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Full-Stokes polarimetric datasets, originating from slit-spectrograph or narrow-band filtergrams, are routinely acquired nowadays. The data rate is increasing with the advent of bi-dimensional spectropolarimeters and observing techniques that allow long-time sequences of high-quality observations. There is a clear need to go beyond the traditional pixel-by-pixel strategy in spectropolarimetric inversions by exploiting the spatiotemporal coherence of the inferred physical quantities. We explore the potential of neural networks as a continuous representation of the physical quantities over time and space (also known as neural fields), for spectropolarimetric inversions. We have implemented and tested a neural field to perform the inference of the magnetic field vector (approach also known as physics-informed neural networks) under the weak-field approximation (WFA). By using a neural field to describe the magnetic field vector, we can regularize the solution in the spatial and temporal domain by assuming that the physical quantities are continuous functions of the coordinates. We investigated the results in synthetic and real observations of the Ca II 8542 A line. We also explored the impact of other explicit regularizations, such as using the information of an extrapolated magnetic field, or the orientation of the chromospheric fibrils. Compared to the traditional pixel-by-pixel inversion, the neural field approach improves the fidelity of the reconstruction of the magnetic field vector, especially the transverse component. This implicit regularization is a way of increasing the effective signal-to-noise of the observations. Although it is slower than the pixel-wise WFA estimation, this approach shows a promising potential for depth-stratified inversions, by reducing the number of free parameters and inducing spatio-temporal constraints in the solution., Comment: 12 pages, 7 figures, Appendix, Submitted to A&A

Astrochemical models are important tools to interpret observations of molecular and atomic species in different environments. However, these models are time-consuming, precluding a thorough exploration of the parameter space, leading to uncertainties and biased results. Using neural networks to simulate the behavior of astrochemical models is a way to circumvent this problem, providing fast calculations that are based on real astrochemical models. In this paper, we present a fast neural emulator of the astrochemical code Nautilus based on conditional neural fields. The resulting model produces the abundance of 192 species for arbitrary times between 1 and 10$^7$ years. Uncertainties well below 0.2 dex are found for all species, while the computing time is of the order of 10$^4$ smaller than Nautilus. This will open up the possibility of performing much more complex forward models to better understand the physical properties of the interstellar medium. As an example of the power of these models, we ran a feature importance analysis on the electron abundance predicted by Nautilus. We found that the electron density is coupled to the initial sulphur abundance in a low density gas. Increasing the initial sulphur abundance from a depleted scenario to the cosmic abundance leads to an enhancement of an order of magnitude of the electron density. This enhancement can potentially influence the dynamics of the gas in star formation sites., Comment: 12 pages, 8 figures, accepted for publication in MNRAS

The study of astronomical phenomena through ground-based observations is always challenged by the distorting effects of Earth's atmosphere. Traditional methods of post-facto image correction, essential for correcting these distortions, often rely on simplifying assumptions that limit their effectiveness, particularly in the presence of spatially variant atmospheric turbulence. Such cases are often solved by partitioning the field-of-view into small patches, deconvolving each patch independently, and merging all patches together. This approach is often inefficient and can produce artifacts. Recent advancements in computational techniques and the advent of deep learning offer new pathways to address these limitations. This paper introduces a novel framework leveraging a deep neural network to emulate spatially variant convolutions, offering a breakthrough in the efficiency and accuracy of astronomical image deconvolution. By training on a dataset of images convolved with spatially invariant point spread functions and validating its generalizability to spatially variant conditions, this approach presents a significant advancement over traditional methods. The convolution emulator is used as a forward model in a multi-object multi-frame blind deconvolution algorithm for solar images. The emulator enables the deconvolution of solar observations across large fields of view without resorting to patch-wise mosaicking, thus avoiding artifacts associated with such techniques. This method represents a significant computational advantage, reducing processing times by orders of magnitude., Comment: 15 pages, 14 figures, accepted for publication in A&A

