Abstract
A general and systematic analysis about the relationship between ABCD optical systems and the fractional Fourier transform (FRT) is provided. It is shown that the FRT can be implemented with an ABCD system but usually different scaling factors for the input and output functions must be used. The requirement for the property of direct additivity of the FRT order is derived for a cascade system; and the method of finding the final order of the FRT for a general cascade ABCD system by using the similarity theorem is discussed. As an application example of the results, an approach to observation of the FRT of continuously variable orders with a scale invariant input is demonstrated.
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