Abstract

We propose a method for diffraction simulation with both shifted destination window and a large oblique illumination. Based on the angular spectrum theory, we first derive a generalized transfer function (GTF) and a generalized point-spread function (GSPF) suitable for free-space diffraction simulation when both a shifted destination window and a large oblique illumination are taken into account. Then we analyze the sampling error caused by sampling of the GTF and the GSPF for numerical simulation based on fast Fourier transform (FFT), and find out an analytical formula for determining a criteria distance of Zc. Theoretical analysis and simulation results prove that the FFT-based GTF sampling algorithm is valid for diffraction simulation with a diffraction distance less than or equal to Zc, while the FFT-based GSPF sampling is only suitable for the simulation with a distance larger than or equal to Zc. Based on theoretical analysis, we propose the hybrid GTF-GSPF algorithm suitable for simulation of both near- and far-field diffractions with shifted destination window and large oblique source illumination at the same time. Finally, some simulation results are given to verify the feasibility of the algorithm.

© 2014 Optical Society of America

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2014 (1)

2013 (6)

2012 (4)

2011 (3)

2010 (3)

2009 (1)

2007 (1)

2006 (2)

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, Phys. Rev. Lett. 97, 025506 (2006).
[CrossRef]

L. Yaroslavsky, Proc. SPIE 6252, 625216 (2006).
[CrossRef]

2005 (1)

Alfieri, D.

Bishara, W.

Bora Esmer, G.

Coskun, A. F.

Dainty, J. C.

de Jonge, M. D.

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, Phys. Rev. Lett. 97, 025506 (2006).
[CrossRef]

De Nicola, S.

Dhal, B. B.

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, Phys. Rev. Lett. 97, 025506 (2006).
[CrossRef]

Eikema, K. S. E.

Endo, Y.

Falaggis, K.

Ferraro, P.

Finizio, A.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005).

Hirayama, R.

Ichihashi, Y.

Ito, T.

Kakue, T.

Koike, C.

Koike, T.

Kou, S. S.

Kozacki, T.

Kujawinska, M.

Kurita, T.

Lin, J.

Lobaz, P.

Makowski, M.

Masuda, N.

Matsushima, K.

Muffoletto, R. P.

Noom, D. W. E.

Nugent, K. A.

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, Phys. Rev. Lett. 97, 025506 (2006).
[CrossRef]

Odate, S.

Oi, R.

Oikawa, M.

Okada, N.

Otaki, K.

Ozcan, A.

Paterson, D.

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, Phys. Rev. Lett. 97, 025506 (2006).
[CrossRef]

Peele, A. G.

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, Phys. Rev. Lett. 97, 025506 (2006).
[CrossRef]

Peng, H.

Pierattini, G.

Qin, Y.

Quiney, H. M.

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, Phys. Rev. Lett. 97, 025506 (2006).
[CrossRef]

Restrepo, J. F.

Rodríguez-Herrera, O. G.

Senoh, T.

Sheppard, C. J. R.

Shimobaba, T.

Su, T.-W.

Sucerquia, J. G.

Sugaya, A.

Sugisaki, K.

Tang, X.

Toba, H.

Tohline, J. E.

Tran, C. Q.

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, Phys. Rev. Lett. 97, 025506 (2006).
[CrossRef]

Tyler, J. M.

Uchikawa, K.

Wang, W.

Williams, G. J.

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, Phys. Rev. Lett. 97, 025506 (2006).
[CrossRef]

Witte, S.

Xiao, Y.

Yamamoto, K.

Yaroslavsky, L.

L. Yaroslavsky, Proc. SPIE 6252, 625216 (2006).
[CrossRef]

Yuan, X.-C.

Appl. Opt. (4)

Opt. Express (11)

Opt. Lett. (5)

Phys. Rev. Lett. (1)

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, Phys. Rev. Lett. 97, 025506 (2006).
[CrossRef]

Proc. SPIE (1)

L. Yaroslavsky, Proc. SPIE 6252, 625216 (2006).
[CrossRef]

Other (1)

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005).

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Figures (4)

Fig. 1.
Fig. 1.

Diffraction geometry with shifted destination window and an oblique illumination.

Fig. 2.
Fig. 2.

Flow chart of the GTF-GSPF algorithm for programming.

Fig. 3.
Fig. 3.

Accuracy of the GTF and GSPF.

Fig. 4.
Fig. 4.

Diffraction intensities simulated by different sampling algorithms when the diffraction distance is taken as 3, 15, and 150 mm, respectively.

Equations (14)

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uo(x,y)=F1{F{ui(x,y)}H(ξ,η)},
H(ξ,η)=exp{jkz1λ2(ξ2+η2)},
uo(x,y)=F1{F{t(xi,yi)exp(jkxisinθ)}H(ξ,η)}.
uo(x,y)=F1{F{t(xi+x0,yi)exp(jk(xi+x0)sinθ)}H(ξ,η)}=F1{T(ξsinθλ,η)exp(j2πx0ξ)H(ξ,η)},
uo(x,y)=exp{jk(x+x0)sinθ}F1{T(ξ,η)Hg(ξ,η)},
Hg(ξ,η)=exp{jk[λx0ξ+z1(λξ+sinθ)2λ2η2]}.
φ(ξ,η)2πξ=x0z(λξ+sinθ)1(λξ+sinθ)2λ2η2,
1δu2|[x0z(λξ+sinθ)1(λξ+sinθ)2]|max.
zZc,
Zc=M(δx)2λ(1+2x0Mδx)(1+2δxsinθλ)1λ24(δx)2(1+2δxsinθλ)2,
uo(x,y)=zjλexp{jkxsinθ}{t(xi,yi)*hg(xi,yi)},
hg(xi,yi)=exp(jkxsinθ)F1{Hg(ξ,η)}exp{jk[xisinθ+z2+(xi+x0)2+yi2]}[z2+(xi+x0)2+yi2].
1δx2|1λ[sinθ+(x+x0)(x+x0)2+z2]|max.
zZc.

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