Direct sampling for diffractive microlens encoding from a rigorous point of view

Rigorous diffraction theory is applied to analyse the direct-sampling (DS) encoding method, which is based on scalar diffraction theory. For given fabrication constraints and constant sampling width of the lens function, the quantized phase profiles obtained with scalar DS are close to the optimum solutions, even for grating period to wavelength ratios (Δb/λ) as small as about 3. For smaller ratios, the phase profiles obtained by DS can be improved by up to 25%, using a straightforward rigorous steepest-gradient optimization. Applied to cylindrical lenses with NA = 0.5 and 0.63, coding with DS and with rigorously improved DS gives quite similar results for the total diffraction efficiency.