Abstract

In this paper the invariance of modulation transfer function (MTF), which describes the insensitivity to perturbation of MTF, is defined to be the evaluating criterion of the wavefront coding system. The rapid optimization of wavefront coding system based on the MTF invariance is proposed by means of introducing the mathematical program Matlab to normal optical design process. The interface called MZDDE between Matlab and Zemax is applied to realize the fast data exchanging and merit function calculating. The genetic algorithm tool (GA) in Matlab is introduced to the optimizing process, which accelerates the converging efficiency considerably. The MTF invariance of optimized system drops to 0.0119 while that of original system is larger than 0.018. If the all the fields of view is taken into consideration, the MTF invariance of optimized system and original system is less than 0.015 and larger than 0.020 respectively. It is proven that the optimization of the unusual optical system with special property can be executed conveniently and rapidly with the help of external program and dynamic data exchange.

© 2009 OSA

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2008 (5)

J. Ojeda-Castañeda, J. E. Landgrave, and C. M. Gómez-Sarabia, “Conjugate phase plate use in analysis of the frequency response of imaging systems designed for extended depth of field,” Appl. Opt. 47(22), E99–E105 (2008).
[CrossRef] [PubMed]

S. Bagheri, P. E. X. Silveira, and D. Pucci de Farias, “Analytical optimal solution of the extension of the depth of field using cubic phase Wavefront Coding,” J. Opt. Soc. Am. 25(5), 1051–1063 (2008).
[CrossRef]

F. Yan, Z. Li-gong, and Z. Xue-jun, “Image Restoration of an Off-axis Three mirror Anastigmatic Optical System with Wavefront Coding Technology,” Opt. Eng. 47(1), 0170081–0170088 (2008).

L. Guang-zhi, X. Zhang, Z. Jian-pin, Y. Hao-ming, H. Feng-yun, and X. Zhang, “Novel optimization method for wavefront coding system,” Opt. Precision Eng. 16(7), 1171–1176 (2008) (in Chinese).

F. Yan, Z. Li-gong, and Z. Xue-jun, “A Design of Off-axis Three Mirror Anastigmatic Optical System with Wavefront Coding Technology,” Opt. Eng. 47(6), 063001 (2008).
[CrossRef]

2007 (2)

Z. Ting-yu, W.-Z. Zhang, Z. Ye, and F.-H. Yu, “Design of wavefront coding system based on evaluation function of fisher information,” Acta Opt. Sin. 27(6), 1096–1101 (2007) (in Chinese).

M. Somayaji and M. P. Christensen, “Frequency analysis of the wavefront-coding odd-symmetric quadratic phase mask,” Appl. Opt. 46(2), 216–226 (2007).
[CrossRef] [PubMed]

2006 (1)

2004 (1)

V. Sudhakar Prasad, P. Panca, R. J. Plemmons, T. C. Torgersen, and J. van der Gracht, “Pupil-phase optimization for extended-focus, aberration-corrected imaging systems,” Proc. SPIE 5559, 335–345 (2004).
[CrossRef]

2003 (1)

2002 (1)

P. Siarry, A. Petrowski, and M. Bessaou, “A multipopulation genetic algorithm aimed at multimodal optimization,” Adv. Eng. Software 33(4), 207–213 (2002).
[CrossRef]

2001 (1)

S. Mezoouari and A. R. Harvey, “Wavefront coding for aberration compensation in thermal imaging systems,” Proc. SPIE 4442, 34–42 (2001).
[CrossRef]

1997 (1)

1996 (1)

D. C. van Leijenhorst, C. B. Lucasius, and J. M. Thijssen, “Optical design with the aid of a genetic algorithm,” Biosystems 37(3), 177–187 (1996).
[CrossRef] [PubMed]

1995 (1)

1983 (1)

K. H. Brenner, A. W. Lohmann, and J. Ojeda-Castaneda, “The ambiguity function as a polar display of the OTF,” Opt. Commun. 44(5), 323–326 (1983).
[CrossRef]

Bagheri, S.

S. Bagheri, P. E. X. Silveira, and D. Pucci de Farias, “Analytical optimal solution of the extension of the depth of field using cubic phase Wavefront Coding,” J. Opt. Soc. Am. 25(5), 1051–1063 (2008).
[CrossRef]

Bessaou, M.

P. Siarry, A. Petrowski, and M. Bessaou, “A multipopulation genetic algorithm aimed at multimodal optimization,” Adv. Eng. Software 33(4), 207–213 (2002).
[CrossRef]

Bradburn, S.

Brenner, K. H.

K. H. Brenner, A. W. Lohmann, and J. Ojeda-Castaneda, “The ambiguity function as a polar display of the OTF,” Opt. Commun. 44(5), 323–326 (1983).
[CrossRef]

Cathey, T.

