/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

The stellar masses, mean ages, metallicities, and star formation histories of galaxies are now commonly estimated via stellar population synthesis (SPS) techniques. SPS relies on stellar evolution calculations from the main sequence to stellar death, stellar spectral libraries, phenomenological dust models, and stellar initial mass functions (IMFs) to translate the evolution of a multimetallicity, multi-age set of stars into a prediction for the time-evolution of the integrated light from that set of stars. Each of these necessary inputs carries significant uncertainties that have until now received little systematic attention. The present work is the first in a series that explores the impact of uncertainties in key phases of stellar evolution and the IMF on the derived physical properties of galaxies and the expected luminosity evolution for a passively evolving set of stars. A Monte Carlo Markov Chain approach is taken to fit near-UV through near-IR photometry of a representative sample of low- and high-redshift galaxies with this new SPS model. Significant results include the following. (1) Including uncertainties in stellar evolution, stellar masses at z ~ 0 carry errors of ~0.3 dex at 95% CL with little dependence on luminosity or color, while at z ~ 2, the masses of bright red galaxies are uncertain at the ~0.6 dex level. (2) Either current stellar evolution models, current observational stellar libraries, or both, do not adequately characterize the metallicity-dependence of the thermally pulsating AGB phase. (3) Conservative estimates on the uncertainty of the slope of the IMF in the solar neighborhood imply that luminosity evolution per unit redshift is uncertain at the ~0.4 mag level in the K band, which is a substantial source of uncertainty for interpreting the evolution of galaxy populations across time. Any possible evolution in the IMF, as suggested by several independent lines of evidence, will only exacerbate this problem. (4) Assuming a distribution of stellar metallicities within a galaxy, rather than a fixed value as is usually assumed, can yield important differences when considering bands blueward of V, but is not a concern for redder bands. Spectroscopic information may alleviate some of these concerns, though uncertainties in the stellar spectral libraries and the importance of nonsolar abundance ratios have not yet been systematically investigated in the SPS context.

The propagation of uncertainties in stellar population synthesis modeling. i. the relevance of uncertain aspects of stellar evolution and the initial mass function to the derived physical properties of galaxies

Course Description This is an advanced course in which we explore the field of Statistical Optics. Topics covered include such subjects as the statistical properties of natural (thermal) and laser light, spatial and temporal coherence, effects of partial coherence on optical imaging instruments, effects on imaging due to randomly inhomogeneous media, and a statistical treatment of the detection of light. Development of this more comprehensive model of the behavior of light draws upon the use of tools traditionally available to the electrical engineer, such as linear system theory and the theory of stochastic processes.

http://ieeexplore.ieee.org/iel5/3/23094/01073023.pdf

Statistical optics

We report an imaging method, termed Fourier ptychographic microscopy (FPM), which iteratively stitches together a
number of variably illuminated, low-resolution intensity images in Fourier space to produce a wide-field, high-resolution
complex sample image. By adopting a wavefront correction strategy, the FPM method can also correct for aberrations and
digitally extend a microscope’s depth of focus beyond the physical limitations of its optics. As a demonstration, we built a
microscope prototype with a resolution of 0.78 µm, a field of view of ∼120 mm^2 and a resolution-invariant depth of focus
of 0.3 mm (characterized at 632 nm). Gigapixel colour images of histology slides verify successful FPM operation. The
reported imaging procedure transforms the general challenge of high-throughput, high-resolution microscopy from one
that is coupled to the physical limitations of the system’s optics to one that is solvable through computation.

Wide-field, high-resolution Fourier ptychographic microscopy

The stellar masses, mean ages, metallicities, and star formation histories of galaxies are now commonly estimated via stellar population synthesis (SPS) techniques. SPS relies on stellar evolution calculations from the main sequence to stellar death, stellar spectral libraries, phenomenological dust models, and stellar initial mass functions (IMFs). The present work is the first in a series that explores the impact of uncertainties in key phases of stellar evolution and the IMF on the derived physical properties of galaxies and the expected luminosity evolution for a passively evolving set of stars. A Monte-Carlo Markov-Chain approach is taken to fit near-UV through near-IR photometry of a representative sample of low- and high-redshift galaxies with this new SPS model. Significant results include the following: 1) including uncertainties in stellar evolution, stellar masses at z~0 carry errors of ~0.3 dex at 95% CL with little dependence on luminosity or color, while at z~2, the masses of bright red galaxies are uncertain at the ~0.6 dex level; 2) either current stellar evolution models, current observational stellar libraries, or both, do not adequately characterize the metallicity-dependence of the thermally-pulsating asymptotic giant branch phase; 3) conservative estimates on the uncertainty of the slope of the IMF in the solar neighborhood imply that luminosity evolution per unit redshift is uncertain at the ~0.4 mag level in the K-band, which is a substantial source of uncertainty for interpreting the evolution of galaxy populations across time; 4) The more plausible assumption of a distribution of stellar metallicities, rather than a fixed value as is usually assumed, can have significant effects on the interpretation of colors blueward of the V-band. (ABRIDGED)

The propagation of uncertainties in stellar population synthesis modeling I: The relevance of uncertain aspects of stellar evolution and the IMF to the derived physical properties of galaxies

The design of the laser-guide-star-based adaptive optics (AO) systems for the Extremely Large Telescopes requires careful study of the issue of elongated spots produced on Shack–Hartmann wavefront sensors. The importance of a correct modeling of the nonuniformity and correlations of the noise induced by this elongation has already been demonstrated for wavefront reconstruction. We report here on the first (to our knowledge) end-to-end simulations of closed-loop ground-layer AO with laser guide stars with such an improved noise model. The results are compared with the level of performance predicted by a classical noise model for the reconstruction. The performance is studied in terms of ensquared energy and confirms that, thanks to the improved noise model, central or side launching of the lasers does not affect the performance with respect to the laser guide stars’ flux. These two launching schemes also perform similarly whatever the atmospheric turbulence strength.

