beam2bl


This IDL facility computes a transfer (or window) function b(l) for a circular beam profile $b(\theta)$.

Location in HEALPix directory tree: src/idl/misc/beam2bl.pro 


FORMAT

IDL> bl=beam2bl( beam, theta, lmax, [/ARCMIN , /DEGREES, /HELP, /RADIANS])


QUALIFIERS

beam
input beam profile $b(\theta)$
theta
angles $\theta$ (in arcmin, degrees or radians) at which the input beam $b(\theta)$ is defined
lmax
maximum multipole on which the output b(l) is to be computed


KEYWORDS

/ARCMIN
if set, $\theta$ is in arcmin
/DEGREES
if set, $\theta$ is in degrees
/HELP
if set, prints out the help header and exits
/RADIANS
if set, $\theta$ is in radians


DESCRIPTION

Since the SH Transform of an arbitrary beam is
\begin{displaymath}
b_{lm} = \int d{\bf {r}}\ b({\bf {r}})\ Y_{lm}^*({\bf {r}})
\end{displaymath} (1)

then, for a circular beam
b(l) = $\displaystyle b_{l0} \sqrt{\frac{4 \pi}{2l+1}}$  
  = $\displaystyle \int b(\theta) P_l(\theta) \sin(\theta)\ d\theta\ 2\pi$ (2)

where Pl is the Legendre Polynomial, b(l) is the beam window (or transfer) function returned by beam2bl and $b(\theta)$ is the beam radial profile expected as input of beam2bl.
IDL's routine INT_TABULATED is used to perform the integration.


RELATED ROUTINES

This section lists the routines related to beam2bl

idl
version 6.4 or more is necessary to run beam2bl.
bl2beam
facility to perform the inverse transform to beam2bl.
bl2fits
facility to write a b(l) window function into a FITS file.
fits2cl
facility to read a b(l) window function from a FITS file


EXAMPLE:

bl = gaussbeam(15.d0, 4000, 1)
theta = dindgen(4000)/100.
beam = bl2beam(bl, theta, /arcmin)
bl1 = beam2bl(beam, theta, 4000, /arcmin)
plot, bl1-bl
the example above generates a beam window function (defined for all l in $\{0,\ldots,4000\}$) for a 15arcmin-FWHM gaussian beam, computes the beam profile for angles in [0,40] arcmin, computes back the beam window function from the beam profile and finally plots the difference between the beam window functions.

Version 3.31, 2017-01-06