<title>Adaptive wavefront control using a nonlinear Zernike filter</title>

A conventional Zernike filter measures wavefront phase by superimposing the aberrated input beam with a phase-shifted version of its zero-order spectral component. The Fourier- domain phase-shifting is performed by a fixed phase-shifting dot on a glass slide in the focal plane of a Fourier- transforming lens. Using an optically-controlled phase spatial light modulator (SLM) instead of the fixed phase-shifting dot, we have simulated and experimentally demonstrated a nonlinear Zernike filter robust to wavefront tilt misalignments. In the experiments, a liquid-crystal light valve (LCLV) was used as the phase SLM. The terminology 'nonlinear' Zernike filter refers to the nonlinear filtering that takes place in the Fourier domain due to the phase change for field spectral components being proportional to the spectral component intensities. Because the Zernike filer output intensity is directly related to input wavefront phase, a parallel, distributed feedback system can replace the wavefront reconstruction calculations normally required in adaptive- optic phase correction systems. Applications include high- resolution phase distortion suppression for atmospheric turbulence, optical phase microscopy, and compensation of aberrations in optical system components. A factor of eight improvement in Strehl ratio was obtained experimentally, and simulation results suggest that even better performance could be obtained by replacing the LCLV with a more sophisticated optically-controlled phase SLM.