These problems and the information needed to solve them come from these two books:
Andrews, Larry C. Laser Beam Propagation through Random Media. 1998. ISBN: 0-8194-2787-X.
Andrews, Larry C. Special Functions of Mathematics for Engineers. 1998. ISBN: 0-8194-2616-4.
The covariance function is defined as (among other things)
The power spectrum is defined as
1. solution Find the associated power spectrum given the covariance function
2. solution Find the associated power spectrum given the covariance function
3. solution Given that the power spectrum and structure function are related by
use the structure function and the integral formula to obtain the Kolmogorov power law spectrum: