Direct reconstruction of spherical harmonics from interferometer observations of the cosmic microwave background polarization

Interferometric observation of the cosmic microwave background (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.