[fitswcs] [Fwd: Re: WCS Paper III comments]

[William Pence]

At the recent ADASS conference, Pedro Osuna gave a talk titled "VOSpec: A 
tool for handling Virtual Observatory Compliant Spectra" in which he made 
some comments related to the WCS papers.  I contacted him for more details, 
and he sent the following reply.  Since this appears to be of general 
interest, I'm forwarding it here to the fitswcs mail list.

Bill Pence

-------- Original Message --------
Subject: Re: WCS Paper III comments
Date: Wed, 03 Nov 2004 15:35:02 +0100
From: Pedro Osuna <Pedro.Osuna at sciops.esa.int>
To: William Pence <William.D.Pence at nasa.gov>
CC: Pedro.Osuna at esa.int, Jesus Salgado <Jesus.Juan.Salgado at esa.int>
References: <4187FD47.10205 at nasa.gov>

Dear Bill,

I send you some very preliminary comments to the paper you mention.

I feel a little bit embarrassed to make comments to such an article
without having devoted time enough to it, as this article has been
checked during years and I have only had some days to look at it.

However, we do believe that something related to what I described in my
talk might be a good candidate to add to the specification.

In my talk, we describe a Dimensional Analysis way to handle units
automatically. By a simple description of the parameters SCALEQ and
DIMEQ in both axes, spectra can be compared easily without having to
care about unit names and string parsing, an always cumbersome  issue in
unit conversion algorithms.

In Paper III, the main items are the "algebraic" relations between the
different possibilities of transformation among the three main possible
spectrum axes, wavelength, frequency and apparent velocity.
I wrote "algebraic" on purpose, in the sense that they describe real
algebraic relationship between quantities, despite their obvious
physical meaning.

In this respect, the dimensional analysis is not very useful. The only
conclusion one can draw from it is the final dimensions of the algebraic
solution for the transformation; what the transformation is doing in
between is not possible to quantify with dimensional analysis.

In the case where the transformations can be expressed as products of
quantities, the dimensional analysis will be able to determine the
conditions to compare the different quantities. In the cases where
algebraic operations appear (e.g.,addition, difference, square root) the
dimensional analysis will only be able to determine the dimensions of
the final transformation.

This means that those conversions appearing in tables 3, 4 and 5 will
still be of importance for algorithms to apply to the different axes
transformations.

However, we still believe that at the end of the day, a Spectrum will
contain some sort of data with some final units, regardless of the
transformations done to get to that spectrum. It is at this point where
the dimensional analysis could be very useful for the comparison of
different spectra.

In looking at the part of the Paper III regarding the units, I got
pointed to Paper I, where there is a description of the recommended
names for units following the IAU Style Manual. Our dimensional analysis
treatement could find a natural place here, in the definition of the
units, where there would be no need to parse strings, as given  proper
SCALEQ and DIMEQ for the units in both axes, the name of the unit would
be irrelevant for the conversions.


We have shown (see our VOSpec tool, e.g.) that this works well with the
most common units in the case of spectral fluxes versus wavelength or
frequency. We have not contemplated yet the velocity in the x-axes, but
will work on it.
  For other general unit transformations, the physical problem might
dictate a different dimensional basis to be chosen, but we still believe
that having the SCALEQ and DIMEQ parameters would be of great use.
Clients for specific and different physical problems will know how to
automatically handle the units once the dimensional basis is known.

Therefore, our comment -in relation with the dimensional analysis I
presented at ADASS- to those two papers would be in the line of
proposing to the FITS community to add one single parameter to the unit
description which would be called:

DIMEQ (for example; in the FITS jargon it might look something like
CDIMEQn)

and that would include for each unit, both the SCALEQ of my presentation
and the DIMEQ in the same line (just to simplify).

Thus, a unit like Jy would be accompanied by a new keyword like:

DIMEQ	'10^-26 MT^-2'

that would combine in a single line the SCALEQ of my presentation (in
this case 10^-26) and the DIMEQ (MT^-2).

This would allow clients to compare units automatically without having
to include logic on a per-case basis, and still human beings will be
able to read the unit name if they wish (useful sometimes when looking
at headers) with the standard CUNIT keyword.


As a summary, we believe that the DIMEQ parameter (including the SCALEQ
factor) is the best way to represent a unit in any case. There will be
cases where the automatic unit handling will be more difficult than in
others, but clients will develop with time and will be able to handle
those units using the dimensional equation. We have been able to
demonstrate the usefulness of this approach in spectra with the VOSpec.
On the other hand, only naming units with a string, even if appearing on
the IAU Style Manual, will be prone to confusions, as people might not
strictly follow the manual (cases like "um", "mu", "micron" or "micra"
are very common when naming the microns).


It would be nice if you could send me your comments to this mail.

Please feel free to send it to whomever this might be of interest.

Thank you very much.

Cheers,
Pedro.
-- 
Pedro Osuna Alcalaya


Software Engineer
European Space Astronomy Center
(ESAC/ESA)
e-mail: Pedro.Osuna at esa.int
Tel + 34 91 8131314
 

European Space Astronomy Center
European Space Agency
P.O. Box 50727
E-28080 Villafranca del Castillo
MADRID - SPAIN