Algorithms, Models, and Methods for SDSS-V Wide-field Robotic Fiber Spectroscopy

Abstract

The field of astronomy has entered an age of big data, and this being driven by dedicated telescopes and instruments built for the sole purpose of conducting broad surveys to catalog the night sky. The highly successful space-based Gaia mission has already cataloged the broadband colors, 3D locations, and trajectories for nearly 2 billion astronomical sources. The much anticipated Legacy Survey of Space and Time (LSST) is projected to catalog an order of magnitude more objects. Imaging surveys like these are providing an unprecedented number of sources available for spectroscopic followup. Spectroscopy reveals a wealth of astrophysical information that imaging alone cannot, but spectroscopy is an inherently slow process. To spectroscopically observe even a small fraction of what is currently available, observations need to be performed as quickly and efficiently as possible. Robotic fiber positioners are a relatively new technology designed to speed up spectroscopic data collection. The fifth iteration of the Sloan Digital Sky Survey (SDSS-V) has built a pair of instruments each with 500 robots carrying optical fibers for multi-object spectroscopy. The first instrument operates from Apache Point Observatory (APO) in New Mexico and saw first light in December 2021. The second instrument operates from Las Campanas Observatory (LCO) in Chile and saw first light in August 2022. These instruments are designed to perform a spectroscopic survey of 6 million sources in a survey duration of five years. Operationally these instruments are complex, and they are required to perform at very high precision. This work describes the mathematics, algorithms, analysis, and general calibration strategies we have developed to make these instruments operational. A robot's fundamental task is to position a 120 $\mu$m diameter optical fiber in the focal plane of the telescope to capture light from an astronomical source. A software package {\tt coordio} was developed to perform the calculations for determining where an astronomical source will land in the focal plane of the telescope and how a robot should be moved to collect light from that object. This package defines a series of coordinate systems and transforms and provides a computational backbone for many pieces of SDSS-V's survey operations and infrastructure codes. SDSS-V has chosen a spatially-agressive layout for the robotic fiber positioner array in which the physical workspace for a robot heavily overlaps with its neighbors. This layout grants more sky coverage to each robot but introduces a high risk of collision between robots during reconfiguration. A software package {\tt kaiju} was developed to compute safe paths for every robot while moving from one spectroscopic target to the next. This path planning algorithm was an important success for the project, and it allowed the instrument to realize its full potential in using every available robot in every spectroscopic exposure. When instrument assembly was completed, a period of lab testing and calibration was performed. A lab test camera was used to measure positions of back-lit optical fibers as robots were moved through many reconfigurations. From this process we derive a kinematic model unique to each robot for use in {\tt coordio} routines to accurately predict fiber locations. This period also served to test and tune {\tt kaiju} path planning parameters while operating the robot array at full scale, ensuring proper operation prior to shipping the instrument to the telescope. After lab calibration, each instrument was installed at the telescope where a Fiber View Camera (FVC) is used to measure and adjust fiber positions during array reconfiguration. A series of camera distortion models were derived to reach sufficient FVC measurement accuracy. On-sky instrument commissioning consisted of spectroscopic observations of Gaia sources using a telescope dither technique, which allowed us to estimate on-sky fiber position errors. Analysis of these data informed additional layers of instrument calibration which improved overall fiber positioning accuracy. The instrument at APO was commissioned first, and is currently placing robotic fibers with an RMS error of 21 $\mu$m relative to astrophysical sources in the focal plane. Spectroscopic targets are generally well centered within the 120 $\mu$m fiber aperture, and normal survey operations are proceeding. We expect that ongoing efforts will further improve survey efficiencies and fiber positioning performance with an end goal of limiting fiber placement error to $\sim$17 $\mu$m. The instrument at LCO is currently in the commissioning and science verification phase, but initial indications suggest that fiber throughput will be sufficient for achieving SDSS-V science goals. SDSS-V is the third project worldwide to successfully deploy a robotic fiber positioner instrument to conduct a multi-year spectroscopic survey, and several other projects of comparable scale are nearing deployment. Throughout the process of designing, building, and using these instruments, the we have developed a number of strategies and techniques that are directly applicable to contemporary instruments today. Robotic fiber positioner arrays will likely continue to grow in importance, and proposals for building instruments with tens of thousands of robots on large aperture telescopes are already in place. The solutions derived from today's robotic multi-object spectrosopic surveys will directly influence the feasibility and design of future projects.