CN101986097A - Method for eliminating defocusing error and tilt error in spherical surface shape interference detection at high precision - Google Patents
Method for eliminating defocusing error and tilt error in spherical surface shape interference detection at high precision Download PDFInfo
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Abstract
The invention discloses a method for eliminating defocusing errors and tilt errors in spherical surface shape interference detection at high precision. Firstly, wave surface data containing defocusing and inclination are obtained through an interferometer, and the curvature radius and the caliber of a spherical surface to be measured are measured to be used as auxiliary data for removing inclination and defocusing. The method of white light interference is used in the test of the spherical radius to be measured, so that the measurement precision is ensured. And then removing constant terms, inclination errors and defocus errors in the wave surface data step by utilizing the wave surface fitting corresponding term coefficients and the relation between the inclination errors and the defocus errors and the accurate relation between defocus amount and optical path difference, and finally removing residual errors of the constant terms, the inclination errors and the defocus errors to obtain high-precision surface shape data. The invention provides a new method for eliminating defocusing and inclination influence in the detection of the spherical surface shape of an optical element through the research on spherical interference detection, particularly small F/# detected surface, and has important application value for the detection and processing of high-quality optical elements.
Description
Technical field
The present invention relates to the interfere measurement technique field of optical element, particularly a kind of in sphere face shape interfere to be detected high precision eliminate the method for defocus error and droop error.
Background technology
Along with the development of optical image technology, spherical surface shaped accuracy of detection demand is also more and more higher.Sphere interferes detection technique can realize spherical optics element high-precision test fast, and the interference detection technique of sphere face shape is updated and is used widely for this reason.In the interference testing of reality, realize that by adjusting mechanism tested sphere sentences the position that zero-bit detects, make that always comprising defocus error and droop error etc. debugs error in the test result but actual mechanism is undesirable.People have proposed to remove corresponding constant term, the out of focus item in the face shape test result and the removal of item to realize debuging error of tilting for this reason, the basic step of this method is that test result data is carried out the Zernike match, debugs error according to coefficient meaning and Zernike fitting of a polynomial character to remove correspondence.This traditional method is simple and convenient, can well satisfy people's demand under the situation that F/# is big and accuracy requirement is not high of plane was seized.But along with diminishing and the raising of accuracy requirement of plane was seized F/#, the influence that traditional mode can not high-precision removal defocus error be brought.Still not having at present suitable high precision in sphere face shape is detected goes out of focus etc. to debug the method for error.
Summary of the invention
The objective of the invention is deficiency at said method, provide a kind of in sphere face shape interfere to be detected high precision eliminate the method for defocus error and droop error.
The method of high precision elimination defocus error and droop error may further comprise the steps in the interference of sphere face shape detects:
1) (x y), determines the tested zone of sphere to utilize interferometer to record the face graphic data W of sphere to be measured;
2) record the radius of curvature R of sphere to be measured by the white light interference method;
3) measure the bore of sphere to be measured and obtain the tested regional any point of sphere to be measured in conjunction with the F number of interferometer index plane (wherein maximum aperture angle is α for x, y) corresponding aperture angle
Max
4) (x y) carries out 36 zernike polynomial matches and obtains constant term coefficient Z to the face graphic data W that records sphere to be measured in the step 1)
0, a Y direction coefficient Z that tilts
1, a directions X coefficient Z that tilts
2With out of focus item coefficient Z
3, (x, y) the inclination item in and constant term obtain face graphic data W to eliminate the face graphic data W of sphere to be measured
1(x, y);
5) utilize out of focus item coefficient Z
3Aperture angle with tested zone
MaxObtain the estimated value of defocusing amount in the sphere test to be checked
6), obtain the tested regional any point of sphere to be checked (x, y) the optical path difference OPD=δ (1-cos α) that in test process, introduces by out of focus by defocusing amount δ and plane was seized aperture angle;
7) removal process 4) the sphere to be measured corrugated data W that obtains
1(x, y) in owing to introduce optical path difference OPD because of out of focus in the face shape test process, removed sphere to be measured corrugated data W after the out of focus for the first time
2(x, y)=W
1(x, y)-OPD;
8) to spherical wave face data W to be measured
2(x y) carries out 36 zernike polynomial matches, obtains
W
2(x，y)＝Z′
0+Z′
1y+Z′
2x+Z′
3[2(x
2+y
2)-1]+Z′
4(y
2-x
2)+......
