Optical differentiation wavefront sensing with binary pixelated transmission filters.

Sensors measuring the spatial phase of optical waves are widely used in optics. The optical differentiation wavefront sensor(ODWS) reconstructs the wavefrontof an optical wave from wavefrontslope measurements obtained by inducing linear field-transmission gradients in the far-field. Its dynamic rangeand sensitivity can be adjusted simply by changing the gradient slope. We numerically and experimentally demonstrate the possibility of implementing the spatially varying transmission gradient using distributions of small pixels that are either transparent or opaque. Binary pixelated filters are achromatic and can be fabricated with high accuracy at relatively low cost using commercial lithography techniques. We study the impact of the noise resulting from pixelation and binarization of the far-field filter for various test wavefrontsand sensor parameters. The induced wavefronterror is approximately inversely proportional to the pixel size. For an ODWS with dynamic rangeof 100 rad/mm over a 1-cm pupil, the error is smaller than λ/15 for a wide range of test wavefrontswhen using 2.5-μm pixels. We experimentally demonstrate the accuracy and consistency of a first-generation ODWS based on binary pixelated filters.