addendum: A comparison of the IWVM and 183 GHz WVR sensitivities (by C. Wilson)

The theoretical calculations presented above suggest the infrared water vapour monitor (IWVM) should be able to achieve a 1 sigma sensitivity of 1 $\mu$m pwv in 1 second. This sensitivity is appropriate for an average pwv of 1 mm; the sensitivity will be 30 percent better when the pwv is 0.5 mm. Now, according to Lay et al. (MMA memo 209), 1 $\mu$m of pwv corresponds to 6 $\mu$m in the optical path. The currently recommended design goal for ALMA is an accuracy of 10(1+w) $\mu$m in optical path per baseline, where w is the atmospheric precipitable water vapour (in millimeters). Since the path difference is determined from measurements at two telescopes, this means the accuracy needed at each telescope is about 14 $\mu$m of path or 2 $\mu$m of pwv when the total pwv is 1 mm. Thus, if the IWVM can achieve the predicted theoretical sensitivity, it should be able to provide the required accuracy. The preliminary analysis of the results from the first run with the IWVM gives a 1 sigma accuracy of 10 $\mu$m pwv (60 $\mu$m of path) in one second of integration. In comparison, the uncooled 183 GHz radiometers on the JCMT and the CSO achieved a 1 sigma accuracy of 0.1-0.2 K in 10 seconds (Wiedner & Hills, Imaging 99 proceedings). From the calibration on a day when the pwv was 2.2 mm, this rms corresponds to a 1 sigma accuracy of 20-40 $\mu$m in path. In comparison, if we were to average the IWVM data over 10 seconds instead of 1 second, the sensitivity from the first run would be 3 $\mu$m pwv or 20 $\mu$m in path. Thus, the current IWVM and the current 183 GHz radiometers likely have similar sensitivities. The expected rms for the existing 183 GHz radiometers from just thermal noise is about 0.06 K; there were substantial fluctuations in the instrumental gain which brought the noise up (Wiedner & Hills 1999). Also, the current plan for ALMA is to cool the 183 GHz radiometers, which will bring the system temperature down by a large factor. As an example, if the system temperature of the uncooled 183 GHz system is 2500 K and that of the cooled system is 400 K, then the thermal noise would drop from 0.06 K to 0.01 K in a 10 second integration or 0.033 K in a one second integration. This means the one sigma accuracy of a cooled 183 GHz radiometer in one second of integration would be 7 $\mu$m in path or about 1 $\mu$m in pwv. However, this sensitivity is appropriate for fairly wet conditions (2.2 mm pwv; 3.9 K/turn or 4.6 K/mm path). From Figure 2 in Wiedner & Hills (1999), when the atmosphere is very dry (0.4 mm pwv), the sensitivity at the line center rises to 40 K/mm path. If the 183 GHz radiometers for ALMA can measure close to the line center, the sensitivity under these conditions would be 0.8 $\mu$m in path or 0.13 $\mu$m in pwv. However, at these levels, the sensitivity would likely be dominated by other factors such as gain stability, uncertainty in the altitude of the water vapour, etc. (see Lay et al., MMA memo 209). In comparison, the expected sensitivity of the IWVM is 4 $\mu$m in path (0.66 $\mu$m in pwv) with an atmosphere of 0.5 mm pwv and 8.5 $\mu$m in path with an atmosphere of 2 mm pwv. (Note that these sensitivities are estimated for Mauna Kea; the sensitivity should be even better at an altitude of 5000 m.) Thus, if the IWVM can achieve the theoretically predicted sensitivity, it could be competitive with the 183 GHz radiometers and should be able to meet the design goals for ALMA.

Figure F1: IWVM Sensitivity versus Water Vapor

Figure F2: Picture of system on the JCMT

Figure F3: Theoretical Curve of Growth

Figure F4: Stability of blackbody reference measurements

Figure F5: Three sky-dips during a 50 scan sequence

Figure F6: Similar to Fig. F5, but on a dry and stable night

Figure F7: Early results of algorithm

Figure F8: Comparison of 183 GHz (lower trace) and infrared system