Calculation of modulation disturbance, caused by homogeneous turbulences in the atmosphere

The phase disturbance caused by homogeneous turbulence is derived for a monochromatic linearly polarised electro - magnetic wave in a medium. The index of refraction is described as n = 1 + δn(x,y,z,t). Assuming homogeneous turbulence, the path is determined using the variation procedure based on Euler-Lagrange, with which the propagation path is derived using Fermat's Principle. The average of the time-derivative of the phase can be derived, when the path and so the phase integral is determined. The average of the second derivative of the phase gives an interesting impression for the phase disturbance. For systems exploiting frequency modulation, a signal is demodulated by differentiation of the instantaneous phase angle as f(time). A variance of the instantaneous phase has been derived using the above mentioned process.