The effect of a finite outer scale on amplitude variance

The effect of the outer scale on intensity fluctuations is generally considered to be small enough to safely ignore. In this work, I use Ishimaru's filter function approach to quantify the effect of two different outer scale models in the weak fluctuation regime by forming the ratio of the amplitude variance with and without a finite outer scale. A ten percent reduction in amplitude variance is adopted as a practical threshold for relevance. Using the von Kármán outer scale model, I find that the outer scale can be ignored when it is larger than about one meter and the propagation distance is smaller than about twenty kilometers at a wavelength of one micron. Changing to an exponential model produces a much weaker effect, approximately equivalent to either more than doubling the outer scale length or increasing the propagation distance by a factor of about five to obtain the same reduction.