Supporting quadric method for designing diffractive optical elements in the scalar diffraction theory framework

We present a formulation of the supporting quadric method (SQM) taking into account diffraction effects and allowing one to calculate the phase function of a diffractive optical element (DOE) generating a prescribed intensity distribution. In the method, the DOE phase is represented as a piecewise smooth function constituted by the phase functions of lenses (quadrics) focusing the incident beam to the points of the required distribution. The quadric parameters are calculated using a gradient method minimizing an error function representing the difference between the generated and required intensity distributions. Importantly, we calculate the gradient of the error function with respect to the quadric parameters in the framework of the scalar diffraction theory (SDT) in an analytical form. The presented examples of DOE design demonstrate good performance of a hybrid approach based on using the geometrical-optics SQM solution as a starting point for the proposed SQM operating in the SDT framework.