Cathey, W. T.

Christensen, M. P.

Dowski, E. R.

Feng-yun, H.

L. Guang-zhi, X. Zhang, Z. Jian-pin, Y. Hao-ming, H. Feng-yun, and X. Zhang, “Novel optimization method for wavefront coding system,” Opt. Precision Eng. 16(7), 1171–1176 (2008) (in Chinese).

Gómez-Sarabia, C. M.

Guang-zhi, L.

L. Guang-zhi, X. Zhang, Z. Jian-pin, Y. Hao-ming, H. Feng-yun, and X. Zhang, “Novel optimization method for wavefront coding system,” Opt. Precision Eng. 16(7), 1171–1176 (2008) (in Chinese).

Hao-ming, Y.

L. Guang-zhi, X. Zhang, Z. Jian-pin, Y. Hao-ming, H. Feng-yun, and X. Zhang, “Novel optimization method for wavefront coding system,” Opt. Precision Eng. 16(7), 1171–1176 (2008) (in Chinese).

Harvey, A. R.

Jian-pin, Z.

L. Guang-zhi, X. Zhang, Z. Jian-pin, Y. Hao-ming, H. Feng-yun, and X. Zhang, “Novel optimization method for wavefront coding system,” Opt. Precision Eng. 16(7), 1171–1176 (2008) (in Chinese).

Landgrave, J. E.

Li-gong, Z.

F. Yan, Z. Li-gong, and Z. Xue-jun, “Image Restoration of an Off-axis Three mirror Anastigmatic Optical System with Wavefront Coding Technology,” Opt. Eng. 47(1), 0170081–0170088 (2008).

F. Yan, Z. Li-gong, and Z. Xue-jun, “A Design of Off-axis Three Mirror Anastigmatic Optical System with Wavefront Coding Technology,” Opt. Eng. 47(6), 063001 (2008).
[CrossRef]

Lohmann, A. W.

K. H. Brenner, A. W. Lohmann, and J. Ojeda-Castaneda, “The ambiguity function as a polar display of the OTF,” Opt. Commun. 44(5), 323–326 (1983).
[CrossRef]

Lucasius, C. B.

D. C. van Leijenhorst, C. B. Lucasius, and J. M. Thijssen, “Optical design with the aid of a genetic algorithm,” Biosystems 37(3), 177–187 (1996).
[CrossRef] [PubMed]

Mezoouari, S.

S. Mezoouari and A. R. Harvey, “Wavefront coding for aberration compensation in thermal imaging systems,” Proc. SPIE 4442, 34–42 (2001).
[CrossRef]

Mezouari, S.

Muyo, G.

Ojeda-Castaneda, J.

K. H. Brenner, A. W. Lohmann, and J. Ojeda-Castaneda, “The ambiguity function as a polar display of the OTF,” Opt. Commun. 44(5), 323–326 (1983).
[CrossRef]

Ojeda-Castañeda, J.

Panca, P.

V. Sudhakar Prasad, P. Panca, R. J. Plemmons, T. C. Torgersen, and J. van der Gracht, “Pupil-phase optimization for extended-focus, aberration-corrected imaging systems,” Proc. SPIE 5559, 335–345 (2004).
[CrossRef]

Petrowski, A.

P. Siarry, A. Petrowski, and M. Bessaou, “A multipopulation genetic algorithm aimed at multimodal optimization,” Adv. Eng. Software 33(4), 207–213 (2002).
[CrossRef]

Plemmons, R. J.

V. Sudhakar Prasad, P. Panca, R. J. Plemmons, T. C. Torgersen, and J. van der Gracht, “Pupil-phase optimization for extended-focus, aberration-corrected imaging systems,” Proc. SPIE 5559, 335–345 (2004).
[CrossRef]

Pucci de Farias, D.

S. Bagheri, P. E. X. Silveira, and D. Pucci de Farias, “Analytical optimal solution of the extension of the depth of field using cubic phase Wavefront Coding,” J. Opt. Soc. Am. 25(5), 1051–1063 (2008).
[CrossRef]

Siarry, P.

P. Siarry, A. Petrowski, and M. Bessaou, “A multipopulation genetic algorithm aimed at multimodal optimization,” Adv. Eng. Software 33(4), 207–213 (2002).
[CrossRef]

Silveira, P. E. X.

S. Bagheri, P. E. X. Silveira, and D. Pucci de Farias, “Analytical optimal solution of the extension of the depth of field using cubic phase Wavefront Coding,” J. Opt. Soc. Am. 25(5), 1051–1063 (2008).
[CrossRef]

Somayaji, M.