The application of machine learning in solar physics has the potential to greatly enhance our understanding of the complex processes that take place in the atmosphere of the Sun. By using techniques such as deep learning, we are now in the position to analyze large amounts of data from solar observations and identify patterns and trends that may not have been apparent using traditional methods. This can help us improve our understanding of explosive events like solar flares, which can have a strong effect on the Earth environment. Predicting hazardous events on Earth becomes crucial for our technological society. Machine learning can also improve our understanding of the inner workings of the sun itself by allowing us to go deeper into the data and to propose more complex models to explain them. Additionally, the use of machine learning can help to automate the analysis of solar data, reducing the need for manual labor and increasing the efficiency of research in this field., Comment: 100 pages, 13 figures, 286 references, accepted for publication as a Living Review in Solar Physics (LRSP)

Ground-based solar image restoration is a computationally expensive procedure that involves nonlinear optimization techniques. The presence of atmospheric turbulence produces perturbations in individual images that make it necessary to apply blind deconvolution techniques. These techniques rely on the observation of many short exposure frames that are used to simultaneously infer the instantaneous state of the atmosphere and the unperturbed object. We have recently explored the use of machine learning to accelerate this process, with promising results. We build upon this previous work to propose several interesting improvements that lead to better models. As well, we propose a new method to accelerate the restoration based on algorithm unrolling. In this method, the image restoration problem is solved with a gradient descent method that is unrolled and accelerated aided by a few small neural networks. The role of the neural networks is to correct the estimation of the solution at each iterative step. The model is trained to perform the optimization in a small fixed number of steps with a curated dataset. Our findings demonstrate that both methods significantly reduce the restoration time compared to the standard optimization procedure. Furthermore, we showcase that these models can be trained in an unsupervised manner using observed images from three different instruments. Remarkably, they also exhibit robust generalization capabilities when applied to new datasets. To foster further research and collaboration, we openly provide the trained models, along with the corresponding training and evaluation code, as well as the training dataset, to the scientific community., Comment: 26 pages, 9 figures, accepted for publication in Solar Physics

Given the widespread availability of grids of models for stellar atmospheres, it is necessary to recover intermediate atmospheric models by means of accurate techniques that go beyond simple linear interpolation and capture the intricacies of the data. Our goal is to establish a reliable, precise, lightweight, and fast method for recovering stellar model atmospheres, that is to say the stratification of mass column, temperature, gas pressure, and electronic density with optical depth given any combination of the defining atmospheric specific parameters: metallicity, effective temperature, and surface gravity, as well as the abundances of other key chemical elements. We employed a fully connected deep neural network which in turn uses a 1D convolutional auto-encoder to extract the nonlinearities of a grid using the ATLAS9 and MARCS model atmospheres. This new method we call iNNterpol effectively takes into account the nonlinearities in the relationships of the data as opposed to traditional machine-learning methods, such as the light gradient boosting method (LightGBM), that are repeatedly used for their speed in well-known competitions with reduced datasets. We show a higher precision with a convolutional auto-encoder than using principal component analysis as a feature extractor.We believe it constitutes a useful tool for generating fast and precise stellar model atmospheres, mitigating convergence issues, as well as a framework for future developments. The code and data for both training and direct interpolation are available online at https://github.com/cwestend/iNNterpol for full reproducibility and to serve as a practical starting point for other continuous 1D data in the field and elsewhere., Comment: Accepted for publication in Astronomy and Astrophysics, 11 pages, 27 figures, 3 tables

Context. Activity on the far side of the Sun is routinely studied through the analysis of the seismic oscillations detected on the near side using helioseismic techniques such as phase shift sensitive holography. Recently, the neural network FarNet was developed to improve these detections. Aims. We aim to create a new machine learning tool, FarNet II, which further increases the scope of FarNet, and to evaluate its performance in comparison to FarNet and the standard helioseismic method for detecting far side activity. Methods. We developed FarNet II, a neural network that retains some of the general characteristics of FarNet but improves the detections in general, as well as the temporal coherence among successive predictions. The main novelties are the implementation of attention and convolutional long short term memory (ConvLSTM) modules. A cross validation approach, training the network 37 times with a different validation set for each run, was employed to leverage the limited amount of data available. We evaluate the performance of FarNet II using three years of extreme ultraviolet observations of the far side of the Sun acquired with the Solar Terrestrial Relations Observatory (STEREO) as a proxy of activity. The results from FarNet II were compared with those obtained from FarNet and the standard helioseismic method using the Dice coefficient as a metric. Results. FarNet II achieves a Dice coefficient that improves that of FarNet by over 0.2 points for every output position on the sequences from the evaluation dates. Its improvement over FarNet is higher than that of FarNet over the standard method. Conclusions. The new network is a very promising tool for improving the detection of activity on the far side of the Sun given by pure helioseismic techniques. Space weather forecasts can potentially benefit from the higher sensitivity provided by this novel method., Comment: Accepted for publication in Astronomy and Astrophysics. Abridged abstract

