Cubic Phase Defocus transfer function for a circular aperture

From Optical Imaging and Spectroscopy (Wiley - OSA 2009)
By David J. Brady
www.opticalimaging.org
Figure 10.6

<<Graphics`Graphics`

u is in units of A/lambda di. x is in units of A . tz is in units of lambda/A^2. alpha is in units of lambda/A^3.

H[u_,tz_ ,alpha_]:=Abs[NIntegrate[Exp[I(2 Pi tz u bx+ 3  alpha u bx^2)]UnitStep[0.5-Abs[bx-u/2]] UnitStep[0.5- Abs[bx+u/2]], {bx,-10,10}]];

Plot[H[u,df,0],{u,0,1}];

df=25;
alf=500;
LogPlot[{H[u,0,0],H[u,df/4,0],H[u,df/2,0],H[u, df,0],H[u, 2 df,0]},{u,0,1},PlotRange->All,Axes->False,Frame->True,PlotPoints->50];

df=20;
alf=750;
LogPlot[{H[u,0,0],H[u,df/2,0],H[u,df,0],H[u,0,alf],H[u,df/2,alf],H[u,df,alf]},{u,0,1},Axes->False,Frame->True,PlotPoints->50,
PlotStyle->Table[Dashing[{.005 x,.01}],{x,6}]];