A third-order aberration theory has been developed for a plane-symmetric double-element optical system that consists of an extended source, two ellipsoidal gratings, and an image plane. The gratings can have any of the groove patterns producible by means of currently available technologies. Analytic formulas of spot diagrams are derived for the system by analytically following a ray-tracing formalism. With these formulas coma, spherical aberration, astigmatism, field curvature, and distortion of the system are discussed in detail together with the focusing conditions. The spot-diagram formulas are critically evaluated in comparison with ray tracing. The result shows their capability in reproducing ray-traced spots with a high degree of accuracy.

© 1999 Optical Society of America

[Optical Society of America ]

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