We study the impact of the loss of axial symmetry around the optical axis on the polarimetric properties of a telescope with segmented primary mirror when each segment is present in a different aging stage. The different oxidation stage of each segment as they are substituted in time leads to non-negligible crosstalk terms. This effect is wavelength dependent and it is mainly determined by the properties of the reflecting material. For an aluminum coating, the worst polarimetric behavior due to oxidation is found for the blue part of the visible. Contrarily, dust -- as modeled in this work -- does not significantly change the polarimetric behavior of the optical system . Depending on the telescope, there might be segment substitution sequences that strongly attenuate this instrumental polarization.

The computational cost of fast non-LTE synthesis is one of the challenges that limits the development of 2D and 3D inversion codes. It also makes the interpretation of observations of lines formed in the chromosphere and transition region a slow and computationally costly process, which limits the inference of the physical properties on rather small fields of view. Having access to a fast way of computing the deviation from the LTE regime through the departure coefficients could largely alleviate this problem. We propose to build and train a graph network that quickly predicts the atomic level populations without solving the non-LTE problem. We find an optimal architecture for the graph network for predicting the departure coefficients of the levels of an atom from the physical conditions of a model atmosphere. A suitable dataset with a representative sample of potential model atmospheres is used for training. This dataset has been computed using existing non-LTE synthesis codes. The graph network has been integrated into existing synthesis and inversion codes for the particular case of \caii. We demonstrate orders of magnitude gain in computing speed. We analyze the generalization capabilities of the graph network and demonstrate that it produces good predicted departure coefficients for unseen models. We implement this approach in \hazel\ and show how the inversions nicely compare with those obtained with standard non-LTE inversion codes. Our approximate method opens up the possibility of extracting physical information from the chromosphere on large fields-of-view with time evolution., Comment: 16 pages, 10 figures, Accepted in ApJ on 01/02/2022 after A&A suggested to be published in a more specialized journal

The non-uniform surface temperature distribution of rotating active stars is routinely mapped with the Doppler Imaging technique. Inhomogeneities in the surface produce features in high-resolution spectroscopic observations that shift in wavelength depending on their position on the visible hemisphere. The inversion problem has been systematically solved using maximum a-posteriori regularized methods assuming smoothness or maximum entropy. Our aim in this work is to solve the full Bayesian inference problem, by providing access to the posterior distribution of the surface temperature in the star. We use amortized neural posterior estimation to produce a model that approximates the high-dimensional posterior distribution for spectroscopic observations of selected spectral ranges sampled at arbitrary rotation phases. The posterior distribution is approximated with conditional normalizing flows, which are flexible, tractable and easy to sample approximations to arbitrary distributions. When conditioned on the spectroscopic observations, they provide a very efficient way of obtaining samples from the posterior distribution. The conditioning on observations is obtained through the use of Transformer encoders, which can deal with arbitrary wavelength sampling and rotation phases. Our model can produce thousands of posterior samples per second. Our validation of the model for very high signal-to-noise observations shows that it correctly approximates the posterior, although with some overestimation of the broadening. We apply the model to the moderately fast rotator II Peg, producing the first Bayesian map of its temperature inhomogenities. We conclude that conditional normalizing flows are a very promising tool to carry out approximate Bayesian inference in more complex problems in stellar physics, like constraining the magnetic properties., Comment: 14 pages, 10 figures, submitted to A&A

