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

TL;DR

This paper determines the optimal telescope focal ratios for microlens-to-fiber integral field spectrographs, balancing optical performance and fabrication constraints, to enhance the design of efficient astronomical instruments.

Contribution

It provides an analytical model for optimizing telescope focal ratios considering aberrations and fiber parameters, validated against ray-tracing simulations.

Findings

Optimal f-ratio range for 200μm fibers is between f/7 and f/12.

Focal ratio of f/8 supports a wide range of fiber sizes and speeds.

Analytical model matches ray-tracing results within +/-4%.

Abstract

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