COLLINSB Collins Chart with track from another file

Internal for COLLINS1 and COLLINS2

           by Chuck DiMarzio
              Northeastern University
              November 2008
 needs zlim and blim to be assigned.  Maxima for plot limits
!! This file may be copied, used, or modified for educational and
!! research purposes provided that this header information is not
!! removed or altered, and provided that the book is cited in
!! publications, as DiMarzio, Charles A., Optics for Engineers,
!! CRC Press, Boca Raton, FL, 2011.
!! http://www.crcpress.com
!! Other distribution is prohibited without permission.

Contents

Start

zstep=0.2;bstep=0.2;zmin=0.2;zmax=6;bmin=0.2;bmax=6;
z=(-zlim:0.2:zlim);
b=(0:0.2:blim);
%
% u = 1/rho, v=-1/b; z + j b = (u + j v)/(u^2 + v^2)
%
bprime=(bmin:bstep:bmax);
rhoinv=(-60:0.02:60);
[u,v]=meshgrid(rhoinv,1./bprime);  % curves of constant b
denom=(u.^2+v.^2);
z1=u./denom;
b1=v./denom;

rho=(zmin:zstep:zmax);
bprimeinv=(0:0.02:60);
[u,v]=meshgrid(1./rho,bprimeinv);  % curves of constant positive rho
denom=(u.^2+v.^2);
z2=u./denom;
b2=v./denom;

rho=-(zmin:zstep:zmax);
bprimeinv=(0:0.02:60);
[u,v]=meshgrid(1./rho,bprimeinv);  % curves of constant negative rho
denom=(u.^2+v.^2);
z3=u./denom;
b3=v./denom;

plot([z;z],[b(1);b(end)],'k--',...
     [z(1);z(end)],[b;b],'k--',...
     z1',b1','k--',...
     z2,b2,'k--',...
     z3,b3,'k--','LineWidth',1)
axis image;axis([-zlim,zlim,0,blim]);
xlabel('z, Axial Distance');ylabel('b, Confocal Parameter');
hold on;

% Once again for integer values with solid lines

zstep=1;bstep=1;zmin=1;bmin=1;
z=[-zlim:1:zlim];
b=(0:1:blim);
%
% u = 1/rho, v=-1/b; z + j b = (u + j v)/(u^2 + v^2)
%
bprime=(bmin:bstep:bmax);
rhoinv=(-60:0.02:60);
[u,v]=meshgrid(rhoinv,1./bprime);  % curves of constant b
denom=(u.^2+v.^2);
z1=u./denom;
b1=v./denom;

rho=(zmin:zstep:zmax);
bprimeinv=(0:0.02:60);
[u,v]=meshgrid(1./rho,bprimeinv);  % curves of constant positive rho
denom=(u.^2+v.^2);
z2=u./denom;
b2=v./denom;

rho=-(zmin:zstep:zmax);
bprimeinv=(0:0.02:60);
[u,v]=meshgrid(1./rho,bprimeinv);  % curves of constant negative rho
denom=(u.^2+v.^2);
z3=u./denom;
b3=v./denom;


plot([z;z],[b(1);b(end)],'k',...
     [z(1);z(end)],[b;b],'k',...
     z1',b1','k',...
     z2,b2,'k',...
     z3,b3,'k','LineWidth',1)