Fringes and Power Spectra from COAST
Overview
After acquiring a star, measurements must be made of the (complex) fringe visibility on each baseline.
Visibility amplitudes are easy to measure with an optical interferometer but the phases are too badly corrupted by the atmosphere. Fortunately, even in the presence of very strong atmospheric turbulence there is a good observable: the phase of the triple product of the visibilities on three baselines, commonly known as the closure phase.
At COAST we proceed as follows: measurements are first made of the visibility amplitude on each baseline by combining the light from each pair of telescopes in turn. During these observations the path length of the baseline of interest is varied in a sawtooth motion in order to allow us to move through the fringes. We then form the power spectrum of the resultant data, and hence estimate the visibility.
A measurement of the closure phase is then made by combining light from three telescopes simultaneously. During this observation the path length is modulated in a similar fashion as before, but at a different frequency in each arm. This serves to separate the fringes from each baseline in frequency, whilst the closure phase is preserved. The closure phase is derived from the phases of the triple products formed from short segments of this data. One triple product is formed for each atmospheric coherence time.
Amplitude Measurements
This figure shows some fringes from Capella on 95/09/13. The sample rate was 5kHz and so the x axis of the graph represents 0.4 seconds of data. Notice that the mean level has been subtracted from this graph. This is achieved by forming the difference of counts between two of the APD detectors, which are out of phase by 180 degrees.
The figure below shows the modulation of the trolley position on this baseline. These data were taken simultaneously with the fringes above.
Finally, the power spectrum is formed:
There are several things to note about this figure. Notice the peak near to the origin – this is due to the atmospheric scintillation, i.e. perturbations in the mean incident intensity, caused by variations in the atmosphere over time.
The peak due to the fringes is at around 700Hz. It is wider than the theoretical width due to the finite passband employed (40nm in this case), and this too is caused by a loss of coherence due to the atmosphere. The area under this peak, above the background noise power, is normalised by the square of the mean photon rate in order to form an estimate of the square of the visibility amplitude.
During fringe acquisition the output from the detectors is directed through an audio amplifier to a loudspeaker. The 700Hz signal is easily recognisable by the ear, and by adjusting the path compensation length until a regular tone is heard every time the trolley passes through the fringes, the centre of the envelope can be found very accurately indeed. That this technique is so successful at locating fringe envelopes is largely a tribute to the ability of the human auditory processing system to isolate an often weak signal amidst a strong background. It also draws odd gazes from people when it is explained that no, you don’t look through your telescope, you listen to it!
Here is a recording of the sound of COAST fringes, in MP3 and WAV formats:
It is worth pointing out the signal to noise ratio is very high, in this case of the order of 10000:1. It is actually difficult on this plot to see the background noise power, which is “white” and attributable to photon noise.
Closure Phase Measurements
The power spectrum of some closure phase data, also taken from the night of 95/09/13, is shown below:
The three peaks due to the fringes on three different baselines can clearly be seen. The scales on the graph are different to before, in order to illustrate the background noise.
Here is a recording of the sound of closure phase data, again in both MP3 and WAV formats. Listen for the three frequencies in the data:
If we choose to sample at 10kHz, the peaks can be spaced further apart, which allows the background level under each peak can be estimated. Thus we can estimate the visibility amplitudes as well as the closure phase from such multiple-baseline data. The visibility amplitudes on all baselines can be measured in a shorter time than would be needed if the amplitude on each baseline were measured separately, at the cost of reduced signal-to-noise in the power spectrum.