healpixwindow

This IDL facility provides the window function in $\ell$ associated with the Healpix pixel of resolution Nside.

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

FORMAT

IDL> wpix=HEALPIXWINDOW(Nside [, Dim, DIRECTORY=, HELP=, LMAX=])

QUALIFIERS

Nside

resolution parameter

Wpix

the pixel window function, computed for the multipoles $\ell$ in {0,...,LMAX}

Dim

scalar integer, optional.
If absent or set to 0 or 1, the output has size (LMAX+1) and is the temperature window function;
if set to $2 \le$ Dim $\le 4$ , the output has size (LMAX+1,Dim) and contains in that order :
the TEMPERATURE window function,
the GRAD/ELECTRIC polarization one
the CURL/MAGNETIC polarization one
the TEMPERATURE*GRAD one.

DIRECTORY=

directory in which the precomputed pixel window file is looked for.
default:!healpix.path.data

HELP=

if set, a documentatin header is printed out, and the routine exits

LMAX=

maximum multipole included in Wpix. Must be in [0, 4 Nside]. Negative values are ignored. default:4 Nside.

DESCRIPTION

healpixwindow computes the $\ell$ space window function due to the finite size of the HEALPix pixels. The typical size of a pixel (square root of its uniform surface area) is $\sqrt{3/\pi}\ 3600/N_{\mathrm{side}}$ arcmin. If a unpixelated sky has a power spectrum $C(\ell)$, the same sky pixelated with a resolution parameter Nside will have the power spectrum $C(\ell)_{\mathrm{pix}} = C(\ell) W(\ell)^2$ where $W(\ell)$ is given by healpixwindow(Nside). The polarized pixel window function is also provided (when Dim > 1). This routine reads some FITS files located in the subdirectory data/ of the HEALPix distribution, unless the keyword Directory is set otherwise.

RELATED ROUTINES

This section lists the routines related to healpixwindow

idl

version 6.4 or more is necessary to run healpixwindow

gaussbeam

computes the $\ell$ space window function associated with a gaussian beam

synfast

F90 code to generate CMB maps of given power spectrum at a given resolution (=pixel size)

anafast

F90 code to compute the power spectrum of a HEALPix sky map

EXAMPLE:

wpix = healpixwindow(256)

wpix contains the window function in {0,...,1024} of the HEALPix pixel with resolution parameter 256 (pixel size of 13.7 arcmin)