Abstract

Nonnull test is often adopted for aspheric testing. But due to its violation of null condition, the testing rays will follow different paths from the reference and aberrations from the interferometer will not cancel out, leading to widely difference between the obtained surface figure and that of the real, which is called the Retrace-error accordingly. In this paper, retrace error of nonnull aspheric testing is analyzed in detail with conclusions that retrace error has much to do with the aperture, F number and surface shape error of the aspheric under test. Correcting methods are proposed according to the manner of the retrace errors. Both computer simulation and experimental results show that the proposed methods can correct the retrace error effectively. The analysis and proposed correction methods bring much to the application of nonnull aspheric testing.

© 2009 Optical Society of America

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References

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2007

D. Liu, Y. Yang, L. Wang, and Y. Zhuo, "Real time diagnosis of transient pulse laser with high repetition by radial shearing interferometer," Appl. Opt. 46, 8305-8314 (2007).
[PubMed]

D. Liu, Y. Yang, J. Weng, X. Zhang, B. Chen, and X. Qin, "Measurement of transient near-infrared laser pulse wavefront with high precision by radial shearing interferometer, " Opt. Commun.  275, 173-178 (2007).

D. Liu, Y. Yang, Y. Shen, J. Weng, and Y. Zhuo, "System optimization of radial shearing interferometer for aspheric testing," Proc. SPIE 6834, 68340U (2007).

J. Weng, Y. Yang, D. Liu, Y. Shen, and Y. Zhuo, "The wavefront aberration analysis and testing accuracy evaluation for the large aberration aspheric system based on the best fit sphere, " Proc. SPIE 6834, 68342V (2007).

Y. Yang, D. Liu, Y. Shen, J. Weng, and Y. Zhuo, "Study on testing larger asphericity in non-null interferometer, " Proc. SPIE 6834, 68340T (2007).

J. J. Sullivan and J. E. Greivenkamp, "Design of partial nulls for testing of fast aspheric surfaces, " Proc. SPIE 6671, 66710W (2007).

2004

2000

T. Kohno, D. Matsumoto, T. Yazawa, and Y. Uda, "Radial shearing interferometer for in-process measurement of diamond turning," Opt. Eng. 39, 2696-2699 (2000).

P. E. Murphy, T. G. Brown, and D. T. Moore, "Interference Imaging for Aspheric Surface Testing," Appl. Opt. 39, 2122-2129 (2000).

1995

1992

J. M. Geary, M. Yoo, and G. Si, "Retrace error: a case study, " Proc. SPIE. 1776, 98-105 (1992).

1980

1963

Anderson, D.

Brown, T. G.

Burge, J.

Chen, B.

D. Liu, Y. Yang, J. Weng, X. Zhang, B. Chen, and X. Qin, "Measurement of transient near-infrared laser pulse wavefront with high precision by radial shearing interferometer, " Opt. Commun.  275, 173-178 (2007).

Gappinger, R. O.

Geary, J. M.

J. M. Geary, M. Yoo, and G. Si, "Retrace error: a case study, " Proc. SPIE. 1776, 98-105 (1992).

Greivenkamp, J. E.

J. J. Sullivan and J. E. Greivenkamp, "Design of partial nulls for testing of fast aspheric surfaces, " Proc. SPIE 6671, 66710W (2007).

J. E. Greivenkamp and R. O. Gappinger, "Design of a Nonnull Interferometer for Aspheric Wave Fronts," Appl. Opt. 43, 5143-5151 (2004).
[PubMed]

Hayslett, C. R.

Kohno, T.

T. Kohno, D. Matsumoto, T. Yazawa, and Y. Uda, "Radial shearing interferometer for in-process measurement of diamond turning," Opt. Eng. 39, 2696-2699 (2000).

Kown, O.

Liu, D.

D. Liu, Y. Yang, J. Weng, X. Zhang, B. Chen, and X. Qin, "Measurement of transient near-infrared laser pulse wavefront with high precision by radial shearing interferometer, " Opt. Commun.  275, 173-178 (2007).

