Imaging systems based on terahertz time-domain spectroscopy offer a range of unique modalities due to the broad bandwidth, sub-picosecond duration, and phase-sensitive detection of the terahertz pulses. Furthermore, an exciting possibility exists to combine spectroscopic characterization and/or identification with imaging because the radiation is broadband in nature. In order to achieve this, novel methods for real-time analysis of terahertz waveforms are required. Unfortunately, both the absorption and the phase delay of a transmitted terahertz pulse vary exponentially with the sample's thickness. We describe a robust algorithm for extracting both the thickness and the complex index of refraction of an unknown sample. In contrast, most spectroscopic transmission measurements require accurate knowledge of the sample's thickness to determine the optical parameters. We also investigate the limits of our method.