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Applied Optics

Applied Optics


  • Vol. 22, Iss. 14 — Jul. 15, 1983
  • pp: 2227–2232

Fourier series approach to synthesis

Sami A. Shakir  »View Author Affiliations

Applied Optics, Vol. 22, Issue 14, pp. 2227-2232 (1983)

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The specified reflectance of a multilayer optical filter is formulated as a Fourier series. The coefficients are related via sample relations to the necessary refractive indices of the layers. The method is approximate but has the advantage of simplicity and efficiency, which makes it a useful design tool. The method is also useful as a companion to the exact methods of synthesis since it can provide the starting values for these exact methods. A versatile design example is solved to demonstrate the utility of the method. It is also shown that once a set of refractive indices is found, an infinite set of solutions can be found by simple scaling of the refractive indices.

© 1983 Optical Society of America

Original Manuscript: January 19, 1983
Published: July 15, 1983

Sami A. Shakir, "Fourier series approach to synthesis," Appl. Opt. 22, 2227-2232 (1983)

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  1. See, for example, the excellent review article by E. Delano, R. J. Pegis, in Progress in Optics, Vol. 4, E. Wolf, Ed. (North-Holland, Amsterdam, 1969), p. 67. [CrossRef]
  2. E. Delano, J. Opt. Soc. Am. 57, 1529 (1967). [CrossRef]
  3. P. H. Berning, Theory and Calculations of Optical Thin Films in Physics of Thin Films, Vol. 1, G. Hass, Ed. (Academic, New York, 1963), p. 69.
  4. See, for example, CRC Standard Mathematical Tables, W. H. Peyer, Ed. (CRC Press, Cleveland, Ohio, 1979), p. 465.
  5. L. D. Faddeev, J. Math. Phys. 4, 72 (1963). [CrossRef]
  6. See, for example, the review article by P. K. Tien, Rev. Mod. Phys. 49, 361 (1977). [CrossRef]

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