B-spline interpolation of scattered phase data of computer generated hologram for null test of freeform surface

Designing methods of null test computer generated hologram (CGH) for freeform surface optical element are researched. Bicubic non-uniform B-spline interpolation is used to fit a continuous phase function from scattered phase compensation data, which is calculated by universal ray tracing numerical method. Matrix representation of bicubic B-spline and monotonicity of CGH phase function are used to calculate the precise intersection lines of planes paralleling to x-y plane and the interpolated B-spline surface, and the positions of fringes of a phase-only CGH are solved with high accuracy. Finally a design example of null test CGH for freeform surface optical element is presented.