Abstract

Hexagonal sampling offers substantial computational efficiency in processing circularly band-limited and/or circularly symmetric functions and also offers a significant reduction of required data storage compared with rectangular sampling. Both Fraunhofer and Fresnel computer-generated holograms utilizing hexagonal sampling are capable of exploiting these properties. Hexagonal fast Fourier transform (FFT) and inverse fast Fourier transform (IFFT) algorithms have been developed along with efficient algorithms for generating the lens transmittance and free-space-transfer matrices that comprise software packages designed to accept hexagonally sampled input arrays and generate hexagonally sampled output arrays suitable for direct encoding into digital holograms.

© 1982 Optical Society of America

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1981

1977

1967

1966

1962

D. P. Petersen and D. Middleton-, "Sampling and reconstruction of wave-number-limited functions in N-dimensional Euclidean spaces," Inf. Control 5, 279–323 (1962).

Agrawal, G. P.

Brown, B. R.

B. R. Brown and A. W. Lohmann, "Complex spatial filtering with binary masks," Appl. Opt. 5, 967–969 (1966).

B. R. Brown and A. W. Lohmann, "Computer-generated binary holograms," IBM J. Res. Dev. 160–168 (1969).

Chan, D. S. K.

D. B. Harris, J. H. McClellan, D. S. K. Chan, and H. W. Schuessler, "Vector radix fast Fourier transform," presented at IEEE Conference on Acoustics, Speech and Signal Processing, May 9–11, 1977, Hartford, Connecticut.

Gold, B.

L. R. Robiner and B. Gold, Theory and Application of Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Harris, D. B.

D. B. Harris, J. H. McClellan, D. S. K. Chan, and H. W. Schuessler, "Vector radix fast Fourier transform," presented at IEEE Conference on Acoustics, Speech and Signal Processing, May 9–11, 1977, Hartford, Connecticut.

Kak, A.

A. Rosenfeld and A. Kak, Digital Picture Processing (Academic, New York, 1976).

Lax, M.

Lohmann, A. W.

McClellan, J. H.

D. B. Harris, J. H. McClellan, D. S. K. Chan, and H. W. Schuessler, "Vector radix fast Fourier transform," presented at IEEE Conference on Acoustics, Speech and Signal Processing, May 9–11, 1977, Hartford, Connecticut.

Mersereau, R. M.

R. M. Mersereau, "The processing of hexagonally sampled two-dimensional signals," Proc. IEEE 67, 930–949 (1979).

Middleton, D.

D. P. Petersen and D. Middleton-, "Sampling and reconstruction of wave-number-limited functions in N-dimensional Euclidean spaces," Inf. Control 5, 279–323 (1962).

Oppenheim, A. V.

A. V. Oppenheim and R. W. Schafer, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975).

Paris, D. P.

Petersen, D. P.

D. P. Petersen and D. Middleton-, "Sampling and reconstruction of wave-number-limited functions in N-dimensional Euclidean spaces," Inf. Control 5, 279–323 (1962).

Robiner, L. R.

L. R. Robiner and B. Gold, Theory and Application of Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975).

Rosenfeld, A.

A. Rosenfeld and A. Kak, Digital Picture Processing (Academic, New York, 1976).

Schafer, R. W.

A. V. Oppenheim and R. W. Schafer, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975).

Schuessler, H. W.

D. B. Harris, J. H. McClellan, D. S. K. Chan, and H. W. Schuessler, "Vector radix fast Fourier transform," presented at IEEE Conference on Acoustics, Speech and Signal Processing, May 9–11, 1977, Hartford, Connecticut.

Siegman, A. E.

Southwell, W. H.

Appl. Opt.

Inf. Control

D. P. Petersen and D. Middleton-, "Sampling and reconstruction of wave-number-limited functions in N-dimensional Euclidean spaces," Inf. Control 5, 279–323 (1962).

J. Opt. Soc. Am.

Opt. Lett.

Other

A. V. Oppenheim and R. W. Schafer, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975).

D. B. Harris, J. H. McClellan, D. S. K. Chan, and H. W. Schuessler, "Vector radix fast Fourier transform," presented at IEEE Conference on Acoustics, Speech and Signal Processing, May 9–11, 1977, Hartford, Connecticut.

B. R. Brown and A. W. Lohmann, "Computer-generated binary holograms," IBM J. Res. Dev. 160–168 (1969).

L. R. Robiner and B. Gold, Theory and Application of Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975).

A. Rosenfeld and A. Kak, Digital Picture Processing (Academic, New York, 1976).

R. M. Mersereau, "The processing of hexagonally sampled two-dimensional signals," Proc. IEEE 67, 930–949 (1979).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

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