[mmaimcal]memo 372 review - d'addario

[Bryan Butler]

Memo Review

Memo: 372 - An Amplitude Calibration Strategy for ALMA
      Moreno & Guilloteau, 2002May10

Reviewer: Larry D'Addario

Date Received: 2002Aug22


Review:

The memo is quite lengthy, and it contains a great deal of useful
material in the form of calculations and anecdotal data.
Unfortunately it is rather confused and disorganized, and therefore it
cannot form the basis of any "strategy" for the ALMA telescope.

Throughout the memo, the authors fail to make some important
distinctions, of which the two most crucial are

1.  Interferometric vs. single-dish techniques; and
2.  Calibration of the instrument vs. measurement of natural variables
(primarily the atmosphere).

These failures cause extensive confusion and prevent useful
conclusions and the development of practical methods.  Regarding
point 2, perhaps the confusion is intentional in view of such
statements as, "Atmospheric correction... is usually performed with
receiver gain calibration, because the two problems do not easily
separate" (page 3).  But this is not at all true.

While section 5 gives formulas and numerical results for
interferometric sensitivity, the only gain calibration methods
discussed (section 6) are single dish techniques.

Although the memo is about "amplitude calibration," some consideration
is given to phase calibration as well (section 10 and elsewhere).
That discussion contains several misconceptions, including that "point
sources are required" (p 25) and "the basic...cycle uses two sky
frequencies, one for observation and one for calibration" (p 4).
Neither of these statements is correct.  The source can be somewhat
extended if the brightness distribution is known.  The two-frequency
technique produces no information about the instrumental phase, which
must be measured with exactly the same setup as the target source
observations.

No consideration at all is given to self-calibration techniques, even
though they will be of critical importance for imaging with ALMA.

Various secondary effects are considered, and each is described as
requiring a separate "calibration."  These include sideband ratio,
delay, bandpass, pointing, and focus.  In each case, the discussion in
the memo contains misconceptions and confusion.  Sideband ratio is
unimportant for continuum observations, provided only that it is the
same for the target and calibrator.  For line observations, very large
suppression of the undesired sideband occurs in the correlator, so
explicit knowledge of the gain ratio of the front end is not
necessary.  "Bandpass" is described as requiring separate "fine,"
"coarse," and "standing wave" calibrations, yet these distinctions are
of little practical value; it is more useful to distinguish the stable
(predictable) and variable parts of the frequency response.  For both
pointing and focus, it is assumed that calibration can be done in a
different band from the observation, yet total offsets (from encoder
readings) are substantially different among bands; not all of the
pointing and focus parameters can be scaled between frequencies.

Most of my comments here apply to interferometric observations.  To
the extent that the target sources will also be observed in total
power or by single-dish spectroscopy, different techniques may be
needed.  Such observations are sensitive to the total system noise,
most of which is uncorrelated between antennas and invisible to
interferometers.  The semi-transparent vane may be useful for this
purpose, even though it is unable to provide the direct measurement of
electronics gain that is desired for interferometry.  Knowledge of the
sideband ratio may also be needed, but only for the case of spectral
line measurements in single dish mode along with gain determination
using continuum calibrators in total power mode; a better approach is
to use interferometry for the calibrator observation.  In any case, a
sensible discussion of calibration strategies must clearly separate
the cases of zero-baseline and non-zero-baseline observations.

Table 12 (p 33) provides suggested "repeat rates" for various
calibrations, yet none of these is justified.  They depend strongly on
the stability of the instrument, which is largely unknown at present.


--------------------------------------------------------------------
[The following notes are a discussion of some principles related to
calibration.  They are not direct comments on Memo 372.]


Let me now return to the second of the two points of distinction
mentioned at the beginning of these notes, namely instrumental
vs. natural effects.  Confusion arises partly because both are
incorrectly called "calibration," not only in this memo but quite
commonly.  We can speak more precisely by using the following
definitions.

Calibration: Determination of those *instrumental* parameters that are
not established to sufficient accuracy by design or from first
principles, and thus must be measured.  [For telescopes, two types of
calibration should be distinguished: internal, based on hardware built
into the instrument for the purpose; and external, based on natural
standards (typically celestial objects).]

Sounding: Determination of *environmental* parameters that affect or
distort the desired measurement, but which do not affect the operation
or accuracy of the instrument.  [For telescopes, these typically
involve the propagation medium between the object under study and the
instrument, and at mm/submm wavelengths this is predominantly the
troposphere.]

Correction: Application of the calibration and sounding information to
the measurements produced by the instrument, so as to produce improved
measurements.  Sometimes correction is accomplished by adjusting the
instrument itself so that future measurements will be better; and
sometimes it is done by numerical modification of the instrument's
output data.

I suggest that the ALMA strategy should proceed in the following
priority order:

a.  Apply all {\it a priori} knowledge based on design and first
principles.  In some cases, this may be enough and no calibration or
sounding is needed.  Amplitudes should be known to 20--30% on this
basis.

b.  Perform internal calibrations and apply to all observations of
calibrators and targets.

c.  Perform all soundings that use instruments separate from the
telescope.  [These include ground based meteorology instruments, water
vapor radiometers (notwithstanding the fact that they are mounted on
the antennas, they are still separate instruments from the telescope),
tipping radiometers, up-looking Fourier transform spectrometers, etc.]
Apply to all observations of calibrators and targets.

d.  Observe one or more calibration sources interferometrically, and
solve for complex gains by antenna and channel.  These observations
must use the same instrumental setup (including, of course, the
observing frequency) as the target source.  Often this will
produce very accurate results (perhaps ~1%) for the relative gains
(ratios among antennas) but with an error in the overall scale due to
uncertainty in the calibrator's flux and/or in the atmospheric
transparency.  The phase part may be in error because of imperfect
knowledge of the atmospheric phase, which may vary across the array
(even though WVR measurements have already been applied per item c).

e.  Rarely, observe a source whose absolute flux is accurately known
so as to transfer that knowledge to other (secondary) calibrators used
in item d.

f.  If necessary, perform additional soundings that use the telescope
itself.  These may involve celestial sources and may use a different
setup than for the target.  Rapid phase calibration is an example of
this; not that it measures atmospheric delay variations on the
assumption that they are non-dispersive, but it does not measure the
instrumental phase (which was calibrated under item d).

g.  If necessary, perform additional external calibrations of
secondary instrumental parameters like focus, pointing, and bandpass.
Notice that this is given low priority.  These things need to be made
rather stable by design.

I believe it is best to keep calibration and sounding measurements
separate as much as possible, and to make maximum use of internal
calibration.  The complex gain of each telescope channel consists of
the cascade of the antenna gain and the electronics gain.  The antenna
gain cannot easily be calibrated internally, but it is made stable by
design and its absolute value is also known rather well by design
(except at the highest frequencies).  The electronics gain may be less
stable, but internal calibration is possible by turning on a known
built-in signal source.  The two-load calibrator accomplishes this,
but the semi-transparent vane does not.  The latter mixes calibration
and sounding, and is thus much less desirable.  Note that it is not
necessary ever to know the system temperature very accurately, but
rather only the gain.  Transparency and delay of the atmosphere should
be determined with separate instruments like WVRs and FTSs.