Measurements from long-baseline interferometry are commonly analysed in terms of the power spectrum and the bispectrum
(or triple-product) of the fringe patterns, as these estimators are invariant in the presence of phase instabilities. At low
light levels, photon and detector noise give rise to systematic "bias" in the power spectrum and bispectrum. This paper extends previous work on computing the expected biases and variances for these quantities by introducing a general method
which can be applied to any fringe-encoding scheme where the measurement equation is linear and to measurements affected
by a combination of photon noise and detector noise. We apply our method to a number of interesting practical
cases, including systems with unevenly-sampled fringe patterns and in the presence of read noise.
For temporally modulated fringe patterns, stellar interferometric fringe acquisition rates must generally exceed 1kHz to avoid significant atmospheric related loss of contrast and cross-talk between fringe components. Furthermore, sufficient travel and high waveform stability in the temporal phase modulation are essential to clean fringe visibility extraction. The authors present a system utilising a piezoelectric actuator that takes advantage of a resonating stage to achieve an accurate and stable high amplitude motion. Nanometre accuracy in waveform optimisation and in continuous waveform stability is demonstrated.
We present a summary of activity at the Cambridge Optical Aperture Synthesis Telescope (COAST) group
during the period 2004-2006. Our main program has focused on technical design and prototyping for future
facility arrays such as the VLTI and Magdalena Ridge Observatory Interferometer, but with a small parallel
effort of focused astronomical observations with COAST, in particular multi-wavelength studies of supergiants.
We report on progress on these and other technical areas over the past 2 years.
We present a formal comparison of the performance of algorithms used for synthesis imaging with optical/infrared long-baseline interferometers. Five different algorithms are evaluated based on their performance with simulated test data. Each set of test data is formatted in the OI-FITS format. The data are calibrated power spectra and bispectra measured with an array intended to be typical of existing imaging interferometers. The strengths and limitations of each algorithm are discussed.
We present a summary of the activity of the Cambridge Optical Aperture
Synthesis Telescope (COAST) team and review progress on the
astronomical and technical projects we have been working on in the
period 2002--2004. Our current focus has now moved from operating
COAST as an astronomical instrument towards its use as a test-bed for
strategic technical development for future facility arrays. We have
continued to develop a collaboration with the Magdalena Ridge
Observatory Interferometer, and we summarise the programmes we expect
to be working on over the next few years for that ambitious
project. In parallel, we are investigating a number of areas for the
European Very Large Telescope Interferometer and these are outlined
The goal of future optical aperture synthesis telescopes is to achieve
model independent imaging of complex sky structure with the success
demonstrated in very long baseline radio interferometry. Tomorrow's
optical interferometers must therefore measure both the powerspectrum
and the bispectrum of a source and with greater baseline coverage than
has so far been achieved. In contrast to VLBI the bispectrum in
optical interferometry is not as readily obtained as the powerspectrum
components. Although it is clear that image reconstruction in general
cannot do without the bispectrum measurements, very little intuition
exists on how many and which bispectrum components in particular are
most important to record. Such knowledge has implications in the
design of the beam combiner and beam handling optics of future interferometers. The authors present results of image reconstruction from simulated optical interferometry data containing a fixed amount of powerspectrum but a varying selection of bispectrum components.
Interferometric fringes are traditionally decomposed using the
Discrete Fourier Transform (DFT). However, the application of the DFT
is only correct in cases where the fringes are sampled evenly with
delay and over integer number of fringe periods. This ideal case is
often not achieved in Optical Interferometry. Fringe spectrography,
non-linear fringe sweeps and image-plane beam combiners are
typical cases of where the DFT approach fails to make most efficient
use of the data. The authors assert that in many cases alternative and more efficient fringe decompositions exist but which may exhibit considerably different noise behaviour to the DFT. The authors present the mathematical results important for correcting for statistical bias in the powerspectrum and bispectrum constructs of a completely general fringe decomposition. An estimator for the noise in the powerspectrum has also been derived. The authors believe this to be the first analytical derivation of statistical bias and noise in interferometry that treats both photon counting noise as well as Gaussian read out noise.
We present a summary of the status of the Cambridge Optical Aperture
Synthesis Telescope, and review developments at the array through the
period 2000-2002. Summaries of the astronomical and technical
programmes completed, together with an outline of those that are
currently in progress are presented. Since our last report two years
ago in 2000, there have been significant changes in the context for
astronomical interferometry in the UK. We review these developments,
and describe our plans for the near and intermediate term at COAST,
and with colleagues in Europe at the VLTI and in the USA at the
Magdalena Ridge Observatory in New Mexico.
The first-generation COAST array is now primarily operated as a tool
for astrophysics, with any development work aimed at improving
observing efficiency and at prototyping hardware for future arrays. In this paper we summarize the full range of astrophysical results
obtained with COAST in the previous two years. Results of a
program to investigate hotspots on red supergiant stars are
presented in detail.