D. Liu, Y. Yang, L. Wang, and Y. Zhuo, "Real time diagnosis of transient pulse laser with high repetition by radial shearing interferometer," Appl. Opt. 46, 8305-8314 (2007).
[PubMed]

D. Liu, Y. Yang, Y. Shen, J. Weng, and Y. Zhuo, "System optimization of radial shearing interferometer for aspheric testing," Proc. SPIE 6834, 68340U (2007).

J. Weng, Y. Yang, D. Liu, Y. Shen, and Y. Zhuo, "The wavefront aberration analysis and testing accuracy evaluation for the large aberration aspheric system based on the best fit sphere, " Proc. SPIE 6834, 68342V (2007).

Y. Yang, D. Liu, Y. Shen, J. Weng, and Y. Zhuo, "Study on testing larger asphericity in non-null interferometer, " Proc. SPIE 6834, 68340T (2007).

Malacara, D.

Malacara, Z.

Matsumoto, D.

T. Kohno, D. Matsumoto, T. Yazawa, and Y. Uda, "Radial shearing interferometer for in-process measurement of diamond turning," Opt. Eng. 39, 2696-2699 (2000).

Moore, D. T.

Murphy, P. E.

Offner, A.

Pan, F. Y.

Poleshchuk, A.

Qin, X.

D. Liu, Y. Yang, J. Weng, X. Zhang, B. Chen, and X. Qin, "Measurement of transient near-infrared laser pulse wavefront with high precision by radial shearing interferometer, " Opt. Commun.  275, 173-178 (2007).

Shen, Y.

D. Liu, Y. Yang, Y. Shen, J. Weng, and Y. Zhuo, "System optimization of radial shearing interferometer for aspheric testing," Proc. SPIE 6834, 68340U (2007).

J. Weng, Y. Yang, D. Liu, Y. Shen, and Y. Zhuo, "The wavefront aberration analysis and testing accuracy evaluation for the large aberration aspheric system based on the best fit sphere, " Proc. SPIE 6834, 68342V (2007).

Y. Yang, D. Liu, Y. Shen, J. Weng, and Y. Zhuo, "Study on testing larger asphericity in non-null interferometer, " Proc. SPIE 6834, 68340T (2007).

Si, G.

J. M. Geary, M. Yoo, and G. Si, "Retrace error: a case study, " Proc. SPIE. 1776, 98-105 (1992).

Sullivan, J. J.

J. J. Sullivan and J. E. Greivenkamp, "Design of partial nulls for testing of fast aspheric surfaces, " Proc. SPIE 6671, 66710W (2007).

Uda, Y.

T. Kohno, D. Matsumoto, T. Yazawa, and Y. Uda, "Radial shearing interferometer for in-process measurement of diamond turning," Opt. Eng. 39, 2696-2699 (2000).

Wang, L.

Weng, J.

D. Liu, Y. Yang, J. Weng, X. Zhang, B. Chen, and X. Qin, "Measurement of transient near-infrared laser pulse wavefront with high precision by radial shearing interferometer, " Opt. Commun.  275, 173-178 (2007).

D. Liu, Y. Yang, Y. Shen, J. Weng, and Y. Zhuo, "System optimization of radial shearing interferometer for aspheric testing," Proc. SPIE 6834, 68340U (2007).

J. Weng, Y. Yang, D. Liu, Y. Shen, and Y. Zhuo, "The wavefront aberration analysis and testing accuracy evaluation for the large aberration aspheric system based on the best fit sphere, " Proc. SPIE 6834, 68342V (2007).

Y. Yang, D. Liu, Y. Shen, J. Weng, and Y. Zhuo, "Study on testing larger asphericity in non-null interferometer, " Proc. SPIE 6834, 68340T (2007).

Wyant, J. C.

Yang, Y.

D. Liu, Y. Yang, J. Weng, X. Zhang, B. Chen, and X. Qin, "Measurement of transient near-infrared laser pulse wavefront with high precision by radial shearing interferometer, " Opt. Commun.  275, 173-178 (2007).

