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.