HigherOrderPSD

MATLAB

[Omega,f,CLow,CHi,HOVarInt,HOVar]=HigherOrderPSD(alpha,...
      lambda,D,LogFMin,LogFMax,NF,S,Atm,[NZ])

Description

This routine computes the PSD of higher order phase aberrations caused by atmospheric turbulence after removal of piston and tilt. The temporal covariance of the phase is averaged over the aperture and Fourier transformed to give a single PSD. Returns a warning if Simpson 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.

HigherOrderPSD(...) with no outputs will generate a LogLog plot of the PSD

Parameters

Parameters	Description
alpha [scalar]	Multiplier on turbulence model
lambda [scalar]	Wavelength of laser (m)
D [scalar]	Aperture Diameter (m)
LogFMin [scalar]	log10 of the minimum frequency for PSD calculation
LogFMax [scalar]	log10 of the maximum 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
Omega [vector]	PSD of higher order aberrations at the frequencies in the input vector f. The PSD is obtained by averaging the pointwise PSDs of the phase AFTER TILT REMOVAL. The units are ${rad}^2/{Hz}$.
f [vector]	Frequencies for which the PSD is calculated.
CLow [scalar]	Coefficient for low frequency limit. In the limit of low frequency, the PSD goes to the constant CLow
CHi [scalar]	Coefficient for high frequency limit. In the limit of high frequency, the PSD goes as ${CHi}*{f}^{-8/3}$.
HOVarInt [scalar]	Higher order phase variance as integrated from the computed PSD.
HOVar [scalar]	Theoretical higher order variance.

Examples

>> [Omega,F,CLow,CHi,HOVarInt,HOVar] = HigherOrderPSD(2.0,...

1e-6,1.0,1,5,10,GeomStruct,AtmStruct)

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

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

>> [Omega,F,CLow,CHi,HOVarInt,HOVar] = HigherOrderPSD(2.0,...

1e-6,1.0,1,5,10,GeomStruct,10,AtmC)

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