19,860 research outputs found
Imaging sub-milliarcsecond stellar features with intensity interferometry using air Cherenkov telescope arrays
Recent proposals have been advanced to apply imaging air Cherenkov telescope
arrays to stellar intensity interferometry (SII). Of particular interest is the
possibility of model-independent image recovery afforded by the good (u,
v)-plane coverage of these arrays, as well as recent developments in phase
retrieval techniques. The capabilities of these instruments used as SII
receivers have already been explored for simple stellar objects, and here the
focus is on reconstructing stellar images with non-uniform radiance
distributions. We find that hot stars (T > 6000 K) containing hot and/or cool
localized regions (T \sim 500 K) as small as \sim 0.1 mas can be imaged at
short wavelengths ({\lambda} = 400 nm).Comment: Accepted for publication in MNRAS. 6 pages, 10 figure
Towards optical intensity interferometry for high angular resolution stellar astrophysics
Most neighboring stars are still detected as point sources and are beyond the
angular resolution reach of current observatories. Methods to improve our
understanding of stars at high angular resolution are investigated. Air
Cherenkov telescopes (ACTs), primarily used for Gamma-ray astronomy, enable us
to increase our understanding of the circumstellar environment of a particular
system. When used as optical intensity interferometers, future ACT arrays will
allow us to detect stars as extended objects and image their surfaces at high
angular resolution.
Optical stellar intensity interferometry (SII) with ACT arrays, composed of
nearly 100 telescopes, will provide means to measure fundamental stellar
parameters and also open the possibility of model-independent imaging. A data
analysis algorithm is developed and permits the reconstruction of high angular
resolution images from simulated SII data. The capabilities and limitations of
future ACT arrays used for high angular resolution imaging are investigated via
Monte-Carlo simulations. Simple stellar objects as well as stellar surfaces
with localized hot or cool regions can be accurately imaged.
Finally, experimental efforts to measure intensity correlations are
expounded. The functionality of analog and digital correlators is demonstrated.
Intensity correlations have been measured for a simulated star emitting
pseudo-thermal light, resulting in angular diameter measurements. The StarBase
observatory, consisting of a pair of 3 m telescopes separated by 23 m, is
described.Comment: PhD dissertatio
Traction force microscopy with optimized regularization and automated Bayesian parameter selection for comparing cells
Adherent cells exert traction forces on to their environment, which allows
them to migrate, to maintain tissue integrity, and to form complex
multicellular structures. This traction can be measured in a perturbation-free
manner with traction force microscopy (TFM). In TFM, traction is usually
calculated via the solution of a linear system, which is complicated by
undersampled input data, acquisition noise, and large condition numbers for
some methods. Therefore, standard TFM algorithms either employ data filtering
or regularization. However, these approaches require a manual selection of
filter- or regularization parameters and consequently exhibit a substantial
degree of subjectiveness. This shortcoming is particularly serious when cells
in different conditions are to be compared because optimal noise suppression
needs to be adapted for every situation, which invariably results in systematic
errors. Here, we systematically test the performance of new methods from
computer vision and Bayesian inference for solving the inverse problem in TFM.
We compare two classical schemes, L1- and L2-regularization, with three
previously untested schemes, namely Elastic Net regularization, Proximal
Gradient Lasso, and Proximal Gradient Elastic Net. Overall, we find that
Elastic Net regularization, which combines L1 and L2 regularization,
outperforms all other methods with regard to accuracy of traction
reconstruction. Next, we develop two methods, Bayesian L2 regularization and
Advanced Bayesian L2 regularization, for automatic, optimal L2 regularization.
Using artificial data and experimental data, we show that these methods enable
robust reconstruction of traction without requiring a difficult selection of
regularization parameters specifically for each data set. Thus, Bayesian
methods can mitigate the considerable uncertainty inherent in comparing
cellular traction forces
Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-like Transforms
We propose a novel method for constructing Hilbert transform (HT) pairs of
wavelet bases based on a fundamental approximation-theoretic characterization
of scaling functions--the B-spline factorization theorem. In particular,
starting from well-localized scaling functions, we construct HT pairs of
biorthogonal wavelet bases of L^2(R) by relating the corresponding wavelet
filters via a discrete form of the continuous HT filter. As a concrete
application of this methodology, we identify HT pairs of spline wavelets of a
specific flavor, which are then combined to realize a family of complex
wavelets that resemble the optimally-localized Gabor function for sufficiently
large orders.
Analytic wavelets, derived from the complexification of HT wavelet pairs,
exhibit a one-sided spectrum. Based on the tensor-product of such analytic
wavelets, and, in effect, by appropriately combining four separable
biorthogonal wavelet bases of L^2(R^2), we then discuss a methodology for
constructing 2D directional-selective complex wavelets. In particular,
analogous to the HT correspondence between the components of the 1D
counterpart, we relate the real and imaginary components of these complex
wavelets using a multi-dimensional extension of the HT--the directional HT.
Next, we construct a family of complex spline wavelets that resemble the
directional Gabor functions proposed by Daugman. Finally, we present an
efficient FFT-based filterbank algorithm for implementing the associated
complex wavelet transform.Comment: 36 pages, 8 figure
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