New modal wave-front sensor: a theoretical analysis

We present a new design of a modal wave-front sensor capable of measuring directly the Zernike components of an aberrated wave front. The sensor shows good linearity for small aberration amplitudes and is particularly suitable for integration in a closed-loop adaptive system. We introduce a sensitivity matrix and show that it is sparse, and we derive conditions specifying which elements are necessarily zero. The sensor may be temporally or spatially multiplexed, the former using a reconfigurable optical element, the latter using a numerically optimized binary optical element. Different optimization schemes are discussed, and their performance is compared.