Fine calibration of large-aperture optical scintillometers and an optical estimate of inner scale of turbulence

Large-aperture optical scintillometers [ Ting-i Wang et al., J. Opt. Soc. Am. 68, 334 ( 1978)] lose their calibration if they are sensitive to portions of the spatial spectrum of temperature fluctuations where κ^−11/3 fails to hold. The model temperature spectrum having the bump [ R. J. Hill, J. Fluid Mech. 88, 541 ( 1978); R. J. Hill and S. F. Clifford, J. Opt. Soc. Am. 68, 892 ( 1978)] is used to find conditions under which the scintillometers maintain their calibration. We find that the aperture size D should be at least twenty times the inner scale l₀ if the contribution of the spectral bump is to be ignored. For application in the surface layer, one needs the height above ground of the optical path to be much greater than three times the aperture size if outer-scale effects are to be negligible. It is shown that the inner scale dependence of a scintillometer having D/l₀ ≃ 2.0 and the lack of such dependence for a scintillometer having D/l₀ ≃ 20.0 can be used to estimate both l₀ and $C_n^2$ if the two systems are used simultaneously on the same path. A preliminary experiment was performed in the atmospheric surface layer with scintillometers having aperture sizes of 2.0 cm, 5.0 cm, and 15.0 cm; the results are consistent with the existence of the spectral bump. The inner scale is estimated by comparing data from the 2.0-cm and 15.0-cm systems. Using this inner scale, the $C_n^2$ values from the 5.0-cm and 15.0-cm scintillometers are corrected for the spectral bump; the corrected values are in agreement. Other turbulence parameters are not deduced from the l₀ and $C_n^2$ estimates because the l₀ values have been found to be insufficiently accurate.