Sensing has been essential for the investigation, understanding, exploitation, and utilization of physical phenomena. Traditional single-point sensing methods are being challenged by the multi-point or distributed sensing capabilities afforded by optical fiber sensors. A powerful technique available for distributed sensing involves the use of the Optical Frequency Domain Reflectometry (OFDR). This work focuses on using OFDR as a means of obtaining distributed vibration measurements using the Rayleigh scatter along a single-mode optical fiber. The effort begins by discussing various distributed measurement techniques currently in use before discussing the OFDR technique. Next, a thorough discussion on how high spatially resolved Rayleigh measurements are acquired and how such measurements can be used to make static strain measurements is presented. A new algorithm to resolve strain at regions of high spatial gradient is developed. This results in enhanced measurement performance of systems using the Rayleigh scatter to determine static strain or temperature measurements by improving measurement fidelity at the high gradient locations. Next, discussions on how dynamic strain (vibration) couples to optical fiber in a single point and in a distributed setting are presented. Lessons learned are then used to develop a new and unique distributed vibration measurement algorithm. Various consequential benefits are then reviewed before concluding remarks are stated. A simulation model was developed and used to supplement this investigation in every step of the discussion. The model was used to gain insight on how various physical phenomena interact with the optical fiber. The simulation was also used to develop and optimize the high gradient and vibration algorithms developed herein. Simple experiments were then used to validate the theory and the simulation models. / Ph. D.