Optimum Truncation of a Gaussian Beam in the Presence of Random Jitter

We consider the far-field or focal-plane irradiance distribution of a Gaussian beam truncated by a circular aperture in the presence of random angular jitter. First, in the absence of jitter, we derive an accurate analytical approximation for the irradiance distribution within the main lobe of the beam for the case where the beam diameter is less than the aperture diameter. We then obtain the corresponding mean irradiance distribution in the presence of circularly symmetric, normally distributed jitter. By maximizing the on-axis intensity, we obtain the optimum ratio of the beam diameter to the aperture diameter in the presence of jitter and present results for the corresponding maximum on-axis intensity and encircled power as a function of the jitter statistics. Gaussian beams, Jitter.