The design of free-form surfaces usually adopts the GS algorithm (Gerchberg-Saxton algorithm). The GS algorithm solves the phase distribution of the free-form surface through an iterative optimization process. The specific steps include:
Give an initial complex amplitude estimate of the input surface, where the input surface is the back surface of the free-form surface, and the initial phase is the phase change introduced by the free-form surface.
The light wave is transmitted to a specified distance by angular spectrum diffraction to obtain the complex amplitude distribution of the output surface.
Appropriate constraints are made in the output surface, and the amplitude of the output surface is replaced with the desired amplitude to obtain the updated complex amplitude of the output surface.
The light wave is transmitted back to the input surface by angular spectrum diffraction to obtain the updated complex amplitude distribution of the input surface.
Appropriate constraints are made in the input surface, and the amplitude of the input surface is replaced with the desired amplitude to obtain the updated complex amplitude estimate of the input surface .