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The Vera C. Rubin Observatory is a unique facility for survey astronomy that will soon be commissioned and begin operations. Crucial to many of its scientific goals is the achievement of sustained high image quality, limited only by the seeing at the site. This will be maintained through an Active Optics System (AOS) that controls optical element misalignments and corrects mirror figure error to minimize aberrations caused by both thermal and gravitational distortions. However, the large number of adjustment degrees of freedom available on the Rubin Observatory introduces a range of degeneracies, including many that are \textit{noise-induced} due to imperfect measurement of the wavefront errors. We present a structured methodology for identifying these degeneracies through an analysis of image noise level. We also present a novel scaling strategy based on Truncated Singular Value Decomposition (TSVD) that mitigates the degeneracy, and optimally distributes the adjustment over the available degrees of freedom. Our approach ensures the attainment of optimal image quality, while avoiding excursions around the noise-induced subspace of degeneracies, marking a significant improvement over the previous techniques adopted for Rubin, which were based on an Optimal Integral Controller (OIC). This new approach is likely to also yield significant benefits for all telescopes that incorporate large numbers of degrees of freedom of adjustment., Comment: 19 pages, 8 figures, 4 tables. Submitted to ApJ

The transient optical sky has remained largely unexplored on very short timescales. While there have been some experiments searching for optical transients from minutes to years, none have had the capability to distinguish millisecond Fast Optical Bursts (FOB). Such very fast transients could be the optical counterparts of Fast Radio Bursts (FRB), the prompt emission from $\gamma$-Ray Bursts (GRB), or other previously unknown phenomena. Here, we investigate a novel approach to the serendipitous detection of FOBs, which relies on searching for anomalous spatial images. In particular, due to their short duration, the seeing distorted images of FOBs should look characteristically different than those of steady sources in a standard optical exposure of finite duration. We apply this idea to simulated observations with the Vera C. Rubin Observatory, produced by tracing individual photons through a turbulent atmosphere, and down through the optics and camera of the Rubin telescope. We compare these simulated images to steady-source star simulations in 15 s integrations, the nominal Rubin exposure time. We report the classification accuracy results of a Neural Network classifier for distinguishing FOBs from steady sources. From this classifier, we derive constraints in duration-intensity parameter space for unambiguously identifying FOBs in Rubin observations. We conclude with estimates of the total number of detections of FOB counterparts to FRBs expected during the 10-year Rubin Legacy Survey of Space and Time (LSST)., Comment: 7 pages, 4 figures, submitted to the Astrophysical Journal

The Vera C. Rubin Observatory will begin the Legacy Survey of Space and Time (LSST) in 2024, spanning an area of 18,000 square degrees in six bands, with more than 800 observations of each field over ten years. The unprecedented data set will enable great advances in the study of the formation and evolution of structure and exploration of physics of the dark universe. The observations will hold clues about the cause for the accelerated expansion of the universe and possibly the nature of dark matter. During the next decade, LSST will be able to confirm or dispute if tensions seen today in cosmological data are due to new physics. New and unexpected phenomena could confirm or disrupt our current understanding of the universe. Findings from LSST will guide the path forward post-LSST. The Rubin Observatory will still be a uniquely powerful facility even then, capable of revealing further insights into the physics of the dark universe. These could be obtained via innovative observing strategies, e.g., targeting new probes at shorter timescales than with LSST, or via modest instrumental changes, e.g., new filters, or through an entirely new instrument for the focal plane. This White Paper highlights some of the opportunities in each scenario from Rubin observations after LSST., Comment: Contribution to Snowmass 2021