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 $a_{\pm 2,lm}$ of the CMB polarization. The linear weight for $a_{\pm 2,lm}$ 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, $a_{\pm 2,lm}$ in the range can be determined by fitting $a_{\pm 2,lm}$ for visibilities of various observational configurations. The formalism presented in this paper enables the determination of $a_{\pm 2,lm}$ 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.