Detailed contributions

sect:ctb-2-4-3-wavefront-corr-sts

For simulations of the StS calibration mode will be important to accuratly model the dependence of tip-tilt angle on wavelength and on the level of wavefront corrugation across the aperture plane in order to determine the following:

1. The mean and RMS differential phase between the two output channels in StS calibration mode, and the dependence of these parameters on the seeing and the atmospheric refraction and dispersion. This is very complicated, as the phase varies rapidly as a function of position in the image plane both before the StS splitting and in the output beams. Generally each speckle in the image has a arbritary phase between $0$ and $2\pi$ radians, independent of the other speckles in the image (see Section 3.3 for examples of this).
2. The mean and RMS colour difference between the light leaving the two output channels in StS calibration mode, and the dependence of these parameters on the seeing and the atmospheric refraction and dispersion. Again, the colour of the light varies as a function of position in the image plane of the StS.

Both of these factors depend on the detailed nature of the wavefront corrugation, and thus depend on all the seeing parameters and the STRAP performance.

Although knife-edge or Schlieren wavefront phase detectors are widely used in astronomy (and microscopy), the effect of such a system on the optical phase at the image plane focus is not well documented. The phase perturbations introduced by the atmosphere will be partially converted into amplitude fluctuations in the pupil plane wavefront. Where the amplitude is very low, substantial changes in the wavefront phase may also be observed. In order to assess the impact of the StS roof mirror on interferometric observations, the simulations discussed in Section 3 were modified to include a knife-edge in the image plane. The pupil plane wavefront properties before and after the knife-edge in one timestep from the simulations can be seen in Figures 15 to 20. Figures 15 and 18 show wavefronts entering the StS for this timestep (identical to Figures 9 and 10, although the amplitude is plotted with a different greyscale). The effect of the wavefront corrugations in the input beam on the wavefront amplitude in the output beams is very strong - this is not surprising as the principle use of image plane knife-edges is in visualising wavefront corrugations (see e.g. [13,14]). These amplitude fluctuations are much larger than those produced by atmospheric scintillation, and may impede the fringe-tracking performance. Note that the knife-edge also diffracts a significant amount of light out of the beam.

Figure: Optical amplitude (upper panel) and phase at $1.97\mbox{ $\mu$m}$ wavelength in the aperture plane before the StS.
Figure: Optical amplitude (upper panel) and phase at $1.97\mbox{ $\mu$m}$ in the aperture plane after an image-plane knife-edge.
Figure 17: Optical amplitude and phase with the opposite knife-edge (corresponding to the other beam from the StS).

Figure: Optical amplitude (upper panel) and phase at $2.43\mbox{ $\mu$m}$ wavelength in the aperture plane before the StS.
Figure: Optical amplitude (upper panel) and phase at $2.43\mbox{ $\mu$m}$ in the aperture plane after an image-plane knife-edge.
Figure 20: Optical amplitude and phase with the opposite knife-edge (corresponding to the other beam from the StS).

It is clear that detailed simulations will be required in order to determine the expected optical phase and colour differences between the two beams output from the StS when it is operating in calibration mode. As the StS calibration mode represents the fundamental calibration of the PRIMA instrument, it will be important to estimate the phase difference expected between the two output beams in this mode. The two output beams will be swapped periodically using the de-rotator, so it will be important to look for effects which couple the differential phase in the output beams to the angle of the de-rotator.