Total Power Calibration

TIP Last Update: JeffMangum - 08 Apr 2005


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Amplitude Calibration Memos (ALMA, EVLA, etc.)

Calibration Plan Section

10 Total Power Calibration

The main use for total power data in ALMA is to add the short spacing data to longer baseline interferometic data for the purpose of making high quality images of large sources that accurately reconstruct all spatial frequencies out to the maximum observed. To this end, the main criterion for total power calibration is to make the total power data accurate and consistent with the interferometer data and to solve for any parameters that will aid in combining the total power and interferometric data. Undoubtedly, there will be some observations that will be made in only total power: for example, a wide field search for emission from some chemical species may determine that there is insufficient signal to perform interferometric imaging in all or part of the region observed first in total power. However, such observations will be the exception.

Total power data will be taken in at least two different scenarios: (a) the four 12m dishes which are part of the ACA will take total power data, and the total power data plus the short interferometric data from the 12 7m dishes will be added to the 64 element ALMA interferometric data, and (b) some or all of the 64 12m ALMA dishes will take total power data, which will be added to the ALMA interferometric data without benefit of the 7m short spacing interferometric data.

Several different calibrations need to be performed to make the total power data useful. These include: focus calibration, pointing calibration, flux scale calibration, flux scale cross-calibration with the interferometric data, bandpass calibration, polarization calibration, removal of atmospheric emission fluctuations, and beam determination. The time that each of these calibrations requires depends strongly upon the total power observing scenario: if 12m dishes in the ACA are measuring total power, it will take much longer to reach the required calibration accuracy than if 12m dishes in the 64 element ALMA array are measuring total power since we will have the benefit of the cross correlations to 63 other antennas. However, it has been decided that this issue is outside the scope of this section. Further, it has been decided that the focus, pointing, flux scale, bandpass, primary beam, and polizarization calibrations are also outside the scope of this document. We note that most of these calibrations can be performed either interferometrically or in total power, and that interferometric determination of these calibrations will be much more efficient.

So, what is left to discuss in this section? It seems we are left with the cross-calibration of the flux scales for total power and interferometric data and correcting for the effects of variable sky emission. We also mention polarization because there currently is no plan for total power polarization, and beam calibration to highlight a potential difference with the interferometrically-determined beams.

10.2 Relative Flux Scale Calibration for Total Power and Interferometric Data

The flux calibration of total power antennas should be similar to the flux calibration of interferometric data, and we assume that the techniques which make possible the interferometric flux calibration to a 3% accuracy at millimeter wavelengths, or 5% accuracy at sub-millimeter wavelengths, will permit flux calibration to the same level of accuracy for the total power data.

However, in order to make high quality mosaics, we need to cross-calibrate the interferometric and total power data to a higher degree of accuracy. Our flux scale will still be off by 3-5%, but the total power and interferometric data must be in error in a consistent manner. (The same requirement applies to the ACA, but that is not in the scope of this section.)

A simple calibration observation can enforce that the flux scales of the interferometric and total power data are similar: simultaneous observation, by both the main interferometric ALMA array and the total power antennas, of a bright and compact source. We need not know the flux of the object. Compact means that the flux seen by the interferometer is the same as the flux seen in total power. Bright means that the SNR is sufficient to reach the desired level of accuracy in the relative flux scales in a reasonable amount of time. The desired level of accuracy will, to some extent, depend upon the possible image quality of the target source -- ie, a weak target source may not need this extra step of cross-calibrating the relative flux scale. A bright target source may require better than 1% agreement of the interferometric and total power flux scales.

The obvious choice for the astronomical objects to be used for the cross-calibration is the flat spectrum quasars. The disadvantage of the quasars is that they are variable over time-scales of hours, days, or weeks -- we may well identify bright quasars which tend to be stable on hours or days, but at the present time, we probably need to count on the interferometric and total power observations being simultaneous or within an hour of each other. This requirement will greatly impact the way the ACA is scheduled, or in some cases, might push the observer to use some of the interferometric ALMA antennas, rather than the ACA antennas, to measure total power rather.

10.2.1 How bright are the quasars?

3C273 is one of the brightest quasars at millimeter wavelengths. The quiescent millimeter spectrum of 3C273 is shown in Table 10.1:

Band Freq S

[#] [Ghz] [Jy]

1 43 20

2 80 16

3 90 15

4 145 11

5 190 10

6 230 9

7 345 5.5

8 500 3.6*

9 680 2.6*

10 880 1.9*

Table 10.1: Flux of 3C273 with Frequency. As the frequencies associated with the ALMA bands were not measured, interpolation ``by eye'' was sometimes used. Data points with ``*'' are extrapolations based on a steepened spectral index of 1.1, which was determined from measurements at 230 and 375~GHz.

We also know a fair bit about quasar counts at 90~GHz and their spectral index distributions. Assuming a spectral steepening of +0.5 above 90~GHz, we can predict how bright a quasar is likely to be within some distance of a random target source. In Table 10.2, we use our source count information to tabulate the median and 10th percentile flux of the brightest source within 15 degrees of a random source.

Freq 10%Flux 50%Flux sigma_64 sigma_sd

[GHz] [Jy] [Jy] [Jy] [Jy]

90 1.15 2.35 0.00016 0.00181

140 0.79 1.58 0.00023 0.00260

170 0.68 1.36 0.00029 0.00329

230 0.55 1.10 0.00035 0.00393

345 0.41 0.83 0.00065 0.00725

490 0.33 0.66 0.00281 0.0313

680 0.27 0.55 0.00258 0.0288

880 0.24 0.48 0.00285 0.0318

Table 10.2: What is the brightest quasar within 15 degrees of my target source, as a function of frequency? The most unlucky 10% of the fields will have a quasar no brighter than the 10%Flux number, and half the fields have a quasar as bright or brighter than the 50% column. The sigma_64 column represents the 1 sigma errors in 60 seconds due to thermal noise on gain solutions obtained from 64 antennas, and the sigma_sd represents the 1 sigma errors in 60 seconds due to thermal noise on a total power observation.

