of the detected mirror can cause a serious non-common optical path of the detected light and the reference light, thereby causing return stroke errors. According to theoretical derivation, the ratio of the spherical aberration coefficient to the defocus coefficient in the difference surface of the two defocus surface types of the measured lens should be constant all the time, however, in practice, it is found that the return error caused by defocus can cause the ratio of the spherical aberration coefficient to the defocus coefficient in the difference surface type to be no longer constant, as shown in fig. 2, and the ratio increases as the defocus amount increases. After the return error is removed by the method of the invention, as shown in fig. 3, the ratio of the spherical aberration coefficient to the defocusing coefficient is closer to the theoretical value.
Claims (1)
1. A method for calibrating return stroke errors simultaneously suitable for a plane and a spherical surface is characterized by comprising the following steps:
the method comprises the following steps: selecting a reflector with negligible surface shape error as the calibration return error of the measured mirror, adjusting the measured mirror and the reference mirror to a confocal position, namely a 'zero stripe' position, and measuring to obtain the surface shape data W 0 ；
Step two: adjusting the azimuth angle of the measured lens to obtain a new set of surface shapes W i Wherein i is 1,2, … N represents the group number of the measured data, N represents the total group number of the measurement, and the tilt coefficient in X direction, the tilt coefficient in Y direction and the defocus coefficient are a1 , i ,a2 , i ,a3 , i ；
Step three: w i W after tilting and defocusing i ', the corresponding return error is WR i ＝W i ’-W 0 Return error is decomposed into WR by zernike i ＝b 4,i *Z4+b 5,i *Z5+…+b 37,i *Z37；
Step four: fitting to obtain each zernike polynomial coefficient and a of return error WR 1 ,a 2 ,a 3 Is respectively expressed as b 4 ＝f 4 (a1,a2,a3)，b 5 ＝f 5 (a1,a2,a3)，…，b 37 ＝f 37 (a1,a2,a3)；
Step five: when the tilt and defocus coefficients, i.e., a1, a2, a3, are determined, the corresponding return error expression is WR-b 4 *Z4+b 5 *Z5+…b 37 Z37; each time a new measured mirror shape is obtained by measurement, the tilt and defocus coefficients are substituted into the function f n The return error can be calculated.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210452516.4A CN114858091B (en) | 2022-04-27 | 2022-04-27 | Method for calibrating return stroke error simultaneously suitable for plane and spherical surface |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210452516.4A CN114858091B (en) | 2022-04-27 | 2022-04-27 | Method for calibrating return stroke error simultaneously suitable for plane and spherical surface |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN114858091A true CN114858091A (en) | 2022-08-05 |
| CN114858091B CN114858091B (en) | 2023-02-14 |
Family
ID=82634196
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202210452516.4A Active CN114858091B (en) | 2022-04-27 | 2022-04-27 | Method for calibrating return stroke error simultaneously suitable for plane and spherical surface |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN114858091B (en) |
Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2009015987A (en) * | 2007-07-06 | 2009-01-22 | Panasonic Corp | Data recording/reproducing device |
| CN101876540A (en) * | 2010-05-07 | 2010-11-03 | 中国科学院光电技术研究所 | Nonspherical absolute measuring system based on multiwave front lens compensator |
| CN101986097A (en) * | 2010-07-09 | 2011-03-16 | 浙江大学 | Method for removing defocusing error and tilt error in spherical surface form interference detection at high accuracy |
| US20130063730A1 (en) * | 2011-09-08 | 2013-03-14 | Zygo Corporation | In situ calibration of interferometers |
| CN103776389A (en) * | 2014-01-10 | 2014-05-07 | 浙江大学 | High-precision aspheric combined interference detection device and high-precision aspheric combined interference detection method |
| CN113091638A (en) * | 2021-03-25 | 2021-07-09 | 中国科学院光电技术研究所 | Device and method for calibrating return error in surface shape measurement by interferometry |
