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The paper presents the metrological setups for the optical measurements of two high quality, large aperture, extremely compact, diffraction limited, relative aperture 1:2.4 free-form telescopes: the CHI and the TIR. The CHI “Compact and Highly Performing Hyperspectral Imager“, is based on a Three-Mirror Anastigmat (TMA) layout and works in the spectral range 0.4-2.5μm with 150 mm aperture. The Thermal Infrared (TIR) Telescope is based on a two-powered-mirror design and works in the spectral range 10-12 μm with 140 mm entrance aperture. Both free-form Telescopes have been designed by OHB Germany and are currently under production at SPACEOPTIX GmbH / Fraunhofer IOF and at VDL ETG / SUMIPRO, respectively. The measurement campaign consists in measuring the wavefront error all over the field of view at 633 nm, the focal length across- and along-track and the geometric distortion. The paper focuses attention on the TIR freeform Telescope. To support the optical tests preparation, the TIR free-form Telescope is analyzed with a pure geometrical optic approach, making also use of the Helmholtz-Lagrange Invariant. The definition of the Helmholtz-Lagrange Invariant for an axial field is recalled from the classic literature. Then the optical invariant of the paraxial optic is extended to the real ray-tracing of the TIR Telescope both in its nominal layout and when subjected to the manufacturing, alignment and integration (MAIT) tolerances. In this way, the optical invariant represents a method, complementary to the commonly used ones, for evaluating the quality of an optical design and for assessing its robustness to the MAIT tolerances.
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