11.5 Current phase correction at IRAM

Remote sounding is done with the astronomical 1mm receivers in the inter-line region at the chosen observing frequency. One uses the total power channel (bandwidth 500 MHz). Advantages of this approach are the close coincidence of observed and monitored line of sight, and the fact that no additional monitoring equipment is needed.

First success was on April 18, 1995, with the installation of the present receiver generation on the PdBI [Bremer 1995]. Critical advantages were the improved total power stability of the receivers and the capability to observe in the 1mm window. The necessary stability for a $30^{\circ}$ phase rms at 230 GHz is about $\Delta M/M=2 \cdot 10^{-4}$.

Figure 11.4: Antenna based total power at 228.3 GHz, the reference value to calculate the differential correction, and the model-based phase shift per antenna at 86.2 GHz.

Steps of the method:

1. Calibration of the total power counts $M_{atm}$ to $T_{sky}$ as given in the lecture on amplitude and flux calibration.
2. Iterate the amount of precipitable water vapor in an atmospheric model to reproduce $T_{sky}$. There is no ``learning phase'' of the algorithm on a quasar, just the model prediction.
3. The amount of water vapor along the line of sight is proportional to the wet path length.

   $$path \approx 6.7 \cdot water({\rm Zenith}) \cdot airmass({\rm Elevation})$$ (11.13)

   
   
   However, wet path length and opacity have different dependencies on frequency, atmospheric pressure and temperature which should be taken into account. The main increase of the refractive index $n$ of water vapor relative to dry air happens in the infrared, which makes it difficult to use the Cramers-Kronig relations linking it to opacity (integration over many transitions). For simplicity, we use the calculations by [Hill & Cliffort 1981] for the frequency dependency and the temperature and pressure dependencies by [Thayer 1974] instead. These references use not $n$ but the refractivity $N$, which is defined over the excess path length $L$ relative to vacuum propagation over the line of sight $s$:

   $$L = 10^{-6} \int N_{\nu} (s) ds$$ (11.14)

   
   

   $$N(P,T) = 77.493 \frac{p_{atm}}{T} - 12.8 \frac{p_V}{T} + 3.776 \times \frac{p_V}{T^2}$$ (11.15)

   
   
   Hill and Cliffort calculate $N(\nu)$ for $T=300$K, $P=1013.3$mbar, 80% humidity

   $$N(p,T,\nu) = 77.493 \frac{p_{atm}}{T} - 12.8 \frac{p_V}{T} + N(\nu) \frac{p_V}{28.2} \left( \frac{300.}{T} \right) ^2$$ (11.16)

   
   

4. Subtract the average over a time interval (default: the duration of a scan) to remove residual offsets due to receiver drift and ground pickup, which can be different for each antenna (see Fig.11.4).
5. Convert the antenna specific path shifts into phase at the observed wavelength, $\Delta \phi_i$
6. Calculate the baseline specific phase shifts $\Delta \phi_{ij} = \Delta \phi_i-\Delta \phi_j$. A corrected and an uncorrected version are calculated and stored during the real time reduction which compresses the spectra over one scan. The precision of the correction in relative pathlength is about $65\mu$m per antenna (hence $90 \mu$m per baseline, i.e. $\sqrt{2}$ larger).
7. During the off-line data reduction, the user can choose freely between the corrected and uncorrected sets. The phase correction can fail under the following conditions:
   • Clouds: the model only works for clear sky conditions, and will over-estimate the phase shifts seriously in the presence of clouds.
   • Very stable winter conditions: The phase noise of the observations can be below $25^\circ$ at 230 GHz, which is the intrinsic noise of the correction method.
   • Total power instabilities: For some frequencies, the receivers are difficult to tune. One can get a nice gain in the interferometric amplitude, but an unstable total power signal with an intrinsic noise well above $25^\circ$ at 230 GHz.
   Even for the cases above, the observer has lost nothing because the uncorrected scans are still there. Software tools are available which help to decide when to apply the correction.

Figure 11.5: Baseline based amplitudes, uncorrected phase and monitor corrected phase at 86.2 GHz with a time resolution of 1 s. The data correspond to the antenna based section in Fig.11.4. The phase calibration applied in columns 2 and 3 was obtained using STORE PHASE /SELF on a one minute time scale, thereby setting the mean phases to zero.