E/B separation paper extra material

See the Harmonic E/B separation example maps.

Also powerpoint file for Paris talk on E/B separation (2004).

CMB polarization codes

Spin-weight spherical harmonics

There is an F90 module for computing spin-weight spherical harmonics. There are thread-safe routines, routines for computing arrays of harmonics, and routines for computing inner products of spherical harmonics over azimuthal cuts. Most basic usage is
lambda = SH_lambdaslm(s,l,m,x)
where sYlm = lambda*e^{i*m*phi}, s is the spin, and x is cos(theta). Sign conventions and documentation in astro-ph/0106536.

Large scale B-mode extraction for asymmetric cuts

In astro-ph/0305545 I presented a method for extracting large scale pure B modes from general cuts (without smoothing). This download has routines for computing coupling matrices from the a_lm of a sky cut, and a sample program to construct the projection matrix into the well supported nearly-pure B modes. Requires BLAS and LAPACK, and (for larger lmax), a 64-bit compiler. Includes Matric_utils module which provides a conventient wrapper around some commonly used BLAS and LAPACK routines.

Exact E/B separation for azimuthal cuts

In astro-ph/0106536 we explain a harmonic method for separating E and B polarization modes on an incomplete sky.

You can download a simple demonstration program. This includes SpinHarmonics.f90, a module for computing spin-weight harmonics and their inner products over an azimuthally symmetric patch of sky.

The sample program itself (dopolar.f90) is very basic and extracts the E or B modes from a file of cut sky a_lms. It reads in a file of parameters (supplied params.ini), which includes a FITS file of the assumed power spectrum. The output is the 'number of sigmas' away from zero, assuming the given isotropic noise. The program is not designed to be realistically useful, but may make a useful starting point.

The program processes a file of a_lms in FITS format, as produced by HEALPIX. You will need FITSIO, HEALPIX and LAPACK installed to compile. You will need to edit the supplied Makefile with the correct location of these files.

The input power spectrum FITS file can be produced by CMBFAST or CAMB.

Antony Lewis May 2003.