Abstract

Figure measuring interferometers generally work in the null condition, i.e., the reference rays share the same optical path with the test rays through the imaging system. In this case, except field distortion error, effect of other aberrations cancels out and doesn’t result in measureable systematic error. However, for spatial carrier interferometry and non-null aspheric test cases, null condition cannot be achieved typically, and there is excessive measurement error that is referenced as retrace error. Previous studies about retrace error can be generally distinguished into two categories: one based on 4th-order aberration formalism, the other based on ray tracing through interferometer model. In this paper, point characteristic function (PCF) is used to analyze retrace error in a Fizeau interferometer working in high spatial carrier condition. We present the process of reconstructing retrace error with and without element error in detail. Our results are in contrast with those obtained by ray tracing through interferometer model. The small difference between them (less than 3%) shows that our method is effective.

© 2015 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Interference imaging for aspheric surface testing

Paul E. Murphy, Thomas G. Brown, and Duncan T. Moore
Appl. Opt. 39(13) 2122-2129 (2000)

Generalized sine condition

Tamer T. Elazhary, Ping Zhou, Chunyu Zhao, and James H. Burge
Appl. Opt. 54(16) 5037-5049 (2015)

Analysis of spurious diffraction orders of computer-generated hologram in symmetric aspheric metrology

Yiwei He, Xi Hou, Fan Wu, Xinxue Ma, and Rongguang Liang
Opt. Express 25(17) 20556-20572 (2017)

References

  • View by:
  • |
  • |
  • |

  1. K. Kinnstaetter, A. W. Lohmann, J. Schwider, and N. Streibl, “Accuracy of phase shifting interferometry,” Appl. Opt. 27(24), 5082–5089 (1988).
    [Crossref] [PubMed]
  2. C. J. Evans and J. B. Bryan, “Compensation for errors introduced by nonzero fringe densities in phase-measuring interferometers,” CIRP Ann. 42(1), 577–580 (1993).
    [Crossref]
  3. C. Huang, “Propagation errors in precision Fizeau interferometry,” Appl. Opt. 32(34), 7016–7021 (1993).
    [Crossref] [PubMed]
  4. P. E. Murphy, T. G. Brown, and D. T. Moore, “Interference imaging for aspheric surface testing,” Appl. Opt. 39(13), 2122–2129 (2000).
    [Crossref] [PubMed]
  5. R. O. Gappinger and J. E. Greivenkamp, “Iterative reverse optimization procedure for calibration of aspheric wave-front measurements on a nonnull interferometer,” Appl. Opt. 43(27), 5152–5161 (2004).
    [Crossref] [PubMed]
  6. D. Liu, Y. Yang, C. Tian, Y. Luo, and L. Wang, “Practical methods for retrace error correction in nonnull aspheric testing,” Opt. Express 17(9), 7025–7035 (2009).
    [Crossref] [PubMed]
  7. E. Garbusi and W. Osten, “Perturbation methods in optics: application to the interferometric measurement of surfaces,” J. Opt. Soc. Am. A 26(12), 2538–2549 (2009).
    [Crossref] [PubMed]
  8. G. Baer, J. Schindler, C. Pruss, J. Siepmann, and W. Osten, “Calibration of a non-null test interferometer for the measurement of aspheres and free-form surfaces,” Opt. Express 22(25), 31200–31211 (2014).
    [Crossref] [PubMed]
  9. M. Born and E. Wolf, Principles of Optics (Publishing House of Electronics Industry, 2009), Ch. 4.
  10. B. D. Stone, “Modeling interferometers with lens design soft-ware,” Opt. Eng. 39(7), 1748–1759 (2000).
    [Crossref]

2014 (1)

2009 (2)

2004 (1)

2000 (2)

1993 (2)

C. J. Evans and J. B. Bryan, “Compensation for errors introduced by nonzero fringe densities in phase-measuring interferometers,” CIRP Ann. 42(1), 577–580 (1993).
[Crossref]

C. Huang, “Propagation errors in precision Fizeau interferometry,” Appl. Opt. 32(34), 7016–7021 (1993).
[Crossref] [PubMed]

1988 (1)

Baer, G.

