Abstract

For applications in the domain of digital holographic microscopy, we present a fast algorithm to propagate scalar wave fields from a small source area to an extended, parallel target area of coarser sampling pitch, using the first Rayleigh-Sommerfeld diffraction formula. Our algorithm can take full advantage of the fast Fourier transform by decomposing the convolution kernel of the propagation into several convolution kernel patches. Using partial overlapping of the patches together with a soft blending function, the Fourier spectrum of these patches can be reduced to a low number of significant components, which can be stored in a compact sparse array structure. This allows for rapid evaluation of the partial convolution results by skipping over negligible components through the Fourier domain pointwise multiplication and direct mapping of the remaining multiplication results into a Fourier domain representation of the coarsly sampled target patch. The algorithm has been verified experimentally at a numerical aperture of 0.62, not showing any significant resolution limitations.

© 2010 Optical Society of America

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2010 (1)

2009 (2)

2008 (2)

2007 (1)

J. Li, Z. Peng, and Y. Fu, "Diffraction transfer function and its calculation of classic diffraction formula," Opt. Commun. 280(2), 243-248 (2007).
[CrossRef]

2006 (1)

2001 (1)

P. P. Vaidyanathan, "Generalizations of the Sampling Theorem: Seven Decades After Nyquist," IEEE Trans. Circ. Syst. I Fundam. Theory Appl. 48, 1094-1109 (2001).
[CrossRef]

1995 (1)

H. J. Kreuzer, "Low energy electron point source microscopy," Micron 26(6), 503-509 (1995).
[CrossRef]

1994 (2)

1972 (1)

R. W. Gerchberg, and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik (Stuttg.) 35, 227-246 (1972).

1967 (1)

1948 (1)

D. Gabor, "A new microscopic principle," Nature 161(4098), 777 (1948).
[CrossRef]

Dong, B.-Z.

Ersoy, O. K.

Ferraro, P.

Finizio, A.

Fu, Y.

J. Li, Z. Peng, and Y. Fu, "Diffraction transfer function and its calculation of classic diffraction formula," Opt. Commun. 280(2), 243-248 (2007).
[CrossRef]

Gabor, D.

D. Gabor, "A new microscopic principle," Nature 161(4098), 777 (1948).
[CrossRef]

Gerchberg, R. W.

R. W. Gerchberg, and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik (Stuttg.) 35, 227-246 (1972).

Graulig, C.

Grjasnow, A.

A. Grjasnow, A. Wuttig, and R. Riesenberg, "Phase resolving microscopy by multi-plane diffraction detection," J. Microsc. 231(1), 115-123 (2008).
[CrossRef]

Gu, B.-Y.

Javidi, B.

Kanka, M.

Kreuzer, H. J.

Li, J.

J. Li, Z. Peng, and Y. Fu, "Diffraction transfer function and its calculation of classic diffraction formula," Opt. Commun. 280(2), 243-248 (2007).
[CrossRef]

Logofatu, P. C.

Memmolo, P.

Miccio, L.

Nascov, V.

Paturzo, M.

Peng, Z.

J. Li, Z. Peng, and Y. Fu, "Diffraction transfer function and its calculation of classic diffraction formula," Opt. Commun. 280(2), 243-248 (2007).
[CrossRef]

Riesenberg, R.

Saxton, W. O.

R. W. Gerchberg, and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik (Stuttg.) 35, 227-246 (1972).

Schnars, U.

Shen, F.

Sherman, G. C.

Tulino, A.

Vaidyanathan, P. P.

P. P. Vaidyanathan, "Generalizations of the Sampling Theorem: Seven Decades After Nyquist," IEEE Trans. Circ. Syst. I Fundam. Theory Appl. 48, 1094-1109 (2001).
[CrossRef]

Wang, A.

Wuttig, A.

M. Kanka, A. Wuttig, C. Graulig, and R. Riesenberg, "Fast exact scalar propagation for an in-line holographic microscopy on the diffraction limit," Opt. Lett. 35(2), 217-219 (2010).
[CrossRef]

A. Grjasnow, A. Wuttig, and R. Riesenberg, "Phase resolving microscopy by multi-plane diffraction detection," J. Microsc. 231(1), 115-123 (2008).
[CrossRef]

Yang, G.-Z.

Zhuang, J.-Y.

Appl. Opt. (3)

IEEE Trans. Circ. Syst. I Fundam. Theory Appl. (1)

P. P. Vaidyanathan, "Generalizations of the Sampling Theorem: Seven Decades After Nyquist," IEEE Trans. Circ. Syst. I Fundam. Theory Appl. 48, 1094-1109 (2001).
[CrossRef]

J. Microsc. (1)

A. Grjasnow, A. Wuttig, and R. Riesenberg, "Phase resolving microscopy by multi-plane diffraction detection," J. Microsc. 231(1), 115-123 (2008).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Micron (1)

H. J. Kreuzer, "Low energy electron point source microscopy," Micron 26(6), 503-509 (1995).
[CrossRef]

Nature (1)

D. Gabor, "A new microscopic principle," Nature 161(4098), 777 (1948).
[CrossRef]

Opt. Commun. (1)

J. Li, Z. Peng, and Y. Fu, "Diffraction transfer function and its calculation of classic diffraction formula," Opt. Commun. 280(2), 243-248 (2007).
[CrossRef]

Opt. Lett. (3)

Optik (Stuttg.) (1)

R. W. Gerchberg, and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik (Stuttg.) 35, 227-246 (1972).

Other (4)

M. Gu, Advanced Optical Imaging Theory, vol. 75 of Optical Sciences (Springer, Berlin, Germany, 1999).

J. W. Goodman, Introduction to Fourier Optics, Electrical and Computer Engineering, 2nd ed. (McGraw-Hill Companies, Inc., USA, 1996).

H. J. Kreuzer, "Holographic microscope and method of hologram reconstruction," US 6,411,406 B1, June 25, 2002 (Canadian Patent CA2376395).

M. Frigo, and S. G. Johnson, "The Design and Implementation of FFTW3," in Proc. IEEE, vol. 93, pp. 216-231 (2005).

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