Abstract

The diffractive processes within an optical system can be simulated by computer to compute the diffraction-altered electric-field distribution at the output of the system from the electric-field distribution at the input. In the paraxial approximation the system can be described by an ABCD ray matrix whose elements in turn can be used to simplify the computation such that only a single computational step is required. We describe two rearrangements of such computations that allow the simulation to be expressed in a linear systems formulation, in particular using the fast-Fourier-transform algorithm. We investigate the sampling requirements for the kernel-modifying function or chirp that arises. We also use the special properties of the chirp to determine the spreading imposed by the diffraction. This knowledge can be used to reduce the computation if only a limited region of either the input or the output is of interest.

© 1998 Optical Society of America

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  12. I. W. Selesnick, C. S. Burrus, “Fast convolution and filterings,” in The Digital Signal Processing Handbook, V. K. Madisetti, D. B. Williams, eds. (IEEE/CRC Press, Boca Raton, Fla., 1998), Chap. 8.
  13. H. Stark, F. B. Tuteur, Modern Electrical Communications—Theory and Systems (Prentice-Hall, Englewood Cliffs, N.J., 1979).
  14. A. J. Lambert, D. Fraser, “An implementation of the fast Fresnel transform,” in IVCNZ’95 Image and Vision Computing New Zealand (Industrial Research Ltd., Christchurch, New Zealand, 1995), pp. 143–148.

1991 (1)

1988 (1)

1987 (1)

1970 (1)

Belanger, P. A.

Beran, M. J.

M. J. Beran, G. B. Perrant, Theory of Partial Coherence (Prentice-Hall, Englewood Cliffs, N.J., 1964).

Burch, J. M.

A. Gerrard, J. M. Burch, Introduction to Matrix Methods in Optics (Wiley, London, 1975).

Burrus, C. S.

I. W. Selesnick, C. S. Burrus, “Fast convolution and filterings,” in The Digital Signal Processing Handbook, V. K. Madisetti, D. B. Williams, eds. (IEEE/CRC Press, Boca Raton, Fla., 1998), Chap. 8.

Cathey, W. T.

W. T. Cathey, Optical Information Processing and Holography (Wiley, New York, 1974).

Collins, S. A.

Fraser, D.

A. J. Lambert, D. Fraser, “An implementation of the fast Fresnel transform,” in IVCNZ’95 Image and Vision Computing New Zealand (Industrial Research Ltd., Christchurch, New Zealand, 1995), pp. 143–148.

Gaskill, J. D.

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978).

Gerrard, A.

A. Gerrard, J. M. Burch, Introduction to Matrix Methods in Optics (Wiley, London, 1975).

Goodman, J. W.

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

Hanson, S. G.

Lambert, A. J.

A. J. Lambert, “Optical image processing and its application,” Ph.D. dissertation (The University of New South Wales, Canberra, Australia, 1996).

A. J. Lambert, D. Fraser, “An implementation of the fast Fresnel transform,” in IVCNZ’95 Image and Vision Computing New Zealand (Industrial Research Ltd., Christchurch, New Zealand, 1995), pp. 143–148.

McKinley, W. G.

Perrant, G. B.

M. J. Beran, G. B. Perrant, Theory of Partial Coherence (Prentice-Hall, Englewood Cliffs, N.J., 1964).

Selesnick, I. W.

I. W. Selesnick, C. S. Burrus, “Fast convolution and filterings,” in The Digital Signal Processing Handbook, V. K. Madisetti, D. B. Williams, eds. (IEEE/CRC Press, Boca Raton, Fla., 1998), Chap. 8.

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

Stark, H.

H. Stark, F. B. Tuteur, Modern Electrical Communications—Theory and Systems (Prentice-Hall, Englewood Cliffs, N.J., 1979).

Tuteur, F. B.

H. Stark, F. B. Tuteur, Modern Electrical Communications—Theory and Systems (Prentice-Hall, Englewood Cliffs, N.J., 1979).

Yura, H. T.

J. Opt. Soc. Am. (1)

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

Opt. Lett. (2)

Other (10)

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

A. J. Lambert, “Optical image processing and its application,” Ph.D. dissertation (The University of New South Wales, Canberra, Australia, 1996).

M. J. Beran, G. B. Perrant, Theory of Partial Coherence (Prentice-Hall, Englewood Cliffs, N.J., 1964).

W. T. Cathey, Optical Information Processing and Holography (Wiley, New York, 1974).

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978).

I. W. Selesnick, C. S. Burrus, “Fast convolution and filterings,” in The Digital Signal Processing Handbook, V. K. Madisetti, D. B. Williams, eds. (IEEE/CRC Press, Boca Raton, Fla., 1998), Chap. 8.

H. Stark, F. B. Tuteur, Modern Electrical Communications—Theory and Systems (Prentice-Hall, Englewood Cliffs, N.J., 1979).

A. J. Lambert, D. Fraser, “An implementation of the fast Fresnel transform,” in IVCNZ’95 Image and Vision Computing New Zealand (Industrial Research Ltd., Christchurch, New Zealand, 1995), pp. 143–148.

A. Gerrard, J. M. Burch, Introduction to Matrix Methods in Optics (Wiley, London, 1975).

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

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