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Optics Letters

Optics Letters


  • Vol. 20, Iss. 10 — May. 15, 1995
  • pp: 1178–1180

Optical interpretation of a complex-order Fourier transform

Chun-Ching Shih  »View Author Affiliations

Optics Letters, Vol. 20, Issue 10, pp. 1178-1180 (1995)

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It is demonstrated that the definition of a fractional-order Fourier transform can be extended into the complex-order regime. A complex-order Fourier transform deals with the imaginary part as well as the real part of the exponential function in the integral. As a result, while the optical implementation of fractional-order Fourier transform involves gradient-index media or spherical lenses, the optical interpretation of complex-order Fourier transform is practically based on the convolution operation and Gaussian apertures. The beam width of a Gaussian beam subjected to the complex-order Fourier transform is obtained analytically with the ABCD matrix approach.

© 1995 Optical Society of America

Original Manuscript: December 13, 1994
Published: May 15, 1995

Chun-Ching Shih, "Optical interpretation of a complex-order Fourier transform," Opt. Lett. 20, 1178-1180 (1995)

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