The effect of the w-term on the visibility correlation and power spectrum estimation

The visibility-visibility correlation has been proposed as a technique for the estimation of the power spectrum, and used extensively for small field of view observations, where the effect of the w-term is usually ignored. We consider power spectrum estimation from large field of view observations, where the w-term can have a significant effect. Our investigation shows that a non-zero w manifests itself as a modification of the primary aperture function of the instrument. Using a Gaussian primary beam, we show that the modified aperture is an oscillating function with a Gaussian envelope. We show that the two-visibility correlation (visibility variance) reproduces the power spectrum beyond a certain baseline given by the width, U_w, of the modified aperture. Further, for a given interferometer, the maximum U_w remains independent of the frequencies of observation. This suggests that the incorporation of a large field of view in radio interferometric observations has a greater effect for larger observing wavelengths.