Defocusing microscopy with an arbitrary size for the aperture of the objective lens

TL;DR

This paper extends defocusing microscopy theory to finite aperture sizes, showing that image intensity depends on phase gradient and phase itself, enabling detection of linear phase objects and increasing contrast with smaller apertures.

Contribution

It generalizes existing defocusing microscopy theory to arbitrary aperture sizes, revealing new dependencies and detection capabilities.

Findings

Image intensity depends on phase gradient and phase for finite apertures.

Smaller apertures increase image contrast of phase objects.

Linear phase variations can be detected with finite aperture sizes.

Abstract

The theoretical approach to describe the defocusing microscopy technique by U. Agero et al. [Phys. Rev. E {\bf 67}, 051904 (2003)] assumes that the size of the objective lens aperture is infinite. This treatment gives that the intensity at the image plane depends on the laplacian of the phase introduced in the field by a pure phase object. In the present paper, we consider an arbitrary size for the aperture of the objective lens and we conclude that the intensity at the image plane depends also on the gradient of the phase introduced by the object and the phase itself. In this case, even an object that introduces only linear variations in the phase can be detected. Furthermore, we show that the contrast of the image of the phase object increases with the use of smaller objective apertures.