Unbiased centroiding of point targets close to the Cramer Rao limit.

Systematic errors affecting center-of-gravity (CoG) measurements may occur from coarse sampling of the point-spread-function (PSF) or from signal truncation at the boundaries of the region-of-interest (ROI). For small ROI and PSF widths, these effects are shown to become dominant, but this can be mitigated by introducing novel unbiased estimators that are largely free of systematic error and perform particularly well for low photon numbers. Analytical expressions for the estimator variances, comprising contributions from photon shot noise, random pixel noise, and residual systematic error, are derived and verified by Monte Carlo simulations.

Probabilistic model to spatially acquire optical links in space under the influence of band-limited beam jitter.

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.

Analysis of performance and robustness against jitter of various search methods for acquiring optical links in space: erratum.

This erratum corrects a typing error in Appl. Opt.60, 3936 (2021)APOPAI0003-693510.

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

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.

Analysis of performance and robustness against jitter of various search methods for acquiring optical links in space.

We discuss various methods for acquiring optical links in space using a dedicated acquisition sensor. Statistical models are developed and simple analytical equations derived that compare the performance between a single- and dual-spiral scan approach as well as between sequential and parallel acquisition of link chains. Simple derived analytical equations allow relating essential search parameters such as track width, variance of the uncertainty distribution, capture radius, and scan speed to the probabilities of acquiring the links within a specific time.

Common mode noise rejection properties of amplitude and phase noise in a heterodyne interferometer.

High precision metrology systems based on heterodyne interferometry can measure the position and attitude of objects to accuracies of picometer and nanorad, respectively. A frequently found feature of the general system design is the subtraction of a reference phase from the phase of the position interferometer, which suppresses low frequency common mode amplitude and phase fluctuations occurring in volatile optical path sections shared by both the position and reference interferometer. Spectral components of the noise at frequencies around or higher than the heterodyne frequency, however, are generally transmitted into the measurement band and may limit the measurement accuracy.

Coupling characterization and noise studies of the optical metrology system onboard the LISA Pathfinder mission.

We describe the first investigations of the complete engineering model of the optical metrology system (OMS), a key subsystem of the LISA Pathfinder science mission to space. The latter itself is a technological precursor mission to LISA, a spaceborne gravitational wave detector. At its core, the OMS consists of four heterodyne Mach-Zehnder interferometers, a highly stable laser with an external modulator, and a phase meter.

Measurement of the absolute wavefront curvature radius in a heterodyne interferometer.

We present an analytical derivation of the coupling parameter relating the angle between two interfering beams in a heterodyne interferometer to the differential phase signals detected by a quadrant photodiode. This technique, also referred to as differential wavefront sensing, is commonly used in space-based gravitational wave detectors to determine the attitude of a test mass in one of the interferometer arms from the quadrant diode signals. Successive approximations to the analytical expression are made to simplify the investigation of parameter dependencies.