Analytical Theory of Arbitrary-Order Achromats
AbstractAn analytical theory of arbitrary-order achromats for
optical systems with mid-plane symmetry is presented. It is based on the
repeated use of identical cells; but besides mere repetition of cells, mirror
symmetry is used to eliminate aberrations. Using mirror imaging of a cell
around the x-y and x-z planes, we obtain four kinds of cells: the forward
cell (F), the reversed cell (R), the cell in which the direction of bend is
switched (S), and the cell where reversion and switching is combined (C).
Representing the linear part of the map by a matrix, and the nonlinear part
by a single Lie exponent, the symplectic symmetry is accounted for and
transfer maps are easily manipulated.
It is shown that independent of the choice and arrangement of such cells,
for any given order, there is a certain minimum number of constraint
conditions that has to be satisfied. It is shown that the minimum number of
cells necessary to reach this optimum level is four, and out of the
sixty-four possible four-cell symmetry arrangements, four combinations yield
such optimal systems. As a proof of principle, the design of a fifth-order
achromat is presented.
W. Wan, M. Berz, Physical Review E
54,3 (1996) 2870-2883
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