Starting from a complex fractional Fourier transformation [Opt. Lett. <b>28</b>, 680 (2003)], it is shown that the integral kernel of a fractional Hankel transformation is equivalent to the matrix element of an appropriate operator in the charge-amplitude state representations; i.e., the fractional Hankel transformation is endowed with a definite physical meaning (definite quantum-mechanical representation transform).
© 2003 Optical Society of America
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing
(070.4690) Fourier optics and signal processing : Morphological transformations
(270.0270) Quantum optics : Quantum optics
Hong-yi Fan, "Fractional Hankel transform studied by charge-amplitude state representations and complex fractional Fourier transformation," Opt. Lett. 28, 2177-2179 (2003)