A novel optical design for wide-field imaging in X-ray astronomy

Over the decades, astronomical X-ray telescopes have utilized the Wolter type-1 optical design, which provides stigmatic imaging in axial direction but suffers from coma and higher-order aberrations for off-axis sources. The Wolter-Schwarzschild design, with stigmatic imaging in the axial direction, while suffering from higher-order aberrations, is corrected for coma, thus performing better than the Wolter type-1. The Wolter type-1 and Wolter-Schwarzschild designs are optimized for on-axis but have reduced angular resolution when averaged over a wide field of view, with the averaging weighted by the area covered in the field of view. An optical design that maximizes angular resolution at the edge of the field of view rather than at the center is more suitable for wide-field X-ray telescopes required for deep-sky astronomical surveys or solar observations. A Hyperboloid-Hyperboloid optical design can compromise axial resolution to enhance field angle resolution, hence providing improved area-weighted average angular resolution over the Wolter-Schwarzschild design, but only for fields of view exceeding a specific size. Here, we introduce a new optical design that is free from coma aberration and capable of maximizing angular resolution at any desired field angle. This design consistently outperforms Wolter-1, Wolter-Schwarzschild, and Hyperboloid-Hyperboloid designs when averaged over any field of view size. The improvement in performance remains consistent across variations in other telescope parameters such as diameter, focal length, and mirror lengths. By utilizing this new optical design, we also present a design for a full-disk imaging solar X-ray telescope.