Abstract

We propose a well-designed reflector, based on the Fermat principle, that is placed on a transmitted optical path to reflect the impinging light on the surface so that the null testing of the interference inspection for the freeform lens can be realized. The design methodology of such a reflector for a freeform lens with rotational symmetry is given and a reflector designed for a high-order aspheric surface is manufactured. Our investigations show that the theoretical accuracy of such an interference inspection can be up to 107mm with the designed reflector. We fabricated the designed reflector by a single point diamond turning machine and a high-order aspheric lens was measured with our methods, showing a good agreement with conventional interference inspection approaches. This might open a way to the fast inspection of freeform surfaces and thus improve the efficiencies of optical testing.

© 2013 Optical Society of America

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2013 (2)

2011 (1)

2010 (3)

O. Cakmakci, O. Thompsona, O. Ocakmakci, K. Thompsona, and P. Vallee, Proc. SPIE 7618, 761803 (2010).
[CrossRef]

X. Q. Jiang, X. C. Zhang, and P. J. Scott, Meas. Sci. Technol. 21, 045101 (2010).
[CrossRef]

C. F. Cheung, L. B. Kong, and M. J. Ren, Meas. Sci. Technol. 21, 115109 (2010).
[CrossRef]

2009 (2)

X. Sun, Z. Zheng, and X. Liu, J. Zhejiang University 43, 1428 (2009).

C. F. Cheung, L. B. Kong, S. To, and W. B. Lee, Meas. Sci. Technol. 20, 105103 (2009).
[CrossRef]

2007 (1)

C. F. Cheung, L. B. Kong, S. To, W. B. Lee, and K. W. Cheng, Meas. Sci. Technol. 18, 2252 (2007).
[CrossRef]

2006 (1)

C. F. Cheung, H. Li, L. Kong, W. B. Lee, and S. To, Meas. Sci. Technol. 17, 488 (2006).
[CrossRef]

1999 (1)

1991 (1)

Arimoto, A.

Baker, J. G.

Cakmakci, O.

O. Cakmakci, O. Thompsona, O. Ocakmakci, K. Thompsona, and P. Vallee, Proc. SPIE 7618, 761803 (2010).
[CrossRef]

Chen, I. M.

Cheng, K. W.

C. F. Cheung, L. B. Kong, S. To, W. B. Lee, and K. W. Cheng, Meas. Sci. Technol. 18, 2252 (2007).
[CrossRef]

Cheung, C. F.

C. F. Cheung, L. B. Kong, and M. J. Ren, Meas. Sci. Technol. 21, 115109 (2010).
[CrossRef]

C. F. Cheung, L. B. Kong, S. To, and W. B. Lee, Meas. Sci. Technol. 20, 105103 (2009).
[CrossRef]

C. F. Cheung, L. B. Kong, S. To, W. B. Lee, and K. W. Cheng, Meas. Sci. Technol. 18, 2252 (2007).
[CrossRef]

C. F. Cheung, H. Li, L. Kong, W. B. Lee, and S. To, Meas. Sci. Technol. 17, 488 (2006).
[CrossRef]

Cordero-Davila, A.

A. Cordero-Davila, J. R. Kantun-Montiel, and J. Gonzalez-Garcia, in Imaging and Applied Optics Technical Digest 2012 (Optical Society of America, 2012), p. 13.

Gao, Z. S.

Gonzalez-Garcia, J.

A. Cordero-Davila, J. R. Kantun-Montiel, and J. Gonzalez-Garcia, in Imaging and Applied Optics Technical Digest 2012 (Optical Society of America, 2012), p. 13.

Guo, W.

Guo, W. J.

Jiang, X. Q.

X. Q. Jiang, X. C. Zhang, and P. J. Scott, Meas. Sci. Technol. 21, 045101 (2010).
[CrossRef]

Joshi, S. Ch.

Kantun-Montiel, J. R.

A. Cordero-Davila, J. R. Kantun-Montiel, and J. Gonzalez-Garcia, in Imaging and Applied Optics Technical Digest 2012 (Optical Society of America, 2012), p. 13.

Kondou, Y.

Kong, L.

C. F. Cheung, H. Li, L. Kong, W. B. Lee, and S. To, Meas. Sci. Technol. 17, 488 (2006).
[CrossRef]

Kong, L. B.

C. F. Cheung, L. B. Kong, and M. J. Ren, Meas. Sci. Technol. 21, 115109 (2010).
[CrossRef]

C. F. Cheung, L. B. Kong, S. To, and W. B. Lee, Meas. Sci. Technol. 20, 105103 (2009).
[CrossRef]

C. F. Cheung, L. B. Kong, S. To, W. B. Lee, and K. W. Cheng, Meas. Sci. Technol. 18, 2252 (2007).
[CrossRef]

Lee, W. B.

C. F. Cheung, L. B. Kong, S. To, and W. B. Lee, Meas. Sci. Technol. 20, 105103 (2009).
[CrossRef]

C. F. Cheung, L. B. Kong, S. To, W. B. Lee, and K. W. Cheng, Meas. Sci. Technol. 18, 2252 (2007).
[CrossRef]

C. F. Cheung, H. Li, L. Kong, W. B. Lee, and S. To, Meas. Sci. Technol. 17, 488 (2006).
[CrossRef]

Li, H.

