27 research outputs found
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 number.
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. The accuracy and computational
speed of the unbiased estimators is compared to those of other common
estimators, including iteratively weighted CoG, thresholded CoG, iterative
least squares fitting, and two-dimensional Gaussian regression. Each estimator
is optimized with respect to ROI size and PSF radius and its error compared to
the theoretical limit defined by the Cramer Rao lower bound (CRLB). The
unbiased estimator with full systematic error correction operating on a small
ROI [3x3] emerges as one of the most accurate estimators while requiring
significantly less computing effort than alternative algorithms.Comment: 11 pages, 7 figures, double column forma
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 photo-diode. This technique,
also referred to as Differential Wavefront Sensing (DWS), 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. Motivated by our findings, we propose
a new measurement method to accurately determine the absolute wave-front
curvature of a single measurement beam. We also investigate the change in
coupling parameter when the interferometer "test-mirror" is moved from its
nominal position, an effect which mediates the coupling of mirror displacement
noise into differential phase-measurements.Comment: double-spaced, 21 pages, 5 figure
Performance analysis of sequential carrier- and code-tracking receivers in the context of high-precision space-borne metrology systems
Future space observatories achieve detection of gravitational waves by
interferometric measurements of a carrier phase, allowing to determine relative
distance changes, in combination with an absolute distance measurement based on
the transmission of pseudo-random noise chip sequences. In addition, usage of
direct-sequence spread spectrum modulation enables data transmission.
Hereafter, we report on the findings of a novel performance evaluation of
planned receiver architectures, performing phase and distance readout
sequentially, addressing the interplay between both measurements. An analytical
model is presented identifying the power spectral density of the chip
modulation at frequencies within the measurement bandwidth as the main driver
for phase noise. This model, verified by numerical simulations, excludes binary
phase-shift keying modulations for missions requiring pico-meter noise levels
at the phase readout, while binary offset carrier modulation, where most of the
power has been shifted outside the measurement bandwidth, exhibits superior
phase measurement performance. Ranging analyses of the delay-locked loop reveal
strong distortion of the pulse shape due to the preceding phase tracking
introducing ranging bias variations. Numerical simulations show that these
variations, however, which originate from data transitions, are compensated by
the delay tracking loop, enabling sub-meter ranging accuracy, irrespective of
the modulation type.Comment: 10 pages, 6 figure