A quasi-discrete Hankel transform (QDHT) is presented as a new and efficient framework for numerical evaluation of the zero-order Hankel transform. A discrete form of Parseval's theorem is obtained for the first time to the authors' knowledge, and the transform matrix is discussed. It is shown that the S factor, defined as the products of a truncated radius, is critical to building the QDHT.

We derive the integral representation of a fractional Hankel transform (FRHT) from a fractional Fourier transform. Some basic properties of the FRHT such as Parseval's theorem and its optical implementation are discussed qualitatively.

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