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function fs_abcd = abcd_free_space( distance)
fs_abcd=[1, distance; 0,1];
endfunction
function lens_abcd =abcd_lens(focal_distance)
lens_abcd = [1, 0; -1/focal_distance, 1];
endfunction
function qnew=q_after_element(q_old,abcd)
qnew=(q_old*abcd(1,1)+abcd(1,2))/(q_old*abcd(2,1)+abcd(2,2));
endfunction
function optics = arrange_optics_along_x(optics_unsorted)
% arrange optics in proper order so its x position increases with consequent index
N=length(optics_unsorted);
% assign x positions
x=zeros(1,N);
for i=1:N
x(i)=optics_unsorted{i}.x;
end
[xs,indx]=sort(x);
cntr=1;
for i=indx
optics{cntr}=optics_unsorted{i};
cntr=cntr+1;
end
end
function waste =q2waste(q, lambda)
waste=sqrt (-lambda./pi./imag(1./q));
endfunction
function radius =q2radius(q, lambda)
radius=(1./real(1./q));
endfunction
function q=waste_r2q(waste,R,lambda)
q=1./(1./R-1i.*lambda./pi./(waste.^2));
endfunction
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