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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_afteer_element(q_old,abcd)
qnew=(q_old*abcd(1,1)+abcd(1,2))/(q_old*abcd(2,1)+abcd(2,2));
endfunction
function q = prop(x_final, q_in, elements)
q(size(x_final,2))=0;
for i=1:size(x_final,2)
x_final_i=x_final(i);
xend=0;
q_end=q_in;
for k=1:size(elements,2)
el=nth(elements,k);
if ( el.x <= x_final_i)
abcd=abcd_free_space(el.x-xend);
q_end=q_afteer_element(q_end,abcd);
q_end=q_afteer_element(q_end,el.abcd);
xend=el.x;
endif
endfor
if (x_final_i > xend);
abcd=abcd_free_space(x_final_i-xend);
q_end=q_afteer_element(q_end,abcd);
xend=x_final_i;
endif
q(i)=q_end;
endfor
endfunction
function waste =q2waste(q, lambda)
for i=1:size(q,2)
waste(i)=sqrt (-lambda/pi/imag(1/q(i)));
endfor
endfunction
function radius =q2radius(q, lambda)
for i=1:size(q,2)
radius(i)=(1/real(1/q(i)));
endfor
endfunction
function q=waste_r2q(waste,R,lambda)
q=1/(1/R-I*lambda/pi/waste/waste);
endfunction
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