Crystal Uniformity

The uniformity of the interferometer components over their aperture, both in terms of surface quality and refractive index uniformity within the crystal, plays an im-portant role in the instrument performance and calibration. Ideally, light passing through any part of the crystal aperture at a given angle should experience an iden-tical phase delay. In reality, thickness variations and refractive index inhomogeneity within the crystal mean that light passing through different parts of the aperture experiences different delays. This has two important effects, the first of which is lowering of the instrument contrast. This occurs because the light arriving at a given point in the image plane has passed through a range of locations in the crystal aperture, and therefore experienced a range of phase delay. The larger the range of phase delay, the lower the fringe contrast at that point in the image. The second

5.3. Interferometer Calibration 117

Figure 5.13: Example of a contrast calibration image using the Cd lamp calibration configuration. The contrast is observed to increase significantly towards the image edges.

effect is to make the interferogram calibration highly sensitive to the pupil illumina-tion. If incoming calibration light does not fill the crystal aperture in the same way as the plasma light, it will sample a different range of delays and therefore could give a different instrument phase and contrast.

In order to measure the non-uniformity of the delay produced by the birefringent components, an experiment was carried out to record the fringe patterns created when only illuminating small sub-apertures of the interferometer. A small square aperture was placed in front of the Cd calibration lamp and imaged on to the interferometer components, which were mounted in the temperature controlled cell but removed from the rest of the diagnostic. This illuminated a small square area of the polarisers and crystals of around 2mm x 2mm (the full crystal aperture is circular with 28mm diameter). The temperature controlled cell was mounted on a 2D linear translation stage setup, such that the illuminated area could be scanned over the components’ clear aperture. A camera with its lens focused at infinity was placed after the cell to record the fringe pattern, using the same fringe scale at the detector as in the complete diagnostic. The illuminated area was then raster scanned over the aperture of the interferometer components using the translation stages, recording the fringe pattern at each location. These images were demodulated to determine the difference in fringe phase between the different positions in the aperture. Since the illumination used had a constant spectrum for all points, these measured differences in fringe phase correspond to the variations in the interferometer phase delay across

5.3. Interferometer Calibration 118 the aperture. Measurements were performed for the baseline crystal configuration consisting of the 6.5mm delay plate, 4mm and 2.2mm Savart polariscopes, and for each of these components separately (always including the polarisers before and after the crystals in order to produce the fringe pattern). Since at least one Savart polariscope is required to produce the fringe pattern which enables the measurement, the delay plate only measurement was obtained using the delay plate and 4mm Savart polariscope together, before subtracting the polariscope measurements. The resulting delay profiles across the crystal apertures are shown in figure 5.14.

Figure 5.14: Measured variations in phase delay across the interferometer aperture, for each component in the baseline interferometer configuration and for the complete system (consisting of one delay plate and two Savart polariscopes).

For the full baseline crystal configuration, the range of the delay variation is ap-proximately 0.7 waves over the aperture. The largest contribution to this is from the 2.2mm Savart polariscope, which displays the largest non-uniformity and the most complex spatial structure, attributed to particularly large manufacturing imperfec-tions in this component (despite all the crystals being provided by one supplier).

In terms of the instrument calibration this amount of phase variation is very large (0.7 waves fringe phase change would be equivalent to a flow measurement of order 100km/s), thus this illustrates the need to ensure the crystal aperture is correctly

5.3. Interferometer Calibration 119 illuminated (i.e. not under-filled) when carrying out calibrations. These results and the known properties of the instrument’s lens configuration also provide a qualita-tive explanation for the observed instrument contrast structure seen in figure 5.13, i.e. the lower contrast near the image centre than at the edges. This occurs because at the centre of the field of view, the entire crystal aperture is illuminated, hence this light samples the full range of phase delay and the fringe contrast is lowest.

Towards the image edges, vignetting due to the imaging lens configuration means a smaller area of the crystals is illuminated, thus the light samples a smaller range of delay and the fringe contrast is higher. This effect appears to be dominant in determining the fringe contrast.

The measurements were repeated with the temperature controlled cell set to dif-ferent temperature values, and the non-uniformity was found to show a weak tem-perature dependence, with the RMS phase variation across the aperture increasing from 0.97 rad at T_crystals = 33.3^◦C to 1.07 rad at 36.9^◦C (without significant change to the spatial structure of the variations). The instrument contrast is therefore expected to decrease slightly with increasing temperature of the crystals, due to increased non-uniformity at higher temperatures. Such an effect is indeed observed, as will be seen in the next section.