Chinese Optics, Volume. 17, Issue 1, 140(2024)
A non-null interferometry for concave aspheric surface
Fig. 1. Schematic diagram of aspheric surface directly tested by non-null interferometry
Fig. 3. Aberration caused by adjustment errors. (a) Distance induced defocusing; (b) tilt error caused by optical axis tilt; (c) coma caused by optical axis offset error
Fig. 4. (a) The experiment setup of non-null test for concave aspheric; data of (b) concave paraboloid surface and (c) concave ellipsoid surface obtained by non-null direct interferometry
Fig. 5. Non-null test results after removing adjustment error and retrace error. (a)Test results of concave parabolic surface; (b) test results of concave ellipsoid surface
Fig. 6. Comparative experiment on concave aspheric. (a) The optical path diagram of plane autocollimation; (b) testing of concave paraboloid surface by autocollimation; (c) testing of concave ellipsoid surface using LUPHOScan
Table 1. Correspondence between the terms of Zernike polynomials and aberrations
View tableView in ArticleTable 1. Correspondence between the terms of Zernike polynomials and aberrations
Term Polynomial Meaning $ {Z_4} $ $ - 1{\text{ + }}2\left( {{x^2} + {y^2}} \right) $ Power $ {Z_7} $ $ \left( { - 2 + 3{x^2} + 3{y^2}} \right)x $ Coma X $ {Z_8} $ $ \left( { - 2 + 3{x^2} + 3{y^2}} \right)y $ Coma Y $ {Z_9} $ $ 1 - 6\left( {{x^2} + {y^2}} \right) + 6{\left( {{x^2} + {y^2}} \right)^2} $ Primary Spherical
Table 2. Parameters of concave paraboloid surface
View tableView in ArticleTable 2. Parameters of concave paraboloid surface
Parameter Value Parameter Value Aspheric type Concave paraboloid Maximum sag/mm 1.67 Diameter/mm 90 Maximum slope/(°) 4.25 Radius curvature of the vertex/mm 606 Maximum asphericity/μm 0.575 Conic coefficient K −1 Best radius of the reference sphere/mm 606.835
Table 3. Parameters of concave ellipsoid surface
View tableView in ArticleTable 3. Parameters of concave ellipsoid surface
Parameter Value Parameter Value Aspheric type Concave ellipsoid Maximum sag/mm 2.91 Diameter/mm 90 Maximum slope/(°) 7.39 Radius curvature of the vertex/mm 348 Maximum asphericity/μm 2.0154 Conic coefficient K −0.66 Best radius of the reference sphere/mm 348.9615
Table 4. Simulation calculation results of retrace error of concave paraboloid surface
View tableView in ArticleTable 4. Simulation calculation results of retrace error of concave paraboloid surface
OA/mm $ O P D $ Power item $ Z_{{\mathrm{OPD}}(4)} $ Primary spherical $Z_{\Delta{{\mathrm{OPD}}(9)}}$ Retrace error 605 606 606.835 607 608
Table 5. Simulation calculation results of retrace error of concave ellipsoid surface
View tableView in ArticleTable 5. Simulation calculation results of retrace error of concave ellipsoid surface
OA/mm $ O P D $ Power item $ Z_{{\mathrm{OPD}}(4)} $ Primary spherical $ Z_{\Delta{{\mathrm{OPD}}(9)}}$ Retrace error 347 348 348.9615 349 350
Table 6. Defocusing error introduced by distance errors in experiments and its removal
(nm) View tableView in ArticleTable 6. Defocusing error introduced by distance errors in experiments and its removal
(nm) Detection result Power is adjusted to a minimum Adjust the distance L1 Adjust the distance L2 Adjust the distance L3 Fringe pattern Surface error before removing Power PV=639.7608RMS=135.4192 PV=4283.4232 RMS=1200.4216 PV=1833.8544 RMS=515.732 PV=1999.0152 RMS=523.3256 Surface error after removing Power PV= 627.1048 RMS=135.4192 PV= 654.3152 RMS=133.5208 PV=721.392 RMS=132.888 PV=656.2136 RMS=137.3176
Table 7. Comet error introduced by optical axis tilt/offset error in experiment and its removal
(nm) View tableView in ArticleTable 7. Comet error introduced by optical axis tilt/offset error in experiment and its removal
(nm) Detection result Coma is adjusted to a minimum Adjust the eccentric θ1 Adjust the eccentric θ2 Adjust the eccentric θ3 Fringe pattern Surface error before removing Coma PV=722.6576 RMS=137.3176 PV=656.8464 RMS=133.5208 PV=641.6592 RMS=134.7864 PV=649.2528 RMS=136.6848 Surface error after removing Coma PV= 510.6696 RMS=125.2944 PV= 489.7872 RMS=123.3960 PV= 491.0528 RMS=125.2944 PV= 488.5216 RMS=126.5600
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Xu ZHANG, Shi-jie LI, Bing-cai LIU, Ai-ling TIAN, Hai-feng LIANG, Chang-long CAI. A non-null interferometry for concave aspheric surface[J]. Chinese Optics, 2024, 17(1): 140
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Received: Mar. 13, 2023
Accepted: --
Published Online: Mar. 28, 2024
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