Practical notes on designing and analysing thick holographic optical elements

Equations for tracing rays through (aspheric) holographic optical elements (HOE) are reviewed, and, in addition, the diffraction efficiency of a thick HOE is taken into account. Expressions for calculating the phase functions of aspheric recording wave fronts of a thick HOE in the presence of a wavelength shift are given. A simple least squares fitting algorithm is used to compute analytic expressions of these phase functions. Finally, a method to calculate a focus of rays is described.