General theory for performing an optical transform

A general theory for making an optical transform is presented using amplitude-phase holographic lenses (masks). It can be shown that an optical system composed of many amplitude-phase masks can do any given linear transform. A set of equations for determining the amplitude-phase distributions of masks is given. A feedback iterative approach to deal with these equations is also suggested. We show that any given optical transform can be achieved even with a single mask by increasing the number of sampling points in the mask. The relevant equations and the necessary conditions satisfied by the mask are also given. To free the fabrication of the mask from difficulty in technique, sometimes the information quantity carried by the single mask must be relaxed. The dual-mask system is discussed in detail. The general theory is demonstrated by examples for performing the four- and eight-sequence Walsh transforms in three different orders. The results agree well with the theory. Some experimental results and relevant applications are also reviewed briefly.