[fitswcs] Paper III: dispersed spectra function GRA

[Mark Calabretta]

On Tue 2001/11/20 12:36:38 PDT, Frank Valdes wrote
in a message to: fitswcs at NRAO.EDU

>regimes) dispersers.  I have finished a first draft.  I would like to
>make this available for comments, particularly from those familiar with
>optical spectroscopy, to insure what I am proposing is reasonable.

Hi Frank,

Looks like a very useful addition to Paper III.  For those of us who are
not familiar with optical spectroscopy I have a few suggestions which may
make it a bit easier.

Cheers, Mark

>>>

* Perhaps "GRI" would be a better algorithm code since it suggests grisms
  as well as gratings.

* Section 1.1, para 2: the concept of "tangent point" is introduced without
  explanation.  I think a schematic diagram here would help greatly, the
  angles alpha, beta and epsilon and the tangent point should be marked.

* Latex typesetting: use \sin, \cos, \tan, \tan^{-1} and \sin^{-1} to get
  proper typefaces for the trig functions.  You also need a roman subscript
  for r since it is not a variable name, e.g. \lambda_{\rm r}.

* The paragraph associated with Eq. 1 says that "For a pure prism the order
  m is zero".   The zero denominator which this produces in Eq. 1, while
  correct, begs clarification.

* n'_r in Eq. 2 is not defined.  I first read it as dn/dlambda (which has
  units of inverse length) but closer inspection shows that it has to be
  lambda_r * dn/dlambda.

* A comment on Paper III in general; I don't think it should preempt the
  name of the intermediate variable, i.e. just use w, not w'.  Paper IV
  will introduce whatever notation is required and we don't want to be
  constrained by what appears in the earlier papers - chances are that it
  will not match this.

* In Eq. 4, it's not clear how theta may be non-zero.  However, the diagram
  may make this clear.

* Typo: "as shown in equations 5".  (Note that A&A has a style rule for this
  it should be Eq. 5 (in latex Eq.~\ref{eq:xyz}) unless at the beginning of
  a sentence when it is spelt in full - Equation~\ref{eq:xyz}.  Similarly
  for Fig. and Sect.)

* Eq. 6 has dw'/dlambda but PVj_7 mysteriously gives dlambda/dw'.  (Doesn't
  the formal notation have a vertical bar to the right of the differential
  rather than parentheses?)

* The intent of Eqs. 1 to 5 is not made clear until the last paragraph of
  Sect. 1.1.  It would clarify matters if that text could be moved much
  earlier in the section.

* You provide the equations for computing lambda as a function of w, but
  what about the inverse?

* Section 1.2: I really wonder about the practicality of this.  As you say,
  grisms are defined naturally in terms of wavelength and perhaps it should
  just be left at that.

* Section 1.3: how about an example of header interpretation as in Paper II,
  i.e. the working for a particular point so that people can check their
  software.  Also perhaps an example or some comments on header
  construction.

* Typo Fig. 1 caption: Coude has an acute accent.

* "l/mm" is a bit obscure, "lines/mm" doesn't take much space.

* Typo: "equvalent".