;+
; NAME:
;	approxwidth.pro
; PURPOSE: 
;	Calculate equivalent widths assuming appoximate forms of 
;	Doppler broadening, Lorentx broadening and Voigt profile. 
;	The equations are from Ch. 4 of Goody & Yung.
; DESCRIPTION:
;	a function to help determine the approx. equivalent width
;	of spectral lines. This was used to check widthv.pro and
;	widtha.pro. 
; CATEGORY: 
; CALLING SEQUENCE: approxwidth, S, N, adop, aL, amf, Wd, Wl, Wv
; INPUTS: 
;	S	-- strength of the line shape, given in cm^-1/(molecules*cm^-2)
;	N	-- Column abundance of molecules which cause the feature,
;		   given in molecules/cm^2.
;	adop	-- Doppler line shape, given in cm^-1
;	aL	-- Lorentzian line shape, given in cm^-1
;	amf	-- air mass factor
; OPTIONAL INPUT PARAMETERS: none
; KEYWORD PARAMETERS:
; OUTPUTS: 
;	Wd	-- the approx. equivalent width using a Doppler profile.
;	Wl	-- the approx. equivalent width using a Lorentz profile.
;	Wv	-- the approx. equivalent width using a Voigt profile.
; SIDE EFFECTS: none
; RESTRICTIONS: 
; PROCEDURE: 
; MODIFICATION HISTORY: Written by Jason Cook, May 4, 1999, BU
;-

function approxwidth, S, N, adop, aL, amf,  Wd, Wl, Wv


w=S*N*amf/(adop*!pi)
print, w

if alog(w) lt 0 then begin 

Wd=S*N

endif else begin

Wd=2*adop*[alog(w)^(1/2.)+0.2886*alog(w)^(-1/2.)-0.2473*alog(w)^(-3/2.)+0.3403*alog(w)^(-5/2.)]

endelse

u=S*N*amf/(2*!pi*aL)
L=u*[1+(!pi*u/2)^(5/4.)]^(-2/5.)
Wl=2*!pi*aL*L

Wv=[Wl^2+Wd^2-(Wl*Wd/(S*N))^2]^(1/2.)


return, Wv

end