Some analytical investigations of phase contrast imaging

An analytical study of phase contrast imaging is performed. It is shown that the complex disturbance in the image plane can be represented as a convolution of the object disturbance and the Fourier transform of the transmission function of the phase plate. The simple theory of the phase contrast microscope is then derived as a limiting case of this more general result that is applicable when the size of the phase object is small compared to the area of the entrance aperture of the system. The response of a general system to several simple large phase objects is also examined, and it is shown that qualitative information about these objects can be obtained from the intensity pattern when the phase perturbations are small, providing the background is sufficiently uniform, and the size of the phase spot on the phase plate is carefully chosen. The study provides insight into the type of performance that can be achieved, for example, if phase contrast imaging is used to extract phase information from an optical memory or if it is used as an experimental tool to study the qualitative behavior of such phenomena as clear air turbulence.