Impact of spectral noise shape and correlations of laser beam jitter on acquiring optical links in space

Abstract

We investigate how the probability of acquiring an optical link between a scanning and a target spacecraft depends on the spectral shape, power and dimensionality of the beam jitter, as well as on the choice of detector integration time, beam detection radius and scan speed. For slow scans and long integration times, the probability of failure (Pfail) is determined by the integrated jitter power up to a critical frequency, which we verify by comparing the results of an analytical model to those of Monte Carlo simulations. Jitter above the critical frequency leads to a loss of correlation between integration windows and decreases Pfail for both, 1d (radial) and 2d (radial and tangential) jitter, as long as the RMS jitter amplitude does not exceed the beam diameter. In the opposite limit of fast scans and short integration times, emergent correlations between jitter fluctuations on two adjacent scanning tracks also decrease Pfail. The analytical model is additionally used to assess the effect of multiple overlapping tracks and the impact of target drifts in the uncertainty plane.

Optical link acquisition for the LISA mission with in-field pointing architecture

“…The analytical model of section 3.3 assumes that a jitter excursion remains quasi constant while the beam passes by SC2, which implies that the beam transit time T pass = 2R d /γ must be much smaller than the width of the jitter auto-correlation function: τ 1/2 2R d /γ. If, on the other hand, the scan speed γ is reduced and the correlation time becomes smaller than T pass , the individual integration windows (in our case ≈ 6) become mutually uncorrelated, which reduces P f ail [16]. Therefore, we expect P f ail to decrease continuously towards lower scan speeds, as also the auto-correlation of the beam jitter evaluated at the transit time r xx (T pass ) decreases with γ.…”

“…However, all these models have in common that the effects of correlations are completely neglected and only RMS values of the amplitudes are used for predicting acquisition probabilities. Therefore, in an extension to our previous analysis, we studied how the spectral distribution and cut-off frequency affect the correlation between integration windows and scanning tracks and found that they strongly impact the acquisition probability [16]. In this paper, we focus on one of the key parameters that may generally be adjusted by the acquisition architect, namely the scan speed, and show it can be tuned to enter 3 different regimes which differ greatly in acquisition probability and duration.…”

“…Here, Q e is the quantum efficiency of the detector, S sl [photons/pixel/s] the background stray light flux , D dark [e − /pixel/s] the detector dark current, and N r [e − /pixel] the readout noise at a frame rate of f s frames per second. We now want to evaluate S sig for the specific conditions of the scanning beam path relative to SC2, for which we introduce the radius of detection R d , as explained in [16]. It defines the maximal angular distance the scanning beam may have (at the point of closest approach) when sweeping past SC2 in order to be detected with sufficient SNR for the given scan speed γ and integration time t int .…”

“…In this case, one must consider that the scanning beam may hit SC2 on multiple adjacent tracks, which requires extending the simple "2 track" model of Eq. 4 to account for N pairs of tracks [16]. The probability of failure P f ail is then found to be: where P x (x) denotes the probability of acquisition failure if SC2 is located at position x in between one track (x = 0) and half the distance to the adjacent track (x = D t /2), and P f ail is the average over P x to account for a random position of SC2.…”

“…We also find very good agreement between the analytical predictions and the results of Monte Carlo (MC) simulations which take the exact SC jitter noise spectrum as input and accurately model the integration of the far-field intensity distribution by the detector, only counting a detected signal of SNR > 40 towards a successful acquisition. For a general description of our Monte Carlo approach see [16]. The red triangles in Fig.…”