Properties of pulsed optical range finders which are affected by the transmitter pulse waveshape have been analyzed. This was done by deriving the probability density functions of the random variable representing range delay time with respect to the start of the transmitter pulse. These functions were used to predict the calibration or bias time, random range errors, the probability that a range measurement is made, and its entropy, all vs signal energy. Noise and other important system properties are treated as parameters, and it is assumed that photoemission is Poisson-distributed. A number of experiments were performed, including a simulation of geodetic satellite conditions. Although more experimental work remains to be done, the agreement between these measurements and theoretical predictions tends to verify the theory, including the basic assumption that photoemission is accurately described by Poisson statistics under almost all likely conditions.
S. Ackerman, "Calibration, Precision, and Efficiency of Optical Range Finders," Appl. Opt. 10, 1051-1056 (1971)