Second-order design methods for definitive studies of plane-symmetric, two-mirror systems

In the early stages of optical design, the consideration of low-order imaging properties significantly simplifies the identification of promising configurations. This process is investigated here for plane-symmetric systems composed of two off-axis sections of conic mirrors. In particular, constraints are derived that ensure sharp imagery through second order for such systems. For completeness, a number of special cases must be treated. In the cases that admit of realizable solutions, the requirement of sharp imagery through second order reduces the dimensionality of the resulting configuration spaces from thirteen to between four and six.