In this study the general algorithm for the fractionalization of the linear
cyclic integral transforms is established. It is shown that there are an i
nfinite number of continuous fractional transforms related to a given cycli
c integral transform. The main properties of the fractional transforms used
in optics are considered. As an example, two different types of fractional
Hartley transform are introduced, and the experimental setups for their op
tical implementation are proposed. (C) 2000 Optical Society of America [S07
40-3232(00)00312-4] OCIS codes: 070.0070, 070.2590, 070.6020.