Optimal reconstruction for closed-loop ground-layer adaptive optics with elongated spots.

Adaptive optics (AO) systems under study for the future generation of telescopes have to cope with a huge number of degrees of freedom. This number N is typically 2 orders of magnitude larger than for the currently existing AO systems. An iterative method using a fractal preconditioning, has recently been suggested for a minimum-variance reconstruction in O ( N ) operations. We analyze the efficiency of this algorithm for both the open-loop and the closed-loop configurations. We present the formalism and illustrate the assets of this method with simulations. While the number of iterations for convergence is around 10 in open-loop, the closed-loop configuration induces a reduction of the required number of iterations by a factor of 3 typically. This analysis also enhances the importance of introducing priors to ensure an optimal command. Closed-loop simulations demonstrate the loss of performance when no temporal priors are used. Besides, we discuss the importance of an accurate model for both the system and its uncertainties, so as to ensure a stable behavior in closed-loop.

FRIM: minimum-variance reconstructor with a fractal iterative method

In ground-based astronomy, the inverse problem of phase retrieval from speckle images is a means to calibrate static aberrations for correction by active optics. It can also be used to sense turbulent wavefronts. However, the number of local minima drastically increases with the turbulence strength, mainly because of phase wrapping ambiguities. Multifocal phase diversity has been considered to overcome some ambiguities of the phase retrieval problem. We propose an effective algorithm for phase retrieval from a single focused image. Our algorithm makes use of a global optimization strategy and an automatically tuned smoothness prior to overcome local minima and phase degeneracies. We push the limit of D/r0=4 achieved by Irwan and Lane [J. Opt. Soc. Am. A.15, 2302 (1998)] up to D/r0=11, which is a major improvement owing to the drastic increase in the problem complexity. We estimate the performances of our approach from consistent simulations for different turbulence strengths and noise levels (down to 1500 photons per image). We also investigate the benefit of temporal correlation.

Phase retrieval from speckle images.

Nulling interferometers such as Darwin or TPF will require a rather sophisticated data processing in order to perform a reliable planet detection and characterization. We propose a Bayesian method, which follows the maximum a posteriori (MAP) approach, to solve this problem. Our method accounts for the noise statistics and optimally combines the data from a nulling interferometer at all observed wavelengths to perform reliable planet detection. The problem to be solved is however multi-modal. We show how, in practice, the global optimum of the MAP criterion can be found by our method; the latter also provides the most likely spectral energy distributions of all planets. Additionally, we show that a proper regularization allows us to achieve an improved robustness of the detection and could lead to shorter observation times.

/pdf/maximum-a-posteriori-planet-detection-and-characterization-v4ni66s5dy.pdf

Maximum a posteriori planet detection and characterization with a nulling interferometer

Context. Exoplanet detection and characterization by direct imaging both rely on sophisticated instruments (adaptive optics and coronagraph) and adequate data processing methods. Angular and spectral differential imaging (ASDI) combines observations at different times and a range of wavelengths in order to separate the residual signal from the host star and the signal of interest corresponding to off-axis sources.Aims. Very high contrast detection is only possible with an accurate modeling of those two components, in particular of the background due to stellar leakages of the host star masked out by the coronagraph. Beyond the detection of point-like sources in the field of view, it is also essential to characterize the detection in terms of statistical significance and astrometry and to estimate the source spectrum.Methods. We extend our recent method PACO, based on local learning of patch covariances, in order to capture the spectral and temporal fluctuations of background structures. From this statistical modeling, we build a detection algorithm and a spectrum estimation method: PACO ASDI. The modeling of spectral correlations proves useful both in reducing detection artifacts and obtaining accurate statistical guarantees (detection thresholds and photometry confidence intervals).Results. An analysis of several ASDI datasets from the VLT/SPHERE-IFS instrument shows that PACO ASDI produces very clean detection maps, for which setting a detection threshold is statistically reliable. Compared to other algorithms used routinely to exploit the scientific results of SPHERE-IFS, sensitivity is improved and many false detections can be avoided. Spectrally smoothed spectra are also produced by PACO ASDI. The analysis of datasets with injected fake planets validates the recovered spectra and the computed confidence intervals.Conclusions. PACO ASDI is a high-contrast processing algorithm accounting for the spatio-spectral correlations of the data to produce statistically-grounded detection maps and reliable spectral estimations. Point source detections, photometric and astrometric characterizations are fully automatized.

/pdf/paco-asdi-an-algorithm-for-exoplanet-detection-and-3q5a9b0dfu.pdf

Éric Thiébaut

Papers

Optimal reconstruction for closed-loop ground-layer adaptive optics with elongated spots.

FRIM: minimum-variance reconstructor with a fractal iterative method

Phase retrieval from speckle images.

Maximum a posteriori planet detection and characterization with a nulling interferometer

PACO ASDI: an algorithm for exoplanet detection and characterization in direct imaging with integral field spectrographs