Stokes inversion techniques are very powerful methods for obtaining information on the thermodynamic and magnetic properties of solar and stellar atmospheres. In recent years, very sophisticated inversion codes have been developed that are now routinely applied to spectro-polarimetric observations. Most of these inversion codes are designed for finding an optimum solution to the nonlinear inverse problem. However, to obtain the location of potentially multimodal cases (ambiguities), the degeneracies, and the uncertainties of each parameter inferred from the inversions, algorithms such as Markov chain Monte Carlo (MCMC), require to evaluate the likelihood of the model thousand of times and are computationally costly. Variational methods are a quick alternative to Monte Carlo methods by approximating the posterior distribution by a parametrized distribution. In this study, we introduce a highly flexible variational inference method to perform fast Bayesian inference, known as normalizing flows. Normalizing flows are a set of invertible, differentiable, and parametric transformations that convert a simple distribution into an approximation of any other complex distribution. If the transformations are conditioned on observations, the normalizing flows can be trained to return Bayesian posterior probability estimates for any observation. We illustrate the ability of the method using a simple Milne-Eddington model and a complex non-LTE inversion. However, the method is extremely general and other more complex forward models can be applied. The training procedure need only be performed once for a given prior parameter space and the resulting network can then generate samples describing the posterior distribution several orders of magnitude faster than existing techniques., Comment: 11 pages, 7 figures, accepted for publication in A&A

We have developed an inversion procedure designed for high-resolution solar spectro-polarimeters, such as Hinode/SP or DKIST/ViSP. The procedure is based on artificial neural networks trained with profiles generated from random atmospheric stratifications for a high generalization capability. When applied to Hinode data we find a hot fine-scale network structure whose morphology changes with height. In the middle layers this network resembles what is observed in G-band filtergrams but it is not identical. Surprisingly, the temperature enhancements in the middle and upper photosphere have a reversed pattern. Hot pixels in the middle photosphere, possibly associated to small-scale magnetic elements, appear cool at the log(tau_500)=-3 and -4 level, and viceversa. Finally, we find hot arcs on the limb side of magnetic pores, which we interpret as the first direct observational evidence of the "hot wall" effect in temperature., Comment: Submitted to Astronomy and Astrophysics. Comments are welcome

Observations from ground based telescopes are affected by the presence of the Earth atmosphere, which severely perturbs them. The use of adaptive optics techniques has allowed us to partly beat this limitation. However, image selection or post-facto image reconstruction methods applied to bursts of short-exposure images are routinely needed to reach the diffraction limit. Deep learning has been recently proposed as an efficient way to accelerate these image reconstructions. Currently, these deep neural networks are trained with supervision, so that either standard deconvolution algorithms need to be applied a-priori or complex simulations of the solar magneto-convection need to be carried out to generate the training sets. Our aim here is to propose a general unsupervised training scheme that allows multiframe blind deconvolution deep learning systems to be trained simply with observations. The approach can be applied for the correction of point-like as well as extended objects. Leveraging the linear image formation theory and a probabilistic approach to the blind deconvolution problem produces a physically-motivated loss function. The optimization of this loss function allows an end-to-end training of a machine learning model composed of three neural networks. As examples, we apply this procedure to the deconvolution of stellar data from the FastCam instrument and to solar extended data from the Swedish Solar Telescope. The analysis demonstrates that the proposed neural model can be successfully trained without supervision using observations only. It provides estimations of the instantaneous wavefronts, from which a corrected image can be found using standard deconvolution technniques. The network model is roughly three orders of magnitude faster than applying standard deconvolution based on optimization and shows potential to be used on real-time at the telescope., Comment: 11 pages, 4 figures, accepted for publication in A&A

The quality of images of the Sun obtained from the ground are severely limited by the perturbing effect of the turbulent Earth's atmosphere. The post-facto correction of the images to compensate for the presence of the atmosphere require the combination of high-order adaptive optics techniques, fast measurements to freeze the turbulent atmosphere and very time consuming blind deconvolution algorithms. Under mild seeing conditions, blind deconvolution algorithms can produce images of astonishing quality. They can be very competitive with those obtained from space, with the huge advantage of the flexibility of the instrumentation thanks to the direct access to the telescope. In this contribution we leverage deep learning techniques to significantly accelerate the blind deconvolution process and produce corrected images at a peak rate of ~100 images per second. We present two different architectures that produce excellent image corrections with noise suppression while maintaining the photometric properties of the images. As a consequence, polarimetric signals can be obtained with standard polarimetric modulation without any significant artifact. With the expected improvements in computer hardware and algorithms, we anticipate that on-site real-time correction of solar images will be possible in the near future., Comment: 16 pages, 12 figures, accepted for publication in A&A

