Memo Review Reply

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

Reviewer: Larry D'Addario
Date Received: 2002Aug22

Reply from: Stephane Guilloteau
Date Received: 2002Sep20


SG comments are interspersed in the original d'addario review, and
are denoted by 'S.G.:'.

> Larry d'Addario writes:
> [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.]

S.G.: Separating "Calibration" from "Sounding" looks attractive, but it 
 leaves the (false) impression the "environmental parameteres" do not 
 affect the accuracy of the measurement. Unfortunately, not only they 
 do, but they even are the dominant factors in many cases.  
 "environmental" parameters also affect the OPERATION of the telescope. 
 For example, in the fast switching scheme, the cycle time depends on 
 the atmospheric phase noise. 

> 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.

S.G.: which is OK for a 5 sigma detection, but of little value for any 
 high S/N image.

> 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).

S.G.: Memo 372 does give time estimate for that stage as a function of
 frequency and desired "accuracy". It turns out to be impossible to get 
 better than 3 % at sub-mm wavelengths by this process.

> 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.

S.G.: "Rarely" is not correct. All (secondary) calibrators are 
 unfortunately time variable. So this must be done at least once for 
 each observation.

> 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.

S.G.: This is an incorrect assumption. The antenna specifications are 
 quite clear from this view point, and it is necessary to calibrate the 
 pointing and focus quite often to reach the accuracy goal. Also, 
 pointing and focus are instrumental parameters which needs not only to 
 be measured for some a-posteriori "calibration", but corrected for in 
 real time to avoid losses. They rather fall under item b) above.  

> I believe it is best to keep calibration and sounding measurements
> separate as much as possible, 

S.G.: If one can demonstrates that it gives a better overall result, 
 then this is the way to go. If one demonstrates it gives a worse 
 result, it should not be done. If we don't know, or if we prove both 
 methods give similar result, it is a matter of taste, or of cost (the 
 ultimate judge...).

> and to make maximum use of internal calibration.  

S.G.: This is always a good idea anyhow.

> The complex gain of each telescope channel consists of
> the cascade of the antenna gain and the electronics gain.  

S.G.: AND THE ATMOSPHERIC TRANSPARENCY.  It is useless to get things
 calibrated out at the 0.1 % level in the receiver or antenna plane, and
 then screw up the whole thing by 15 to 20 % because the atmosphere is 
 there.

> 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.  

S.G.: It should be possible to build a receiver with an electronic gain 
 stable to 0.5 % on the "medium" timescales (several hours). This has 
 already been done.  The ASAC repeatedly asks to get 0.01 % stability 
 on "short"  timescales (minutes): this is much more difficult.

> 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.  

S.G.: unless one gives better result than the other, it does not matter.

> Note that it is not necessary ever to know the system temperature 
> very accurately, but rather only the gain.  

S.G.: if you define the gain as Jy per Correlator count, yes... But 
 this involves the atmospheric transparency correction.

> Transparency and delay of the atmosphere should
> be determined with separate instruments like WVRs and FTSs.

S.G.: We ought to have a separate sounding device. The total 
 atmospheric delay is irrelevant.


S.G.: There is one important category of calibration "actions" which is 
 not defined and considered in the above description. These are the 
 real-time actions which cannot be undone or superseded. These includes 
 pointing, focus, but also WVR correction. The list is not exhaustive, 
 and can depend on details of the implementation of the calibration
 process.