| CN113804122A (en) * | 2021-09-06 | 2021-12-17 | 中国科学院光电技术研究所 | Method for detecting plane mirror shape containing defocusing aberration by using translation and rotation absolute detection method |
-
2022
- 2022-04-27 CN CN202210452516.4A patent/CN114858091B/en active Active
Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2009015987A (en) * | 2007-07-06 | 2009-01-22 | Panasonic Corp | Data recording/reproducing device |
| CN101876540A (en) * | 2010-05-07 | 2010-11-03 | 中国科学院光电技术研究所 | Nonspherical absolute measuring system based on multiwave front lens compensator |
| CN101986097A (en) * | 2010-07-09 | 2011-03-16 | 浙江大学 | Method for removing defocusing error and tilt error in spherical surface form interference detection at high accuracy |
| US20130063730A1 (en) * | 2011-09-08 | 2013-03-14 | Zygo Corporation | In situ calibration of interferometers |
| CN103776389A (en) * | 2014-01-10 | 2014-05-07 | 浙江大学 | High-precision aspheric combined interference detection device and high-precision aspheric combined interference detection method |
| CN113091638A (en) * | 2021-03-25 | 2021-07-09 | 中国科学院光电技术研究所 | Device and method for calibrating return error in surface shape measurement by interferometry |
| CN113804122A (en) * | 2021-09-06 | 2021-12-17 | 中国科学院光电技术研究所 | Method for detecting plane mirror shape containing defocusing aberration by using translation and rotation absolute detection method |
Non-Patent Citations (2)
| Title |
|---|
| I.DE ARRIBA-RUIZ: "Multipath reflectivity estimation in urban environments for Synthetic Aperture Radar images", 《2010 - MILCOM 2010 MILITARY COMMUNICATIONS CONFERENCE》 * |
| 邓婷等: "X射线柱面反射镜的非零位干涉测量", 《光学学报》 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN114858091B (en) | 2023-02-14 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| EP3220099B1 (en) | Calibration device, calibration method, optical device, imaging device, projection device, measurement system, and measurement method | |
| EP1869401B1 (en) | Method for accurate high-resolution measurements of aspheric surfaces | |
| CN109307480B (en) | Method for detecting multi-surface shape of transmission element | |
| CN108507495B (en) | Free-form surface detection method based on reverse Hartmann detection | |
| WO2003021184A1 (en) | Rapid in-situ mastering of an aspheric fizeau | |
| JP5971965B2 (en) | Surface shape measuring method, surface shape measuring apparatus, program, and optical element manufacturing method | |
| CN103353388A (en) | Method and device for calibrating binocular integrated microscopy imaging system with camera shooting function | |
| CN104570621A (en) | Feedback regulation method for optical grating diffraction wave surface error in double-beam exposure system | |
| CN111157226A (en) | Method and device for measuring point spread function of microscope | |
| US20020057495A1 (en) | Measuring system for performance of imaging optical system | |
| CN111650747A (en) | Method and device for real-time correction of defocusing aberration of collimator | |
| CN113091653B (en) | Device and method for measuring angle freedom degree error of linear guide rail based on pentaprism | |
| CN113251953B (en) | Mirror included angle measuring device and method based on stereo deflection technology | |
| CN114636373A (en) | Laser galvanometer calibration method based on binocular camera | |
| JPH1163946A (en) | Methods for measuring shape and manufacturing high-precision lens | |
| CN114858091B (en) | Method for calibrating return stroke error simultaneously suitable for plane and spherical surface | |
| CN102589472A (en) | Method for highly precisely eliminating adjustment error in spherical surface shape interference detection | |
| KR20110065365A (en) | Method and apparatus for measuring aspherical body | |
| CN113900250B (en) | Alignment method of adaptive optical system deformable mirror and Hartmann wavefront sensor | |
| CN107687933A (en) | A kind of distorting lens system high accuracy rigid body displacement detection method and device | |
| JP2000097663A (en) | Interferometer | |
| CN110793465B (en) | Multi-surface large-dynamic-range synchronous measurement method for micro-transmission element | |
| JP7191632B2 (en) | Eccentricity measurement method | |
| CN110332883A (en) | The removing method of fizeau interferometer hysterisis error | |
| Harding et al. | Calibration methods for 3D measurement systems |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |