Lens Design with Aspheric and Freeform Mirrors

Abstract

This Master thesis discusses selected lens designs with aspheric and freeform mirrors. Chapter 3 reviews the theory of obscured 2-mirror telescopes and discusses the Aplanatic Cassegrain (AC) Thirty Meter Telescope (TMT) and the Aplanatic Gregorian (AG) Giant Magellan Telescope (GMT). An analysis of the coma free point and of field tilt due to misalignment of the secondary mirror is given. Chapter 4 discusses Dave Shafer’s freeform 5-mirror unobscured anastigmat with external pupil, optimized for use as an ultraviolet (UV) camera for a fiber-fed spectrograph on TMT. It features a large, 291 mm diameter, external pupil for a transmissive dispersive element, a field of view of diameter equal to 18.6deg, and a focal ratio equal to f|1.35. The top-level performance requirement for the camera is specified as delivering at least 90% extended source encircled energy (EE) within the paraxial image at the detector of a fiber core, which in terms of root mean square (RMS) wavefront error (WFE) corresponds to at most 40% of a wave. We show that the nominal performance of the freeform five-mirror anastigmat exceeds this top-level specification. A preliminary Monte Carlo tolerance analysis has been carried out for tolerances on spacing, tilt, decenter and radius of curvature of each mirror. For a 95% confidence level, the design delivers about 40% EE within the paraxial image of a fiber core. Finally, Chapter 5 discusses a high-performance, f|3, 200 mm long, wide-field Offner relay. We show that the use of aspheric or freeform mirrors enables a spectacular increase from the 12 mm x 0.5 mm diffraction-limited field of the classical telecentric relay with spherical concentric mirrors to field sizes as large as 100 mm x 1 mm or 25 mm x 15 mm. Such freeform Offner relay could be used as a diffraction-limited wide-field spectrograph featuring a reflective freeform disperser or as an adaptive optics relay. Chapter 6 provides a summary of the main results for each design, Chapter 7 provides a summary of first-order properties of each design, and Chapter 8 provides a list of references.