ALMA Calibration Outline Draft 3-Apr-2001 v0.1 S. Myers -------------------------------------------------------------------------------- Before setting down the offline (and pipeline) requirements for calibration, it would be a good idea to come up with an outline of the ALMA calibration process. It is the goal of this outline to list the various ALMA calibration operations, and to delineate the possible calibration procedures with either a set of flow charts or sequences of operations and states. -------------------------------------------------------------------------------- Online Calibration: -------------------------------------------------------------------------------- These occur in the on-line system and are applied to control parameters of the system such that the output of the correlator is a correct representation of the correlation coefficient. We will not be concerned with these here, but list a subset of them for completeness. To some extent getting these wrong online will be corrected for in later operations. -------------------------------------------------------------------------------- Delay Pointing Focus Level Control Quantization Corrections -------------------------------------------------------------------------------- Real Time Calibrations: -------------------------------------------------------------------------------- These are based on environmental information, monitor data, noise tube measurements, calibration vane measurements, WVR measurements and are meant to be applied to the data stream (though possibly well after the fact). -------------------------------------------------------------------------------- Applies To: (C=continuum S=spectrum) Inf TP Code C S C S What Comes From Produces -------------------------------------------------------------------------------- TA x x x x Temperature Scale Noise tubes/vanes CC -> Ta WV x x Atmospheric Phase WVR Phase-stable OP x x x x Atmospheric Opacity WVR? FTS? Tip Ta -> Ta* (@) RP x x Polarization Cor. Cal signal? Orthogonal (@@) (@ Probably using parallel tip curve observations taken in a subarray. Timescale would be longer than most of these Real Time corrections) (@@ This is if a cal signal is used to correct polarization products in real time) -------------------------------------------------------------------------------- A Priori Calibrations: -------------------------------------------------------------------------------- These require some previously known calibration information (eg. from baseline determinations, gain curves) usually not part of the observations themselves. -------------------------------------------------------------------------------- Applies To: Inf TP Code C S C S What Comes From Produces -------------------------------------------------------------------------------- GC x x x x Antenna Gain Eff. vs. Elev. Normalized gain IB x x Baseline Correction Calibration run Phase-stable PB x x x x Primary Beam Holography PB Correct (+) (+ incorporated into imaging, includes polarization primary beam) -------------------------------------------------------------------------------- A Posteriori Calibrations: -------------------------------------------------------------------------------- These are usually determined from the data itself or calibrations taken along with the data, and usually require a-priori calibration of the data before determination. Some of these (bandpass, leakage) could be done as a-priori if they were sufficiently stable. -------------------------------------------------------------------------------- Applies To: Inf TP Code C S C S What Comes From Produces -------------------------------------------------------------------------------- FL x x x x Flux Scale Source Calibration(&) Flux Density GA x x Interferometer Gain Phase&Amp Referencing Phase Coherence BP x x Bandpass Bright Source Flat bandpass PD x x Pol. Phase Difference Pol. Cal. Source Orthogonal (*) PL x x x x Polarization Leakage Pol. Cal. Source Stokes (**) (& or conversion from Tant to Flux using aperture efficiency, as is standard in VLBI) (* eg. R/L phase diff for circular. In single dish case applied online.) (** after conversion from polarization products to Stokes parameters) -------------------------------------------------------------------------------- Calibration States: -------------------------------------------------------------------------------- The data can be considered to be in one of a number of "calibration states" at a given time, depending on what has been applied to that point. The order in which some of these are applies in not critical (eg. RW can be applied after RT, you might be able to skip temperature and go directly to flux if the system were stable enough). The following is a possible flow of states during the calibration procedure: State Units Input Apply Notes -------------------------------------------------------------------------------- Raw Correlation coefficient raw only online short integ RawGain Correlation coefficient Raw WV longer integ RawTemp Antenna Temperature (Ta) RawGain TA NorTemp Antenna Temperature (Ta*) RawTemp OP RawFlux Flux density (PolProd) NorTemp FL NorFlux Flux density RawFlux GA NorGain Flux density NorFlux GC NorPol Flux density (Stokes) NorGain PD,PL for poln data NorSpec Flux density NorPol BP for spectral line or NorFlux We can write these in operator notation, starting from Raw data or an intermediate state: NorTemp = TA*WV NorFlux = GA*FL*NorTemp = GA*FL*TA*WV Some alternative formulations: Spectra in K.km/s: TemSpec = BP*GC*GA*NorTemp One could make a set of flow charts, but I think the operator notation works pretty well. These in some sense correspond to matrices in the measurement equation, for example. If you think of the input streams of LTA output (frequency channels x bands x polarization products), these are preserved by the operations (scaling) until application of PD/PL, which mix the products into Stokes (a rotation).