The application of auto focus, using an optical beam deflection technique, to existing live cell interferometry measurements was developed and examined. The benefit to relevant experiments, currently being performed, is shown as well as its performance across various magnifications. Enough information is given so that the system can be reproduced to fit any end users needs.

The Phase Gradient Autofocus (PGA) algorithm is widely used in spotlight mode SAR for motion compensation. The Maximum Likelihood PGA (ML PGA) algorithm has been shown to be a superior autofocus method. The PGA is restricted to high altitude aircraft. Since lower altitude SARs have significant range dependencies that cannot be ignored, the PGA could not be used. This thesis eliminates the high altitude restriction and extends the PGA for use with all spotlight SARs. The new algorithm is tested with three images. Each image has a unique quality. A desert image provides a low signal to clutter ratio with no distinct targets and the mountain image has areas with high signal-to-clutter and areas with low signal-to-clutter. Each image was corrupted with a low frequency and high frequency motion induced low altitude phase error. The new Phase Weighted Estimation (PWE) low altitude autofocus method converged to a lower standard deviation than the ML PGA, but required more iterations. Another limitation of the PGA is that it will only work for spotlight SAR. In this thesis, the spotlight PGA is extended to stripmap by using a conversion similar to spotlight mode. With the space frequency relationship an altered PGA is used to extend the PGA to stripmap mode SAR. The stripmap SAR, range dependant PGA allows for focusing of low altitude low cost stripmap SARs. The phase weighted estimation method is extended to range dependent stripmap. The stripmap mode estimator is most successful with high signal-to-noise images.