Bright-Field Microscopy of Transparent Objects: A Ray Tracing Approach

Abstract

The formation of a bright-field microscopic image of a transparent phase object is described in terms of elementary geometrical optics. Our approach is based on the premise that the image replicates the intensity distribution (real or virtual) at the front focal plane of the objective. The task is therefore reduced to finding the change in intensity at the focal plane caused by the object. This can be done by ray tracing complemented with the requirement of energy conservation. Despite major simplifications involved in such an analysis, it reproduces some results from the paraxial wave theory. In addition, our analysis suggests two ways of extracting quantitative phase information from bright-field images: by vertically shifting the focal plane (the approach used in the transport-of-intensity analysis) or by varying the angle of illumination. In principle, information thus obtained should allow reconstruction of the object morphology.

Keywords: Optical theory; quantitative phase imaging; transmission microscopy; transport-of-intensity equation.