Two new analysis techniques used to characterize a non-diffraction-
limited pulsed laser system whose focal spot is too intense to record photographically and whose pointing varies in time are described. The data to be analyzed were collected by moving the focal point in three dimensions and recording the fraction of the incident energy that passed through a pinhole. Analyzing the data in two different ways provides two independent estimates of the properties of the laser beam that are in reasonable agreement. One method estimates the average size of the focal volume over the measurement period, whereas the other estimates its minimum size. The difference between the average and the minimum then indicates the range of variation in size. Two different estimates of the random motion of the beam are also obtained. Both analysis methods employ statistics to account for pulse-to-pulse variations in the size, location, and total energy of the pulses. Beam widths at different points along the beam axis can then be fit with the M2 model, which describes beams that are not diffraction limited, to provide a simple expression for the irradiance at any point in the focal volume.