Abstract

This Letter presents a new method for modeling of complex optical setups illuminated by quasi monochromatic spatially incoherent light. The algorithm provides better performance and quality than other modeling methods both for isoplanatic and nonisoplanatic systems. The algorithm maintains energy relations, image orientation, and magnification of the system. Computer modeling and experimental results are presented.

© 2012 Optical Society of America

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References

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  1. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).
  2. M. Mansuripur, Classical Optics and its Applications, 2nd ed. (Cambridge University, 2009).
  3. K. Kakarenko, I. Ducin, M. Makowski, A. Siemion, A. Siemion, J. Suszek, M. Sypek, D. Wojnowski, and A. Kolodziejczyk, Proc. SPIE 7746, 77460N (2010).
    [CrossRef]
  4. M. Sypek, Opt. Commun. 116, 43 (1995).
    [CrossRef]
  5. M. Sypek, C. Prokopowicz, and M. Górecki, Opt. Eng. 42, 3158 (2003).
    [CrossRef]
  6. Z. Jaroszewicz, A. Kolodziejczyk, M. Sypek, and C. Gomez-Reino, J. Mod. Opt. 43, 617 (1996).
    [CrossRef]

2010 (1)

K. Kakarenko, I. Ducin, M. Makowski, A. Siemion, A. Siemion, J. Suszek, M. Sypek, D. Wojnowski, and A. Kolodziejczyk, Proc. SPIE 7746, 77460N (2010).
[CrossRef]

2003 (1)

M. Sypek, C. Prokopowicz, and M. Górecki, Opt. Eng. 42, 3158 (2003).
[CrossRef]

1996 (1)

Z. Jaroszewicz, A. Kolodziejczyk, M. Sypek, and C. Gomez-Reino, J. Mod. Opt. 43, 617 (1996).
[CrossRef]

1995 (1)

M. Sypek, Opt. Commun. 116, 43 (1995).
[CrossRef]

Ducin, I.

K. Kakarenko, I. Ducin, M. Makowski, A. Siemion, A. Siemion, J. Suszek, M. Sypek, D. Wojnowski, and A. Kolodziejczyk, Proc. SPIE 7746, 77460N (2010).
[CrossRef]

Gomez-Reino, C.

Z. Jaroszewicz, A. Kolodziejczyk, M. Sypek, and C. Gomez-Reino, J. Mod. Opt. 43, 617 (1996).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Górecki, M.

M. Sypek, C. Prokopowicz, and M. Górecki, Opt. Eng. 42, 3158 (2003).
[CrossRef]

Jaroszewicz, Z.

Z. Jaroszewicz, A. Kolodziejczyk, M. Sypek, and C. Gomez-Reino, J. Mod. Opt. 43, 617 (1996).
[CrossRef]

Kakarenko, K.

K. Kakarenko, I. Ducin, M. Makowski, A. Siemion, A. Siemion, J. Suszek, M. Sypek, D. Wojnowski, and A. Kolodziejczyk, Proc. SPIE 7746, 77460N (2010).
[CrossRef]

Kolodziejczyk, A.

K. Kakarenko, I. Ducin, M. Makowski, A. Siemion, A. Siemion, J. Suszek, M. Sypek, D. Wojnowski, and A. Kolodziejczyk, Proc. SPIE 7746, 77460N (2010).
[CrossRef]

Z. Jaroszewicz, A. Kolodziejczyk, M. Sypek, and C. Gomez-Reino, J. Mod. Opt. 43, 617 (1996).
[CrossRef]

Makowski, M.

K. Kakarenko, I. Ducin, M. Makowski, A. Siemion, A. Siemion, J. Suszek, M. Sypek, D. Wojnowski, and A. Kolodziejczyk, Proc. SPIE 7746, 77460N (2010).
[CrossRef]

Mansuripur, M.

M. Mansuripur, Classical Optics and its Applications, 2nd ed. (Cambridge University, 2009).

Prokopowicz, C.

M. Sypek, C. Prokopowicz, and M. Górecki, Opt. Eng. 42, 3158 (2003).
[CrossRef]

Siemion, A.