Sudhakar Prasad, V.

V. Sudhakar Prasad, P. Panca, R. J. Plemmons, T. C. Torgersen, and J. van der Gracht, “Pupil-phase optimization for extended-focus, aberration-corrected imaging systems,” Proc. SPIE 5559, 335–345 (2004).
[CrossRef]

Thijssen, J. M.

D. C. van Leijenhorst, C. B. Lucasius, and J. M. Thijssen, “Optical design with the aid of a genetic algorithm,” Biosystems 37(3), 177–187 (1996).
[CrossRef] [PubMed]

Ting-yu, Z.

Z. Ting-yu, W.-Z. Zhang, Z. Ye, and F.-H. Yu, “Design of wavefront coding system based on evaluation function of fisher information,” Acta Opt. Sin. 27(6), 1096–1101 (2007) (in Chinese).

Torgersen, T. C.

V. Sudhakar Prasad, P. Panca, R. J. Plemmons, T. C. Torgersen, and J. van der Gracht, “Pupil-phase optimization for extended-focus, aberration-corrected imaging systems,” Proc. SPIE 5559, 335–345 (2004).
[CrossRef]

van der Gracht, J.

V. Sudhakar Prasad, P. Panca, R. J. Plemmons, T. C. Torgersen, and J. van der Gracht, “Pupil-phase optimization for extended-focus, aberration-corrected imaging systems,” Proc. SPIE 5559, 335–345 (2004).
[CrossRef]

van Leijenhorst, D. C.

D. C. van Leijenhorst, C. B. Lucasius, and J. M. Thijssen, “Optical design with the aid of a genetic algorithm,” Biosystems 37(3), 177–187 (1996).
[CrossRef] [PubMed]

Xue-jun, Z.

F. Yan, Z. Li-gong, and Z. Xue-jun, “A Design of Off-axis Three Mirror Anastigmatic Optical System with Wavefront Coding Technology,” Opt. Eng. 47(6), 063001 (2008).
[CrossRef]

F. Yan, Z. Li-gong, and Z. Xue-jun, “Image Restoration of an Off-axis Three mirror Anastigmatic Optical System with Wavefront Coding Technology,” Opt. Eng. 47(1), 0170081–0170088 (2008).

Yan, F.

F. Yan, Z. Li-gong, and Z. Xue-jun, “Image Restoration of an Off-axis Three mirror Anastigmatic Optical System with Wavefront Coding Technology,” Opt. Eng. 47(1), 0170081–0170088 (2008).

F. Yan, Z. Li-gong, and Z. Xue-jun, “A Design of Off-axis Three Mirror Anastigmatic Optical System with Wavefront Coding Technology,” Opt. Eng. 47(6), 063001 (2008).
[CrossRef]

Ye, Z.

Z. Ting-yu, W.-Z. Zhang, Z. Ye, and F.-H. Yu, “Design of wavefront coding system based on evaluation function of fisher information,” Acta Opt. Sin. 27(6), 1096–1101 (2007) (in Chinese).

Yu, F.-H.

Z. Ting-yu, W.-Z. Zhang, Z. Ye, and F.-H. Yu, “Design of wavefront coding system based on evaluation function of fisher information,” Acta Opt. Sin. 27(6), 1096–1101 (2007) (in Chinese).

Zhang, W.-Z.

Z. Ting-yu, W.-Z. Zhang, Z. Ye, and F.-H. Yu, “Design of wavefront coding system based on evaluation function of fisher information,” Acta Opt. Sin. 27(6), 1096–1101 (2007) (in Chinese).

Zhang, X.

L. Guang-zhi, X. Zhang, Z. Jian-pin, Y. Hao-ming, H. Feng-yun, and X. Zhang, “Novel optimization method for wavefront coding system,” Opt. Precision Eng. 16(7), 1171–1176 (2008) (in Chinese).

L. Guang-zhi, X. Zhang, Z. Jian-pin, Y. Hao-ming, H. Feng-yun, and X. Zhang, “Novel optimization method for wavefront coding system,” Opt. Precision Eng. 16(7), 1171–1176 (2008) (in Chinese).

Acta Opt. Sin. (1)

Z. Ting-yu, W.-Z. Zhang, Z. Ye, and F.-H. Yu, “Design of wavefront coding system based on evaluation function of fisher information,” Acta Opt. Sin. 27(6), 1096–1101 (2007) (in Chinese).

