ISO Spectral access and QUANTITY discussion

[posuna at iso.vilspa.esa.es]

Dear all,


some days ago, we posted a mail to the DAL announcing our extension of
SIAP to Spectrum access to the ISO data.

In that mail, we made an exposition of how we managed the problem of
the axes/units in the representation of spectra using some sort of
dimensional equations.

In view of the recent discussions on the QUANTITY issue, we thought it
might be of interest to the DM group, and thus we attach the mail
below.

Our dimensional analysis trick might be applied to other "quantities"
and models as it is a very general way of describing physical
quantities.


Hope this is of interest.

Best regards,
P.


======================================================================

From: posuna at iso.vilspa.esa.es
To: dal at ivoa.net
Cc: Pedro.Osuna at esa.int, Jesus.Juan.Salgado at esa.int,
Christophe.Arviset at esa.int, Alberto.Salama at esa.int Reply-To:
posuna at iso.vilspa.esa.es Subject: Simple access to ISO Spectra (+images)
using ISO AIO in SIAP mode Date: Fri, 7 Nov 2003 11:23:25 +0100
Sender: owner-dal at eso.org
X-Mailer: Sylpheed version 0.9.2 (GTK+ 1.2.9; sparc-sun-solaris2.8)


Dear all,

 at the Strasbourg IVOA meeting, we proposed a simple access to spectra
 using a similar protocol to the SIAP. We have modified our system in
 this line for accessing both ISO images and spectra in a SIAP-like way.

 You can access an example at:

http://pma.standby.vilspa.esa.es:8080/aio/jsp/siap.jsp?id_target=M51&imageType=spectrum

 (as usual in our system, a "format=html" can be input to see a
 human-readable html page with the outputs)

 We have included an "imagetype" parameter that can either be:

 - spectrum
 - image
 - all

 with obvious meanings.

 By default (i.e., not including the imagetype), the answer will only be
 images, fully SIAP compatible thus.


 For the metadata information for the spectra in the VOTable output,
this is what we have put in:

 - FIELD_ID="AXES" ucd=VOX:Spectrum_axes datatype="char" arraysize="*"
   
   This one indicates the axes names (in our case corresponding to the
   keyword names in our fits files) that ought to be used from the
   spectrum product  to do a display of the spectrum

 - FIELD ID="UNITS" ucd="VOX:Spectrum_units" datatype="double"
   arraysize="*"

   This one indicates the units in which each of the axes is represented

 - FIELD ID="FORMAT" ucd="VOX:Spectrum_Format
   

   This is a mime format for spectrum products in fits format.



 As the aforementioned quantities would not be enough to be able to
 overlap or represent different spectra coming from different
 instruments, etc., we believe that we have found a solution by
 introducing the following fields:


 - FIELD ID="DIMEQ" ucd="VOX:Spectrum_dimeq" datatype="char"
   arraysize="*"/>

   This one represents the dimensional equation of the units in each of
   the axes. More on this later.
   The dimesnional equation is based on the fundamental dimesnionless
   quantities M,L,T,Q for Mass, Length, Time and Charge respectively.
   We represent the equation by, e.g: 

 	MLT-2 

   where any number after the quantity means (exponential), i.e, the
   equation above should be read MLT^-2

   (this could be changed if it does not result too clear)  



 - FIELD ID="SCALEQ" ucd="VOX:Spectrum_scaleq" datatype="char"
   arraysize="*"/>
   
   This one represents the scaling factor needed to transform the
   dimensional equation (dimensionless by definition) to the
   International System of Units. More on this later.

 With these two quantities, one can always transform from any system of
 units to other, and with the scaling factor it is possible to display
 and overlay diffrent scaled spectra. We give some explanation of what
we mean below with a working example.



 --------------------------------------------
 Use of dimensional equation for the metadata
 --------------------------------------------

 Our data fluxes, in the case of LWS, are given in "w/cm^2/um", whereas
 the data for SWS are given in Jy.

 We thus need a way to convert from one to the other. Let's try
 to convert the LWS spectrum units (w/cm^2/s) to the SWS spectrum units
 (in Jy) and then display both in the same browse tool.   

 According to our server, the SWS flux (in Jy) dimensional equation is:

 [SWS] = MT-2

 and the LWS (w/cm^2/um) dimensional equation is:

 [LWS] = MLT-3


 So, to represent one with respect to the other, we will have to divide
 both dimensional equations:

 [SWS]     MT-2
 ----- = ------- = LT 
 [LWS]   ML-1T-3


 as the only quantities we can use in the transformation are those
coming from the conversion between "wavelength" and "frequency", to go
from one to the other we will have to use a combination of "LAMBDA" and
"c" (wavelength and light velocity). So the above equation has to be
equal to:

 LT = [LAMBDA]^n [c]^m  = L^n [LT-1]^m = L^(n+m) T^-m


 Which means (by equaling the exponents):

 n+m=1
 -m=1

 and thus:

 m=-1
 n=2



 so to go from SWS spectrum to LWS one, we will have to multiply by:

 [LAMBDA]^2/[c]

 which is as expected from physical reasonings (please check page 82 of
 the ISO Handbook - Vol 1. MISSION OVERVIEW at
 http://www.iso.vilspa.esa.es/manuals/HANDBOOK/I/gen_hb/).


 (In case the above 2x2 system of equations is not solvable, then the
two spectra could not be comparable).




 This would give the dimensionless equation. To get to International
 System units, we would simply have to do:


 FLUX(SWS units) = Flux(LWS units) [LAMBDA]^2 [c]^-1 [SWS scale] / [LWS
 scale]

 FLUX(SWS units)  = Flux(LWS units) [LAMBDA]^2 [c]^-1 10^-26 10^-10
                  = 10^-36 Flux(LWS units) [LAMBDA]^2 [c]^-1


    
 where obviously, LAMBDA and c should be given in international system
 units (LAMBDA in International Units is deducible from the LAMBDA given
 in the spectrum times its Spectrum_scaleq factor).


 This procedure might look cumbersome, but once the algorithm is
 understood a computer can do it without problems.


------------------------------------------------------------------------


 We believe this way of presenting metadata in this type of simple
access a la SIAP makes it easy to access our spectra and might be used
for other spectra as well, at least for those in fits format. 

 This does not clash in our view with the more complicated and general
 SSAP work which is going thoroughly on, but simply tries to give access
 to our spectra products in an easy way.


 Please let us know if you have any comments.

 Best regards,
 Pedro Osuna and Jesus Salgado.






--


Pedro Osuna Alcalaya


SOFTWARE Development Group
XMM-Newton Science Archive				
e-mail: Pedro.Osuna at esa.int
Tel + 34 91 8131314  				

European Space Agency
VILLAFRANCA Satellites Tracking Station
P.O. Box 50727 
E-28080 Villafranca del Castillo
MADRID - SPAIN