The functions in this section compute parameters which characterize the atmosphere.
Name 
Description 
Computes anisoplanatic beam jitter components (in rad) given turbulence multiplier alpha, Tx/Rx aperture diameter D, anisoplanatic beam path displacement d, and atmospheric modeling data in Atm. Jitter is resolved in target P axis and T axis. Beam displacement vector should be obtained via PathDisp to include appropriate anisoplanatic effects (angular, aperture, chromatic, etc.)  
Calculates the Strehl ratio due to the effect of angular anisoplanatism given turbulence multiplier, Tx/Rx aperture diameter, anisoplanatic beam path displacement, and atmospheric modeling data. Beam displacement vector should be obtained via PathDisp to include appropriate anisoplanatic effects (angular, aperture, chromatic, etc.)  
Computes the optical transfer function (OTF) and point spread function (PSF) for ensembleaveraged exposure through Kolmogorov turbulence. If not specified, the following default values are used in modeling: lambda = 1 micron, D = 1 m, r0 = D/4, di = 1 m, alpha =1.  
Computes the section size of a laser guide star beacon (d0) given turbulence assumptions, propagation geometry, and wavelength. Output is appropriate for computing residual phase variance for compensation from laser guide star beacon as $(D/d0)^{5/3}$. Assumes the target object is at a finite range as specified by Geom. Hence propagation calculations are made using spherical wave analysis. Returns NaN if propagation path intersects earth surface.  
Computes the irradiance covariance for a beam wave given turbulence multiplier alpha, point spacings d, atmospheric modeling data in Atm, and wavelength in wvl. In this calculation, the light propagates from the target to the platform. Uses the weak turbulence assumption. Use with caution  function is numerically unstable.  
Computes beam spread in 2 axes (image row and column) given input image. Beam spread is quantified as least squares fit for Sigma with Gaussian form $exp(0.5(x/sigma)^2)$. Image is averaged down rows and across columns, normalized to the peak, and fit is made to normalized irradiance above RelThresh. If there is an input for N that is greater than 0, it is interpolated over N points, centered about the centroid. Fit can be displayed by setting DisplayPlot=1.  
Maps input altitudes in the interval [hInt(1) hInt(2)] into altitudes in the interval [hhInt(1) hhInt(2)]. Intended to facilitate using atmospheric models in the earth's boundary layer where certain altitudes should be referenced to ground level, and other altitudes should be referenced to sea level. Generally, hInt(end) = hhInt(end) = boundarylayer altitude limit. However, code will accept other inputs and use them accordingly. Altitudes in interval hInt are set according to: hh = hhInt(1)+(diff(hhInt)/diff(hInt)).*(hhInt(1)); Input altitudes less than hInt(1) are set to hhInt(1).  
Computes the complex field resulting from the Fresnel diffraction of a circular aperture illuminated by an onaxis point source R0 meters from the aperture at an observation plane R meters from the aperture.  
DistortionNumber calculates the thermal blooming distortion number (Nd) for a propagation path with specified absorption, scattering, and temperature models. If the input atmospheric model is continuous, Nd represents the integrated effect of thermal blooming, and NdScreen = []. If the input atmospheric model is discrete, Nd is computed by summing the distortion numbers for each phase screen slab as given in NdScreen. The calculation of Nd is welldocumented in literature. NdIpk is a scaling parameter anchored to wave optics for estimation of peak irradiance due to thermal blooming. NdPkShft is a scaling parameter for estimation of the amount of peak... more  
Computes Strehl ratio (peak irradiance decrease) for a beam focused at FocusRange but incident at TargetRange. Based on Gaussian beam model for beam spread of defocused beam.  
Computes the Greenwood frequency for propagation given turbulence assumptions, engagement parameters, and wavelength. Returns NaN if propagation path intersects earth surface.  
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... more  
Computes weighting of Cn2 (turbulence strength) over propagation path for the irradiance covariance. Handles plane, spherical, and Gaussian beam cases (can be numerically unstable in beam wave cases). Uses the weak turbulence assumption.  
Computes covariance matrix of Zernike polynomials with N >= 2 for propagation through Kolmogorov turbulence (no anisoplanatism). Diagonal elements are the modal variance of each atmospheric Zernike mode.  
Computes the jitter of a laser propagated through atmospheric turbulence. Returns the standard deviation (1*sigma) for a Gaussian probability density of atmospheric tilt.  
Computes the Strehl ratio of a laser propagated through a turbulent medium. Returns the Strehl ratio for tiltincluded, and the Strehl ratio for a tiltremoved beam (higherorder only).  
