bl2beam

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

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

FORMAT

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

QUALIFIERS

bl

input $b(\ell)$ 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

$$b({\textbf{r}}) = \sum_{\ell m} b_{\ell m} Y_{\ell m}({\textbf{r}}),$$ (3)

a circular beam has a radial profile (as returned by bl2beam)

$$b(\theta) = \sum_\ell b(\ell) P_\ell(\theta) \frac{2\ell+1}{4 \pi},$$ (4)

where P_l is Legendre Polynomial and

$$b(\ell)=b_{\ell 0} \sqrt{\frac{4 \pi}{2\ell+1}}$$ (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 $b(\ell)$ window function into a FITS file.

fits2cl

facility to read a $b(\ell)$ 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.