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