Eliminate constant term coefficient Z
0', a Y direction coefficient Z that tilts
1', directions X inclination coefficient Z
2' and out of focus item coefficient Z
3', obtain the face graphic data W of sphere to be measured
3(x, y)=Z '
4(y
2-x
2)+...
The described radius of curvature R step that records sphere to be measured by the white light interference method is:
Utilize light source for the white light expansion light source and have the white light interference zero level dark fringe location of the Michelson interferometer of compensating plate, the reference planes of mobile Michelson interferometer are measured twice crossing radius of a circle r of plane and sphere
1And r
2And the value D of the difference of two positions sphere rise, the radius of curvature R of plane was seized is:
Describedly measure sphere bore to be measured and obtain the tested regional any point of sphere to be measured that (wherein maximum aperture angle is α for x, y) corresponding aperture angle in conjunction with interferometer index plane F number
MaxStep is:
1) measures the bore of tested sphere
2) plane was seized aperture angle
The index plane aperture angle is
The aperture angle in tested zone then
MaxFor:
Any point aperture angle is on the plane was seized:
It is described that (x y) carries out 36 zernike polynomial matches and obtains constant term coefficient Z to the face graphic data W that records sphere to be measured in the step 1)
0, a Y direction coefficient X that tilts
1, directions X inclination coefficient Z
2With out of focus item coefficient Z
3, (x, y) the inclination item in and constant term obtain face graphic data W to eliminate the face graphic data W of sphere to be measured
1(x, y) step is:
W(x，y)＝Z
0+Z
1y+Z
2x+Z
3[2(x
2+y
2)-1]+Z
4(y
2-x
2)+......
Z in the formula
0, Z
1And Z
2Represent the constant term and the item that tilts of gained face shape respectively, with coefficient Z in the following formula
0, Z
1And Z
2Zero setting obtains removing the face graphic data of constant term and inclination item
W
1(x，y)＝Z
3[2(x
2+y
2)-1]+Z
4(y
2-x
2)+......
The present invention has considered the higher order term of defocus error to the influence of test surfaces shape, estimates defocusing amount to remove out of focus by convenient mode.Treating method when the present invention has considered also that there is error in defocusing amount in estimating is promptly directly removed remaining defocus error item by match once more and is removed.This method can effectively remove sphere detect in by out of focus and the test error that tilts to introduce, be specially adapted to face form height accuracy detection hour as plane was seized F/#, processing has directive significance to optics.
Description of drawings
Fig. 1 is that the embodiment of the invention is at detecting bore
Radius of curvature R=25mm spherical mirror detects gained face graphic data figure, and data are the face shape error data that the optical element that utilizes interferometer to record is measured;
Fig. 2 eliminate for the face shape error data of measuring in the embodiment of the invention and constant term after face graphic data figure;
Fig. 3 is the synoptic diagram of defocusing amount and optical path difference OPD in the embodiment of the invention;
Fig. 4 is treated final face shape result in the embodiment of the invention.
Embodiment
1) (x y), determines sensing range (as shown in Figure 1), the used laser wavelength lambda of interferometer=0.6328 μ m to utilize the GPI interferometer of Zygo company to record the face graphic data W of tested sphere
2) utilize the white light interference zero level dark fringe location of light source for the Michelson interferometer of white light expansion light source, the reference planes of mobile Michelson interferometer are measured twice crossing radius of a circle of plane and sphere and are respectively r
1=10.52mm=and r
2The value D=24.6 μ m of the difference of=7.71mm and two positions sphere rise, the radius of curvature R=25.12mm of plane was seized.
3) measure the plane was seized bore
And combined standard face F number calculates tested regional aperture angle
MaxAnd plane was seized any point aperture angle;
Use Zygo GPI interferometer in the test, used index plane F number is 0.65, can get tested regional aperture angle
Max=47.33 °, can calculate any point aperture angle.
4) to 1) in obtain the corrugated data W (x, y) carry out 36 zernike polynomial fitting results and be:
W
2(x，y)＝Z
0+Z
1y+Z
2x+Z
3[2(x
2+y
2)-1]+Z
4(y
2-x
2)+......
