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UBC Theses and Dissertations

Reconstruction of stellar images from correlations Shi, Xiaotian


The problem of object reconstruction from a series of short-exposure astronomical image data observed by ground-based telescopes is addressed. The observations are seriously degraded by atmospheric turbulence as well as corrupted by photon noise, detection noise and background noise. An approach for the reconstruction of the unknown object using the "self cross correlation” is proposed and implemented. This self cross correlation is defined as the cross correlation between an image observation and a truncated part of it. The relation amongst the phase of the cross spectrum, the phase of the object and the edges in the object are established. Based on these relations some efficient and effective algorithms for retrieving the unknown phase of the object and its modulus are developed. These algorithms are found to be insensitive to the presence of noise. Writing the Fourier transform (FT) of an image a as IA en)°, we call the inverse FT of the phasor part eie° as the phasor-image of a. We show that the phasor-image of the self cross correlation preserves the edges of the unknown object. If the object does not contain edges then its phasor-image represents an estimate of the Fourier phase of the unknown object. If all the stars and sub-objects in the object have edges then a phase retrieval method based on the iterative FT method is proposed. In this case the iterative FT method uses the edges obtained from the phasor-image of the average cross spectrum as object support bounds constraints. If some of the stars or sub-objects have edges then a non iterative phase retrieval method is developed. If none of the stars has edges then a modified version of this method is used to retrieve the object phase. We also address the anisoplanatic atmospheric turbulence case. We show that our approach can be extended to deal with the object reconstruction problem under such a condition. This is unlike the existing methods which only apply to the isoplanatic case. We evaluate the performance of our algorithms by comparing the signal-to-noise ratios with those of existing reconstruction methods. The results from both simulated and real astronomical data demonstrate the superiority of our methods in accuracy and computational speed.

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