Differential Zernike filter for phasing of segmented mirror and image processing
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The major objective of this thesis is to study the differential Zernike filter and its applications in phasing segmented mirror and image processing. In terms of phasing, we provide both theoretical analysis and simulation for a differential Zernike filter based phasing technique, and find that the differential Zernike filter perform consistently better than its counterpart, traditional Zernike filter. We also combine the differential Zernike filter with a feedback loop, to represent a gradient-flow optimization dynamic system. This system is shown to be capable of separating (static) misalignment errors of segmented mirrors from (dynamical) atmospheric turbulence, and therefore compress the effects of atmospheric turbulence. Except for segmented mirror phasing, we also apply the Zernike feedback system in image processing. For the same system dynamics as well as in segment phasing, the Zernike filter feedback system is capable of compress the static noisy background, and makes the single particle tracking algorithm even working in case of very low signal-to-noise ratio. Finally, we apply an efficient multiple-particle tracking algorithm on a living cell image sequence. This algorithm is shown to be able to deal with higher particle density, while the single particle tracking methods are not working under this condition.