16,115 research outputs found
Non-Convex Phase Retrieval from STFT Measurements
The problem of recovering a one-dimensional signal from its Fourier transform
magnitude, called Fourier phase retrieval, is ill-posed in most cases. We
consider the closely-related problem of recovering a signal from its phaseless
short-time Fourier transform (STFT) measurements. This problem arises naturally
in several applications, such as ultra-short laser pulse characterization and
ptychography. The redundancy offered by the STFT enables unique recovery under
mild conditions. We show that in some cases the unique solution can be obtained
by the principal eigenvector of a matrix, constructed as the solution of a
simple least-squares problem. When these conditions are not met, we suggest
using the principal eigenvector of this matrix to initialize non-convex local
optimization algorithms and propose two such methods. The first is based on
minimizing the empirical risk loss function, while the second maximizes a
quadratic function on the manifold of phases. We prove that under appropriate
conditions, the proposed initialization is close to the underlying signal. We
then analyze the geometry of the empirical risk loss function and show
numerically that both gradient algorithms converge to the underlying signal
even with small redundancy in the measurements. In addition, the algorithms are
robust to noise
Compensation for the setup instability in ptychographic imaging
The high-frequency vibration of the imaging system degrades the quality of
the reconstruction of ptychography by acting as a low-pass filter on ideal
diffraction patterns. In this study, we demonstrate that by subtracting the
deliberately blurred diffraction patterns from the recorded patterns and adding
the properly amplified subtraction to the original data, the high-frequency
components lost by the vibration of the setup can be recovered, and thus the
image quality can be distinctly improved. Because no prior knowledge regarding
the vibrating properties of the imaging system is needed, the proposed method
is general and simple and has applications in several research fields.Comment: 13pages, 10figure
Atmospheric hydroxyl radical (OH) abundances from ground-based ultraviolet solar spectra: an improved retrieval method
The Fourier Transform Ultraviolet Spectrometer (FTUVS) instrument has recorded a long-term data record of the atmospheric column abundance of the hydroxyl radical (OH) using the technique of high resolution solar absorption spectroscopy. We report new efforts in improving the precision of the OH measurements in order to better model the diurnal, seasonal, and interannual variability of odd hydrogen (HOx) chemistry in the stratosphere, which, in turn, will improve our understanding of ozone chemistry and its long-term changes. Until the present, the retrieval method has used a single strong OH absorption line P1(1) in the near-ultraviolet at 32,341 cm−1. We describe a new method that uses an average based on spectral fits to multiple lines weighted by line strength and fitting precision. We have also made a number of improvements in the ability to fit a model to the spectral feature, which substantially reduces the scatter in the measurements of OH abundances
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
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