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.

The behaviour of ODS 12Cr steel under thermal treatment is studied in this report at micro and macro level. ODS 12Cr steel is always in the ferrite phase and has a melting point at 1500 ºC. Before studying,
the retrieved samples were metallographically prepared in four steps: mounting, grinding, mechanically polishing and electrolytically polishing. A measurement was done to analyse the effect of electrolytically polishing on bulk S and W parameters. This showed that mechanically polishing with 0.04 μm alumina particles has the same effect as electrolytically polishing. Next, the alloy was studied with three different measurement techniques: positron annihilation Doppler broadening spectroscopy, Vickers hardness test and positron lifetime measurements. Before these measurements the samples were annealed at selected temperatures for 10 minutes and naturally cooled.

The Doppler broadening spectroscopy was done with the Variable Energy Positron beam (VEP) at the Reactor Institute Delft (RID). With this set-up the S and W parameter were measured at different im-
plantation energies and converging bulk values of them were determined. The results were fitted with VEPFIT. This measurement was done in the as received state and after annealing from 200 ºC up to
1300 ºC in steps of 100 ºC. The Vickers hardness test was done with a load of 0.3 kgf and in the same temperature range as the VEP measurements but with steps of 200 ºC. A lifetime spectrum was measured in the as received state with two sample sandwiching a 22Na source packed with kapton. The average lifetime was determined by fitting the spectrum with LT 9.2. This measurement was repeated
after annealing for 10 minutes from 200 ºC up to 700 ºC in steps of 100 ºC.

The three different measurement techniques show corresponding results. Up to annealing temperatures of 1000 ºC the results stay constant. The bulk S and W parameters are respectively 0.475 and 0.078.
The Vickers hardness stays at 395 HV and is comparable to literature values. The average lifetime is approximately 208 ps, which corresponds with defects with sizes comparable to or at least larger than
that of divacancies. At this temperatures most thermal vacancies are trapped by the nano-oxide particles and are not able to liberate themselves which causes the constant results. At higher temperatures (larger than 1100 ºC) the thermal vacancy concentration increases and the vacancies gain enough energy to be liberated. This causes, in combination with oxide particles clustering, more defects in the material and explains the increasing bulk S value for temperatures up from 1100 ºC. The high bulk S values, compared with an iron alloy with less chromium, can also originate from clustering of chromium atoms. The surface S parameters are also increased in this temperature domain due to the formation of an oxide layer which can be seen with the naked-eye. Finally, the hardness value decreases to 374 HV after annealing at 1200 ºC which is a significant decrease and indicates that the pinning of the nano-particles decreases, resulting in grains growing easier.