Abstract

A new type of phase-only filter is described for wave-front construction, in which both the amplitude and phase information necessary to construct an arbitrary image over a limited field are encoded. It is shown that this phase-only filter can duplicate the performance of an ideal complex-valued spatial filter (a filter that controls both amplitude and phase transmittance). This phase-only filter controls the amplitude transmittance by the use of a modulated high-frequency phase carrier that diffracts a controlled amount of light into the image. This type of filter is particularly useful in the implementation of computational wave-front construction, because the maximum spatial frequency that must be plotted is associated with the image and not the carlier. The performance of the filter is examined both numerically and experimentally.

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  1. E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962).
  2. A. Vander Lugt, IEEE Trans. IT-10, 139 (1964).
  3. W. T. Cathey, Jr., Appl. Opt. 9, 1478 (1970).
  4. In general, complicated wave fronts will be filtered. When used to form an image, the incident wave front will usually be plane or spherical.
  5. R. M. Bracewell, The Fourier Transform and Its Applications (McGraw—Hill, New York, 1965).
  6. If [equation] then [equation].
  7. H. M. Smith, J. Opt. Soc. Am. 58, 533 (1968).
  8. The system we used accommodated 256-point transforms.
  9. APL/360 is available from IBM as a program product.
  10. G. C. Danielson and C. Lanczos, J. Franklin Inst. 233, 365 (1942).
  11. J. W. Cooley and J. W. Tukey, Math. Comp. 19, 297 (1965).
  12. L. B. Lesem, P. M. Hirsch, and J. A. Jordan, Jr., IBM J. Res. Develop. 13, 150 (1969).
  13. D. Kermisch, J. Opt. Soc. Am. 60, 15 (1970).

Bracewell, R. M.

R. M. Bracewell, The Fourier Transform and Its Applications (McGraw—Hill, New York, 1965).

Cathey, Jr., W. T.

W. T. Cathey, Jr., Appl. Opt. 9, 1478 (1970).

Cooley, J. W.

J. W. Cooley and J. W. Tukey, Math. Comp. 19, 297 (1965).

Danielson, G. C.

G. C. Danielson and C. Lanczos, J. Franklin Inst. 233, 365 (1942).

Hirsch, P. M.

L. B. Lesem, P. M. Hirsch, and J. A. Jordan, Jr., IBM J. Res. Develop. 13, 150 (1969).

Jordan, Jr., J. A.

L. B. Lesem, P. M. Hirsch, and J. A. Jordan, Jr., IBM J. Res. Develop. 13, 150 (1969).

Kermisch, D.

D. Kermisch, J. Opt. Soc. Am. 60, 15 (1970).

Lanczos, C.

G. C. Danielson and C. Lanczos, J. Franklin Inst. 233, 365 (1942).

Leith, E. N.

E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962).

Lesem, L. B.

L. B. Lesem, P. M. Hirsch, and J. A. Jordan, Jr., IBM J. Res. Develop. 13, 150 (1969).

Lugt, A. Vander

A. Vander Lugt, IEEE Trans. IT-10, 139 (1964).

Smith, H. M.

H. M. Smith, J. Opt. Soc. Am. 58, 533 (1968).

Tukey, J. W.

J. W. Cooley and J. W. Tukey, Math. Comp. 19, 297 (1965).

Upatnieks, J.

E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962).

Other

E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962).

A. Vander Lugt, IEEE Trans. IT-10, 139 (1964).

W. T. Cathey, Jr., Appl. Opt. 9, 1478 (1970).

In general, complicated wave fronts will be filtered. When used to form an image, the incident wave front will usually be plane or spherical.

R. M. Bracewell, The Fourier Transform and Its Applications (McGraw—Hill, New York, 1965).

If [equation] then [equation].

H. M. Smith, J. Opt. Soc. Am. 58, 533 (1968).

The system we used accommodated 256-point transforms.

APL/360 is available from IBM as a program product.

G. C. Danielson and C. Lanczos, J. Franklin Inst. 233, 365 (1942).

J. W. Cooley and J. W. Tukey, Math. Comp. 19, 297 (1965).

L. B. Lesem, P. M. Hirsch, and J. A. Jordan, Jr., IBM J. Res. Develop. 13, 150 (1969).

D. Kermisch, J. Opt. Soc. Am. 60, 15 (1970).

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