Simulations of X-ray Propagation in Guiding Structures and Light Scattering From Coccoliths Using Finite Difference Methods

Abstract

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 light scattering from calcite shells from phytoplankton. X-ray imaging is a valuable tool within many scientific fields, for example in medical imaging and industrial product inspection. Several optical elements routinely available for visible light are hard to realize in the X-ray regime as the refractive index is close to unity. 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 critical reflection angle, and waveguides can therefore be an important extension to current X-ray technology. In this thesis, a computer program for solving the paraxial wave equation in both 2D and 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 both Fourier 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 curved waveguides is calculated for 2D slab waveguides, allowing estimation of the maximum deflection angle that can be achieved with a waveguide approach. Furthermore, losses as- sociated with the connection between two waveguide segments are treated in detail using perturbation 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 that deviations from the first Born approximation is expected for large scatterers, even in the absence of absorption. Deviations in the far field intensity pattern are indeed seen in the simulations. 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 a calcite 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 to the enormous number of coccolithophores in the ocean, these calcite producing creatures play an important role in the global CO 2 cycle. Increasing CO 2 levels in the atmosphere alter 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 fully understood. Knowlegde about the function of the coccoliths is important to predict how they will respond to environmental changes, which further is crucial for modelling marine ecosystems and the global CO 2 cycle. Here, the optical scattering properties of coccoliths are investigated to see if they for instance protect the organism agains harmful UV-radiation or contribute to accelerated photosynthesis. The polarization properties of the scattered light is assessed by computing the Müller matrix, and the wavelength dependence of the total scattering cross section is computed.