bl2beam


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

Location in HEALPix directory tree: src/idl/misc/bl2beam.pro 


FORMAT

IDL> beam=bl2beam( bl, theta, [/ARCMIN , /DEGREES, /HELP, /RADIANS])


QUALIFIERS

bl
input b(l) window function of beam (defined for all integer multipoles l starting at 0)
theta
angles $\theta$ (in arcmin, degrees or radians) at which the output beam $b(\theta)$ 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 an arbitrary beam is related to its SH Transform via
\begin{displaymath}
b({\bf {r}}) = \sum_{lm} b_{lm} Y_{lm}({\bf {r}}),
\end{displaymath} (3)

a circular beam has a radial profile (as returned by bl2beam)
\begin{displaymath}
b(\theta) = \sum_l b(l) P_l(\theta) \frac{2l+1}{4 \pi},
\end{displaymath} (4)

where Pl is Legendre Polynomial and
\begin{displaymath}
b(l)=b_{l0} \sqrt{\frac{4 \pi}{2l+1}}
\end{displaymath} (5)

is the beam window (or transfer) function, expected as input to bl2beam.


RELATED ROUTINES

This section lists the routines related to bl2beam

idl
version 6.4 or more is necessary to run bl2beam.
beam2bl
facility to perform the inverse transform to bl2beam.
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(3000)/100.
beam = bl2beam(bl, theta, /arcmin)
plot, theta, beam
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 [0,30] arcmin and then plots it.

Version 3.31, 2017-01-06