In this Thesis we present imaging systems modified for the purpose of enhanced defocus, and consequently depth estimation. The imaging systems are modified by use of a mask in the Fourier plane, causing the point spread function (PSF) of the system to appear as two intense spots that rotate with defocus.

We establish a criterion for comparing PSFs for the task of estimating depth using the Cramer-Rao bound, and examine why a rotating PSF is well suited to this task. Using this criterion, we show a theoretical ten-fold increase in the precision with which depth can be estimated compared to a standard clear, circular aperture PSF. We also discuss how specifically the estimation of defocus is performed, and how the point spread function is implemented. We show experimental results for a variety of objects, in a variety of geometries that confirm our theoretical predictions.

We divide the experiments in this Thesis into two categories. First, in axial position sensing, we measure the PSF directly. This is done using either a point source object, which approximates a fluorescent bead or colloid, or by scanning across a more complex object with a focused beam. The second category is wide field three-dimensional imaging. Here we use the image generated by the rotating PSF system, and deconvolve it with a second standard image to recover the rotating PSF. In both cases, defocus, and correspondingly depth, is computed by estimating the angle of rotation of the point spread function.