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We present the optical design of the Red arm (operating at 2-5 µm) of the Planetary Systems Imager (PSI). At the heart of this arm of PSI is a 180x180 silicon lenslet array which will allow diffraction-limited low- resolution integral field spectroscopy over a field of view of 1.5 arcseconds on the Thirty Meter Telescope. The entrance window, lenslet array, and dispersing prisms are the only refractive optics; all other optics are diamond-turned, off-axis, aspherical, gold-coated aluminum and designed with a ‘bolt-and-go’ opto-mechanical approach. We use a homologous material design, meaning we have guaranteed exquisite coefficient of thermal expansion matching which allows us to test, align, and adjust the optics (apart from the lenslet array) in ambient laboratory conditions. Several ‘plug-and-play’ upgrades that increase the scientific capabilities of the instrument are also included in the design such that they can be integrated into the instrument at a later stage without much rework and redesign required. A novel upgrade is an image slicer that sits behind the lenslet array and is illuminated with an insertable fold mirror; this allows us to boost the spectral resolution to 2000-10000 for a field of view of 0.15x0.15 square arcseconds depending on the bandpass. This is a new realm of spectral resolution with ‘large field of view’ IFU instrumentation at these wavelengths and present a novel opportunity for exoplanet characterization. This hybrid lenslet/image slicer combination trades spatial coverage for vastly increased spectral resolution by geometrically rearranging a subset of 23x23 lenslets into a pseudo-slit which is then dispersed using selectable 1st order gratings.
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