[OPTICAL REVIEW Vol. 18, No. 6 (2011) 441-447]
© 2011 The Japan Society of Applied Physics

Closed-Form Representations for Third-Order Aberrations of Two-Aspherical Mirror Aplanats with the Mirror Tilt and Decenter

Mitsunori TOYODA

Laboratory of Soft X-ray Microscopy, Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai 980-8577, Japan

(Received January 11, 2011; Accepted August 22, 2011)

Approximate equations are derived for imaging aberrations of two-aspherical-mirror aplanats for soft X-ray imaging. These expressions include the Seidel terms for unperturbed states and the axial coma resulting from the tilt and decenter of the mirror surface. A simple analytical method for reducing both the Seidel terms and the axial coma enables us to design novel soft X-ray imaging systems utilizing a wide field of view with reduced sensitivity to mirror misalignments. The method is illustrated by applying it to a two-mirror system for soft X-ray microscopy with a magnification m=-1/50. The design example showed an appreciable reduction in sensitivity, as compared with the existing anastigmatic designs that include a standard Schwarzschild configuration. Imaging aberrations of the novel system are also confirmed by a numerical ray tracing method.

Key words: aplanat, axial coma, aspherical mirror, misalignment, soft X-ray, microscopy