Z in the formula
0=0.0253 λ, Z
1=-0.1622 λ and Z
2=-0.0456 λ represents the constant term and the item that tilts of gained face shape respectively, with coefficient Z in the following formula
0, Z
1And Z
2Zero setting obtains removing the face graphic data W of constant term and inclination item
1(x, y) (as shown in Figure 2):
W
1(x，y)＝Z
3[2(x
2+y
2)-1]+Z
4(y
2-x
2)+......
5) utilize the out of focus item coefficient Z of match in the step 3)
3The aperture angle in=0.2430 λ and tested zone
MaxObtain defocusing amount estimated value δ, computing formula is: δ=0.75 λ
6), calculate out of focus according to the relation (as shown in Figure 3) of aperture angle, defocusing amount and optical path difference and introduce optical path difference OPD=δ (1-cos α) by defocusing amount that estimates and plane was seized aperture angle;
7) with 4) in obtain eliminate to tilt and the corrugated data W of constant term
1(x y) eliminates out of focus and introduces optical path difference OPD and removed corrugated data W after the out of focus for the first time
2(x, y)=W
1(x, y)-OPD;
8) to 7) in the result that obtains adopt 36 zernike polynomial matches, fitting result is
W
2(x，y)＝Z′
0+Z′
1y+Z′
2x+Z′
3[2(x
2+y
2)-1]+Z′
4(y
2-x
2)+......
Eliminate and constant term and out of focus item, the gained result is as final data (as shown in Figure 4): net result is compared the influence of removing out of focus and inclination well with the face shape result who initially records as can be seen, gained peak-to-valley value PV=0.0505 λ.
Claims (4)
- One kind in sphere face shape interfere to be detected high precision eliminate the method for defocus error and droop error, it is characterized in that may further comprise the steps:1) (x y), determines the tested zone of sphere to utilize interferometer to record the face graphic data W of sphere to be measured;2) record the radius of curvature R of sphere to be measured by the white light interference method;3) measure the bore of sphere to be measured and obtain the tested regional any point of sphere to be measured in conjunction with the F number of interferometer index plane (wherein maximum aperture angle is α for x, y) pairing aperture angle Max4) (x y) carries out 36 zernike polynomial matches, obtains constant term coefficient Z to the face graphic data W that records sphere to be measured in the step 1) 0, a Y direction coefficient Z that tilts 1, a directions X coefficient Z that tilts 2With out of focus item coefficient Z 3, (x, y) the inclination item in and constant term obtain face graphic data W to eliminate the face graphic data W of sphere to be measured 1(x, y);5) utilize out of focus item coefficient Z 3Aperture angle with tested zone MaxObtain the estimated value of defocusing amount in the sphere test to be checked
6), obtain the tested regional any point of sphere to be checked (x, y) the optical path difference OPD=δ (1-cos α) that in test process, introduces by out of focus by defocusing amount δ and plane was seized aperture angle;7) removal process 4) in the sphere to be measured corrugated data W that obtains 1(x, y) in owing to introduce optical path difference OPD because of out of focus in the face shape test process, removed sphere to be measured corrugated data W after the out of focus for the first time 2(x, y)=W 1(x, y)-OPD;8) to spherical wave face data W to be measured 2(x y) adopts 36 zernike polynomial matches, obtainsW 2(x，y)＝Z′ 0+Z′ 1y+Z′ 2x+Z′ 3[2(x 2+y 2)-1]+Z′ 4(y 2-x 2)+......Eliminate constant term coefficient Z 0', a Y direction coefficient Z that tilts 1', a directions X coefficient Z that tilts 2' and out of focus item coefficient Z 3', obtain the face graphic data W of sphere to be measured 3(x, y)=Z ' 4(y 2-x 2)+... - 2. according to claim 1 a kind of in sphere face shape interfere to be detected high precision eliminate the method for defocus error and droop error, it is characterized in that the described radius of curvature R step that records sphere to be measured by the white light interference method is:Utilize light source for the white light expansion light source and have the white light interference zero level dark fringe location of the Michelson interferometer of compensating plate, the reference planes of mobile Michelson interferometer are measured twice crossing radius of a circle r of plane and sphere 1And r 2And the value D of the difference of two positions sphere rise, the radius of curvature R of plane was seized is:
