Two Scintillation Methods of Measuring the Inner Scale

Let σ2 (L, k, Cn2, ℓo) be the irradiance variance of a monochromatic spherical wave of wavelength λ and wavenumber k = 2π/λ after propagating along a path of length L. The turbulence is assumed isotropic with refractive-index structure constant Cn2 and inner scale ℓo. Similarly let σ122(L, k1, k2, Cn2, ℓo) be the irradiance correlation, <(I1-) (I2-)>/ for iradiances I1 and I2 from spherical waves of wavelengths λ1, and λ2. Let σLA2(L, D, Cn2, ℓo) be the irradiance variance of radiation propagating along the same path and transmitted through a circular, uniformly-illuminated, phase-incoherent aperture of diameter D and measured using a receiving aperture of diameter D. It is assumed that D exceeds two Fresnel-zone sizes so σLA2 is approximately independent of the optical wavenumber.