| Abstract: This research lays the groundwork for building the Replicated Spectroscopic Array, demonstrating that high-resolution spectroscopy can be achieved using compact, budget-friendly, and easily reproducible instruments for various astronomy projects. Building a cost-effective, compact, high-resolution spectrograph with radial velocity (RV) capabilities enables its use in arrayed telescope concepts and in long-term RV monitoring for exoplanet science cases. Such a facility can make a significant contribution to time-domain astronomy and exoplanet research, particularly in the follow-up of bright targets from TESS and the Vera Rubin Observatory.
Our design process combined analytical calculations for the echelle grating and prism cross-disperser with thorough ray-tracing simulations in Zemax. This combination enables us to verify that our theoretical predictions are actually feasible with basic optical components. We developed a comprehensive theoretical model for the echelle grating and prism system, derived from the necessary design equations. The Zemax ray-tracing verification is used to verify several grating and prism design parameters, and it also enables the conclusion of the design configurations used for different grating and prism combinations. We also ensured that we found commercially available components that would meet our performance targets while keeping costs reasonable for building multiple copies.
The spectrograph is in a double-pass configuration, providing significantly higher resolving power (R ~ 20,000-25,000) by allowing rays to traverse the cross-disperser twice. This level of performance is crucial for tasks such as accurately measuring radial velocities to detect exoplanets, tracking the changes in stars over time, and conducting large-scale spectroscopic surveys to study the history of our galaxy. The fiber-fed setup maintains stability and compactness, and the cross-dispersed echelle format optimizes the use of the detector. Because the design is scalable, we can build multiple identical units and create a network of distributed telescopes, all connected to affordable, compact echelle spectrographs.
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