Simulations of X-ray Propagation in Guiding Structures and Light Scattering From Coccoliths Using Finite Difference Methods
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- Institutt for fysikk 
This thesis consists of two major parts. First, future applications of waveguides in the X-ray regime has been studied numerically. The second part is devoted to the study of lightscattering from calcite shells from phytoplankton.X-ray imaging is a valuable tool within many scientific fields, for example in medicalimaging and industrial product inspection. Several optical elements routinely availablefor visible light are hard to realize in the X-ray regime as the refractive index is close tounity. Examples of such elements include mirrors, beam splitters and delay lines. Re-cently, waveguides have been used to deflect X-rays to angles much larger than the criticalreflection angle, and waveguides can therefore be an important extension to current X-raytechnology.In this thesis, a computer program for solving the paraxial wave equation in both 2Dand 3D has been developed in order to perform wave optical simulations of X-ray prop-agation. The program is called Paraxial X-ray Propgation (PaXPro), and includes bothFourier Transform based and finite difference solvers. Testing of several boundary con-ditions shows that the implementation of Transparent Boundary conditions efficiently su-press artificial reflections from the domain boundary. Attenuation coefficients for curvedwaveguides is calculated for 2D slab waveguides, allowing estimation of the maximumdeflection angle that can be achieved with a waveguide approach. Furthermore, losses as-sociated with the connection between two waveguide segments are treated in detail usingperturbation theory. The calculations show that for X-rays connection losses are negligi-ble, which is further supported by simulations.Results from X-ray scattering studies are then presented. It is argued theoretically thatdeviations from the first Born approximation is expected for large scatterers, even in theabsence of absorption. Deviations in the far field intensity pattern are indeed seen in thesimulations.At last results from scattering studies from visible light on coccoliths are presented.The simulations were carried out using a realistic 3D model reconstructed from X-ray to-mography. A large fraction of the phytoplankton are coccolithophores, which produce acalcite shell known as coccoliths. Furthermore, falling coccoliths are responsible for asignificant part of the overall transport of calcite from the surface to the seabed. Due tothe enormous number of coccolithophores in the ocean, these calcite producing creaturesplay an important role in the global CO 2 cycle. Increasing CO 2 levels in the atmospherealter the pH level in the sea, which in turn may affect the calcite production of coccol-ithophores. The reason why coccolithophores produce these calcite shells is not fullyunderstood. Knowlegde about the function of the coccoliths is important to predict howthey will respond to environmental changes, which further is crucial for modelling marineecosystems and the global CO 2 cycle.Here, the optical scattering properties of coccoliths are investigated to see if they forinstance protect the organism agains harmful UV-radiation or contribute to acceleratedphotosynthesis. The polarization properties of the scattered light is assessed by computingthe Müller matrix, and the wavelength dependence of the total scattering cross section iscomputed.