Adaptive optics in speckle interferometry and in super-resolution

This thesis describes innovative techniques for reducing speckle noise and improving the intensity profile of the speckle correlation fringes. The methods are based on reducing the range of the modulation intensity values of the speckle interference pattern. After the fringe pattern is corrected adaptively at each pixel, a simple morphological filtering of the fringes is sufficient to obtain smoothed fringes. The concepts are presented both analytically and by simulation by using computer-generated speckle patterns and experimental verifications are performed wherever possible. A new generalized method for designing continuous amplitude-only pupil filters for transverse superresolution using a nonlinear programming method is also presented. The thesis emphasises the principal advantage of amplitude-only filters over their phase-only counterparts, that the side lobe intensities can be highly reduced along with the spot size. A quantitative comparison with continuous phase-only filters as well as the two-zone binary phase filter is shown with respect to spot size and ratio of side lobe to central peak intensity. The work is extended to combine the advantages of amplitude and phase filters in one complex filter that performs better than either phase or amplitude filters designed so far. The performance here refers to having a smaller spot size along with higher peak to side lobe intensity ratio. Using numerical simulation the limitations of phase and amplitude filters are assessed. The experimental verification of the designed combination filter is performed with two LCD spatial light modulators used for displaying separately the phase and amplitude part of the filter. Results obtained from this setup confirm the simulation. Finally, the effect of optical superresolution on speckle correlations is studied. Simulations reveal that using a lateral super-resolution pupil filter more than twice the out of plane correlation length of the clear pupil can be achieved. This means that the measurement range in speckle correlation measurements doubles. To verify the correlation length an experiment is performed using a liquid crystal (LCD) spatial light modulator as a programmable superresolution filter. The results corroborate the simulation.