For heterodyne observations, there are three types of calibrations: temperature (chopper) calibration, telescope efficiency, and (if necessary) AOS frequency calibration. It is best to calibrate regularly.
UIP> planet planet
UIP> chop 2
UIP> oo 1 /step offset
REMEMBER Observers must decide how important the calibration is to them and how to deal with it.
Several authors (Tom Phillips, Ken [Taco] Young, and Todd Groesbeck) contributed to this description of the calibration procedure.
Heterodyne observations are calibrated with the chopper method first discussed for millimeter astronomy by Penzias and Burrus (1973 ARA&A 11, 51 ADS). Two measurements are made: one of the sky and one of an ambient temperature absorber (hot load or chopper) placed into the beam at a point between the receiver and the secondary mirror. As shown below, these measurements provide the information necessary to determine TA*, the antenna temperature corrected for atmospheric absorption and ambient temperature telescope losses, including hot spillover and blockage.
Temperature calibration is performed with the
Cal command. This is done automatically at the start of the next scan after changing sources, retuning the receiver, etc. The results of the most recent appropriate
Cal measurement are automatically applied so the recorded data are calibrated on the TA* scale.
Define the following:
|α||= hot spillover efficiency|
|= 1 - (fraction of power falling on ground, etc.)|
|β||= cold spillover efficiency|
|= 1 - (fraction of power falling on sky, but not forming part of the beam)|
|γ||= source coupling efficiency|
|TRX||= receiver noise temperature||[K]|
|Th||= hot load temperature (= ground temperature = air temperature)||[K]|
|Tc||= cold load temperature||[K]|
|Ts,sig||= source temperature, signal sideband||[K]|
|Ts,img||= source temperature, image sideband||[K]|
|TA*||= corrected antenna temperature, SSB||[K]|
|Vh||= hot load signal||[V]|
|Vc||= cold load signal||[V]|
|Y||= Vh / Vc|
|Vsky||= sky (off position) signal||[V]|
|Vs||= source and sky (on position) signal||[V]|
|G||= Gsig + Gimg = overall system gain||[V K-1]|
|Gsig||= system gain, signal sideband||[V K-1]|
|Gimg||= system gain, image sideband||[V K-1]|
|τz||= zenith atmospheric optical depth at the observing frequency|
|τsig||= zenith atmospheric optical depth at the signal frequency|
|τimg||= zenith atmospheric optical depth at the image frequency|
|CSB||= Sideband atmospheric correction ratio|
|A||= secant (zenith angle) = airmass|
Several assumptions simplify the theory. The major ones are:
At the CSO, all the receivers are double sideband (DSB). Continuum (broad band) sources, such as calibrators, spillover, the atmosphere, and planets, contribute to the measured signal in both sidebands. Spectral lines, however, only contribute in one sideband.
Looking at the calibrator (hot load or chopper), the measured signal includes contributions from the receiver and the load,
Looking at the sky (off position) and at the source and sky (on position), the measured signal include contributions from the receiver, the atmosphere, the ground (hot) spillover, the sky (cold) spillover, and the source,
|Vsky||= (Gsig+Gimg)||× [TRX||+ (1 - α)Th ]||+ Gsig αβ (1 - e-τsigA )Th||+ Gimg αβ (1 - e-τimgA )Th||+ Gsig α(1 - β)(1 - e-τsigA )Th||+ Gimg α(1 - β)(1 - e-τimgA )Th||,|
|Vs||= (Gsig+Gimg)||× [TRX||+ (1 - α)Th ]||+ Gsig αβ (1 - e-τsigA )Th||+ Gimg αβ (1 - e-τimgA )Th||+ Gsig α(1 - β)(1 - e-τsigA )Th||+ Gimg α(1 - β)(1 - e-τimgA )Th||+ αβγ [ Gsig Ts,sig e-τsigA + Gimg Ts,img e-τimgA ].|
|receiver||hot spillover||atmosphere||cold spillover||source|
|Vsky||= (Gsig+Gimg) TRX||+ Gsig (1 - αe-τsigA )Th||+ Gimg (1 - αe-τimgA )Th||,|
|Vs||= (Gsig+Gimg) TRX||+ Gsig (1 - αe-τsigA )Th||+ Gimg (1 - αe-τimgA )Th||+ αβγ [ Gsig Ts,img e-τsigA + Gimg Ts,img e-τimgA ].|
Observations are made with some switching scheme, i. e., position switching. The observing procedure measures
OO= (Vs - Vsky)/Vsky = αβγ [ Gsig Ts,sig e-τsigA + Gimg Ts,img e-τimgA ] / Vsky ,
the calibration procedure measures
Cal= (Vh - Vsky)/Vsky = α Th [ Gsig e-τsigA + Gimg e-τimgA ] / Vsky .
When the sideband gains are equal, Gsig = Gsig, the ratio
Cal is independent of the hot spillover efficiency, α, and of the system gain, Gsig + Gimg. The data are recorded as SSB antenna temperature, corrected for atmospheric absorption and hot spillover,
Cal) = 2βγ (Ts,sig e-τsigA + Ts,img e-τimgA ) / ( e-τsigA + e-τimgA ).