We present MOLPOP-CEP, a universal line transfer code that allows the exact calculation of multi-level line emission from a slab with variable physical conditions for any arbitrary atom or molecule for which atomic data exist. The code includes error control to achieve any desired level of accuracy, providing full confidence in its results. Publicly available, MOLPOP-CEP employs our recently developed Coupled Escape Probability (CEP) technique, whose performance exceeds other exact methods by orders of magnitude. The program also offers the option of an approximate solution with different variants of the familiar escape probability method. As an illustration of the MOLPOP-CEP capabilities we present an exact calculation of the Spectral Line Energy Distribution (SLED) of the CO molecule and compare it with escape probability results. We find that the popular large-velocity gradient (LVG) approximation is unreliable at large CO column densities. Providing a solution of the multi-level line transfer problem at any prescribed level of accuracy, MOLPOP-CEP is removing any doubts about the validity of its final results., Comment: 10 pages, 3 figures, accepted for publication in A&A

The Helioseismic and Magnetic Imager (HMI) provides continuum images and magnetograms with a cadence better than one per minute. It has been continuously observing the Sun 24 hours a day for the past 7 years. The obvious trade-off between full disk observations and spatial resolution makes HMI not enough to analyze the smallest-scale events in the solar atmosphere. Our aim is to develop a new method to enhance HMI data, simultaneously deconvolving and super-resolving images and magnetograms. The resulting images will mimic observations with a diffraction-limited telescope twice the diameter of HMI. Our method, which we call Enhance, is based on two deep fully convolutional neural networks that input patches of HMI observations and output deconvolved and super-resolved data. The neural networks are trained on synthetic data obtained from simulations of the emergence of solar active regions. We have obtained deconvolved and supper-resolved HMI images. To solve this ill-defined problem with infinite solutions we have used a neural network approach to add prior information from the simulations. We test Enhance against Hinode data that has been degraded to a 28 cm diameter telescope showing very good consistency. The code is open source., Comment: 13 pages, 10 figures. Accepted for publication in Astronomy & Astrophysics

We show that it is possible to measure polarization with a polarimeter that gets rid of the seeing while still measuring at a frequency well below that of the seeing. We study a standard polarimeter made of two retarders and a beamsplitter. The retarders are modulated at $\sim 500$ Hz, a frequency comparable to that of the variations of the refraction index in the Earth atmosphere, what is usually termed as seeing in astronomical observations. However, we assume that the camera is slow, so that our measurements are time integrations of these modulated signals. In order to recover the time variation of the seeing and obtain the Stokes parameters, we use the theory of compressed sensing to solve the demodulation by impose a sparsity constraint on the Fourier coefficients of the seeing. We demonstrate the feasibility of this sub-Nyquist polarimeter using numerical simulations, both in the case without noise and with noise. We show that a sensible modulation scheme is obtained by randomly changing the fast axis of the modulators or their retardances in specific ways. We finally demonstrate that the value of the Stokes parameters can be recovered with great precision at almost maximum efficiency, although it slightly degrades when the signal-to-noise ratio of the observations increase, a consequence of the multiplexing under the presence of photon noise., Comment: 9 pages, 6 figures, accepted for publication in Applied Optics

We describe a simple technique for the acceleration of spectro-polarimetric inversions based on principal component analysis (PCA) of Stokes profiles. This technique involves the indexing of the database models based on the sign of the projections (PCA coefficients) of the first few relevant orders of principal components of the four Stokes parameters. In this way, each model in the database can be attributed a distinctive binary number of $2^{4n}$ bits, where $n$ is the number of PCA orders used for the indexing. Each of these binary numbers (indexes) identifies a group of "compatible" models for the inversion of a given set of observed Stokes profiles sharing the same index. The complete set of the binary numbers so constructed evidently determines a partition of the database. The search of the database for the PCA inversion of spectro-polarimetric data can profit greatly from this indexing. In practical cases it becomes possible to approach the ideal acceleration factor of $2^{4n}$ as compared to the systematic search of a non-indexed database for a traditional PCA inversion. This indexing method relies on the existence of a physical meaning in the sign of the PCA coefficients of a model. For this reason, the presence of model ambiguities and of spectro-polarimetric noise in the observations limits in practice the number $n$ of relevant PCA orders that can be used for the indexing., Comment: accepted for publication on the Astrophysical Journal

