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Elucidation

The classes SkyModel, SkyJones, VisJones, MJones, ACoh, XCorr are base classes from which concrete classes must be derived. For example, the most useful form of SkyModel is ImageSkyModel which can be constructed from an image or set of images. Similarly, we envisage a ComponentSkyModel which implements Sky Brightness modeling via a set of discrete components such as Gaussians. Note that the interface to SkyEquation is via images, but that the internal workings of a SkyModel are not prescribed. Similarly, the two types of Jones classes, SkyJones and VisJones, interface to the VisEquation via actual matrices but may be implemented internally in any way desired.

Fourier transforms are implemented by the FTCoh and IFTCoh objects.

None of the matrices is required. For single dish processing, E must be present to implement summation over a primary beam. We have chosen a specific number and set of slots to make integration of different matrices part of the services supplied by the SkyEquationand VisEquation.

The use of SkyModel is subtle and deserves some description.

Prediction

The SkyEquation calls the get method of SkyModel to get a set of Images for which it can do a prediction of the coherences in a VisSet. Note that because of the form of the measurement equation, Images are required and, in particular, a collection of e.g. Gaussian components cannot be used directly. To obtain the predicted coherences, one uses the predict method of SkyEquation.

Solution

To solve for a SkyModel, one uses the solve of the SkyEquation. This calls the solve method of the SkyModel. This will usually be an iterative procedure that in turn calls the gradientsChiSquared method of SkyEquation which accumulates $\chi^{2}_{}$ and first and second gradients into the SkyModel. The gradients are with respect to the set of Images. Conversion of the gradients to be with respect to the internal variables of the SkyModel is the responsibility of the particular SkyModel and is not visible outside of that SkyModel. Thus, for example, ComponentSkyModel has to take the image form of the gradient of $\chi^{2}_{}$ and convert it to be with respect to the parameters of the various components.

Thus although SkyModel is very general, the interface between the SkyEquation and SkyModel is quite simple and is based upon Images. The apply method can apply a correction to an Image.

A similar scheme works for Jones classes. Here the interface is in terms of the coherence vector.

Prediction

The apply method of a Jones class applies the interferometer gain term (i.e. the direct product of the Jones Matrices).

Solution

The gradients are with respect to these same matrices. These are accumulated into a Jones classes by the gradientsChiSquared method of the VisEquation. The solve method of the Jones class is responsible for calling gradientsChiSquared. The particular Jones class, e.g. PhaseScreenVisJones is responsible for converting the gradients of $\chi^{2}_{}$ with respect to the matrices $\sf J^{vis}$ into gradients with respect to the internal variables of the Jones class e.g. parameters of a phase screen across a synthesis array.

Correction

The applyInv of a Jones class applies the inverse of the interferometer gain term (i.e. the direct product of the Jones Matrices).