6 Illustrative examples from the model

In this section we show some results of the simulations of the VLTI. These are based on ESO's optomechanical End-to-End model.

Figure16 shows the global instrumental visibility as measured by an idealized pupil plane instrument. The visibility measured by a true instrument will be severely effected by thermal background at 10 $\mu$m and high spatial frequency wavefront corrugations due to the turbulent atmosphere at the shorter wavelengths which are both not included here. The peaks with a period of 0.5seconds in the 0.6$\mu$m visibilities arise from the residual tracking errors of the telescopes under wind load, which lets the two Airy disks overlap only from time to time. These residual errors can be corrected by increasing the gain of the fast tracking loop which has been set to low values here on purpose. The first 100ms of each time series are dominated by the model initialization phase and are not usable.

Figure 16: Time-dependent visibility amplitude computed for an idealized pupil plane instrument combining two beams of the VLTI. The visibility has been computed for three different wavelengths (10$\mu$m, 2.2$\mu$m, and 0.6$\mu$m) with the exposure times $T_{{\rm exp}}$ matching the atmospheric coherence time $\tau {}_0$ for each wavelength ($\tau {}_0$=290ms, 50ms, 10ms, respectively)

Residual tilt is dominating the degradation of the visibility at short wavelengths. Figure17 shows the effect of residual tilt present in the exit pupil plane on the resulting interferometric image for three different wavelengths. While for 10$\mu$m the Airy disks overlap perfectly, at 2$\mu$m one can see a slight elongation, and for 500nm the Airy disks are separated.

Figure 17: Coaxially combined interferograms at a) 10$\mu$m, b) 2$\mu$m, and c) 500nm (see text)

Another aspect that we studied is the influence of the detector when using the interferometer at low light levels. We added noise to a multiaxially combined interferogram, corresponding to 10 000 photons and 20 e^- readout noise. In Fig.18 the modulus of the corresponding Fourier spectrum can be seen. The interferometric peaks which carry the signal we want to measure are blurred, thus degrading the visibility significantly.

Figure 18: Fourier spectrum of an image plane combined interferogram at 2$\mu$m with 10 000 photons and 20e- readout noise (square root display)