The quantum electrodynamics of a medium

By using the Feynman diagram technique, a unified analysis is given of the Quantum Electrodynamics of a Medium. We consider both an atomic medium and an electron gas. The photon propagator in a medium is calculated by summing the most highly divergent diagrams in each term of the perturbation series expansion of the photon propagator. An explicit form for the interaction amplitude of two arbitrary currents in a medium is given. From this amplitude a complete complex dielectric function iris defined (at the pole of a photon propagator). Furthermore, we have examined the photon propagator for its poles in order to obtain dispersion relations which yield the energy-momentum relation for free motion of the system. We have considered, in detail, an atomic system and an electron gas. In both cases explicit dispersion relations are found over a wide range of energy and momentum variables. Effects of finite temperatures are discussed. Also we have obtained the energy loss of fast incident charged particles passing through an atomic medium from the self energy of the incident particle in the medium. The energy loss so obtained consists of three parts: loss due to excitation of atoms, loss due to ionization of atoms, and a Cerenkov loss. General features of the energy loss are discussed. We also give a number of expressions for the loss for various incident particles

Finding small displacements of recorded speckle patterns: revisited

An analytical expression for the bias effect in digital speckle correlation is derived based on a Gaussian approximation of the spatial pixel size and array extent. The evaluation is carried out having assumed an incident speckle field. The analysis is focused on speckle displacements in the order of one pixel, thus having no speckle decorrelation. Furthermore, sensitivity is a main issue wherefore we need speckles close to the pixel size, which means that speckle averaging becomes important, and that Nyquist’s criteria may not be fulfilled. Based on these observations, a new correlation method is introduced, which alleviates the need to know the expected shape of the crosscovariance between the original and the off-set recorded speckle pattern. This concept calls for correlating the crosscovariance with the auto covariance, which essentially carries information on the expected shape of the crosscovariance