Study of Adaptive Optics Images by means of Multiscalar Transforms

Adaptive optics (AO) systems are used to increase the spatial resolution achieved by ground-based telescopes, which are limited by the atmospheric motion of air layers above them. Therefore, the real cut-off frequency is extended closer to the theoretical diffraction limit of the telescope thus allowing more high-frequency information from the object to be present in the image. Nevertheless, although the goal of image reconstruction and deconvolution algorithms is basically the same (i.e., to recover a “real” diffracted limit image, free of noise, from the object), and since the correction of AO is not complete (i.e., the effective cut-off frequency achieved by AO is still below the theoretical diffraction limit), the simultaneous use of such deconvolution algorithms over dataset acquired with AO is possible and desirable to further enhance their contrast. On the other hand, multiresolution tools like the wavelet transform (WT) have been historically introduced into multiple deconvolution schemes improving their performance with respect to their non-wavelet counterparts. The ability of such transforms to separate image components depending on their frequency content results in solutions that are generally closer to the real object. On the other hand, AO community generally states that, due to the high variability of AO PSFs is necessary to update the PSF estimate during the reconstruction process. Hence, the use of blind and myopic deconvolution algorithms should be unavoidable and yields to better results than those obtained by the static-PSFs codes. Therefore, being the aforementioned paragraphs the current state-of-art of AO imaging, this thesis yields the following topics/goals: 1. The static-PSF algorithm AMWLE has been applied over binary systems simulated for the 3-m Shane telescope to evaluate the photometric accuracy of the reconstruction. Its performance is compared with the PSF-fitting algorithm StarFinder, commonly used by the AO community, as well as other algorithms like FITSTAR, PDF deconvolution and IDAC. Results shown that AWMLE is able to produce better results than StarFinder and FITSTAR, and very similar results with respect to the rest of codes, especially for high Strehl ratios (SR) and matched PSFs. 2. A new deconvolution algorithm called ACMLE, based on the curvelet transform (CT) and a maximum likelihood estimator (MLE), has been designed for the reconstruction of extended and/or elongated objects. ACMLE has been tested together with AMWLE and blind/myopic codes such as MISTRAL and IDAC over Saturn and galaxy simulated images for the 5-m. Hale telescope. It is shown that the performance in the presence of noise of the multiresolution static-PSF algorithms is better than myopic and blind algorithms, thus showing that the control of noise is as important as the update of the PSF estimate during the reconstruction process. 3. A unidimensional WT has been applied in the spectral deconvolution of integral field spectroscopy (IFS) datacubes for direct imaging of exoplanets with EPICS instrument, which will be installed at the forthcoming 39-m E-ELT telescope. When this approach is compared with the classical non-wavelet one, an improvement of 1 mag from angle separations equal to 73 mas is devised. Furthermore, detection of close-in planets, between 43 and 58 mas also benefit of the application of wavelets. The use of WT allows the APLC chronograph to obtain similar results with respect to the apodizer-only solution, especially with increasing Talbot length, thus showing that WT classify planet frequency components and chromatic aberrations in different scales. Preliminary results for HARMONI spectrograph are also shown. This thesis opens several lines of research that will be addressed in future: - The world of multiresolution transforms is extremely huge and has produced dozens of new mathematical tools. Among many other, it is worthwhile to mention the shearlet transform, which is an extension/improvement of CT, and the waveatom tool, which is intended to classify textures in the image. They should be studied and compared to establish their best performance and their best field of application over AO images. - Blind and myopic algorithms have proved their ability for large mismatches between the “real” PSF that has created the image and the PSF that is used as a first estimate in the reconstruction process. However, their performance in the presence of noise is highly affected. Hence, it is convenient to investigate if it is possible to introduce (and how to do it) multiresolution transforms into these algorithms to improve their behavior. - For the study of IFS datacubes, other father scaling functions with different shapes could be proposed, in particular, it can be considered a “dynamic” scaling function with the ability to modulate its shape according to the low frequency signal to be removed from the spaxel. This could potentially improved the final photometry of the detected faint source. Besides, the design of a dictionary of wavelets, which increase the decomposing resolution across the spaxel, instead of a single dyadic decomposition, can improve the photometric accuracy of detected planets as well as their spectral characterizations, taking full advantage of the information contained in the IFS datacubes