Computes the section size of a laser guide star beacon (d0) given turbulence assumptions, propagation geometry, and wavelength. Output is appropriate for computing residual phase variance for compensation from laser guide star beacon as $(D/d0)^{5/3}$. Assumes the target object is at a long range compared to the beacon and hence plane wave analysis is appropriate. However, integration of Cn2 is done over the propagation path to target specified by Geom. Returns NaN if propagation path intersects earth surface.  
Computes the irradiance covariance for a plane wave given turbulence multiplier alpha, point spacings d, atmospheric modeling data in Atm, and wavelength in wvl. In this calculation, the light propagates from the target to the platform, which is consistent with calculations of PlaneRytov and PlaneR0. Uses the weak turbulence assumption.  
Computes the plane wave coherence diameter (Fried parameter) given turbulence assumptions, propagation geometry, and wavelength. Also calculates screen r0 if input Atm is a discrete structure from AtmStruct. Returns NaN if propagation path intersects earth surface.  
Computes the plane wave Rytov number given turbulence assumptions, propagation geometry, and wavelength. Returns NaN if propagation path intersects earth surface.  
Computes the wave structure function for a plane wave in units of rad^2 given turbulence multiplier alpha, point spacings d, atmospheric modeling data in Atm, and wavelength in wvl. In this calculation, the light propagation direction does not matter.  
Returns an output structure containing values for atmospheric propagation parameters computed for the input geometry, atmospheric models, and optional turbulence multiplier alpha, wavelength, aperture, and laser power. If not specified, defaults to alpha = 1, lambda = 1 micron, D = 1 m, Power = 1 MW. Any or all of the inputs values may be arrays, in which case output p is a struct array. However, if any are arrays, all inputs must be either scalar or the same length.  
Computes the irradiance distribution after propagation from a uniformly illuminated annular aperture. Allows for propagation through Kolmogorov phase screens of arbitrary strength distributed arbitrarily over the propagation path. Defaults to vacuum propagation if screens not specified. When turbulence is specified, returns the average irradiance over random phase screen realizations.  
Given original altitudes of a light (laser beam) propagating along a certain path between a platform (hp) and a target (ht), RefractAlt calculates the new altitudes (h) due to refraction of light along the path, and the differences between these altitudes and the original refractionfree altitudes. Issues a warning if any of the new heights intersects earth surface.  
Computes the coherence diameter (Fried parameter) for each phase screen given turbulence assumptions, propagation geometry, and wavelength. Returns NaN if propagation path intersects earth surface.  
Computes the irradiance covariance for a spherical wave given turbulence multiplier alpha, point spacings d, atmospheric modeling data in Atm, and wavelength in wvl. In this calculation, the light propagates from the target to the platform, which is consistent with calculations of SphericalRytov and SphericalR0. Uses the weak turbulence assumption.  
Computes the spherical wave normalized irradiance variance given turbulence assumptions, propagation geometry, and wavelength. Returns NaN if propagation path intersects earth surface. Propagation is from platform to the target and this function returns the target plane variance. Accounts for strong turbulence conditions.  
Computes the large and small scale logirradiance covariance for a spherical wave given turbulence multiplier alpha, point spacings d, atmospheric modeling data in Atm, and wavelength in wvl. In this calculation, the light propagates from the platform to the target.  
Computes weighting of Cn2 (turbulence strength) over propagation path for the logirradiance 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.  
Computes the spherical wave coherence diameter (Fried parameter) given turbulence assumptions, propagation geometry, and wavelength. Returns NaN if propagation path intersects earth surface.  
Computes the spherical wave Rytov number given turbulence assumptions, propagation geometry, and wavelength. Returns NaN if propagation path intersects earth surface.  
Computes the spherical wave isoplanatic angle given turbulence assumptions, propagation geometry, and wavelength. Returns NaN if propagation path intersects earth surface.  
Computes the wave structure function for a spherical wave in units of rad^2 given turbulence multiplier alpha, point spacings d, atmospheric modeling data in Atm, and wavelength in wvl. In this calculation, the light propagates from the target to the platform.  
Computes a focusing range for a laser beam that gives equivalent Strehl ratio for propagation through vacuum as that specified by the input S. Since this can be accomplished by focusing past the target or by focusing prior to the target, both solutions are given. If the input Strehl is very small, FocusRangePast may give a negative focus range (indicating a divergent beam).  
