Freeform Optical Design of Smooth Hermite Radial Basis Function Implicit Surface under Point-Normal Constraints

The freeform surface has become a primary optical design method due to its higher degree of freedom,and the quadratic supporting method is one of the mainstream methods of freeform optical design because of its inherent integrability.Nevertheless,the quadratic supporting surface is usually not smooth,and its smooth enveloping surface needs to be further solved to satisfy the optical manufacturing requirements.The sampling value points and corresponding unit normal vectors on the quadratic supporting surface are used as constraints,and the implicit surface method based on the Hermite radial basis is adopted to successfully generate a smooth freeform optical surface that can project a uniform square spot on the target screen.The point-normal constraints are optimized in terms of value point interpolation and increasing the supporting sub-surface array.And the optical simulation results show that proposed algorithm has more minor errors of value point and normal vector,and better shapes the light beam.