- 3. according to claim 1 a kind of in sphere face shape interfere to be detected high precision eliminate the method for defocus error and droop error, it is characterized in that described measure sphere bore to be measured and in conjunction with interferometer index plane F number obtain the tested regional any point of sphere to be measured (x, y) institute corresponding aperture angle wherein maximum aperture angle be α MaxStep is:1) measures the bore of tested sphere
2) plane was seized aperture angleThe index plane aperture angle is
The aperture angle in tested zone then MaxFor:
Any point aperture angle is on the plane was seized:
- 4. according to claim 1 a kind of in sphere face shape interfere to be detected high precision eliminate the method for defocus error and droop error, it is characterized in that described (x y) carries out 36 zernike polynomial matches and obtains constant term coefficient Z to recording sphere face graphic data W to be measured in the step 1) 0, a Y direction coefficient Z that tilts 1, a directions X coefficient Z that tilts 2With out of focus item coefficient Z 3, (x, y) the inclination item in and constant term obtain face graphic data W to eliminate the face graphic data W of sphere to be measured 1(x, y) step is:W(x，y)＝Z 0+Z 1y+Z 2x+Z 3[2(x 2+y 2)-1]+Z 4(y 2-x 2)+......Z in the formula 0, Z 1And Z 2Represent the constant term and the item that tilts of gained face shape respectively, with coefficient Z in the following formula 0, Z 1And Z 2Zero setting obtains removing the face graphic data of constant term and inclination itemW 1(x，y)＝Z 3[2(x 2+y 2)-1]+Z 4(y 2-x 2)+......。
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Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102853780A (en) * | 2012-09-07 | 2013-01-02 | 厦门大学 | Separation method for errors of all frequency sections of surface outline of polishing workpiece |
| CN104748670A (en) * | 2013-12-26 | 2015-07-01 | 南京理工大学 | Method of correcting tilt offset high-order adjustment errors of to-be-detected spherical surface in spherical surface figure detection |
| CN105890541A (en) * | 2016-04-12 | 2016-08-24 | 中国科学院上海光学精密机械研究所 | High-precision planar sub-aperture stitching detection method |
| CN107941165A (en) * | 2017-11-08 | 2018-04-20 | 中科院南京天文仪器有限公司 | Local sampling face shape restoration methods based on influence matrix Ritchey-Common test |
| CN110531379A (en) * | 2019-09-02 | 2019-12-03 | 中国科学院新疆天文台 | Pose adjustment method for determination of amount, pose method of adjustment and the device of subreflector |
| CN114858091A (en) * | 2022-04-27 | 2022-08-05 | 中国科学院光电技术研究所 | Method simultaneously suitable for calibrating return error of plane and spherical surface |
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Cited By (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102853780A (en) * | 2012-09-07 | 2013-01-02 | 厦门大学 | Separation method for errors of all frequency sections of surface outline of polishing workpiece |
| CN104748670A (en) * | 2013-12-26 | 2015-07-01 | 南京理工大学 | Method of correcting tilt offset high-order adjustment errors of to-be-detected spherical surface in spherical surface figure detection |
| CN105890541A (en) * | 2016-04-12 | 2016-08-24 | 中国科学院上海光学精密机械研究所 | High-precision planar sub-aperture stitching detection method |
| CN105890541B (en) * | 2016-04-12 | 2018-04-17 | 中国科学院上海光学精密机械研究所 | A kind of high precision plane sub-aperture stitching detection method |
| CN107941165A (en) * | 2017-11-08 | 2018-04-20 | 中科院南京天文仪器有限公司 | Local sampling face shape restoration methods based on influence matrix Ritchey-Common test |
| CN110531379A (en) * | 2019-09-02 | 2019-12-03 | 中国科学院新疆天文台 | Pose adjustment method for determination of amount, pose method of adjustment and the device of subreflector |
| CN110531379B (en) * | 2019-09-02 | 2022-07-08 | 中国科学院新疆天文台 | Determination method of pose adjustment amount of subreflector, pose adjustment method and device |
| CN114858091A (en) * | 2022-04-27 | 2022-08-05 | 中国科学院光电技术研究所 | Method simultaneously suitable for calibrating return error of plane and spherical surface |
| CN114858091B (en) * | 2022-04-27 | 2023-02-14 | 中国科学院光电技术研究所 | Method for calibrating return stroke error simultaneously suitable for plane and spherical surface |
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