Turbulent scattering in an exponential atmosphere - A wave-optical solution

The thin-screen model for scattering of radiation by a turbulent atmosphere is generalized to the case where the mean phase change decreases exponentially as a function of distance across the screen. This is of interest because it models the effect of turbulent scattering in an isothermal average atmosphere. We present both the change in average intensity and average bending angle in terms of the r-m-s scattering angle introduced by the turbulence. We find, for example, that the effect of turbulent scattering on the mean scattering angle (and hence Doppler residuals) is approximately the same as that obtained from more heuristic calculations. The effect depends on wavelength only to the extent that the refractivity is a function of wavelength.