C. F. Cheung, H. Li, L. Kong, W. B. Lee, and S. To, Meas. Sci. Technol. 17, 488 (2006).
[CrossRef]

Li, X.

Liu, X.

X. Sun, Z. Zheng, and X. Liu, J. Zhejiang University 43, 1428 (2009).

Malacara, D.

D. Malacara, Optical Shop Testing, 3rd ed. (Wiley, 2007).

Mochizuki, T.

Moriyama, S.

Ocakmakci, O.

O. Cakmakci, O. Thompsona, O. Ocakmakci, K. Thompsona, and P. Vallee, Proc. SPIE 7618, 761803 (2010).
[CrossRef]

Plummer, W. T.

Pun, E.

Ren, M. J.

C. F. Cheung, L. B. Kong, and M. J. Ren, Meas. Sci. Technol. 21, 115109 (2010).
[CrossRef]

Saitoh, S.

Scott, P. J.

X. Q. Jiang, X. C. Zhang, and P. J. Scott, Meas. Sci. Technol. 21, 045101 (2010).
[CrossRef]

Shen, H.

Sun, X.

X. Sun, Z. Zheng, and X. Liu, J. Zhejiang University 43, 1428 (2009).

Tassell, J. V.

Thompsona, K.

O. Cakmakci, O. Thompsona, O. Ocakmakci, K. Thompsona, and P. Vallee, Proc. SPIE 7618, 761803 (2010).
[CrossRef]

Thompsona, O.

O. Cakmakci, O. Thompsona, O. Ocakmakci, K. Thompsona, and P. Vallee, Proc. SPIE 7618, 761803 (2010).
[CrossRef]

To, S.

C. F. Cheung, L. B. Kong, S. To, and W. B. Lee, Meas. Sci. Technol. 20, 105103 (2009).
[CrossRef]

C. F. Cheung, L. B. Kong, S. To, W. B. Lee, and K. W. Cheng, Meas. Sci. Technol. 18, 2252 (2007).
[CrossRef]

C. F. Cheung, H. Li, L. Kong, W. B. Lee, and S. To, Meas. Sci. Technol. 17, 488 (2006).
[CrossRef]

Vallee, P.

O. Cakmakci, O. Thompsona, O. Ocakmakci, K. Thompsona, and P. Vallee, Proc. SPIE 7618, 761803 (2010).
[CrossRef]

Wong, W.

Zhang, X. C.

X. Q. Jiang, X. C. Zhang, and P. J. Scott, Meas. Sci. Technol. 21, 045101 (2010).
[CrossRef]

Zhao, L.

Zheng, Z.

X. Sun, Z. Zheng, and X. Liu, J. Zhejiang University 43, 1428 (2009).

Zhu, R.

Zhu, X. L.

Appl. Opt. (3)

Chin. Opt. Lett. (1)

J. Zhejiang University (1)

X. Sun, Z. Zheng, and X. Liu, J. Zhejiang University 43, 1428 (2009).

Meas. Sci. Technol. (5)

C. F. Cheung, H. Li, L. Kong, W. B. Lee, and S. To, Meas. Sci. Technol. 17, 488 (2006).
[CrossRef]

X. Q. Jiang, X. C. Zhang, and P. J. Scott, Meas. Sci. Technol. 21, 045101 (2010).
[CrossRef]

C. F. Cheung, L. B. Kong, S. To, and W. B. Lee, Meas. Sci. Technol. 20, 105103 (2009).
[CrossRef]

C. F. Cheung, L. B. Kong, S. To, W. B. Lee, and K. W. Cheng, Meas. Sci. Technol. 18, 2252 (2007).
[CrossRef]

C. F. Cheung, L. B. Kong, and M. J. Ren, Meas. Sci. Technol. 21, 115109 (2010).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (1)

O. Cakmakci, O. Thompsona, O. Ocakmakci, K. Thompsona, and P. Vallee, Proc. SPIE 7618, 761803 (2010).
[CrossRef]

Other (2)

D. Malacara, Optical Shop Testing, 3rd ed. (Wiley, 2007).

A. Cordero-Davila, J. R. Kantun-Montiel, and J. Gonzalez-Garcia, in Imaging and Applied Optics Technical Digest 2012 (Optical Society of America, 2012), p. 13.

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Figures (6)

Fig. 1.
Fig. 1.

Design principle of the reflector.

Fig. 2.
Fig. 2.

Optical path for testing.

Fig. 3.
Fig. 3.

(a) Profile of the designed reflector. The radius approaching a sphere is 12.454 mm; the maximum deviation with the sphere surface is 0.544 μm. (b) Simulation results.

Fig. 4.
Fig. 4.

(a) Fabricated reflector. (b) The lens used in the measurement.

Fig. 5.
Fig. 5.

Measurement results from the conventional interference inspection method.

Fig. 6.
Fig. 6.

Measurement results from our method.

Equations (2)

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

{axi3+bxi2+cxi+d=zi,axi+13+bxi+12+cxi+1+d=zi+1,3axi2+2bxi+c=1dzxi,3axi+12+2bxi+1+c=1dzxi+1.
f(x)=cx21+1(1+k)c2x2+i=110aix2i,

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