10.2.2 Cross-calibration strategies

We can see from these tables that it will be straightforward to cross-calibrate the interferometric and total power flux scales at 345 GHz and below in 60 seconds or less. Above 345 GHz thermal noise is getting higher and our quasar fluxes are decreasing. The situation for single dish is not actually as dire as it looks: if we have four different total power antennas, the random noise fluctuations will be different, and a SNR of 50:1 for each dish's flux scale will result in 100:1 for the flux scale of the combined total power image. Of course, if we are using 64 antennas for total power, we gain a factor of 8, and cross-calibration is quick and easy.

If we are just using four total power antennas, considering the extra factor of 2 in the total SNR, we have three options for sub-millimeter cross-calibration: (a) observe longer in total power (using the 50% quasar fluxes, this is 6 minutes at 490 GHz, but this comes 40 minutes at 880 GHz), (b) go farther away than 15 degrees to obtain a brighter quasar requiring less observing time (this puts demands on the accuracy of the gain curves and the monitoring of opacity with time, possibly for each antenna), or (c) live with less accurately cross-calibrated data in the submillimeter. We will be able to take advantage of all of these strategies, observing a bit longer, going a bit farther to find a brighter calibrator source, and perhaps living with larger errors in cross-calibration.

10.2.3 How long and how often

Non mosaiced observations will not need flux scale cross-calibration. Low accuracy mosaic observations will probably skip the flux scale cross-calibration (ie, the 3% or 5% accuracy may be good enough). Note that low accuracy mosaics are then free to be observed at different times on interferometric ALMA and on the ACA. Modest accuracy mosaic observations will need to perform the cross-calibration once during the observations. Interferometrically, this will take perhaps 20 seconds at 345 GHz and below, or up to 60 seconds above 345 GHz. For single dish, this will take about 60 seconds at 345 GHz and below, or around 5 minutes (or more) above 345 GHz. The most demanding mosaic imaging observations might require multiple cross-calibration observations, but we assume this will be rare. Whenever flux scale cross-calibration is required, we must be observing interferometrically and with total power during the same block of time, which either restricts the ACA and ALMA scheduling, or requires that we use the regular ALMA antennas for total power.

10.3 Variable Sky Emission and 1/f gain fluctuations

As water vapor is a main contributor to atmospheric opacity at millimeter wavelengths, it is also a strong emitter. The sky emission usually is much stronger than the celestial signals we aim to detect, so we must have some sort of ON-OFF switching to detect our source. However, inhomogeneously distributed water vapor in the atmosphere results in variable sky emission, which can limit the success of our ON-OFF switching in the case of continuum observations. Fortunately, ALMA antennas are designed to move fast enough that on-the-fly (OTF) observing can usually push the residual sky brightness fluctuations (after ON-OFF subtraction) below the thermal noise. As the residual brightness fluctuations tend to be random from one OTF scan to the next, residuals that are below thermal noise level do not appreciably increase the image noise level (see Holdaway, 2004, ALMA Memo 490).

A similar effect that must be considered is 1/f gain fluctuations. If the gain changes between an ON and an OFF observation, we cannot distinguish this fluctuation from a residual atmospheric fluctuation or a celstial signal. 1/f gain fluctuations of the order 1e-4 in 300 s marginally limit the sensitivity of the ALMA single dishes. The current spec of 5e-4 gain fluctuations will surpass both residual atmospheric emission fluctuations and thermal noise for fast OTF (0.5~deg/s) and beam switching continuum observations.

10.4 Polarization

There is no mention of polarization calibration of total power in the polarization section, so we at least mention it here.

In spite of the requirement to be able to image polarization, there is currently no plan for total power polarization measurement and calibration. Traditionally, this requires some extra hardware, such as a rotatable polarizing grid in front of the feeds. Another possibility is to perform cross-correlation of the X and Y signals from the same antenna, but we have very little experience with this approach. Presumably the correlator can be configured to make this cross-correlation, and we will be able to debug and calibrate that process for the eventual use of polarization total power data. A third possibility is to observe a source in total power over a wide range of parallactic angles. Differences in the X and Y data would indicate a polarized celestial signal. However, this method requires long observations and is inconsistent with other plans for using ALMA in small time blocks to optimize sensitivity by observing near transit and when the atmospheric conditions are most favorable. Much less than a plan, this paragraph points to the lack of a plan but the possibilities for future plans.

10.5 Total Power Beam Measurement

A 12m dish measuring total power could have a different beam pattern than the interferometric beam pattern. The illuminations could be different. Also, at high frequencies where the reflector's surface errors come into play, the sidelobes could be different. Large scale surface deformations will put power into the close sidelobes. If the large scale deformations of different antennas are not identical, the phases and nulls of the sidelobes in the voltage pattern will differ among antennas, resulting in some amount of destructive interference in the primary beam's sidelobes. No such interference will occur for the total power primary beam. Hence the total power and interferometric primary beams could be different at the highest frequencies, especially in the sidelobes. If this were an important effect, it would be possible to measure by observing a slow raster of the brightest quasars on the sky, as can be inferred from Tables 10.1 and 10.2. This could take over an hour, and would be done during test time.

-- MarkHoldaway - 09 Sep 2004
Topic revision: r4 - 2005-04-08, JeffMangum
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