Abstract

In calculations of optical propagation through the turbulent atmosphere, one often requires knowledge of the spectrum of the refractivity fluctuations. Several forms of the spectrum are typically used. The Kolmogorov spectrum is a pure −11/3 power law in wavenumber and does not include inner scale effects. The Tatarski spectrum includes a Gaussian taper at high wavenumbers to account for inner scale effects. The Hill spectrum is the result of a rigorous derivation of the spectrum, and includes a bump near the inner scale. Unfortunately, it does not have an analytic form. However, it can be reasonably approximated by multiplying the Kolmogorov spectrum by exp(−70.5K²) + 1.45 exp[−0.97(lnK + 1.55)²], where K is the product of the Kolmogorov microscale (0.135 times the inner scale) and the wavenumber. This formula is within a few percent of the Hill spectrum except at very high wavenumbers where the values are very small.

© 1989 Optical Society of America