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Theory and Applications of Arbitrary-Order Achromats

A Dissertation

In partial fulfillment of the requirements for the degree of Doctor of Philosophy from Michigan State University.


An analytical theory of arbitrary-order achromats for optical systems with midplane symmetry is presented. Besides repetition of cells, mirror symmetry is used to eliminate aberrations. Using mirror imaging 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 easily accounted for and maps are easily manipulated.

It is shown that, independent of the choice and arrangement of such cells, there is a certain minimum number of conditions for a given order; for example, this number is five for the first order, four for the second order, fifteen for the third order, fifteen for the fourth order, and thirty-nine for the fifth and sixth orders. It is shown that the minimum number of cells necessary to reach this optimum level is four, and four of the sixty-four possible four-cell symmetry arrangements are optimal systems. Various third-, fourth- and fifth-order achromats are designed and potential applications are discussed.

W. Wan (1995)


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