Hybrid RBF and local φ-polynomial freeform surfaces

Abstract

Advances in slow-servo single point diamond turning enables fabrication of freeform optical elements. Freeform optical elements, which are by definition rotationally non-symmetric, will have a profound importance in the future of optical technology. Historically, ortho gonal polynomials added onto conic sections have been extensively used for description of optical surface shapes. More recently, local shape descriptors, specifically radial basis functions, have been investigated for optical shape description. In this paper, we reveal an efficient and accurate localized hybrid method combining in one implementation assets of both radial basis functions and φ-polynomials for freeform shape description, uniquely applicable across any aperture shape. Initial results show that the proposed method yields subnanometer accuracy with as few as 25 terms of φ-polynomials. Subnanometer accuracy is required for the stringent conditions of lithography and related precision optics applications. Less stringent conditions are also shown to be achieved with as few as 16 terms φ-polynomials.