SphericalLogIrrPathWeight
MATLAB
`[Wx,Wy] = SphericalLogIrrPathWeight(xi,dhat,Rytov,[type])`

Computes weighting of Cn2 (turbulence strength) over propagation path for the log-irradiance covariance for a spherical wave. Can return the large scale (Wx), small scale (Wy), both (Wx,Wy), or Wx + Wy (single output with type = 'both'). This function uses the integral formulation from Andrews and Phillips and can be computationally intensive.

 Parameters Description xi [vector] Normalized location along the propagation path. dhat [vector] Normalized (by sqrt(L/k)) separation of points in the observation plane Rytov [scalar] Spherical wave Rytov number from SphericalRytov. type [string] (Optional) Scale of covariance to output if the number of outputs is one. Ignored for two outputs. Specify 'large' (default), 'small', or 'both' for combined.
 Return Values Description Wx [vector] Large scale path weighting (or Wx + Wy if type is 'both' and single output) evaluated along the path Wy [vector] (Optional) Small scale path weighting evaluated along the path

• L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. Bellingham, Wash.: SPIE Press, 2005.
• L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications. Bellingham, WA: SPIE, 2001.
• L. C. Andrews, R. L. Phillips, and C. Young Hopen, "Scintillation model for a satellite communication link at large zenith angles", Opt. Eng., vol. 39(12), pp. 3272-3280, 2000.

>> Atm = AtmStruct(0, 2e4, 0, 100, 'Cn2', 'HV57');

>> wvl = 0.5e-6;

>> dhat = [1 2 3 4 5].*0.02./sqrt(Atm.L*wvl/(2*pi));

>> Rytov = SphericalRytov(1,wvl,Atm);

>> W = SphericalLogIrrPathWeight(Atm.z/Atm.L,dhat,Rytov,'both');

• Path weighting functions for irradiance covariance with wavelength of 500 nm, point source at 20 km propagating straight down, pupil-plane separation of multiples of 2 cm, and atmospheric model Atm.