Polarizing microscopy brought about many advancements in the science of liquid crystals and other soft materials, including those of biological origin. Recent developments in optics and computer-based analysis enabled a new generation of quantitative polarizing microscopy which produces spatial maps of the optic axis. Unfortunately, most of the available approaches require a long acquisition time of multiple images which are then analyzed to produce the map. We describe a polychromatic polarizing microscope, which allows one to map the patterns of the optical axis in a single-shot exposure, thus enabling a fast temporal resolution. We present a comparative analysis of the new microscope with alternative techniques such as a conventional polarizing optical microscope and MicroImager of Hinds Instruments.