Phased-array performance degradation due to mirror misfigures, piston errors, jitter, and polarization errors

Abstract

The purpose of this paper is to develop relationships between the normalized far-field peak intensity (Strehl ratio) and system perturbations, such as mirror misfigure, piston errors, jitter, and polarization errors, for phased-array transmitters. Some of these sources of degradation are unique to phased arrays, whereas others are shared in common with single-aperture transmitters. It was found that for a phased array with many apertures, piston errors must be controlled to within ~λ/20 to ensure a Strehl ratio of 0.9. However, if adaptive optics is used to adjust the path lengths optimally in the free-space regions, then the gain lengths need only be controlled to within λ/(20δn) for a master-oscillator power-amplifier system. The factor δn = (δn/δk)δk is simply the variation of the gain’s index of refraction within one standard deviation in the wave number of the lasing lines. The results found for the effects of jitter are valid for arbitrary-shaped apertures as well as for arbitrary array patterns. For identical apertures and uncorrelated jitter among the apertures, the Strehl ratio is independent of the number of apertures and their arrangement. On the other hand, for correlated jitter, the far-field degradation is sensitive to the array pattern and is least sensitive for a close-packed array. Both the case of isolated perturbations for one element of the array and that of random errors in all the elements of the array are studied.