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Single-pulse and double-pulse methods for measuring the cross-correlation (two polarizations transmitted and received) or auto-correlation (one polarization only) function of the scattered signal are described. The statistical errors associated with various forms of multi-bit (no quantization errors in the sampling process), one-bit, and hybrid estimators of the correlation function are calculated and compared, both for large and small signal-to-noise ratios. Roughly speaking, when the signal correlation is small, the hybrid estimators require π/2 and the one-bit π2/4 times as many independent samples as the multi-bit estimators to achieve the same statistical accuracy, but this disadvantage is often more than compensated for by an increase in the effective sampling rate. When the correlation is 0.5 or more, there may be a substantial difference between estimators of the same class (multi-bit, for example). Systematic distortions of the correlation function and limitations on resolution associated with the finite receiver bandwidth and transmitted pulse length are calculated. The effect of a refractive index slightly less than unity is mentioned.