D. Liu, Y. Yang, L. Wang, and Y. Zhuo, "Real time diagnosis of transient pulse laser with high repetition by radial shearing interferometer," Appl. Opt. 46, 8305-8314 (2007).
[PubMed]

J. Weng, Y. Yang, D. Liu, Y. Shen, and Y. Zhuo, "The wavefront aberration analysis and testing accuracy evaluation for the large aberration aspheric system based on the best fit sphere, " Proc. SPIE 6834, 68342V (2007).

D. Liu, Y. Yang, Y. Shen, J. Weng, and Y. Zhuo, "System optimization of radial shearing interferometer for aspheric testing," Proc. SPIE 6834, 68340U (2007).

Y. Yang, D. Liu, Y. Shen, J. Weng, and Y. Zhuo, "Study on testing larger asphericity in non-null interferometer, " Proc. SPIE 6834, 68340T (2007).

Yazawa, T.

T. Kohno, D. Matsumoto, T. Yazawa, and Y. Uda, "Radial shearing interferometer for in-process measurement of diamond turning," Opt. Eng. 39, 2696-2699 (2000).

Yoo, M.

J. M. Geary, M. Yoo, and G. Si, "Retrace error: a case study, " Proc. SPIE. 1776, 98-105 (1992).

Zhang, X.

D. Liu, Y. Yang, J. Weng, X. Zhang, B. Chen, and X. Qin, "Measurement of transient near-infrared laser pulse wavefront with high precision by radial shearing interferometer, " Opt. Commun.  275, 173-178 (2007).

Zhuo, Y.

D. Liu, Y. Yang, L. Wang, and Y. Zhuo, "Real time diagnosis of transient pulse laser with high repetition by radial shearing interferometer," Appl. Opt. 46, 8305-8314 (2007).
[PubMed]

D. Liu, Y. Yang, Y. Shen, J. Weng, and Y. Zhuo, "System optimization of radial shearing interferometer for aspheric testing," Proc. SPIE 6834, 68340U (2007).

Y. Yang, D. Liu, Y. Shen, J. Weng, and Y. Zhuo, "Study on testing larger asphericity in non-null interferometer, " Proc. SPIE 6834, 68340T (2007).

J. Weng, Y. Yang, D. Liu, Y. Shen, and Y. Zhuo, "The wavefront aberration analysis and testing accuracy evaluation for the large aberration aspheric system based on the best fit sphere, " Proc. SPIE 6834, 68342V (2007).

Appl. Opt.

Opt. Commun.

D. Liu, Y. Yang, J. Weng, X. Zhang, B. Chen, and X. Qin, "Measurement of transient near-infrared laser pulse wavefront with high precision by radial shearing interferometer, " Opt. Commun.  275, 173-178 (2007).

Opt. Eng.

T. Kohno, D. Matsumoto, T. Yazawa, and Y. Uda, "Radial shearing interferometer for in-process measurement of diamond turning," Opt. Eng. 39, 2696-2699 (2000).

Proc. SPIE

D. Liu, Y. Yang, Y. Shen, J. Weng, and Y. Zhuo, "System optimization of radial shearing interferometer for aspheric testing," Proc. SPIE 6834, 68340U (2007).

Y. Yang, D. Liu, Y. Shen, J. Weng, and Y. Zhuo, "Study on testing larger asphericity in non-null interferometer, " Proc. SPIE 6834, 68340T (2007).

J. J. Sullivan and J. E. Greivenkamp, "Design of partial nulls for testing of fast aspheric surfaces, " Proc. SPIE 6671, 66710W (2007).

J. Weng, Y. Yang, D. Liu, Y. Shen, and Y. Zhuo, "The wavefront aberration analysis and testing accuracy evaluation for the large aberration aspheric system based on the best fit sphere, " Proc. SPIE 6834, 68342V (2007).

Proc. SPIE.

J. M. Geary, M. Yoo, and G. Si, "Retrace error: a case study, " Proc. SPIE. 1776, 98-105 (1992).

Other

N. Gardner and A. Davies, "Retrace error evaluation on a figure-measuring interferometer," Proc. SPIE 5869, 58690V.1-8 (2005).