The derivation of the effective temperature of a star is a critical first step in a detailed spectroscopic analysis. Spectroscopic methods suffer from systematic errors related to model simplifications. Photometric methods may be more robust, but are exposed to the distortions caused by interstellar reddening. Direct methods are difficult to apply, since fundamental data of high accuracy are hard to obtain. We explore a new approach in which the spectrum is used to characterize a star's effective temperature based on a calibration established by a small set of standard stars. We perform principal component analysis on homogeneous libraries of stellar spectra, then calibrate a relationship between the principal components and the effective temperature using a set of stars with reliable effective temperatures. We find that our procedure gives excellent consistency when spectra from a homogeneous set of observations are used. Systematic offsets may appear when combining observations from different sources. Using as reference the spectra of stars with high-quality spectroscopic temperatures in the Elodie library, we define a temperature scale for FG-type disk dwarfs with an internal consistency of about 50 K, in excellent agreement with temperatures from direct determinations, but distinct from widely used scales based on the infrared flux method., Comment: Pages 1-9 Article and pages 9-22 Table. 7 Figures

Extracting magnetic and thermodynamic information from spectropolarimetric observations is a difficult and time consuming task. The amount of science-ready data that will be generated by the new family of large solar telescopes is so large that we will be forced to modify the present approach to inference. In this contribution, I propose several possible ways that might be useful for extracting the thermodynamic and magnetic properties of solar plasmas from such observations quickly., Comment: 11 pages, 4 figures, proceedings of "2nd ATST-EAST Workshop in Solar Physics: Magnetic Fields from the Photosphere to the Corona"

Double-peaked line profiles are commonly considered a hallmark of rotating disks, with the distance between the peaks a measure of the rotation velocity. However, double-peaks can arise also from radiative transfer effects in optically thick non-rotating sources. Utilizing exact solutions of the line transfer problem we present a detailed study of line emission from geometrically thin Keplerian disks. We derive the conditions for emergence of kinematic double peaks in optically thin and thick disks, and find that it is generally impossible to disentangle the effects of kinematics and line opacity in observed double-peaked profiles. Unless supplemented by additional information, a double-peaked profile alone is not a reliable indicator of a rotating disk. In certain circumstances, triple and quadruple profiles might be better indicators of rotation in optically thick disks., Comment: MNRAS, to be published

The weak-field approximation is one of the simplest models that allows us to relate the observed polarization induced by the Zeeman effect with the magnetic field vector present on the plasma of interest. It is usually applied for diagnosing magnetic fields in the solar and stellar atmospheres. A fully Bayesian approach to the inference of magnetic properties in unresolved structures is presented. The analytical expression for the marginal posterior distribution is obtained, from which we can obtain statistically relevant information about the model parameters. The role of a-priori information is discussed and a hierarchical procedure is presented that gives robust results that are almost insensitive to the precise election of the prior. The strength of the formalism is demonstrated through an application to IMaX data. Bayesian methods can optimally exploit data from filter-polarimeters given the scarcity of spectral information as compared with spectro-polarimeters. The effect of noise and how it degrades our ability to extract information from the Stokes profiles is analyzed in detail., Comment: 16 pages, 5 figures, accepted for publication in ApJ

Accurate astrophysical polarimetry requires a proper characterization of the polarization properties of the telescope and instrumentation employed to obtain the observations. Determining the telescope and instrument Muller matrix is becoming increasingly difficult with the increase in aperture size of the new and upcoming solar telescopes. We have carried out a detailed multi-wavelength characterization of the Dunn Solar Telescope (DST) at the National Solar Observatory/Sacramento Peak as a case study and explore various possibilites for the determination of its polarimetric properties. We show that the telescope model proposed in this paper is more suitable than that in previous work in that it describes better the wavelength dependence of aluminum-coated mirrors. We explore the adequacy of the degrees of freedom allowed by the model using a novel mathematical formalism. Finally, we investigate the use of polarimeter calibration data taken at different times of the day to characterize the telescope and find that very valuable information on the telescope properties can be obtained in this manner. The results are also consistent with the entrance window polarizer measurements, opening very interesting possibilities for the calibration of future large-aperture solar telescopes such as the ATST or the EST., Comment: To be submitted to A&A (instrumentation section)