Adv. Eng. Software (1)

P. Siarry, A. Petrowski, and M. Bessaou, “A multipopulation genetic algorithm aimed at multimodal optimization,” Adv. Eng. Software 33(4), 207–213 (2002).
[CrossRef]

Appl. Opt. (4)

Biosystems (1)

D. C. van Leijenhorst, C. B. Lucasius, and J. M. Thijssen, “Optical design with the aid of a genetic algorithm,” Biosystems 37(3), 177–187 (1996).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

S. Bagheri, P. E. X. Silveira, and D. Pucci de Farias, “Analytical optimal solution of the extension of the depth of field using cubic phase Wavefront Coding,” J. Opt. Soc. Am. 25(5), 1051–1063 (2008).
[CrossRef]

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

Opt. Commun. (1)

K. H. Brenner, A. W. Lohmann, and J. Ojeda-Castaneda, “The ambiguity function as a polar display of the OTF,” Opt. Commun. 44(5), 323–326 (1983).
[CrossRef]

Opt. Eng. (2)

F. Yan, Z. Li-gong, and Z. Xue-jun, “A Design of Off-axis Three Mirror Anastigmatic Optical System with Wavefront Coding Technology,” Opt. Eng. 47(6), 063001 (2008).
[CrossRef]

F. Yan, Z. Li-gong, and Z. Xue-jun, “Image Restoration of an Off-axis Three mirror Anastigmatic Optical System with Wavefront Coding Technology,” Opt. Eng. 47(1), 0170081–0170088 (2008).

Opt. Lett. (1)

Opt. Precision Eng. (1)

L. Guang-zhi, X. Zhang, Z. Jian-pin, Y. Hao-ming, H. Feng-yun, and X. Zhang, “Novel optimization method for wavefront coding system,” Opt. Precision Eng. 16(7), 1171–1176 (2008) (in Chinese).

Proc. SPIE (2)

V. Sudhakar Prasad, P. Panca, R. J. Plemmons, T. C. Torgersen, and J. van der Gracht, “Pupil-phase optimization for extended-focus, aberration-corrected imaging systems,” Proc. SPIE 5559, 335–345 (2004).
[CrossRef]

S. Mezoouari and A. R. Harvey, “Wavefront coding for aberration compensation in thermal imaging systems,” Proc. SPIE 4442, 34–42 (2001).
[CrossRef]

Other (3)

http://www.mathworks.com/matlabcentral/fileexchange/7507 .

J. van der Gracht, J. G. Nagy, V. Pauca, and R. J. Plemmons, “Iterative restoration of wavefront coded imagery for focus invariance,” in Integrated Computational Imaging Systems, OSA Technical Digest Series (Optical Society of America, 2001), paper ITuA1.

W. Chi, and N. George, “Smart Camera with Extended Depth of Field,” Proc. SPIE 6024, 602424–1—602424–6(2005).

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Figures (8)

Fig. 1
Fig. 1

The layout and main parameters of the off-axis TMA system under research, where PM is primary mirror, SM is secondary mirror, TM is tertiary mirror and FM is folded mirror; F# is F-number; EFL stands for effective focal length, FOVx stands for field of view in x-direction while FOVy stands for field of view in y-direction and Fcut-off stands for the cut-off frequency of the system.

Fig. 2
Fig. 2

The comparison of MTF curves between wavefront coding system (left) and traditional system (right) when the defocus aberration varies from 1.25λ to 1.25λ with increment of 0.25λ defocus

Fig. 3
Fig. 3

The schematic explanation of the definition of MTF invariance

Fig. 4
Fig. 4

The RMSMTF curve of the WFC system before optimazition with different defocus aberration in the extended DOF with increment of 0.25λ defocus

Fig. 5
Fig. 5

The schematic explanation of location of the extended DOF

Fig. 6
Fig. 6

The RMSMTF curve of the optimized system with different defocus aberration in the extended DOF with increment of 0.25λ defocus

Fig. 7
Fig. 7

The MTF curves of optimized wavefront coding system with different defocus aberration varying from 1.25λ to 1.25λ with increment of 0.25λ defocus

Fig. 8
Fig. 8

The comparison of RMSMTF curve of different FOV between optimized system (left) and original system (right) when the defocus aberration varies from 1.25λ to 1.25λ with increment of 0.25λ defocus

Equations (6)

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

MTFm,nw020=0,
z(x,y)=c(x2+y2)1+1(1+k)c2(x2+y2)+β(x3+y3),
P(x,y)={12exp{j[w020(x2+y2)+α(x3+y3)]}  for (x2+y2)1/21 0otherwiseα=24,
MTF similarity{PVMTF=max(ΔMTFi)RMSMTF=[(Σn1ΔMTFi2)/n(Σn1ΔMTFi/n)2]1/2,
opt_cri=max(RMSjMTF),
z(x,y)=c(x2+y2)1+1(1+k)c2(x2+y2)+a1x3+a2x2y+a3xy2+a4y3,

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