Optimum telescope focal ratios for microlens-to-fiber coupled integral field spectrographs

We describe the optimum telescope focal ratio for a two-element, three-surface, telecentric image-transfer microlens-to-fiber coupled integral field unit within constraints imposed by microoptics fabrication and optical aberrations. create generalized analytical description of parameters from first principles. find that performance, including all aberrations, design constrained an analytic model considering only spherical aberration diffraction matches ± 4 % optimized ray-tracing software such as Zemax. The does not require any compromise on available clear aperture; about 90% mechanical aperture hexagonal microlens is light collection. f-ratio 200-μm core fiber-fed at f / 3.5 between 7 12. changes function fiber diameter input beam speed. A 8 would support largest range diameters (100 to 500 μm) injection speeds (between 3 5). optimization lenslet-coupled fibers relevant high-efficiency dedicated survey telescopes, retrofitting existing facilities via introducing macro-optics match instrument requirements.