Thermal blooming and turbulence combined effects waveoptics propagation. Models propagation of a laser source with arbitrary wavelength, power, focus distance, size/type to be propagated given an atmospheric specification structure (Atm) and the engagement geometry velocity decomposition. Must have Atm.Abs, Atm.Scat, and Atm.Temp in order to model thermal blooming. If Atm.Cn2 is specified, waveoptics propagation will also include turbulence phase screens as specified by Atm.z. Input Atm struct may also include models for inner and outer scale given the Cn2 model employed. Returns mensurated target irradiance (${W}/{m}^2$), relative peak irradiance, peak shift, beam spread and waveoptics configuration information. Waveoptics modeling may... more  
Computes the effect of thermal blooming using the specified analysis method for the propagation scenario described by the inputs. The optional input parameters P1, P2, P3,..., PN are those required for the analysis method. Currently supported analysis methods are 'SCALING' and 'WAVEOPTICS'. 'SCALING' method computes angular peak shift, beam spread (relative to diffraction), and Strehl ratio using empirical scaling laws derived from wave optics modeling of thermal blooming effects for a Gaussian or Uniform beam. The output structure TB contains metrics for modeling the incident irradiance. The output structure TBPhase has the same form as TB, but models the effect... more  
Computes the covariance scale lengths for modeling Kolmogorov angular tilt anisoplanatism as a Markov random process in 2 dimensions. Returns angular scale lengths and tilt variance quantities for modeling tilt angular covariance as: $C_{X}(a,0) = tvar*exp(a/thetaCovX)$ and $C_{Y}(a,0) = tvar*exp(a/thetaCovY)$  
Computes angularequivalent Zernike tilt covariance matrix in units of ${rad}^2$ given turbulence multiplier alpha, Tx/Rx aperture diameter D, anisoplanatic beam path displacement d, and atmospheric modeling data in Atm. Optionally, user may specify a particular combination of tilt components 'P' or 'T' for which the covariance is to be calculated.  
Computes weighting of Cn2 (turbulence strength) over propagation path for Zerniketilt covariance for the specified positions x normalized to the path length (01), and the accompanying aperture diameter normalized beam separation vector sigma. Path weighting is computed for covariance of C1 component with C2 component.  
Computes the temporal covariance scale lengths for modeling Kolmogorov tilt fluctuations as a Markov random process in time. Returns temporal scale lengths and tilt variance quantities for modeling tilt temporal covariance as: $C_{X}(t,0) = tvar*exp(t/TauX)$ and $C_{Y}(t,0) = tvar*exp(a/TauY)$  
This function calculates tilt variance in a limited band and the ratio of the bandlimited tilt variance to the full band tilt variance. The input PropDir sets the direction of propagation and indicates at which point tilt is to be measured. 'BACKWARD' and 'FORWARD' calculate tilt on a focal plane. 'BACKWARDAP' and 'FORWARDAP' calculate tilt in the aperture plane.  
Computes atmospheric transmission given input atmospheric model. Returns transmission given extinction model, absorption model, and scattering model separately. If both Abs and Scat models are specified, and if the transmission calculated from the extinction model does not equal the transmission calculated from the sum of the absorption model and scattering model, then the function will issue a warning. If Ext model is not specified, then ExtTrans will be set equal to TotTrans.  
Returns the exact value of constants that appear frequently in turbulence calculations given the approximate value often written in equations.  
Computes the Tyler frequency for propagation given turbulence assumptions, engagement parameters, and wavelength. Returns NaN if propagation path intersects earth surface.  
Computes weighting of Cn2 (turbulence strength) over propagation path for the wave structure function.  
Calculates the weighting term of Cn2 for the calculation of anisoplanatic Strehl ratio. For further clarification see the documentation inside the function.  
Computes the weighting matrix (W) associated with the discrete profile such that P = K*W*Cn2 where P is a vector with elements $r_0^{5/3}$ (Fried Parameter), $theta_0^{5/3}$ (isoplanatic angle), $sigma_{chi}^2$ (Rytov), and $M_0$ (integrated Cn2). K is a diagonal matrix with the appropriate scaling constants and Cn2 is a vector of Cn2 values. W is a matrix of dimension 4 by length dx (number of screens).  
Returns the transverse direction cosines for natural wind.  
Returns path weighting function of Cn2 for the BLS900 scintillometer. To be used to compute a pathweighted value of Cn2 as follows: Cn2Wt = sum(Cn2.*wt)./sum(wt)  
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:
 
Computes Zernike coefficients for given Zernike modes when provided with the phase screen and radial coordinates.  
Returns radial and azimuthal coordinate system to use with Zernike polynomial functions. Also returns mask to be applied to coordinate system for the aperture as well as rectangular coordinates. X coordinate is down the rows, Y coordinate is across the columns.  
Computes weighting of Cn2 (turbulence strength) over propagation path for covariance of Zernike coefficients for the specified positions x normalized to the path length (01), and the accompanying aperture diameter normalized beam separation vector sigma. Path weighting is computed for the covariance of the ith and jth Zernike coefficients.  
Returns the value of the Zernike polynomial of order noll_order at normalized radius rho and angle theta: 0<=rho<=1 0<=theta<=2pi. rho and theta may be scalar or matrix quantity.  
Produces phase screen given Zernike orders to be used and their corresponding magnitudes (coefficients)  
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 twosided 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... more 
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