The calibration and imaging formalism used in AIPS++is based closely
on the generic instrument model of Hamaker, Bregman and Sault
(1996). This formalism, referred to as the Measurement Equation (ME),
is instrument-independent and represents calibration effects in both
the visibility and image plane as Jones matrices, with arbitrary
parametrization and polarization basis. It's use in AIPS++is
described by Cornwell (1995) and Noordam (1995), and references
The calibration table format used in AIPS++was designed to support
the fundamental principles on which the ME formalism is based. The
definition of a standard calibration table format allows calibration
components to be stored permanently for subsequent retrieval,
application or modification. The current calibration table format
revision level is v2.0.
The underlying principles on which the calibration table data format
is based are described below.
Data representation:AIPS++calibration tables are stored
as AIPS++Tables, in keeping with the general rule in AIPS++
for all data visible to end users. As such, there is full user access
to all data stored in a calibration table. These data can be
retrieved, inspected and modified in the general user interface. The
implementation of the calibration tables also uses other common Tables infrastructure such as TableMeasures.
ME formalism: the calibration table format was chosen to
support the key assumptions of the ME formalism, including support for:
i) arbitrary polarization bases; ii) arbitrary Jones matrix
parametrization; and, iii) generic, instrument-independent
representation of calibration components.
Unified calibration: the calibration table format has been
designed to support both single-dish and synthesis calibration,
antenna- and baseline-based Jones matrices, as well as
visibility-plane and image-plane calibration components in a common
format, with specialization where appropriate. This was chosen to
maximize the re-use of calibration information and allow it to be
transferred between different observing contexts.
MS integration: the calibration table format is fully
integrated with the MeasurementSet (MS) data format, supports all data
representations possible in the MS, and re-uses all applicable column
and keyword names for common underlying physical concepts. A
calibration table can be attached to one or more MeasurementSets, but
exists as a stand-alone table with a user-specified name. This
supports both single-project and multi-project calibration schemes.
History tracking: the calibration table format supports
full tracking of the calibration history attached to each calibration
solution or step in the calibration process.
This section describes and defines all fields in the calibration table
format. At the highest level, the calibration table consists of a main
table, CAL_MAIN, and two sub-tables stored as table keywords
CAL_DESC and CAL_HISTORY. The CAL_DESC sub-table describes the
shape and coordinates of the array columns in the main calibration
table. CAL_HISTORY references the associated calibration history for
each row in the main table. All tables are described separately below.
The ME contains several different Jones matrix calibration components
which are enumerated in the references listed above. In general,
the Jones matrix calibration components fall into the following broad
Antenna-based, visibility-plane, non-solvable: i) P
- parallactic angle; and, ii) C - polarization configuration.
Antenna-based, visibility-plane, solvable: i) T -
atmospheric correction; ii) G - electronic gain; iii) D -
instrumental polarization; iv) B - bandpass; and v) F -
Interferometer-based, visibility-plane, solvable: The only
supported interferometer-based correction at present is a
multiplicative, solvable term (M). An additive term is also
allowed by the ME.
Antenna-based, image-plane, non-solvable: i) P -
Antenna-based, image-plane, solvable: i) T -
atmosphere correction; ii) D - instrumental polarization; iii)
F - ionosphere correction; and iv) E - voltage pattern.
Note that the same Jones matrix can appear as both a visibility-plane
and image-plane correction in the ME, as appropriate. In addition, an
individual Jones matrix component may either be discretely sampled or
modeled using arbitrary parameters.
Jones matrices of different types (time-variable, solvable,
baseline-based, antenna-based and parametrized) share as many common
sections in the CAL_MAIN table as appropriate, thus representing the
inheritance and specialization inherent to the family of Jones matrix
types. This inheritance relationship is illustrated by the VisJones and SkyJones class families in the AIPS++library.
Each calibration table holds only Jones calibration matrices of one
type (e.g. GJones, or PJones etc.).
The key sections in the CAL_MAIN table are as follows:
Primary MS indices: The first section contains the MS
indices representing the MS data from which the calibration solution
was derived or which otherwise label the calibration data. Fundamental
amongst these are the time and interval of each row. Indices over
which the MS data were averaged prior to the solution, or which are
not applicable, are set to -1.
Secondary MS fields: The primary MS indices can be used to
retrieve any secondary MS information by direct lookup in the
associated MS. However, a limited subset of MS information is stored
directly in the calibration table, to minimize the need for lookup in
the MS for the most common secondary information. This breaks database
normalization, but as is commonly the case, is warranted when dictated
by efficiency. This also allows the calibration table to be used in
many cases when the associated MS is not available. Where these column
names are not unique within the MS as a whole, they are prefixed by
the associated MS subtable name (e.g. SOURCE_CODE).
Gain values: The calibration gain factors, represented as
sampled complex (1x1), (2x2) or (4x4) Jones matrices, in
array format over optional axes of spectral window identifier,
frequency channel and sky coordinates, are stored in a GAIN
column. This column is optional for parametrized calibration
Reference frame: A section is provided to represent the
reference antenna, feed, receptor, frequency and direction for
calibration parameters, where appropriate.
Solution statistics: A section is defined to contain the
statistical properties of each calibration solution. This includes
boolean flags for the calibration gain arrays and the fit and fit
weight, both per array element and for the solution interval as a
Jones matrix parametrization: Customized columns required
to represent parametrized Jones matrices are defined in a separate
section. These are different for each parametrized type.
Sub-table pointers: Indices per CAL_MAIN row, into
the CAL_DEC and CAL_HISTORY sub-tables, are defined separately.
The CAL_DESC sub-table defines the dimensions of the array-based
columns in CAL_MAIN, and specifies the coordinates of the array axes.
These coordinates include frequency, receptor polarization, and for
image-plane components, directions and regions in the image-plane.
The frequency labeling of discretely sampled calibration gain values,
as well as parametrized calibration models, may differ from the
frequency labeling in the associated MS, if calibration is derived by
aggregating or sub-dividing the MS spectral windows. Hence, the
spectral windows and frequency channels along the calibration array
axes, as described in CAL_DESC, may differ from the MS itself. Where
there is a direct mapping to MS spectral windows and channel ranges,
this is recorded.
The polarization axis is defined in terms of a list of receptor
polarizations. As an enumerated coordinate, these overlap with those
used in the associated MS.
For parametrized calibration components, the coordinate axes in
CAL_DESC define the coordinate ranges over which the parameters are
valid, and also the dimensions of the model parameters stored as
arrays. In this case, the frequency and direction coordinates also
define the units and frame for the parameters.
The image-plane direction array axis is defined by specifying an array
or directions and associated regions about each direction in the image
plane. This allows arbitrary discrete sampling of image-plane Jones
calibration matrices, as well as arbitrary parameter domains for
image-plane calibration models.
The CAL_HISTORY sub-table records the calibration context for the
solutions recorded in each main calibration table row. This includes
the parameters used by the calibration solver, the other calibration
tables which may have been applied in the solution, any data
selection, as well as an arbitrary set of notes the user may wish to
attach to the calibration entry for future reference. All CAL_HISTORY
fields are in string form, with a general keyword-value format.