Ron Maddalena reports on calibration with the GBT: "Bob Garwood, Jim Braatz, and Joe McMullin
? forwarded some e-mails that showed you had an interest in how Tsys is used by the calibration routines for GBT data. You might not have seen my discussions with Bob, Jim, and Joe or some of the draft memos that are being distributed. I also don't know how many others might be interested in the subject so feel free to distribute this to the interested parties.
"I'll use DISH as a way to describe where we have been and where we need to go. Essentially, d.calib in DISH determines and applies an average Tsys over the full spectrum, regardless of the bandwidth. For most types of observations, d.calib does:
[(SIG-REF)/REF] * Tsys_REF
d.calib assumes the observer is firing the noise diode throughout the observations. It determines Tsys_REF from:
Tsys_REF = MEAN [ Tcal(f) * REF / (REF_CALON - REF_CALOFF) ]
where Tcal(f) is some estimate of the noise diode's temperature as a function of frequency across the band
"Since we know that Tsys can vary greatly in a few 10's of MHz, the simplistic assumptions of DISH lead to the miscalibration of spectral lines, especially if there are multiple lines within a band. It's also very obvious one cannot calculate Tsys on a channel-by-channel basis since the radiometer noise in the determined Tsys would be greater than in (SIG-REF)/REF. Thus, the Tsys one needs to use has to be either averaged over some range of frequency, averaged over time, or some combination of both. The need for a well-determined, non-mean Tsys that varies across a wide band was first suggested at least three years ago in the calibration memo that was used by those developing d.calib.
"The first attempts to implement this failed for a few of reasons. First, the Tcal values provided by the engineers vary from one frequency to another by 10% due to the inaccuracies of the methods they employ in the measurements of Tcal. This leads to structures in the bandpass that are not real. I also made a mistake in the estimate of the number of channels one has to average over to keep the statistical noise in Tsys below that in (S-R)/R. This led to nosier data than if one applied a mean Tsys. The DISH 'boxcar' routine for a proper averaging of Tsys was very, very slow and switching to the use of 'mean' gave DISH a heft performance boast. Finally, at that time we were using a first-cut calibration for our NOD observing technique. The preliminary algorithm led to baseline shapes that were falsely attributed to using a non-mean Tsys. Since time was tight and we wanted to move on, the temporary 'solution' was to just have d.calib do the above 'mean' calculation. Unfortunately, the splintering of the Aips++ project last year meant that the temporary solution persists.
"I'm in the process of writing a calibration manifesto that goes into all the grizzly details. I'm about 2/3rds done and already the beast is longer than the text part of my thesis. A good approximation for the number of scans or number of channels one needs to average over is:
N_scans * N_channels >> ( Tsys / Tcal ) ^ 2
Typically, Tsys~10*Tcal, so N_scans * N_channels must be >> 100. Let's say 500 channels or 500 scans or some combination of these. Essentially, one must average Tsys over a range of channels that is smaller than the frequency structure of Tsys and, at the same time, average Tsys over a range of time that is smaller than the time for Tsys to change appreciably. To me, there's no one combination of time or frequency averaging that will work for all receivers, observing techniques, or observed object. Rather, it has to be the observer that has to make that decision.
"This still doesn't address the issue of the engineer's Tcal values and it's influence on the frequency structure of the determined Tsys. I'm working on an astronomical method which provides Tcal values with high frequency resolution and a relative accuracy of less than 1% and an absolute accuracy of about 5%. Take a look at http://www.gb.nrao.edu/~rmaddale/GBT/Commissioning/Rcvr_Tcal/memo22_NoiseDiode.pdf
for what my thoughts were a couple of years ago.
"I've recently extended the technique of the above memo to include the determination of Tsys with high accuracy and frequency resolution. I'm hoping this technique will help with the removal of some of the residual baseline structure in wide bandpass observations. If you think of SIG as being: Tatmosphere + Tline(f) + Tcmb + ... +Tcontinuum + Treceiver(f), only Treceiver has any substantial frequency shape across a typical band. REF would be similar except Tcontinuum or Tatmosphere might be different. In the numerator of (SIG-REF)/REF, the contributions of everything cancel out except for: Delta_Tatmos + Delta_Tcont + Tline(f). But, Treceiver(f) remains in the denominator. Whenever Delta_Tatmos or Delta_Tcont aren't zero, (S-R)/R will contain traces of Treceiver(f). The larger the deltas, the more you'll see Treceiver(f). But, if one had a great model of Tsys(f), then Tsys(f) could cancel the frequency structure of the denominator when you take the product: [(S-R)/R]*Tsys. I should know by the end of March or so how well this technique works. But I'm hopeful since it's very close to what is behind the scenes in the 'template' fitting algorithm of Solomon, Vanden Bout and Maddalena that got us a z=2.6 detection of HCN with the GBT.
"There's more nuances to the topic than I can present in this e-mail. But, I hope I've provided you with the direction we will be heading for future calibration algorithms."
- 07 Dec 2004