B. Thomas and B. Markus, "Interferometric asphere testing in a spherical test setup," Proc. SPIE 5965, 596514.1-8 (2005).

D. Malacara, Editor, Optical shop testing, 3rd Ed. (John Wiley and Sons, Inc., New Jersey 2007).

T.-C. Poon and T. Kim. "Geometrical Optics" in Engineering Optics with Matlab, Ting-Chung Poon ed., World Scientific Publishing Co.Pte.Ltd (2006).

J. C. Wyant and K. Creath, "Two-wavelength phase-Shifting interferometer and method," U.S. Patent No.4,832,489 (1989).

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Figures (11)

Fig. 1.
Fig. 1.

Scheme of the testing arm of a nonnull aspheric testing system

Fig. 2.
Fig. 2.

The test rays reflected from the aspheric cannot follow their original paths due to the large deviation between the aspheric under test and the reference sphere.

Fig. 3.
Fig. 3.

shows the testing error when the spherical principle is adopted to test an f/2 paraboloid with the aspheric is positioned in the vertex matched position. (a) Half of the PV (Peak-to-Valley) value of the wavefront detected by the detector W/2 and the deviation between the aspheric under test and the reference sphere N 0. (b) The absolute testing error when the CTP is adopted in nonnull aspheric testing. (c) The relative testing error when the CTP is adopted in nonnull aspheric testing.

Fig. 4.
Fig. 4.

The testing error when the spherical principle is adopted to test a 550mm paraboloid with the aspheric is positioned in the vertex matched position. (a) Half of the PTV value of the wavefront detected by the detector W/2 and the deviation between the aspheric under test and the reference sphere N 0. (b) The absolute testing error when the CTP is adopted in nonnull aspheric testing. (c) The relative testing error when the CTP is adopted in nonnull aspheric testing.

Fig. 5.
Fig. 5.

Wavefront with large deformation will change its shape as it travels

Fig. 6.
Fig. 6.

The regularized coordinates of the testing rays at the aspheric surface and the detect plane, respectively (The aspheric under test is an f/2 , 160mm parabloid, positioned in the vertex match position and the detector is at the focal plane of the imaging lens.). (a) The regularized coordinates of the testing rays at the aspheric surface, sampled at equal spaced zones. (b) The corresponding regularized coordinates of the testing rays at the detect plane.(The same marker means the same zone rays)

Fig. 7.
Fig. 7.

Computer simulation for non null testing of a paraboloid (f/1.8, 150mm) with some surface figure. (a) Deviation between the theoretical aspheric and its vertex sphere; (b) Surface figure of the paraboloid under test; (c) Half of the wavefornt on the detector plane; (d) Testing result by adopting CTP

Fig. 8.
Fig. 8.

Reverse transformation between the coordinates of the aspheric and that of the detector

Fig. 9.
Fig. 9.

Error correction for the nonnull aspheric testing in section 2.3. (a) Axial error induced by the deviation between the theoretic aspheric and the reference wavefront; (b) Result after eliminating retrace phase error from the wavefront in Fig. 7(c); (c) Result after eliminating retrace coordinate error from the wavefront in Fig. 9(b)

Fig. 10.
Fig. 10.

Diagrammatic layout of error correction experiment

Fig. 11.
Fig. 11.

Comparison of testing results in nonnull interferometer and that of ZYGO interferometer. (a) Testing result by ZYGO interferometer in spherical setup; (b) Testing result by nonnull interferometer in planar setup

Tables (2)

Tables Icon

Table 1 Numerical results of computer simulation(the wavelength of the testing rays is 1.064μm)

Tables Icon

Table 2. Experimental results of retrace error correction

Equations (6)

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

N 0 = AS = { x 2 + [ R f ( x ) ] 2 } 1 / 2 R Sp ,
OPD = OPL h OPL 0 ,
W = 2 N 0 ,
Err = W / 2 N 0 ,
ε = Err / N 0 .
W test = Z R E 2

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