Probabilistic model for spatially acquiring optical links in space under influence of band-limited beam jitter

TL;DR

This paper develops an analytical probabilistic model to predict the failure rate of acquiring space-based optical links affected by band-limited beam jitter, accounting for correlations and optimizing scan parameters.

Contribution

It introduces a novel analytical model that incorporates jitter spectrum and correlation effects, providing insights for optimizing optical link acquisition in space.

Findings

P-fail decreases with higher correlation strength.

Model predictions match Monte Carlo simulations.

Optimal track width minimizes acquisition time.

Abstract

An analytical model is derived for the probability of failure (P-fail) to spatially acquire an optical link with a jittering search beam. The analytical model accounts for an arbitrary jitter spectrum and considers the associated correlations between jitter excursions on adjacent tracks of the search spiral. An expression of P-fail in terms of basic transcendental functions is found by linearizing the exact analytical model with respect to the correlation strength. Predictions from the models indicate a strong decrease of P-fail with increasing correlation-strength, which is found to be in excellent agreement to results from Monte Carlo simulations. The dependency of P-fail on track-width and scan speed is investigated, confirming previous assumptions on the impact of correlations. Expressions and applicable constraints are derived for the limits of full and no correlations, and the optimal track width to minimize the acquisition time is computed for a range of scan speeds. The model is applicable to optical terminals equipped with a fast beam steering mirror, as often found for optical communication missions in space.