The image degradation produced by atmospheric turbulence and optical aberrations is usually alleviated using post-facto image reconstruction techniques, even when observing with adaptive optics systems. These techniques rely on the development of the wavefront using Zernike functions and the non-linear optimization of a certain metric. The resulting optimization procedure is computationally heavy. Our aim is to alleviate this computationally burden. To this aim, we generalize the recently developed extended Zernike-Nijboer theory to carry out the analytical integration of the Fresnel integral and present a natural basis set for the development of the point spread function in case the wavefront is described using Zernike functions. We present a linear expansion of the point spread function in terms of analytic functions which, additionally, takes defocusing into account in a natural way. This expansion is used to develop a very fast phase-diversity reconstruction technique which is demonstrated through some applications. This suggest that the linear expansion of the point spread function can be applied to accelerate other reconstruction techniques in use presently and based on blind deconvolution., Comment: 10 pages, 4 figures, accepted for publication in Astronomy & Astrophysics

We demonstrate through numerical simulations with real data the feasibility of using compressive sensing techniques for the acquisition of spectro-polarimetric data. This allows us to combine the measurement and the compression process into one consistent framework. Signals are recovered thanks to a sparse reconstruction scheme from projections of the signal of interest onto appropriately chosen vectors, typically noise-like vectors. The compressibility properties of spectral lines are analyzed in detail. The results shown in this paper demonstrate that, thanks to the compressibility properties of spectral lines, it is feasible to reconstruct the signals using only a small fraction of the information that is measured nowadays. We investigate in depth the quality of the reconstruction as a function of the amount of data measured and the influence of noise. This change of paradigm also allows us to define new instrumental strategies and to propose modifications to existing instruments in order to take advantage of compressive sensing techniques., Comment: 11 pages, 9 figures, accepted for publication in A&A

In order to get a significant Zeeman signature in the polarised spectra of a magnetic star, we usually 'add' the contributions of numerous spectral lines; the ultimate goal is to recover the spectropolarimetric prints of the magnetic field in these line additions. Here we want to clarify the meaning of these techniques of line addition; in particular, we try to interpret the meaning of the 'pseudo-line' formed during this process and to find out why and how its Zeeman signature is still meaningful. We create a synthetic case of line addition and apply well tested standard solar methods routinely used in the research on magnetism in our nearest star. The results are convincing and the Zeeman signatures well detected; Solar methods are found to be quite efficient also for stellar observations. We statistically compare line addition with least-squares deconvolution and demonstrate that they both give very similar results as a consequence of the special statistical properties of the weights. The Zeeman signatures are unequivocally detected in this multiline approach. We may anticipate the outcome that magnetic field detection is reliable well beyond the weak-field approximation. Linear polarisation in the spectra of solar type stars can be detected when the spectral resolution is sufficiently high., Comment: 8 pages, accepted for publication in A&A

Our aim is to present a fast and general Bayesian inference framework based on the synergy between machine learning techniques and standard sampling methods and apply it to infer the physical properties of clumpy dusty torus using infrared photometric high spatial resolution observations of active galactic nuclei. We make use of the Metropolis-Hastings Markov Chain Monte Carlo algorithm for sampling the posterior distribution function. Such distribution results from combining all a-priori knowledge about the parameters of the model and the information introduced by the observations. The main difficulty resides in the fact that the model used to explain the observations is computationally demanding and the sampling is very time consuming. For this reason, we apply a set of artificial neural networks that are used to approximate and interpolate a database of models. As a consequence, models not present in the original database can be computed ensuring continuity. We focus on the application of this solution scheme to the recently developed public database of clumpy dusty torus models. The machine learning scheme used in this paper allows us to generate any model from the database using only a factor 10^-4 of the original size of the database and a factor 10^-3 in computing time. The posterior distribution obtained for each model parameter allows us to investigate how the observations constrain the parameters and which ones remain partially or completely undetermined, providing statistically relevant confidence intervals. As an example, the application to the nuclear region of Centaurus A shows that the optical depth of the clouds, the total number of clouds and the radial extent of the cloud distribution zone are well constrained using only 6 filters., Comment: 12 pages, 7 figures, accepted for publication in ApJ