Direct reconstruction of spherical harmonics from interferometer observations of the CMB polarization

Interferometric observation of the CMB polarization can be expressed as a linear sum of spherical harmonic coefficients a±2,lm of the CMB polarization. The linear weight for a±2,lm depends on the observational configuration such as antenna pointing, baseline orientation, and spherical harmonic number l,m. Since an interferometer is sensitive over a finite range of multipoles, a±2,lm in the range can be determined by fitting a±2,lm for visibilities of various observational configurations. The formalism presented in this paper enables the determination of a±2,lm directly from spherical harmonic spaces without spherical harmonic transformation of pixellized maps. The result of its application to a simulated observation is presented with the formalism.