Analytical and numerical comparison of encoding methods for computer-generated diffractive optical elements

We present a new, to our knowledge, analysis of the performances of common encoding schemes that are used to design computer-generated diffractive optical elements. A statistical analysis of the fringe width and the positional errors, which are introduced by the encoding process, is used to calculate their effects on the diffraction efficiency and the noise. The analysis is applied to interferogram-type encoding methods that are most suited to analytically designed elements, in particular, the polygon-fringe-tracing and the bitmap, or mosaic, methods. Predictions are verified by use of both numerical simulation and existing empirical results. The analysis is used to compare the relative merits of the different encoding schemes quantitatively in terms of optical performance and computational efficiency criteria.