Solutions to common issues in widefield microscopy: vignetting, mosaicing and depth of focus

In this thesis we have developed solutions to common issues regarding widefield microscopes, facing the problem of the intensity inhomogeneity of an image and dealing with two strong limitations: the impossibility of acquiring either high detailed images representative of whole samples or deep 3D objects. First, we cope with the problem of the non-uniform distribution of the light signal inside a single image, named vignetting. In particular we proposed, for both light and fluorescent microscopy, non-parametric multi-image based methods, where the vignetting function is estimated directly from the sample without requiring any prior information. After getting flat-field corrected images, we studied how to fix the problem related to the limitation of the field of view of the camera, so to be able to acquire large areas at high magnification. To this purpose, we developed mosaicing techniques capable to work on-line. Starting from a set of overlapping images manually acquired, we validated a fast registration approach to accurately stitch together the images. Finally, we worked to virtually extend the field of view of the camera in the third dimension, with the purpose of reconstructing a single image completely in focus, stemming from objects having a relevant depth or being displaced in different focus planes. After studying the existing approaches for extending the depth of focus of the microscope, we proposed a general method that does not require any prior information. In order to compare the outcome of existing methods, different standard metrics are commonly used in literature. However, no metric is available to compare different methods in real cases. First, we validated a metric able to rank the methods as the Universal Quality Index does, but without needing any reference ground truth. Second, we proved that the approach we developed performs better in both synthetic and real cases.

The rupture process of recent tsunamigenic earthquakes by geophysical data inversion

Subduction zones are the favorite places to generate tsunamigenic earthquakes, where friction between oceanic and continental plates causes the occurrence of a strong seismicity. The topics and the methodologies discussed in this thesis are focussed to the understanding of the rupture process of the seismic sources of great earthquakes that generate tsunamis. The tsunamigenesis is controlled by several kinematical characteristic of the parent earthquake, as the focal mechanism, the depth of the rupture, the slip distribution along the fault area and by the mechanical properties of the source zone. Each of these factors plays a fundamental role in the tsunami generation. Therefore, inferring the source parameters of tsunamigenic earthquakes is crucial to understand the generation of the consequent tsunami and so to mitigate the risk along the coasts. The typical way to proceed when we want to gather information regarding the source process is to have recourse to the inversion of geophysical data that are available. Tsunami data, moreover, are useful to constrain the portion of the fault area that extends offshore, generally close to the trench that, on the contrary, other kinds of data are not able to constrain. In this thesis I have discussed the rupture process of some recent tsunamigenic events, as inferred by means of an inverse method. I have presented the 2003 Tokachi-Oki (Japan) earthquake (Mw 8.1). In this study the slip distribution on the fault has been inferred by inverting tsunami waveform, GPS, and bottom-pressure data. The joint inversion of tsunami and geodetic data has revealed a much better constrain for the slip distribution on the fault rather than the separate inversions of single datasets. Then we have studied the earthquake occurred on 2007 in southern Sumatra (Mw 8.4). By inverting several tsunami waveforms, both in the near and in the far field, we have determined the slip distribution and the mean rupture velocity along the causative fault. Since the largest patch of slip was concentrated on the deepest part of the fault, this is the likely reason for the small tsunami waves that followed the earthquake, pointing out how much the depth of the rupture plays a crucial role in controlling the tsunamigenesis. Finally, we have presented a new rupture model for the great 2004 Sumatra earthquake (Mw 9.2). We have performed the joint inversion of tsunami waveform, GPS and satellite altimetry data, to infer the slip distribution, the slip direction, and the rupture velocity on the fault. Furthermore, in this work we have presented a novel method to estimate, in a self-consistent way, the average rigidity of the source zone. The estimation of the source zone rigidity is important since it may play a significant role in the tsunami generation and, particularly for slow earthquakes, a low rigidity value is sometimes necessary to explain how a relatively low seismic moment earthquake may generate significant tsunamis; this latter point may be relevant for explaining the mechanics of the tsunami earthquakes, one of the open issues in present day seismology. The investigation of these tsunamigenic earthquakes has underlined the importance to use a joint inversion of different geophysical data to determine the rupture characteristics. The results shown here have important implications for the implementation of new tsunami warning systems – particularly in the near-field – the improvement of the current ones, and furthermore for the planning of the inundation maps for tsunami-hazard assessment along the coastal area.