Matrix description of near-field diffraction and the fractional Fourier transform
JOSA A, Vol. 16, Issue 2, pp. 316-322 (1999)
http://dx.doi.org/10.1364/JOSAA.16.000316
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Abstract
We describe a matrix multiplication procedure for evaluating the pixelated version of the near-field pattern of a discrete, one- or two-dimensional input. We show that for an input with N×N pixels, in an area d×d, it is necessary to evaluate the Fresnel diffraction pattern at distances z≥d2/λN. Our numerical algorithm is also useful for evaluating the fractional Fourier transform by multiplying by a special phase matrix with fractional parameter ε. If the phase matrix is evaluated at ε=1, we find the discrete Fourier transform matrix.
© 1999 Optical Society of America
OCIS Codes
(050.1960) Diffraction and gratings : Diffraction theory
(350.6980) Other areas of optics : Transforms
Citation
Sara Bradburn Tucker, Jorge Ojeda-Castañeda, and W. Thomas Cathey, "Matrix description of near-field diffraction and the fractional Fourier transform," J. Opt. Soc. Am. A 16, 316-322 (1999)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-2-316
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