Total Power Calibration
Last Update: JeffMangum - 08 Apr 2005
Specification
Contents
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