Fast & Furious focal-plane wavefront sensing

We present two complementary algorithms suitable for using focal-plane measurements to control a wavefront corrector with an extremely high-spatial resolution. The algorithms use linear approximations to iteratively minimize the aberrations seen by the focal-plane camera. The first algorithm, Fast & Furious (FF), uses a weak-aberration assumption and pupil symmetries to achieve fast wavefront reconstruction. The second algorithm, an extension to FF, can deal with an arbitrary pupil shape; it uses a Gerchberg–Saxton (GS)-style error reduction to determine the pupil amplitudes. Simulations and experimental results are shown for a spatial-light modulator controlling the wavefront with a resolution of 170×170  pixels. The algorithms increase the Strehl ratio from ∼0.75 to 0.98–0.99, and the intensity of the scattered light is reduced throughout the whole recorded image of 320×320  pixels. The remaining wavefront rms error is estimated to be ∼0.15  rad with FF and ∼0.10  rad with FF-GS

Calibrating a high-resolution wavefront corrector with a static focal-plane camera

We present a method to calibrate a high-resolution wavefront (WF)-correcting device with a single, static camera, located in the focal-plane; no moving of any component is needed. The method is based on a localized diversity and differential optical transfer functions to compute both the phase and amplitude in the pupil plane located upstream of the last imaging optics. An experiment with a spatial light modulator shows that the calibration is sufficient to robustly operate a focal-plane WF sensing algorithm controlling a WF corrector with 40,000 degrees of freedom. We estimate that the locations of identical WF corrector elements are determined with a spatial resolution of 0.3% compared to the pupil diameter

Focal-plane wavefront sensing with high-order adaptive optics systems

We investigate methods to calibrate the non-common path aberrations at an adaptive optics system having a wavefront-correcting device working with an extremely high resolution (larger than 150x150 correcting elements). We use focal-plane images collected successively, the corresponding phase-diversity information and numerically efficient algorithms to calculate the required wavefront updates. Different approaches are considered in numerical simulations, and laboratory experiments are shown to confirm the results. We compare the performances of the standard Gerchberg-Saxton algorithm, Fast and Furious (use of small-phase assumption to take advantage of linearisation) and recently proposed phase-retrieval methods based on convex optimisation. The results indicate that the calibration task is easiest with algorithms similar to Fast and Furious, at least in the framework we considered.