MATLAB
`ZCov = ZernikeCoeffCov(alpha,D,s,i,j,Atm,[Norm])`

Computes Zernike coefficient covariance for mode i with mode j in units of \$m^2\$ given turbulence multiplier alpha, Tx/Rx aperture diameter D, anisoplanatic beam path displacement s, and atmospheric modeling data in Atm.

The optional input 'Norm' determines whether covariance is normalized and output in appropriate units. The following options are available:

• 'N': normalized to \$(D/r0)^{5/3}\$ for spherical-wave r0, phase \${rad}^2\$,
• 'A': converted to angular \${rad}^2\$, natural for i,j = 2,3.

 Parameters Description alpha [vector] Turbulence strength multiplier D [scalar] Tx/Rx Aperture diameter (m) s [matrix] Separation of beam paths along propagation path (m). Resolved for the P axis and T axis, as calculated from PathDisp. Column 1 is separation in P axis, col 2 is separation in T axis, i.e., d=[d_P,d_T] i..j [scalars] Mode numbers of Zernike coefficients (Noll's ordering) Atm [struct] Atmospheric modeling structure from AtmStruct Norm [string] (Optional) Flag to indicate whether covariance should be normalized. If omitted, output is not normalized
 Return Values Description ZCov [vector/matrix] Zernike Coefficient covariance (\${rad}^2\$) or normalized to \$(D/r0)^{5/3}\$

>> d = [linspace(0,0.02,10)' zeros(10,1)];

>> Atm = AtmStruct(0,2e4,0,10,'Cn2','HV57')

>> ZCov = ZernikeCoeffCov(1.0, 1.0, d, 2, 2, Atm,'N')

• Normalized Zernike coefficient covariance for turbulence multiplier of 1, 1 m Tx/Rx aperture, separation vector d, zernike coefficient orders 2 and 2 (tilt), and atmospheric model Atm. The covariance data is normalized to (D/r0)^(5/3).
>> ZCov = ZernikeCoeffCov(1.0, 2.0, d, 7, 3, Atm)

• Unnormalized covariance for a turbulence multiplier of 1 of the Zernike coefficient of order of 7 with the Zernike coefficient of order 3 for separation vector d, a 2 m Tx/Rx aperture and atmospheric model Atm.

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