Superresolution and increased depth of focus: An inverse problem of vector diffraction

Abstract

Using vector diffraction theory, we have addressed the issue of finding the pupil function when the rate of decay of the intensity in the vicinity of the Gaussian focus along the optical axis is prescribed. The problem posed here reduces to a Fredholm integral equation, which is then solved to obtain the pupil function. We show that the diffraction integrals, as formulated by Wolf, are invariant if they are expressed in terms of the zth (the direction of the optical axis) component of the unit normal to the aberrated wave front. This makes it possible to obtain the pupil function from the solution of the Fredholm integral equation. We present results for lenses with high numerical aperture and show that the depth of focus is significantly increased without any loss of transmitted energy. Results further indicate that the FWHM of the primary lobe is significantly narrower than the clear aperture.