Progress in freeform mirror design for space applications

Abstract

Off-axis systems with freeform mirrors is a design approach of increasing importance for space instruments. While the off-axis reflective approach allows simple, versatile and obstruction free designs, the use of freeform surfaces allows to achieve better optical performance and/or compactness. In recent years, many such instruments have been designed and manufactured at TNO. Some important examples are the Tropomi (S5/precursor) and TSBOA (Sentinel-5) telescopes and several pushbroom spectrometers of the Spectrolite family. Despite the recognized potential of these systems, there is to our knowledge no available theory that allows to describe and predict the aberrations of plane symmetrical (off-axis) systems with freeform mirrors. In this context, an effort has been started 4 years ago at TNO to develop an approach that can describe and explore systematically off-axis freeform mirror systems with an arbitrary geometry. Since then the developed theory has been proven to be very useful in scanning the solution space for better starting designs, folding geometries and correction of lower aberrations in an early design phase. To circumvent difficulties linked to a wavefront formalism, generalized ray-tracing equations were derived, that include aberration terms up to 3rd order in X/Y object and pupil coordinates. These equations were recently published in two papers for the case of pure mirror systems [1,2]. The theory was also expanded to describe flat reflective gratings, opening a way to a complete description of reflective freeform spectrometers. In the present paper, after providing a high-level description and introduction to the aberration theory for freeform mirror systems, we will report some of its outcomes that have some practical relevance for space instruments. In particular: - two-mirror telescope designs for slit spectrometers (thus having a 1D field along the slit) that are inherently corrected for spatial smile will be presented. For these designs the slit projection in object space is exactly straight. - a new family of mirror spectrometers will be introduced that uses flat gratings and no collimator. In a collimator-less spectrometer, the aberrations induced by the grating under diverging light are corrected with freeform mirrors. The presented designs are entirely calculated from theory, with only optimization of the higher order freeform terms. A simpler architecture than traditional designs is obtained, with less optical surfaces. - finally we present a systematic classification of distortions in imaging slit spectrometers. The difference between distortions originating in the collimator and at the grating or in the imager is clarified and described mathematically. We discuss aberration-induced non-linear dispersion, as well as distortions from the keystone and smile families. The proposed classification also applies to catadioptric and refractive systems, the only requirement being to have a plane of symmetry.