Calculation of the Transmission Function of a Generalized Spiral Phase Plate to Form a Given Curve

We consider the inverse diffraction problem for a generalized spiral phase plate. For a given luminous curve in the focal plane, the transmission function of the plate forming this curve is calculated. It is assumed that the curve is specified analytically in polar coordinates in the form of an explicit dependence of the radius on the angle. We give the conditions imposed on the curve under which the problem certainly has a solution. Also there are examples of solving the direct problem when curves that do not satisfy these conditions are formed.