Analytic Computer Generated Hologram Design

TL;DR

This paper presents an analytic method for designing computer generated holograms that transform spherical wavefronts into aspheric shapes for interferometric metrology, combining theoretical derivation with potential numerical implementation.

Contribution

It introduces an analytic approach to CGH design for aspheres using the grating equation, enhancing precision in interferometric measurements.

Findings

Analytic derivation of CGH design for aspheres

Method accommodates complex aspheric shapes

Potential for numerical implementation in complex cases

Abstract

For a given asphere the grating equation is used to derive the design for a Computer Generated Hologram (CGH), sometimes referred to as a diffractive null corrector. The CGH converts a spherical wavefront to the shape appropriate for the given asphere as required for interferometric metrology. The derivation is effectively analytic but may require numerical implementation in certain cases depending on the complexity of the shape of the asphere and the accuracy required.