Characterization of a phase camera for the Virgo gravitational wave detector

Abstract

Gravitational waves predicted by Einstein have been measured in a few observatories worldwide. These detectors are complex interferometers with sizes of kilometers. Misalignments and aberrations in their optical set-up can create higher-order modes in the laser beam. These higher-order mode effects should be compensated to improve the sensitivity of the interferometer. Such a compensating control system requires a real-time wavefront sensor. The phase cameras developed for the Virgo gravitational wave detector can simultaneously create intensity and phase images of the laser wavefront at 11 demodulation frequencies. Currently, the phase images are not used due to difficulties in the interpretation. Therefore, the goal of this research is to improve the understanding of the phase images of a phase camera for the Virgo gravitational wave detector.

A prototype set-up of the phase camera was built at Nikhef. The beam is modulated and sidebands are created such that a beat signal of 80 MHz and the first upper and lower sidebands at 75 and 85 MHz are measured. Images are created by scanning the laser beam across a pinhole diode and digital demodulation. In the chosen optical set-up only one of the two beams that give the measurable beat signal is scanned. This leads to systematic phase effects caused by length differences in the optical path as a function of the scanning angle. To predict the phase images, the interference of two Gaussian beams with a scanning mirror is mathematically derived. Phase images are created with a simulation, which matches within 10 to 20% compared to measurements. To improve the results, the input parameters of the simulation should be measured more accurately and the optical set-up layout should be checked. Also, the phase stability of the prototype set-up is measured. Due to the high sensitivity of the phase camera, very small optical path length differences, for example caused by airflow or temperature differences, lead to significant phase offsets. The long timescale fluctuations in the phase measurements can be reduced by covering the optical set-up. The measured high-frequency phase resolution is Δ𝜙 = 7.1 ± 0.4 mrad and behaves as a function of power as expected.