SED Data Model: Questions and Comments
Ed Shaya
edward.j.shaya.1 at gsfc.nasa.gov
Fri Feb 18 12:43:38 PST 2005
David Berry wrote:
>AST can determine and evaluate mappings between any two equivalent
>units strings based on FITS-WCS paper I, with a range of tolerated
>variations (cm2->cm^2, micron->um, etc). This includes the log, ln, and
>exp functions which FITS-WCS paper I specified. But I cannot currently
>see how to do a dimensional analysis of say "log(Jy)/sr". Anyone got any
>ideas?
>
>
I don't think you should try to handle log(Jy)/sr. Nor should you
handle [Jy + 7]/sr. These both break the rules of a physical formula.
During scientific manipulations you should only take log, exponents,
or trigonometric functions of unitless variables. If you have exp(kt),
k needs to have dimension 1/T. One sees the seriousness of taking
the logarithm of a unit when you look at the expansion:
ln(x) = (x-1)/x + 1/2[(x-1)/x]^2 + 1/3[(x-1)/x]^3 ...
There is just no defineable resulting dimension to this.
Now, log(Jy)/sr is particularly insidious, because you can not recover
back to Jy/sr unless you know what number of sr was used to derive this
value. If you took 10 Jy, and take the log(Jy)=1 and divided by 1 sr,
then to undo you just exponentiate. But you took 15 Jy and tak
log(Jy)=1.17, and divide by 1.5 sr you get 0.784. So log(15Jy)/1.5 sr
is not the same as log(10Jy)/1sr. So what does it mean physically, nothing.
So, you ask, what about the thousands of tables and plots with
log(whatever) in them? It is fine for display or as a compact form to
store or show anything after you take its log. But, if you are going to
do any further processing of it, you need to undo it (exponentiate).
Think about FITS integer format, it takes the values and adds a constant
and then multiplies by a constant. You can't do dimensional analysis
with these numbers because, what are the units of (Jy + 7)?
Bottom line, <units name="Jy/sr" factor="1e7"
storageAlgorighm="log($v)+17">
I hope that helps,
Ed
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