ZTiltPSD

MATLAB

[XPSD,YPSD,F,Xvar,Yvar,Tvar]=ZTiltPSD(alpha,D,LogFMin,...
                                      LogFMax,NF,S,Atm,[NZ])

Description

This routine computes the PSD of Zernike tilt phase aberrations caused by atmospheric turbulence after. The temporal covariance of the phase is averaged over the aperture and Fourier transformed to give a single PSD for each direction. Returns a warning if Simpson's Rule integration does not include at least 85% of the theoretical variance.

The PSD calculated in this routine is one half of a two-sided PSD. The integral under the PSD as computed must be doubled to account for power at negative frequencies. There is a convenient way to calculate the total power when the PSD is generated for a vector of logarithmically spaced frequencies.

ZTiltPSD(...) with no outputs generates a Log plot of the PSD

Parameters

Parameters	Description
alpha [scalar]	Multiplier on turbulence model
D [scalar]	Aperture Diameter (m)
LogFMin [scalar]	log10 of the min frequency for PSD calculation
LogFMax [scalar]	log10 of the max frequency for PSD calculation
NF [scalar]	Number of frequencies per decade (logarithmically spaced) for PSD calculation
S [struct]	Engagement parameters. Can be a structure from EngagementStruct or GeomStruct. If a structure from GeomStruct is passed in as S, the engagement structure will be computed.
Atm [struct]	Atmospheric modeling parameter structure from AtmStruct. Can be a continuous or a discrete model.
NZ [scalar]	Number of evaluation points for the numerical integral (using Simpson's rule integration) with range. If Atm is a structure defining a discrete atmospheric model, NZ is ignored.

Return Values

Return Values	Description
XPSD [vector]	PSD of X-Tilt aberrations at the frequencies in the input vector f. The PSD is obtained by averaging the pointwise PSDs of the phase Tilt. The units are ${rad}^2/{Hz}$.
YPSD [vector]	PSD of Y-Tilt aberrations at the frequencies in the input vector f. The PSD is obtained by averaging the pointwise PSDs of the phase Tilt. The units are ${rad}^2/{Hz}$.
F [vector]	Frequencies for which the PSD is calculated (1/s).
Xvar [scalar]	X-Tilt variance from the computed PSD ${rad}^2$.
Yvar [scalar]	Y-Tilt variance from the computed PSD ${rad}^2$.
Tvar [scalar]	Theoretical tilt variance ${rad}^2$. If the spacing of the base 10 logarithm is dlogf, then the total
variance is given by ${TVar}	2{dlogf}ln(10) sum(fomega)$.

Examples

>> [XPSD,YPSD,F,Xvar,Yvar,Tvar] = ZTiltPSD(1.0,...

1.0,1,5,10,GeomStruct,AtmStruct)

Compute PSD for tilt phase aberrations for a discrete Atm model at 1 micron wavelength and 1 m aperture diameter

>> AtmC = AtmStruct(GeomStruct,inf,'Cn2','HV57');

>> [XPSD,YPSD,F,Xvar,Yvar,Tvar] = ZTiltPSD(1.0,...

1.0,1,5,10,GeomStruct,10,AtmC)

Compute PSD for tilt phase aberrations for a continuous Atm model specifying 10 phase screens at 1 micron wavelength and 1 m aperture diameter