Individual spectral lines appear only in one sideband, so Ts,img = 0 and
where the sideband atmospheric correction ratio
The correction ratio may be calculated with an atmospheric model. Note the correction ratio depends on the observing zenith angle.
If the atmospheric transmission in the two sidebands is equal, τsig = τimg and CSB = 1, independent of zenith angle, and the recorded data are properly calibrated.
If the atmospheric transmission in the two sidebands is unequal, τsig ≠ τimg, then for proper calibration the recorded data should be multiplied by CSB ≠ 1.
If the atmospheric transmission in the image sideband is better than in the signal sideband, τsig > τimg and C > 1. In this case the atmospheric contribution to the system noise in the image sideband is less than the contribution in the signal sideband.
For continuum sources, the source temperature is the same in both sidebands, Ts,sig = Ts,img = Ts, so
This is independent of the relative atmospheric transmission in the two sidebands.
The system temperature, Tsys, indicates the system noise level corrected for atmospheric absorption and hot spillover. Among other things, it is used for weighting scans when summing them. The system temperature includes contributions in both sidebands from the receiver, from the atmosphere, and from hot spillover. For line (SSB) observations,
If the air temperature and spillover temperature are the same, Tatm = Tspill = Th, then
The system temperature can be determined from a calibration measurement,
Cal= [α (e-τsigA + e-τimgA) Th] / [2TRX + (2 - αe-τsigA - αe-τimgA)Th] ,
Cal= CSB 2Th /
The observatory software assumes the atmospheric transmission in the two sidebands is equal, τsig = τimg, i. e., CSB = 1, and reports
The receiver temperature, TRX, and Y factor may be determined from measurements of two loads, hot (ambient) and cold (LN2).
They may also be determined by substituting a cold load for the sky when making a (manual) calibration.
Cal= (Vh - Vc)/Vc ,
Cal= 1 + 2 Th / Tsys , and
For a piece of Eccosorb drenched in LN2, it is usually assumed that Tc = 80 K.
To correct for cold spillover and for the coupling of the beam to the source, it is necessary to measure the telescope efficiency, βγ. Then the source temperature may be determined,
The actual value of βγ, and what you may wish to call it, depends on the size of the source. There are three typical cases: sources large, similar, or small compared to the beam.
For line observations :
|TA*|| = 2Th × ( ||recorded data|
|TA*(Moon-corrected)||= TA* / βγ (Moon),||large source|
|TMB||= TA* / βγ (Main Beam)||smallish source|
The efficiencies vary with the receiver and, strictly speaking, with frequency for each receiver. It is best to measure the efficiency yourself, but approximate values are:
|Receiver||230 GHz||345 GHz||492 GHz||650 GHz||850 GHz|
|βγ (Main beam)||76%||65%||53%||32% ??|
We will use many of the same quantities and some of the results of the previous section. In addition, let us define the following quantities:
|Tspillover||= spillover temperature ≡ (1 - ηhot) Th|
|τz||= atmospheric opacity at zenith|
|A|| = airmass at a given zenith angle = 1/cos(
|Y||= Vh/Vc = Receiver Y factor|
[ηhot) ≡ α.]
As noted, we assume a plane-parallel model for the atmosphere, so for a given zenith angle we have
τ = τz A.
We will be comparing measurements at different zenith angles rather than on- and off-source measurements. The entire passband of the receiver is treated as a single channel (the total power output is used), and we assume that the contribution of any source to the total power is negligible in comparison with the contributions of the receiver, spillover, and the atmosphere.
From the previous section, we have
|Vh||= G [TRX + Th ]|
|Vc||= G [TRX + Tc ]|
Vsky = G [TRX + (1 - ηhote-τ )Th ].
If we now form the quantity
|S||= ln [(Vh - Vc)/(Vh - Vsky)]|
|= ln [(Th - Tc)/ ηhot e-τ Th ]|
|= τ + ln [(Th - Tc)/ ηhot Th ]|
|= τzA + ln [(Th - Tc)/ ηhot Th ] ,|
we see that A is a linear function of airmass with slope τZ. With Th and Tc known, ηhot can be found from the intercept as
ηhot = (1 - Th/Tc) e-(intercept).
Tspillover can then be calculated from its definition. Note that for any measurement of Vsky we may define a Tequiv by requiring
Vsky = G [ TRX + Tequiv ].
Tspillover can then also be thought of as the Tequiv that would be measured for an airmass of zero.
If Vc (or Tc) is unknown, τz can be found by defining
|S'||= ln [Vh/(Vh - Vsky)]|
|= ln [(Th + TRX)/ ηhot e-τ Th ]|
|= τzA + ln [(Th + TRX) / ηhot Th ] ,|
where now S' is linear in airmass with a slope of τz. If TRX is known, this intercept can be used to find ηhot. However, it is more likely that TRX will be determined from hot and cold load measurements of Vh and Vc at known temperatures as follows:
Y = Vh/Vc = (TRX + Th)/(TRX + Tc)
TRX = (Th - Y Tc)/(Y - 1) .
