A multiplier combined with an integrator which produces the complex visibility from the detected complex electric fields. For continuum observations, the average correlation over the signal bandwidth is measured, so measurements are made only for zero-delay offsets. A complex correlator is used to obtain the real and imaginary parts. In spectral line observations, measurements at different frequencies across the signal band are required. This is most commonly implemented by measuring the correlation of the signals as a function of time offset (lag). The Fourier transform of this quantity is the complex visibility as a function of frequency (cross power spectrum). The correlator provides visibilities at N frequency intervals called frequency channels. According to Thompson et al. (1986), it suffices to use a single-multiplier correlator, although the more complicated complex correlator can also be used.
Complex Correlator, Quantization Efficiency Eric Weisstein's World of Math
References
D'Addario, L. R. "Cross Correlators." Ch. 4 in Synthesis Imaging in Radio Astronomy: Third NRAO Summer School, 1988 (Ed. R. A. Perley, F. R. Schwab, and A. H. Bridle). San Francisco, CA: Astronomical Society of the Pacific, 1989.
Thompson, A. R.; Moran, J. M.; and Swenson, G. W. Jr. Interferometry and Synthesis in Radio Astronomy. New York: Wiley, 1986.
