A Fast Gridded Method for the Estimation of the Power Spectrum of the Cosmic Microwave Background from Interferometer Data with Application to the Cosmic Background Imager

We describe an algorithm for the extraction of the angular power spectrum of an intensity field, such as the cosmic microwave background (CMB), from interferometer data. This new method, based on the gridding of interferometer visibilities in the aperture plane followed by a maximum likelihood solution for band powers, is much faster than direct likelihood analysis of the visibilities and deals with foreground radio sources, multiple pointings, and differencing. The gridded aperture-plane estimators are also used to construct Wiener-filtered images using the signal and noise covariance matrices used in the likelihood analysis. Results are shown for simulated data. The method has been used to determine the power spectrum of the CMB from observations with the Cosmic Background Imager, and the results are given in companion papers.