(This is of course unrelated to doing a skydip except insofar as measurements are typically made of Vh and Vc.)
Whether S or S' is used, it is necessary to make more than one measurement in order to find the slope and the intercept. The usual way of doing this is outlined below.
N. B. This section is obsolete. The
SKYDIP macro will position the telescope to successive airmasses.
A skydip is usually performed at the CSO using the
1.5M, etc., macros under the
UIP. Issuing one of these macros causes the telescope to go to the corresponding zenith angle for 1, 1.5, 2, 3, 4, or 5 airmasses. The total power must be recorded at each of these positions (some day it may be automated, but not yet) and for the hot and cold loads.
A utility program called TAUPLOT exists at the CSO which will do all of the necessary calculations and produce pretty plots. This may be run by simply typing
tauplot at either the
UIP> prompt or the
$ prompt. The program will then prompt you for an airmass and voltage, and will repeat the prompt after the values are entered. A simple carriage return will cause the program to go on, and you are prompted for Vh and then Vc. Default values for Th and Vc will be used unless other values are specified at the next prompt.
IMPORTANT NOTE - The program is set up under the assumption that G is positive (it checks that Vsky is always less than Vh). This means that although the total power voltage may be displayed as negative, the absolute value of this should be used. Furthermore, it is often more convenient to use integral values though this is not necessary. Thus, if the meter reads -0.142, a value of 142 should be entered.
Once the data entry is complete, the program calculates τz, the intercept, ηhot, Tspillover, Y, and TRX, as well as equivalent temperatures Tequiv for all of the measured Vsky. These are displayed on the screen, and you are asked if you wish to plot the results. The default is to produce first a screen plot and then hardcopy, but you may specify otherwise if you desire. All of the calculated values are also displayed on the plot.
If for some reason, Vc is not measured, the program may be run using the A' formalism outlined above by not entering a value at the Vc prompt. In this case, τz is the only value calculated and is displayed with a message to that effect.
N. B. This section is obsolete.
Frequency calibration of the AOS backends at the CSO is done using a multiplied crystal oscillator to generate a comb with peaks separated by 100 MHz for the 500 MHz AOS or 10 MHz for the 50 MHz AOS. These allow one to determine the relationship between the IF frequency υIF and channel number of the AOS. (This relationship is assumed to be linear and experience shows this to be so.)
LO command is issued, the LO frequency υLO is set so that the desired line frequency will correspond to the center of the passband, or approximately channel 512. This will take into account velocity and frequency offsets as well as the correct υIF. A default relationship between channel number and frequency is then written into the observation headers. However, because the AOS exhibits some variation in response to temperature changes, the calibration comb should be used to determine the precise relationship as follows:
FCALmacro to record a scan showing the response of the AOS to the comb. Then use CLASS to look at this scan using units of channel numbers.
If after determining the correct values for the reference channel number (corresponding to the desired line frequency) and the width of the channels you desire to change from the default values to the correct values, you can do this within CLASS for data taken in the IRAM format. At the present time, there is no provision made for changing the default values that will be written as you observe, so corrections must be made after the fact. As you will want to write out the scans after they have been corrected, this means you must first open a new data file for writing. See the CLASS manual for a description of the
FILE OPEN command if you are not sure how to do this.
Variables exist corresponding to the reference channel location and the channel spacing in both frequency and velocity which are used by CLASS in plotting, etc. The names of these variables are
VELO_STEP. The command
EXAMINE variable_name can be used to display the current values, while the command
LET variable_name = value can be used to change the values. Unfortunately, these new values do not become effective until the scan is written out to a data file and the new scan then read back in. Alternatively, the command
MODIFY can be used (with conveniently different variable names, of course). To change the reference channel, type
MODIFY RECENTER value; to change the channel frequency spacing, type
MODIFY WIDTH value. Using
MODIFY has some advantages: the values become effective immediately, and changing the frequency spacing automatically causes the velocity spacing to be changed correctly. However, with either
MODIFY the scan must be written to a data file or the changes will be lost. This can be done using either
UPDATE. Again, see the CLASS manual for more details on these commands.
Some conditions for which having the correct values is essential would include: adding together spectra where a line has been observed in different parts of the passband; observing weak or narrow lines which might be lost if any smearing were to occur because of AOS drifts; observing lines near the edge of the passband, or very wide lines. Note that because all values are calculated from the reference channel at around 512, errors in the channel width value become progressively more important as you move toward the edge of the passband.
At the present time, the frequency calibration comb is switched in only upon the user's request (or if the antenna is sent on a very long slew). The
FCAL macro in the
UIP program does this; to do this in a command file you must give the actual series of commands which correspond to the
FCAL macro. Type
DEFINE/LIST FCAL to see this series of commands.