Comparison of scintillation methods for measuring the inner scale of turbulence

One method of inner scale measurement uses the irradiance variance of a diverging monochromatic wave (the irradiance being obtained through a small aperture at the receiver position) and the irradiance variance of a large-aperture C(2)(n) scintillometer. The ratio of these two variances depends on the inner scale of turbulence l(0) but not on the refractive-index structure parameter C(2)(n). Another method uses the bichromatic correlation of irradiances from waves having two different wavelengths, transmitted through a common small aperture (the irradiance being obtained through a small aperture at the receiver position) and the two corresponding monochromatic irradiance variances. The ratio of the bichromatic correlation to the geometric mean of the two monochromatic variances depends on l(0) but not on C(2)(n). A third method is to obtain the ratio of the two monochromatic variances without using the bichromatic correlation. These methods are compared graphically using calculations based on an accurate atmospheric refractive-index spectrum. A scaling analysis is performed to determine the minimum number of parameters needed to describe the methods. It is suggested that systematic errors, rather than signal-to-noise limitations, determine the accuracy with which inner scale is measured. The effects of refractive-index dispersion between the two wavelengths must be taken into account. The results indicate that the bichromatic method has advantages when l(0) less, similar0.6 radicalL/k, whereas the method using small and large apertures has the advantage when l(0) greater, similar0.6 radicalL/k were L is the propagation path length and k is the optical wave number.