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The Wigner distribution function (WDF) offers the representation of a signal function in terms of position and spatial-frequency variables simultaneously. The fractional Fourier transform (FRT) corresponds to the rotation of the WDF in phase space. This paper considers the special affine Fourier transformation (SAFT) in phase space and the corresponding integral transformation of the signal function. The SAFT is then applied to standard operations in geometric optics, where the operations of lens, free-space propagation, magnification and the FRT are seen to be the Abelian subgroups of the SAFT. The SAFT is then applied to an optical system with small imperfections, to the filtering problem (wavelet and widowed FT) and to afocal imaging systems.

Additional information

Authors: ABE S, Nihon University, College of Science and Technology, Narashinodai, Chiba (JP);SHERIDAN J T, JRC Ispra (IT)
Bibliographic Reference: Paper presented: Focus on Microscopy '95, Taipei (TW), April 18-20, 1995
Availability: Available from (1) as Paper EN 38907 ORA
Record Number: 199510642 / Last updated on: 1995-07-07
Original language: en
Available languages: en