/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

We address the data processing methods needed for imaging with a long baseline optical interferometer. We first describe parametric reconstruction approaches and adopt a general formulation of nonparametric image reconstruction as the solution of a constrained optimization problem. Within this framework, we present two recent reconstruction methods, Mira and Wisard, representative of the two generic approaches for dealing with the missing phase information. Mira is based on an implicit approach and a direct optimization of a Bayesian criterion while Wisard adopts a self-calibration approach and an alternate minimization scheme inspired from radio-astronomy. Both methods can handle various regularization criteria. We review commonly used regularization terms and introduce an original quadratic regularization called ldquosoft support constraintrdquo that favors the object compactness. It yields images of quality comparable to nonquadratic regularizations on the synthetic data we have processed. We then perform image reconstructions, both parametric and nonparametric, on astronomical data from the IOTA interferometer, and discuss the respective roles of parametric and nonparametric approaches for optical interferometric imaging.

/pdf/advanced-imaging-methods-for-long-baseline-optical-2j6dqqgz50.pdf

Advanced Imaging Methods for Long-Baseline Optical Interferometry

The emergence of optical interferometers with three and more telescopes allows image reconstruction of astronomical objects at the milliarcsecond scale. However, some objects contain components with very different spectral energy distributions (SED; i.e. different temperatures), which produces strong chromatic effects on the interferograms that have to be managed with care by image reconstruction algorithms. For example, the gray approximation for the image reconstruction process results in a degraded image if the total (u, v)-coverage given by the spectral supersynthesis is used. The relative flux contribution of the central object and an extended structure changes with wavelength for different temperatures. For young stellar objects, the known characteristics of the central object (i.e., stellar SED), or even the fit of the spectral index and the relative flux ratio, can be used to model the central star while reconstructing the image of the extended structure separately. Methods. We present a new method, called SPARCO (semi-parametric algorithm for the image reconstruction of chromatic objects), which describes the spectral characteristics of both the central object and the extended structure to consider them properly when reconstructing the image of the surrounding environment. We adapted two image-reconstruction codes (Macim, Squeeze, and MiRA) to implement this new prescription. SPARCO is applied using Macim, Squeeze and MiRA on a young stellar object model and also on literature data on HR5999 in the near-infrared with the VLTI. This method paves the way to improved aperture-synthesis imaging of several young stellar objects with existing datasets. More generally, the approach can be used on astrophysical sources with similar features such as active galactic nuclei, planetary nebulae, and asymptotic giant branch stars.

SPARCO : a semi-parametric approach for image reconstruction of chromatic objects

This paper provides a general introduction to the problem of image reconstruction from interferometric data. A simple model of the interferometric observables is given, and the issues arising from sparse Fourier data are discussed. The effects of various regularizations are described. In the proposed general framework, most existing algorithms can be understood. For an astronomer, such an understanding is crucial not only for selecting and using an algorithm but also to ensure correct interpretation of the resulting image.

/pdf/principles-of-image-reconstruction-in-optical-interferometry-4s41i9vjm6.pdf

Principles of image reconstruction in optical interferometry: tutorial

The potential of in-line digital holography to locate and measure the size of particles distributed throughout a volume (in one shot) has been established. These measurements are fundamental for the study of particle trajectories in fluid flow. The most important issues in digital holography today are poor depth positioning accuracy, transverse field-of-view limitations, border artifacts and computational burdens. We recently suggested an 'inverse problem' approach to address some of these issues for the processing of particle digital holograms. The described algorithm improves axial positioning accuracy, gives particle diameters with sub-micrometer accuracy, eliminates border effects and increases the size of the studied volume. This approach for processing particle holograms pushes back some classical constraints. For example, the Nyquist criterion is no longer a restriction for the recording step and the studied volume is no longer confined to the field of view delimited by the sensor borders. In this paper we present a review of the limitations commonly found in digital holography. We then discuss the benefits of the 'inverse problem' approach and the influence of some experimental parameters in this framework.

/pdf/digital-holography-of-particles-benefits-of-the-inverse-48ack44dd9.pdf

Digital holography of particles: benefits of the 'inverse problem' approach

Image deblurring is essential to high resolution imaging and is therefore widely used in astronomy, microscopy or computational photography. While shift-invariant blur is modeled by convolution and leads to fast FFT-based algorithms, shift-variant blurring requires models both accurate and fast. When the point spread function (PSF) varies smoothly across the field, these two opposite objectives can be reached by interpolating from a grid of PSF samples. Several models for smoothly varying PSF co-exist in the literature. We advocate that one of them is both physically-grounded and fast. Moreover, we show that the approximation can be largely improved by tuning the PSF samples and interpolation weights with respect to a given continuous model. This improvement comes without increasing the computational cost of the blurring operator. We illustrate the developed blurring model on a deconvo-lution application in astronomy. Regularized reconstruction with our model leads to large improvements over existing results.

/pdf/fast-model-of-space-variant-blurring-and-its-application-to-4sfi2c5sva.pdf

Éric Thiébaut

Papers

Advanced Imaging Methods for Long-Baseline Optical Interferometry

SPARCO : a semi-parametric approach for image reconstruction of chromatic objects

Principles of image reconstruction in optical interferometry: tutorial

Digital holography of particles: benefits of the 'inverse problem' approach

Fast model of space-variant blurring and its application to deconvolution in astronomy