Optimizing interferometer experiments for CMB B mode measurement

The sensitivity of interferometers with linear polarizers to the CMB E and B mode are variant under the rotation of the polarizer frame, while interferometer with circular polarizers are equally sensitive to E and B mode. We present analytically and numerically that the diagonal elements of window functions for CMB E/B power spectra are maximized in interferometric measurement of linear polarization, when the polarizer frame is in certain rotation from the associated baseline. We also present the simulated observation to show that the 1-$\sigma$ errors on E/B mode power spectrum estimation are variant under the polarizer frame rotation in the case of linear polarizers, while they are invariant in the case of circular polarizers. Simulation of the configuration similar to the DASI shows that minimum 1-$\sigma$ error on B mode in interferometer measurement with linear polarizers is 26% of that in interferometric measurement with circular polarizers. The simulation also shows that the E/B mixing in interferometer measurement with linear polarizers can be as low as 23% of that in interferometric measurement with circular polarizers. It is not always possible to physically align the polarizer frame with all the associated baselines in the case of an interferometer array (N$>$2). There exist certain linear combinations of visibilities, which are equivalent to visibilities of the optimal polarizer frame rotation. We present the linear combinations, which enables B mode optimization for an interferometer array (N$>$2).