Super-resolution and apodization with discrete adaptive optics.

High-resolution imaging is of great importance in various fields. The use of pupil phase-only filters (PPF) exceeds the diffraction limit of the imaging system in a simple way. When dealing with distorted wavefronts, however, PPF require that aberrations be compensated for. In this paper, we introduce a novel technique consisting of the use of discrete adaptive optics with PPFs so that the compensating device implements the PPF at the same time. Analysis of the theory for point spread function reshaping using PPFs has enabled us to develop a new approach to characterizing apodizing filters. A validation experiment has been carried out, the first of its kind to our knowledge, in which a number of PPFs were combined with two levels of compensation. Our experimental results are discussed.

Amplitude image processing by diffractive optics.

In contrast to the standard digital image processing, which operates over the detected image intensity, we propose to perform amplitude image processing. Amplitude processing, like low pass or high pass filtering, is carried out using diffractive optics elements (DOE) since it allows to operate over the field complex amplitude before it has been detected. We show the procedure for designing the DOE that corresponds to each operation. Furthermore, we accomplish an analysis of amplitude image processing performances. In particular, a DOE Laplacian filter is applied to simulated astronomical images for detecting two stars one Airy ring apart. We also check by numerical simulations that the use of a Laplacian amplitude filter produces less noisy images than the standard digital image processing.

Non-Gaussian speckle statistics in adaptive-optics partial compensation.

Wave fronts distorted by the atmosphere can be partially reconstructed by use of adaptive-optics systems. The intensity statistics at the image plane is a function of the ratio D/r(0) and of the level of compensation performed by the adaptive-optics system. We show that a non-Gaussian statistics is obtained when the aperture diameter is slightly greater than the Fried parameter. This situation can frequently be found when one is working in the IR. The light statistics is obtained by use of a simple model to describe the atmosphere and application of the same procedure used in the analysis of scattered light. Special attention is paid to very high- and very low-compensation regimes.

Speckle statistics in partially corrected wave fronts.

Wave fronts distorted by the atmosphere preserve high-spatial-frequency information. This information can be retrieved by use of adaptive optics systems to correct the incoming wave front. This correction should be as nearly complete as possible. In experiments performed in the visible, only partial compensation is attainable. We provide a theoretical model to predict the intensity statistics of the light in the image center as a function of the number of Zernike polynomials corrected.

Rician distribution to describe speckle statistics in adaptive optics.

Adaptive optics systems allow us to retrieve high-spatial-frequency information that is preserved in the wave fronts distorted by the atmosphere. Although wave-front correction should be as complete as possible, only partial compensation is attainable in the visible. We provide a procedure that uses the Rician distribution to predict the intensity statistics of the light at the image center as a function of the number of corrected Zernike polynomials.