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The study of accurate methods to estimate the distribution of stellar rotational velocities is important for understanding many aspects of stellar evolution. From such observations we obtain the projected rotational speed v sin(i) in order to recover the true distribution of the rotational velocity. To that end, we need to solve a difficult inverse problem that can be posed as a Fredholm integral of the first kind. n this work we have used a novel approach based on Maximum likelihood (ML) estimation to obtain an approximation of the true rotational velocity probability density function expressed as a sum of known distribution families. In our proposal, the measurements have been treated as random variables drawn from the projected rotational velocity probability density function. We analyzed the case of Maxwellian sum approximation, where we estimated the parameters that define the sum of distributions. The performance of the proposed method is analyzed using Monte Carlo simulations considering two theoretical cases for the probability density function of the true rotational stellar velocities: i) an unimodal Maxwellian probability density distribution and ii) a bimodal Maxwellian probability density distribution. The results show that the proposed method yielded more accurate estimates in comparison with the Tikhonov regularization method, especially for small sample length N=50. Our proposal was evaluated using real data from three sets of measurements, and our findings were validated using three statistical tests. The ML approach with Maxwellian sum approximation is a accurate method to deconvolve the rotational velocity probability density function, even when the sample length is small (N= 50)

In the era of high-angular resolution astronomical instrumentation, where long and very long baseline interferometers (constituted by many, $\sim$ 20 or more, telescopes) are expected to work not only in the millimeter and submillimeter domain, but also at near and mid infrared wavelengths (experiments such as the Planet Formation Imager, PFI, see Monnier et al. 2018 for an update on its design); any promising strategy to alleviate the costs of the individual telescopes involved needs to be explored. In a recent collaboration between engineers, experimental physicists and astronomers in Valparaiso, Chile, we are gaining expertise in the production of light carbon fiber polymer reinforced mirrors. The working principle consists in replicating a glass, or other substrate, mandrel surface with the mirrored adequate curvature, surface characteristics and general shape. Once the carbon fiber base has hardened, previous studies have shown that it can be coated (aluminum) using standard coating processes/techniques designed for glass-based mirrors. The resulting surface quality is highly dependent on the temperature and humidity control among other variables. Current efforts are focused on improving the smoothness of the resulting surfaces to meet near/mid infrared specifications, overcoming, among others, possible deteriorations derived from the replication process. In a second step, at the validation and quality control stage, the mirrors are characterized using simple/traditional tools like spherometers (down to micron precision), but also an optical bench with a Shack-Hartman wavefront sensor. This research line is developed in parallel with a more classical glass-based approach, and in both cases we are prototyping at the small scale of few tens of cms. We here present our progress on these two approaches., Comment: 13 pages, SPIE Proceedings Volume 10700, Ground-based and Airborne Telescopes VII; 107003X (2018). Event: SPIE Astronomical Telescopes + Instrumentation, 2018, Austin, Texas, United States

We present an algorithm for a class of statistical inference problems. The main idea is to reformulate the inference problem as an optimization procedure, based on the generation of surrogate (auxiliary) functions. This approach is motivated by the MM algorithm, combined with the systematic and iterative structure of the Expectation-Maximization algorithm. The resulting algorithm can deal with hidden variables in Maximum Likelihood and Maximum a Posteriori estimation problems, Instrumental Variables, Regularized Optimization and Constrained Optimization problems. The advantage of the proposed algorithm is to provide a systematic procedure to build surrogate functions for a class of problems where hidden variables are usually involved. Numerical examples show the benefits of the proposed approach., Comment: 18 pages, 3 figures

The availability and performance of laser-based adaptive optics (AO) systems are strongly dependent on the power and quality of the laser beam before being projected to the sky. Frequent and time-consuming alignment procedures are usually required in the laser systems with free-space optics to optimize the beam. Despite these procedures, significant distortions of the laser beam have been observed during the first two years of operation of the Gemini South multi-conjugate adaptive optics system (GeMS). A beam shaping concept with two deformable mirrors is investigated in order to provide automated optimization of the laser quality for astronomical AO. This study aims at demonstrating the correction of quasi-static aberrations of the laser, in both amplitude and phase, testing a prototype of this two-deformable mirror concept on GeMS. The paper presents the results of the preparatory study before the experimental phase. An algorithm to control amplitude and phase correction, based on phase retrieval techniques, is presented with a novel unwrapping method. Its performance is assessed via numerical simulations, using aberrations measured at GeMS as reference. The results predict effective amplitude and phase correction of the laser distortions with about 120 actuators per mirror and a separation of 1.4 m between the mirrors. The spot size is estimated to be reduced by up to 15% thanks to the correction. In terms of AO noise level, this has the same benefit as increasing the photon flux by 40%., Comment: 20 pages, 12 figures