Optical coherence tomography is a coherent ranging method that images into biological tissues to 2 mm deep and with micron-scale resolution.  I present signal processing solutions that mitigate imaging artifacts of OCT including speckle, sidelobes, material dispersion, and defocus, which may have applications for other coherent ranging methods such as ultrasound imaging and synthetic aperture radar.  From this work, a method called Interferometric Synthetic Aperture Microscopy has evolved that is a general solution for the inverse scattering problem in coherent microscopy.  In particular, ISAM eliminates the depth-of-field limitation common to most microscopic techniques.