Abstract

A brief description is given of a method for approximate synthesis of multilayer filters consisting of either homogeneous layers or inhomogeneous films. The method is based on the fact that the amplitude reflectance is the approximate Fourier transform of the function ½U′(p)/U(p), where U(p) is the effective refractive index as a function of the optical thickness p. Two forms of the sampling theorem are applied to obtain explicit expressions for the film parameters in terms of the specified reflectivity at certain sampling values of the frequency. Numerical examples are included.

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  1. E. Delano, Ph. D. thesis, University of Rochester, June 1966.
  2. 2 O. S. Heavens, Optical Properties of Thin Solid Films (Dover Publications, Inc., New York, 1965), Sec. 4.10, p. 80.
  3. C. H. Greenewalt, W. Brandt, and D. D. Friel, J. Opt. Soc. Am. 50, 1005 (1960).
  4. R. J. Pegis, J. Opt. Soc. Am. 51, 1255 (1961).
  5. R. J. Pegis (Private communication, July 1962).
  6. Z. Knittl, Appl. Opt. 6, 331, (1967).
  7. H. Wolter, in Progress in Optics, Vol. I, E. Wolf, Ed. (North-Holland Publ. Co., Amsterdam, 1961), Ch. V, p. 157.
  8. D. A. Linden, Proc. IRE 47, 1219 (1959).
  9. W. Weinstein, Vacuum 4, 3 (1954).
  10. E. H. Linfoot, Fourier Methods in Optical Image Evaluation (Focal Press, London, 1964), Appendix, p. 75.
  11. A. Papoulis, The Fourier Integral and its Applications (McGraw-Hill Book Co., New York, 1962), Appendix 1, p. 269.
  12. S. Goldman, Information Theory (Prentice-Hall, Inc., New York, 1954), Secs. 2.1, 2.2; see also Appendix XII, p. 368.
  13. R. Bracewell, The Fourier Transform and its Applications (McGraw-Hill Book Co., New York, 1965), Ch. 10.
  14. C. Lanczos, Applied Analysis (Prentice-Hall, Inc., Englewood Cliffs, N. J., 1964) Ch. IV.

Bracewell, R.

R. Bracewell, The Fourier Transform and its Applications (McGraw-Hill Book Co., New York, 1965), Ch. 10.

Brandt, W.

C. H. Greenewalt, W. Brandt, and D. D. Friel, J. Opt. Soc. Am. 50, 1005 (1960).

Delano, E.

E. Delano, Ph. D. thesis, University of Rochester, June 1966.

Friel, D. D.

C. H. Greenewalt, W. Brandt, and D. D. Friel, J. Opt. Soc. Am. 50, 1005 (1960).

Goldman, S.

S. Goldman, Information Theory (Prentice-Hall, Inc., New York, 1954), Secs. 2.1, 2.2; see also Appendix XII, p. 368.

Greenewalt, C. H.

C. H. Greenewalt, W. Brandt, and D. D. Friel, J. Opt. Soc. Am. 50, 1005 (1960).

Heavens, O. S.

2 O. S. Heavens, Optical Properties of Thin Solid Films (Dover Publications, Inc., New York, 1965), Sec. 4.10, p. 80.

Knittl, Z.

Z. Knittl, Appl. Opt. 6, 331, (1967).

Lanczos, C.

C. Lanczos, Applied Analysis (Prentice-Hall, Inc., Englewood Cliffs, N. J., 1964) Ch. IV.

Linden, D. A.

D. A. Linden, Proc. IRE 47, 1219 (1959).

Linfoot, E. H.

E. H. Linfoot, Fourier Methods in Optical Image Evaluation (Focal Press, London, 1964), Appendix, p. 75.

Papoulis, A.

A. Papoulis, The Fourier Integral and its Applications (McGraw-Hill Book Co., New York, 1962), Appendix 1, p. 269.

Pegis, R. J.

R. J. Pegis (Private communication, July 1962).

R. J. Pegis, J. Opt. Soc. Am. 51, 1255 (1961).

Weinstein, W.

W. Weinstein, Vacuum 4, 3 (1954).

Wolter, H.

H. Wolter, in Progress in Optics, Vol. I, E. Wolf, Ed. (North-Holland Publ. Co., Amsterdam, 1961), Ch. V, p. 157.

Other (14)

E. Delano, Ph. D. thesis, University of Rochester, June 1966.

2 O. S. Heavens, Optical Properties of Thin Solid Films (Dover Publications, Inc., New York, 1965), Sec. 4.10, p. 80.

C. H. Greenewalt, W. Brandt, and D. D. Friel, J. Opt. Soc. Am. 50, 1005 (1960).

R. J. Pegis, J. Opt. Soc. Am. 51, 1255 (1961).

R. J. Pegis (Private communication, July 1962).

Z. Knittl, Appl. Opt. 6, 331, (1967).

H. Wolter, in Progress in Optics, Vol. I, E. Wolf, Ed. (North-Holland Publ. Co., Amsterdam, 1961), Ch. V, p. 157.

D. A. Linden, Proc. IRE 47, 1219 (1959).

W. Weinstein, Vacuum 4, 3 (1954).

E. H. Linfoot, Fourier Methods in Optical Image Evaluation (Focal Press, London, 1964), Appendix, p. 75.

A. Papoulis, The Fourier Integral and its Applications (McGraw-Hill Book Co., New York, 1962), Appendix 1, p. 269.

S. Goldman, Information Theory (Prentice-Hall, Inc., New York, 1954), Secs. 2.1, 2.2; see also Appendix XII, p. 368.

R. Bracewell, The Fourier Transform and its Applications (McGraw-Hill Book Co., New York, 1965), Ch. 10.

C. Lanczos, Applied Analysis (Prentice-Hall, Inc., Englewood Cliffs, N. J., 1964) Ch. IV.

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