COLLINS Generates a Collins Chart

           by Chuck DiMarzio
              Northeastern University
              November 2008
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!! 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; % Adjust these to
                                                     % determine which
                                                     % curves are plotted
z=(-2:0.2:2);
b=(0:0.2:2);
%
% 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;

fig16=figure;
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([-2,2,0,2]);
xlabel('z, Axial Distance');ylabel('Confocal Parameter');
hold on;

% Once again for integer values with solid lines

zstep=1;bstep=1;zmin=1;bmin=1;
z=(-2:1:2);
b=(0:1:2);
%
% 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)
hold off;
%print -deps 9-16-collins.eps