2.1

Signal

To understand the signal we first looked at all the different transmission effects, shown in Figure 1. One major component here is the atmospheric transmission for which we used a modeled curve from ATRAN. As shown in the top left image of Figure 1, the transmission is high in most of the K-Band with strong absorption features to the edges. Another major component is the transmission of the actual beam combiner of GRAVITY. This has bean measured directly¹ and is shown in the lower left image of Figure 1 for the low and medium resolution. Of course one also has to account for the transmission of the VLTI up to the lab where GRAVITY is located. This transmission is accounted with a constant factor of 0.35.⁶

Figure 1.

Spectrally resolved inputs for the simulated signal. Top left: atmospheric transmission over the spectral range. Top right: Response function for the 14 used channels in the low resolution mode. Bottom left: transmission curves of the beam combiner in low (red) and medium (blue) resolution mode. Bottom right: Full transmission of atmosphere, telescopes and beam combiner. Fully resolved in red and for the 14 channels in low resolution mode shown as black diamonds. The full transmission for the medium mode is shown in blue.

Taking all this into account we computed the full transmission for the whole K-Band in the lower right figure of Figure 1 as well the average transmission for the 14 channels in the low resolution mode. In general the transmission in the medium resolution mode is about a factor two smaller than in the low resolution mode, which is due to the different gratings used in GRAVITY.¹ For a full determination of the signal strength one furthermore has to account for losses for example due to an imperfect fiber placement in GRAVITY and for the actual performance of the AO system.

In general all considerations in this proceeding are done for the unit telescopes (UTs) but can be easily adapted to the auxiliary telescopes (ATs) but using the correct transmission⁶ and a higher loss due to the worse correction of the atmospheric turbulence.

With the understanding of the transmission we can now simulate any source signal. We do this by using a given source magnitude and spectral power index as an input and calculate the actual received number of photons per spectral channel. With this information and the transmission curves we get the actual received signal at GRAVITY by integrating the signal, multiplied with the transmission, over the used channel response functions. For the example of the S2 star⁴ in the galactic center this is shown in Figure 2. One can see that the simulated signal is in good agreement with the data and can therefore be used for further analysis and tests.

Figure 2.

Comparison of simulated signal of S2 and a real observation. The figure shows the low resolution case with the simulated signal in red and real data in black.

2.2

Noise

Another important part of our system model is to model the expected noise on the detector. In order to do this we used a lot of flat field images from recent GRAVITY observations and analyzed them in terms of pixel-to-pixel noise as well as temporal effects.

An example of the pixel-to-pixel noise of a typical measurement can be seen in Figure 3. The noise is shown for an one and a ten second integration, as well as the square root of the corresponding signal. From that one can see that the photon noise clearly dominates for the ten second integration, while the one second integration still has a clear amount of readout noise. With this data we did a noise estimation for each individual channel by fitting a read-out and a photon noise component to the noise from data of different integration times. While the photon noise increases linearly with time, the read-out noise of a non-destructive read detector decreases with increasing integration time. Such a simulated noise is then shown by the blue curve in Figure 4. From this we can clearly identify two major noise sources: In the low wavelength the noise is dominated by the backscatter of the metrology laser,⁷ while the noise a high wavelength comes from the black body emission of the background. Scaled with the throughput of the beam combiner, this gives the actual measured noise signal as shown as a blue curve in Figure 4.

Figure 3.

The dots show the measured pixel-to-pixel noise for a ten second integration (red) and a one second integration (black). The lines in the same color show the square root of the corresponding signal as an estimation of the photon noise.

Figure 4.

Estimation of the main photon noise sources of GRAVITY. The red line shows the noise from the laser backscatter, while the black line is the noise from the black body emission of the background. The typical noise at the detector is shown in blue.

2.3

Usage & further work

With a simulated and spectrally resolved signal and noise estimation we can use this now to better plan observations with GRAVITY. We for example tested what the best integration time for the observations of the galactic center is. For a total exposure of five minutes we simulated the signal and noise for each individual frame for frame exposures between 1 and 20 seconds. Figure 5 shows the corresponding SNR normalized by the SNR from the 1 second integration time. One can therefore see how much the SNR increases when one observes longer. From this we concluded that with an integration time of 10 seconds we are in the photon noise regime and do not gain much by integrating longer. We did a similar estimation for the medium resolution which helped us to estimate the feasibility of observations in this instrumental mode.

Figure 5.

Signal to noise ratio estimation for different integration times, normalized by the SNR of a 1 second integration. The black lines show the SNR with an integration time between 1 and 20 seconds. The lines with 1 and 10 seconds are shown in red.

As we are usually not interested in the actual measured flux but rather in the visibilities and phases we are currently also expanding this work, to estimate the SNR in this modes. This will further help us to better plan observations and to identify the effect of the different noise sources for these measurements.

3.1

Sky frames

To run these tests we used a good dataset from the end of 2017 and rereduced the data with a varying number of sky frames. To get a measurable result we then used the usual binary fitting to the closure phases and squared visibilities¹ as well as the imaging⁸ of the data and checked how much the error and the scatter for the point changed for the different data reductions. We also looked at the time series of the data points in order to check if the quality decreases around the omitted sky frames.

When reducing the number of sky frames to only two per night, we could not see a clear change in the result of the test. This gave us the first impression that we actually could significantly reduce the number of sky frames.

This included also using sky frames from previous nights and averaged over several nights. In order to see if there is any dependence on the sky frame we then used a frame from a different month. This significantly changed the scatter of the fitting results and changed the actual separation by a few milliarcseconds. From this we conclude that there is a dependence on the sky frame under current conditions but the frequency of frames can be reduced.

This furthermore strengthens our previous results, that the signal in the sky frame is dominated by the laser backscatter and the black body emission, probably mostly from the lab. However, there is some dependence on the sky frame which excludes ideas such as simulating a general sky frame. This dependency could come from variation in the metrology laser as well as from background signal from the actual sky.

3.2

Calibrator frames

The same test as for the sky frames was then repeated for the calibrator frames. Here we saw a similar effect as before: The results did not change noticeably for a fewer number of calibrator frames but changed significantly when a a calibration from a very different night was used. This was even stronger than for the sky frames, which was expected as the calibrator should be more dependent on the actual conditions.

With the results from these tests we changed our observing strategy in a way that we now usually observe six frames with five minutes each, and do one sky and one calibrator observation for those six frames. A comparison of the on source fraction of the old and new scheme is shown in Figure 6. This new scheme increased our on source time by around 10 %.

Figure 6.

Comparison of the old and new observation scheme. The percentage of object, calibrator and sky schemes is shown for the original scheme on the left and the new scheme on the right.