Abstract

The angular spectrum method (ASM) calculates diffraction calculation in a high numerical aperture, unlike Fresnel diffraction. However, this method does not allow us to calculate at different sampling rates on source and destination planes. In this Letter, we propose a scaled ASM that calculates diffraction at different sampling rates on source and destination planes using the nonuniform fast Fourier transform.

© 2012 Optical Society of America

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References

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  1. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts, 2005).
  2. M. K. Kim, SPIE Rev. 1, 018005 (2010).
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  10. Q. H. Liu and N. Nguyen, IEEE Microw. Guided Wave Lett. 8, 18 (1998).
    [CrossRef]
  11. Q. H. Liu, N. Nguyen, and X. Y. Tang, Proc. IEEE Geosci. Remote Sens. Symp. 1, 288 (1998).
  12. T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, Comput. Phys. Commun. 183, 1124 (2012).
    [CrossRef]

2012

T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, Comput. Phys. Commun. 183, 1124 (2012).
[CrossRef]

2011

2010

2007

2004

1998

Q. H. Liu and N. Nguyen, IEEE Microw. Guided Wave Lett. 8, 18 (1998).
[CrossRef]

Q. H. Liu, N. Nguyen, and X. Y. Tang, Proc. IEEE Geosci. Remote Sens. Symp. 1, 288 (1998).

1993

A. Dutt and V. Rokhlin, SIAM J. Sci. Comput. 14, 1368 (1993).
[CrossRef]

Dutt, A.

A. Dutt and V. Rokhlin, SIAM J. Sci. Comput. 14, 1368 (1993).
[CrossRef]

Garcia-Sucerquia, J.

Goodman, J. W.

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

Greengard, L.

L. Greengard and J. Y. Lee, SIAM Rev. 46, 443 (2004).
[CrossRef]

Ito, T.

T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, Comput. Phys. Commun. 183, 1124 (2012).
[CrossRef]

Kim, M. K.

M. K. Kim, SPIE Rev. 1, 018005 (2010).
[CrossRef]

Koike, C.

Koike, T.

Lee, J. Y.

L. Greengard and J. Y. Lee, SIAM Rev. 46, 443 (2004).
[CrossRef]

Liu, Q. H.

Q. H. Liu and N. Nguyen, IEEE Microw. Guided Wave Lett. 8, 18 (1998).
[CrossRef]

Q. H. Liu, N. Nguyen, and X. Y. Tang, Proc. IEEE Geosci. Remote Sens. Symp. 1, 288 (1998).

Masuda, N.

T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, Comput. Phys. Commun. 183, 1124 (2012).
[CrossRef]

Matsushima, K.

Muffoletto, R. P.

Nguyen, N.

Q. H. Liu, N. Nguyen, and X. Y. Tang, Proc. IEEE Geosci. Remote Sens. Symp. 1, 288 (1998).

Q. H. Liu and N. Nguyen, IEEE Microw. Guided Wave Lett. 8, 18 (1998).
[CrossRef]

Nishitsuji, T.

T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, Comput. Phys. Commun. 183, 1124 (2012).
[CrossRef]

Odate, S.

Okada, N.

T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, Comput. Phys. Commun. 183, 1124 (2012).
[CrossRef]

Otaki, K.

Restrepo, J. F.

Rokhlin, V.

A. Dutt and V. Rokhlin, SIAM J. Sci. Comput. 14, 1368 (1993).
[CrossRef]

Sakurai, T.

T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, Comput. Phys. Commun. 183, 1124 (2012).
[CrossRef]

Shimobaba, T.

T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, Comput. Phys. Commun. 183, 1124 (2012).
[CrossRef]

Shiraki, A.

T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, Comput. Phys. Commun. 183, 1124 (2012).
[CrossRef]

Sugaya, A.

Sugisaki, K.

Takada, N.

T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, Comput. Phys. Commun. 183, 1124 (2012).
[CrossRef]

Tang, X. Y.

Q. H. Liu, N. Nguyen, and X. Y. Tang, Proc. IEEE Geosci. Remote Sens. Symp. 1, 288 (1998).

Toba, H.

Tohline, J. E.

Tyler, J. M.

Uchikawa, K.

Weng, J.

T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, Comput. Phys. Commun. 183, 1124 (2012).
[CrossRef]

Yamaguchi, I.

Yaroslavsky, L. P.

Zhang, F.

Appl. Opt.

Comput. Phys. Commun.

T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, Comput. Phys. Commun. 183, 1124 (2012).
[CrossRef]

IEEE Microw. Guided Wave Lett.

Q. H. Liu and N. Nguyen, IEEE Microw. Guided Wave Lett. 8, 18 (1998).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. IEEE Geosci. Remote Sens. Symp.

Q. H. Liu, N. Nguyen, and X. Y. Tang, Proc. IEEE Geosci. Remote Sens. Symp. 1, 288 (1998).

SIAM J. Sci. Comput.

A. Dutt and V. Rokhlin, SIAM J. Sci. Comput. 14, 1368 (1993).
[CrossRef]

SIAM Rev.

L. Greengard and J. Y. Lee, SIAM Rev. 46, 443 (2004).
[CrossRef]

SPIE Rev.

M. K. Kim, SPIE Rev. 1, 018005 (2010).
[CrossRef]

Other

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

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Figures (6)

Fig. 1.
Fig. 1.

Outline of scaled ASM. (a) R<1 and (b) R>1.

Fig. 2.
Fig. 2.

Correction term (R<1).

Fig. 3.
Fig. 3.

Intensity and phase profiles of RS diffraction and the scaled ASM when R=1.

Fig. 4.
Fig. 4.

Intensity and phase profiles of RS diffraction and the scaled ASM when R=0.8.

Fig. 5.
Fig. 5.

Intensity and phase profiles of the scaled ASM and RS diffraction when R=1.6.

Fig. 6.
Fig. 6.

Reconstructed images calculated by the scaled ASM from a hologram. (a) R=1 and (b) R=1/2.3.

Equations (6)

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A(f,0)=u1(x1)exp(2πx1f)dx1,A(f,z)=A(f,0)exp(2πiz(1λ2f2)),u2(x2)=A(f,z)exp(2πx2f)df,
A(mf,0)=FFT[u1(m1)],A(mf,z)=A(mf,0)exp(2πiz(1λ2(mfΔf)2)),u2(m2)=FFT1[A(mf,z)],
A(mf,0)=FFT[u1(m1)],A(mf,z)=A(mf,0)exp(2πiz(1λ2(mfΔf)2ϕc)),u2(m2)=mfA(mf,z)exp(2πiRmfm2N)=NUFFT2[A(mf,z)],
F(k)=NUFFT1[f(xj)]=jf(xj)exp(iπkxj),
f(xj)=NUFFT2[F(k)]=kF(k)exp(iπkxj).
A(mf,0)=m1u1(m1)exp(2πim1mfRN)=NUFFT1[u1(m1)],A(mf,z)=A(mf,0)exp(2πiz(1λ2(mfΔf)2ϕc))u2(m2)=FFT1[A(mf,z)],

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