K. Kakarenko, I. Ducin, M. Makowski, A. Siemion, A. Siemion, J. Suszek, M. Sypek, D. Wojnowski, and A. Kolodziejczyk, Proc. SPIE 7746, 77460N (2010).
[CrossRef]

K. Kakarenko, I. Ducin, M. Makowski, A. Siemion, A. Siemion, J. Suszek, M. Sypek, D. Wojnowski, and A. Kolodziejczyk, Proc. SPIE 7746, 77460N (2010).
[CrossRef]

Suszek, J.

K. Kakarenko, I. Ducin, M. Makowski, A. Siemion, A. Siemion, J. Suszek, M. Sypek, D. Wojnowski, and A. Kolodziejczyk, Proc. SPIE 7746, 77460N (2010).
[CrossRef]

Sypek, M.

K. Kakarenko, I. Ducin, M. Makowski, A. Siemion, A. Siemion, J. Suszek, M. Sypek, D. Wojnowski, and A. Kolodziejczyk, Proc. SPIE 7746, 77460N (2010).
[CrossRef]

M. Sypek, C. Prokopowicz, and M. Górecki, Opt. Eng. 42, 3158 (2003).
[CrossRef]

Z. Jaroszewicz, A. Kolodziejczyk, M. Sypek, and C. Gomez-Reino, J. Mod. Opt. 43, 617 (1996).
[CrossRef]

M. Sypek, Opt. Commun. 116, 43 (1995).
[CrossRef]

Wojnowski, D.

K. Kakarenko, I. Ducin, M. Makowski, A. Siemion, A. Siemion, J. Suszek, M. Sypek, D. Wojnowski, and A. Kolodziejczyk, Proc. SPIE 7746, 77460N (2010).
[CrossRef]

J. Mod. Opt. (1)

Z. Jaroszewicz, A. Kolodziejczyk, M. Sypek, and C. Gomez-Reino, J. Mod. Opt. 43, 617 (1996).
[CrossRef]

Opt. Commun. (1)

M. Sypek, Opt. Commun. 116, 43 (1995).
[CrossRef]

Opt. Eng. (1)

M. Sypek, C. Prokopowicz, and M. Górecki, Opt. Eng. 42, 3158 (2003).
[CrossRef]

Proc. SPIE (1)

K. Kakarenko, I. Ducin, M. Makowski, A. Siemion, A. Siemion, J. Suszek, M. Sypek, D. Wojnowski, and A. Kolodziejczyk, Proc. SPIE 7746, 77460N (2010).
[CrossRef]

Other (2)

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

M. Mansuripur, Classical Optics and its Applications, 2nd ed. (Cambridge University, 2009).

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Figures (4)

Fig. 1.
Fig. 1.

Results of modeling the isoplanatic system with spatially incoherent illumination using the convolution method (a) and TDRP algorithm with 10 (b), 50 (c), 100 (d) and 1000 (e) iterations.

Fig. 2.
Fig. 2.

Results of simulating the imaging in 2f2f setup with Fresnel lens with f=4mm and aperture d=3mm with nonparaxial propagation. (a) Input image and (b) TDRP, Σ500.

Fig. 3.
Fig. 3.

Scheme of the experimental setup. The optimal sharpness of the image was adjusted by changing the distance between the lens and the microbolometer array.

Fig. 4.
Fig. 4.

Results of numerical modeling of the imaging with nonparaxial propagation in setup shown in Fig. 3 with numerical equivalent of the thick germanium lens with f=25.4mm and aperture d=25.4mm and results of experimental verification. (a) Numerical modeling and (b) experimental results.

Tables (1)

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Table 1. Measured Values of Radii of Boundaries of the Contrast Inversion Region

Equations (4)

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t(x,y)=exp[iϕ],ϕ=2πiλ(x2+y2)2f,
ϕBIN={0forϕ[0,π)πforϕ[π,2π).
νi(r)=322πr,
Δνi(r)=322πr2Δr,

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