Spatial filtering radio astronomical data: One-dimensional case

Radio astronomical measurements of radio brightness are made by pointing an antenna at a regular array of points in the sky and measuring the received noise power at each point. In the absence of receiver noise, the measured brightness is the convolution of the true brightness distribution with the antenna effective area (i.e., receiving power pattern), evaluated at the point of observation. Front-end noise in the radiometer receiver adds fluctuations inversely proportional to the observing time at each measured point. From such data, we calculate optimum mean-square estimates for two quantities: measured brightness between observations, and true brightness at and between observations. The first is interpolation; the second, called restoration, partially deconvolves the antenna pattern from the measured data. We determine the errors associated with each, as functions of: (1) receiving antenna pattern, (2) separation between observations, and (3) radiometer output signal-to-noise ratio. These results permit the construction of maps of measured and true brightness, with known mean-square errors. In this paper we study the one-dimensional version of this problem, assuming a large number of measured points. We find that measured points should be separated by about half the (full) 3-dB beamwidth for conventional antennas. Restoration is more costly than interpolation.