Brown, T. G.

Bryan, J. B.

C. J. Evans and J. B. Bryan, “Compensation for errors introduced by nonzero fringe densities in phase-measuring interferometers,” CIRP Ann. 42(1), 577–580 (1993).
[Crossref]

Evans, C. J.

C. J. Evans and J. B. Bryan, “Compensation for errors introduced by nonzero fringe densities in phase-measuring interferometers,” CIRP Ann. 42(1), 577–580 (1993).
[Crossref]

Gappinger, R. O.

Garbusi, E.

Greivenkamp, J. E.

Huang, C.

Kinnstaetter, K.

Liu, D.

Lohmann, A. W.

Luo, Y.

Moore, D. T.

Murphy, P. E.

Osten, W.

Pruss, C.

Schindler, J.

Schwider, J.

Siepmann, J.

Stone, B. D.

B. D. Stone, “Modeling interferometers with lens design soft-ware,” Opt. Eng. 39(7), 1748–1759 (2000).
[Crossref]

Streibl, N.

Tian, C.

Wang, L.

Yang, Y.

Appl. Opt. (4)

CIRP Ann. (1)

C. J. Evans and J. B. Bryan, “Compensation for errors introduced by nonzero fringe densities in phase-measuring interferometers,” CIRP Ann. 42(1), 577–580 (1993).
[Crossref]

J. Opt. Soc. Am. A (1)

Opt. Eng. (1)

B. D. Stone, “Modeling interferometers with lens design soft-ware,” Opt. Eng. 39(7), 1748–1759 (2000).
[Crossref]

Opt. Express (2)

Other (1)

M. Born and E. Wolf, Principles of Optics (Publishing House of Electronics Industry, 2009), Ch. 4.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1 A schematic diagram of a Fizeau interferometer.
Fig. 2
Fig. 2 The simplified imaging system.
Fig. 3
Fig. 3 Schematic map of opt .
Fig. 4
Fig. 4 Retrace error comparison. The first row is the results of α= 0.04 , the second one is the results of α= 0.02 , and the third one is the results of α= 0.01 . The first column is the results constructed as 3.1 section, the second column is the results obtained by ray tracing, and the third column is their difference.
Fig. 5
Fig. 5 Comparison between PCF and ray tracing. The test plat is tilted about α= 0.04 . A figure error term Z 11 =λ 5 (6 ρ 2 6ρ+1) is introduced to a surface of the imaging system where the test rays deviate the most from the reference rays. The first column is the result calculated as 3.1 section, the second column is the result gained by ray tracing, and the third column is their difference.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

V( x 0 , y 0 , z 0 ; x 1 , y 1 , z 1 )= ( x 0 , y 0 , z 0 ) ( x 1 , y 1 , z 1 ) nds ,
V( x 0 , y 0 , z 0 ; x 1 , y 1 , z 1 )=S( x 1 , y 1 , z 1 )S( x 0 , y 0 , z 0 ),
n d r ds =grad(S),
gra d 0 (V)= n 0 e 0 gra d 1 (V)= n 1 e 1 },
u= h x 2 + h y 2 v= h x p xi + h y p yi w= p xi 2 + p yi 2 }.
V= ijk f ijk u i v j w k .
cos( ξ 0 )= V r h h x cos( η 0 )= V r h h y cos( ξ 1 )= V r pi p xi cos( η 1 )= V r pi p yi },
f 001 = r pi 2 2l .
( p x , p y )=( cos( ξ 0 ) r p , cos( η 0 ) r p ) h xi = ( r pi p xi +l cos( ξ 1 ) 1cos ( ξ 1 ) 2 cos ( η 1 ) 2 ) / r hi h yi = ( r pi p yi +l cos( η 1 ) 1cos ( ξ 1 ) 2 cos ( η 1 ) 2 ) / r hi }.
h xi = ijkm a ijkm h x i h y j p x k p y m h yi = ijkm b ijkm h x i h y j p x k p y m p xi = ijkm c ijkm h x i h y j p x k p y m p yi = ijkm d ijkm h x i h y j p x k p y m }.

Metrics