[QUANTITY] Justification for Matrix Quantities (Was: Re: [QUANTITY] Requirements and apology)

David Berry dsb at ast.man.ac.uk
Tue Nov 4 02:26:05 PST 2003

```Ed,

> You are discussing a flux quantity that is dependent on frequency (I
> prefer hasArgument but they are synonomous).  Frequency is also a
> quantity.  It is something that is measured (in this case, by measurements
> on a calibration lamp).  Normally one would simply have an array of flux
> and an array of frequencies and you would say the flux (quantity array)
> is dependent on the frequency (quantity array).

If you have a simple 1D array of numbers, your starting point is surely
to say the pixel value is dependent on the pixel index. The measured
discrete pixel values are the fundamental thing we are describing here,
not the underlying continuous physical function of flux on frequency. The
Quantity meta-data should allow you to move from what you *have* (i.e. the
dependancy of pixel value on pixel index) to what you *want* (e.g. the
dependancy of flux on frequency).

One point to note is that whilst "what we have" is always the same (i.e.
we have the dependancy of pixel value on pixel index), there may be
several options for "what we want". For instance, for a simple CCD image
of the sky, we may want the dependancy of (RA,DEC) on pixel index, or
alternatively we may want the dependancy of focal plane position on pixel
index. Presumably, in your model you would express this by saying that
flux is a function of sky position, which is a function of focal plane
position, which is a function of pixel index? How do you decide on the
dependancy order? Why not say that flux is a function of focal plane
position, which is a function of sky position, which is a function of
pixel index? I'll reiterate that in my opinion, the only truely
independant variable we have here is pixel index, since that is what is
used to access the actual numerical values, and that the best way to model
this is to store both the dependancy of sky position on pixel index and
also the dependancy of focal plane position on pixel index.

So far this message has talked exclusively about transformations based on
pixel *index*, but the model should provide equivalent facilities for
pixel *value* - i.e. it should describe how to move from what we have (pixel
value) to what we want (e.g. flux). One example scenario is if the pixel
array in the quantity holds uncalibrated raw data values, the associated
meta-data could describe the transformation from raw data value to
calibrated flux value (potentially you could have transformations into
several different systems; flux, antenna temperature, etc). If the
calibration was then ever improved, a new transformation could be added
into the Quantity (or the old one replaced).

In summary, I would like to see a data model which recognises that
the only two independant variables we have are pixel value and pixel
index, and which stores meta data describing the transformations from
pixel value/index into a selection of other systems.

David

----------------------------------------------------------------------
Dr David S. Berry    (dsb at ast.man.ac.uk)