  A statistical method for the estimation of spatial correlation lengths of
Gaussian-shaped fluctuating signals with two measurement points is examined to
quantitatively evaluate its reliability (variance) and accuracy (bias error).
The standard deviation of the correlation value is analytically derived for
randomly distributed Gaussian shaped fluctuations satisfying stationarity and
homogeneity, allowing us to evaluate, as a function of fluctuation-to-noise
ratios, sizes of averaging time windows and ratios of the distance between the
two measurement points to the true correlation length, the goodness of the
two-point measurement for estimating the spatial correlation length. Analytic
results are confirmed with numerically generated synthetic data and real
experimental data obtained with the KSTAR beam emission spectroscopy
diagnostic. Our results can be applied to Gaussian-shaped fluctuating signals
where a correlation length must be measured with only two measurement points.
