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