rsalm

Description

rsalm convolves the map with a symmetric beam via

$$a^{'}_{{\ell}m} = B_{{\ell}}\cdot a_{{\ell}m}$$ (19)

, where $B_{{\ell}}$ is the expansion in Legendre polynomials of a symmetric beam. The symmetric beam can be input by reading in an ASCII file containing the profile of $B_{{\ell}}$, or by providing the FWHM for a symmetric Gaussian beam, where

$$B_{{\ell}}= \exp[- \sigma^2 {\ell}({\ell}+1) / 2 ]$$ (20)

and

$$\sigma = \frac{{\rm FWHM}} {\sqrt{8 \ln 2}}.$$ (21)

For deconvolution, a simple Tikhonov regularization scheme is always applied via

$$a^{''}_{{\ell}m}=\frac{a_{{\ell}m}}{B_{{\ell}}+ \alpha},$$ (22)

where $\alpha$ is the regularization parameter.

Examples

1. Convolution:
   • rsalm alm.fits -fw 10 -o alm.sm.fits
     convolves the map with its $a_{{\ell}m}$ in file ' alm.fits' with a symmetric Gaussian beam (FWHM 10 arcmin). The result is output in ' alm.sm.fits'.

   • rsalm alm.fits -b beamprofile.dat -o alm.beam.fits
     convolves the map with its $a_{{\ell}m}$ in file ' alm.fits' with a given beam profile ' beamprofile.txt', which contains $B_{{\ell}}$. The output is in ' alm.beam.fits'.

2. De-convolution with Tikhonov regularization:
   • rsalm alm.fits -alp 0.001 -fw 60 -o alm.decon.fits
     deconvolves the map with its $a_{{\ell}m}$ in file ' alm.fits' with a symmetric Gaussian beam (FWHM 60 arcmin). The Tikhonov regularization scheme is used with the parameter $\alpha$ = 0.001. The output is in ' alm.decon.fits'.

   • rsalm alm.fits -alp 0.001 -b beamprofile.dat -o alm.decon.fits
     deconvolves the map with its $a_{{\ell}m}$ in file ' alm.fits' with a given beam profile in ' beamprofile.dat'. The Tikhonov regularization scheme is used with the parameter $\alpha$ = 0.001. The output is in ' alm.decon.fits'.