Band volume for a circular aperture

From Optical Imaging and Spectroscopy (Wiley - OSA 2009)
By David J. Brady
www.opticalimaging.org
Figures 6.14 and 6.15

B[dx_,dy_,q_]:=(2/(dx^2+dy^2+10^(-17))) Re[Sqrt[(dx^2+dy^2)-(dx^2+dy^2+2 Abs[q])^2]];
qlimit[r_]:=(1/4) (-(r^2)+(Sqrt[4 (r^2)-3 (r^4)]));

DensityPlot[B[r Cos[(π/6)],r Sin[(π/6)],q],{r,(1/(10^4)),1},{q,-0.3,0.3},PlotPoints->100,Mesh->False,FrameLabel->{Δx,q}]

Plot3D[B[r Cos[(π/6)],r Sin[(π/6)],q],{r,(1/(10^4)),1},{q,-0.3,0.3},AxesLabel->{Δx,q,B},PlotPoints->200,PlotRange->{0,20},Mesh->False]

Plot[{qlimit[r],-qlimit[r]},{r,0.001,1}]

ax=ParametricPlot3D[{r Cos[t],r Sin[t],qlimit[r]},{r,0.001,1},{t,0,2 π},PlotPoints->100,Lighting->{{"Ambient",GrayLevel[.8,.5],{{5,5,4},{5,5,0}}}}]

bx=ParametricPlot3D[{r Cos[t],r Sin[t],-qlimit[r]},{r,0.001,1},{t,0,2 π},Lighting->{{"Ambient",GrayLevel[.8,.5],{{5,5,4},{5,5,0}}}}]

Show[{bx,ax},AxesLabel->{Δx,Δy,q},PlotRange->All]

<<Version5`Graphics`

Plot3D[B[u,0,q],{u,0.0001,1},{q,-1/8,1/8},AxesLabel->{Δx,q,B},PlotPoints->50,PlotRange->{0,10},ColorOutput->GrayLevel,MeshStyle->Gray]