Simulation Results

The simulations discussed in this section are widely used throughout the remainder of the document. A few very basic results are presented here to provide a better understanding of the simulations and of the variation of the optical wavefront properties with position in the image plane.

Figure 4 shows the short exposure image quality expected when using an AT to look at a point source $30^{\circ}$ above the horizon under mediocre conditions. The effects of atmospheric refraction were ignored when generating this image. Note that the image is coloured - this means that the spectral energy distribution reaching the detectors will depend strongly on the position of the FSU spatial filter (or in other words on the tip-tilt error). If the StS is put into calibration mode, the light from one half of the PSF will be sent to one FSU, and the light from the other half of the PSF will be sent to the other PSF. The colour of the light sent to the two FSUs will be different, and hence the astrometric measurements on the two FSUs will also be different. The average colour of the light reaching the FSUs will vary with the seeing conditions and with the performance of the STRAP unit (as the size and shape of the mean PSF is strongly wavelength dependent).

Figure 5 is identical to Figure 4 except that atmospheric refraction has been ``switched on'' (including both the lateral shift of the beam in the atmosphere and the change in the angle-of-arrival with wavelength). Note that the colours are slightly different to the case with atmospheric refraction switched off (Figure 4). As the angle of refraction remains relatively constant with time during an observation, this colour shift will be systematically applied to a whole observation. If the StS is put into calibration mode, the two FSUs will receive light which has systematically different colours (and hence systematically different astrometric observables). As the flux distribution in the image depends on the seeing, the magnitude of the colour difference between the two channels will vary with the seeing conditions (i.e. on timescales of minutes and hours). This will lead to drifts in the differential phase between the two beams on similar timescales. In order to calibrate out this effect, the atmospheric seeing, STRAP unit performance, air density and humidity may have to be monitored at the ATs, particularly when using the StS calibration mode. A good knowledge of the coupling of the FSU spatial filter as a function of image-plane position and wavelength will be required for such a simulation. If the StS roof mirror is aligned with the direction of the bulk atmospheric dispersion the systematic effects may be substantially reduced.

	Figure 4: Simulated short exposure image through an AT pointing at the zenith with $4r_{0}$ across the aperture diameter.	Figure 5: Identical to Figure 4 but including the effects of atmospheric refraction for a zenith angle of $60$ degrees.

The three FSU spectral channels are shown in red, green and blue.

Another area where numerical simulations are essential is in the assessment of fringe tracking performance when there are wavefront corrugations across the AT apertures. In early optical interferometers the apertures were usually stopped-down in order to keep the variance in the wavefront phase across the aperture below $\sim1$ radian. With the introduction of spatial filters larger aperture sizes have come into common usage, and hence the variance of the wavefront phase is often much larger than $1$ radian. It will be important to assess the effect of these wavefront corrugations on the temporal properties of the interferometric fringes and hence determine the expected fringe tracking performance. In order to highlight the detrimental effect of wavefront corrugations, maps of the optical phase and intensity in the image plane of a single telescope are shown for a large ($9r_{0}$) aperture in Figure 6 for a series of closely-spaced time-steps. Each speckle in the image plane has a different (random) phase, and the speckles in the image change rapidly. If a spatial filter was used to select light from one speckle and use it in an interferometer, the phase of the light would vary as quickly as the phases of the speckles in the image plane. This is in stark contrast to the piston mode component (see e.g. [9]) which in this case does not change significantly from one time-step to the next, and thus contributes little to the high-frequency fluctuations in the fringe phase.

Figure 6: Phase and light intensity as a function of position in the image plane for a $9r_{0}$ diameter aperture. Three closely-separated time-points are shown starting on the top row (the piston mode changes by $<1$ radian over the total time shown). The legend at the lower right indicates the dependence of hue and brightness on optical phase and intensity respectively.