Optimal Defocus for Phase Diversity Wave Front Retrieval

Phase diversity techniques are widely employed in solar astronomy to evaluate and correct the aberrations stemming from atmospheric turbulences, the telescope, and its instruments. The method uses information provided by a pair of images. One of them is usually focused while the other one is defocused. The amount of defocus to be induced is somehow arbitrary, though. In this work we carry out a series of numerical experiments with artificial solar images to investigate the performance of phase diversity for different choices of the relative defocus among the two images. The experiments allow us to determine the amount of defocus that produces the best wave front restoration when changing: (1) the number of Zernike polynomials of the retrieved and/or incident wave fronts; (2) the signal-to-noise ratio of the images; (3) the amplitude of the incident aberrations; and (4) the observed scene. We find a correlation between the amount of defocus needed for optimal restorations and the number of Zernike polynomials employed in the optimization. Values larger than the typically accepted choice of 1λ (peak to peak) are obtained in most cases.