A new method for detecting solar atmospheric gravity waves.

Internal gravity waves have been observed in the Earth's atmosphere and oceans, on Mars and Jupiter, and in the Sun's atmosphere. Despite ample evidence for the existence of propagating gravity waves in the Sun's atmosphere, we still do not have a full understanding of their characteristics and overall role for the dynamics and energetics of the solar atmosphere. Here, we present a new approach to study the propagation of gravity waves in the solar atmosphere. It is based on calculating the three-dimensional cross-correlation function between the vertical velocities measured at different heights. We apply this new method to a time series of co-spatial and co-temporal Doppler images obtained by SOHO/MDI and Hinode/SOT as well as to simulations of upward propagating gravity wave-packets. We show some preliminary results and outline future developments. This article is part of the Theo Murphy meeting issue 'High-resolution wave dynamics in the lower solar atmosphere'.

Atmospheric tomography for artificial satellite observations with a single guide star.

Estimation of wavefront errors in three dimensions is required to mitigate isoplanatic errors when using adaptive optics or numerical restoration algorithms to recover high-resolution images from blurred data taken through atmospheric turbulence. Present techniques rely on multiple beacons, either natural stars or laser guide stars, to probe the atmospheric aberration along different lines of sight, followed by tomographic projection of the measurements. In this Letter, we show that a three-dimensional estimate of the wavefront aberration can be recovered from measurements by a single guide star in the case where the aberration is stratified, provided that the telescope tracks across the sky with nonuniform angular velocity. This is generally the case for observations of artificial Earth-orbiting satellites, and the new method is likely to find application in ground-based telescopes used for space situational awareness.

High-resolution speckle imaging through strong atmospheric turbulence.

We demonstrate that high-resolution imaging through strong atmospheric turbulence can be achieved by acquiring data with a system that captures short exposure ("speckle") images using a range of aperture sizes and then using a bootstrap multi-frame blind deconvolution restoration process that starts with the smallest aperture data. Our results suggest a potential paradigm shift in how we image through atmospheric turbulence. No longer should image acquisition and post processing be treated as two independent processes: they should be considered as intimately related.

Deconvolution from wave front sensing using the frozen flow hypothesis.

Deconvolution from wave front sensing (DWFS) is an image-reconstruction technique for compensating the image degradation due to atmospheric turbulence. DWFS requires the simultaneous recording of high cadence short-exposure images and wave-front sensor (WFS) data. A deconvolution algorithm is then used to estimate both the target object and the wave front phases from the images, subject to constraints imposed by the WFS data and a model of the optical system. Here we show that by capturing the inherent temporal correlations present in the consecutive wave fronts, using the frozen flow hypothesis (FFH) during the modeling, high-quality object estimates may be recovered in much worse conditions than when the correlations are ignored.

Compact multiframe blind deconvolution.

We describe a multiframe blind deconvolution (MFBD) algorithm that uses spectral ratios (the ratio of the Fourier spectra of two data frames) to model the inherent temporal signatures encoded by the observed images. In addition, by focusing on the separation of the object spectrum and system transfer functions only at spatial frequencies where the measured signal is above the noise level, we significantly reduce the number of unknowns to be determined. This "compact" MFBD yields high-quality restorations in a much shorter time than is achieved with MFBD algorithms that do not model the temporal signatures; it may also provide higher-fidelity solutions.

Fast and optimal multiframe blind deconvolution algorithm for high-resolution ground-based imaging of space objects.

We report a multiframe blind deconvolution algorithm that we have developed for imaging through the atmosphere. The algorithm has been parallelized to a significant degree for execution on high-performance computers, with an emphasis on distributed-memory systems so that it can be hosted on commodity clusters. As a result, image restorations can be obtained in seconds to minutes. We have compared and quantified the quality of its image restorations relative to the associated Cramér-Rao lower bounds (when they can be calculated). We describe the algorithm and its parallelization in detail, demonstrate the scalability of its parallelization across distributed-memory computer nodes, discuss the results of comparing sample variances of its output to the associated Cramér-Rao lower bounds, and present image restorations obtained by using data collected with ground-based telescopes.

A computational method for the restoration of images with an unknown, spatially-varying blur.

In this paper, we present an algorithm for the restoration of images with an unknown, spatially-varying blur. Existing computational methods for image restoration require the assumption that the blur is known and/or spatially-invariant. Our algorithm uses a combination of techniques. First, we section the image, and then treat the sections as a sequence of frames whose unknown PSFs are correlated and approximately spatially-invariant. To estimate the PSFs in each section, phase diversity is used. With the PSF estimates in hand, we then use a technique by Nagy and O'Leary for the restoration of images with a known, spatially-varying blur to restore the image globally. Test results on star cluster data are presented.

Sensing wave-front amplitude and phase with phase diversity.

We show in benchtop experiments that wave-front phase estimation by phase diversity can be significantly improved by simultaneous amplitude estimation. Processing speed, which will be important for real-time wave-front control applications, can be enhanced by use of small-format detectors with pixels that do not fully sample the diffraction limit. Using an object-independent phase-diversity algorithm, we show that, for both pointlike and extended objects, the fidelity of the phase and amplitude estimates degrades gracefully, rather than catastrophically, as the sampling becomes coarser. We show in simulation that the same algorithm also improves the fidelity of image reconstruction of complex targets.

Blind deconvolution in optical diffusion tomography.

We use blind deconvolution methods in optical diffusion tomography to reconstruct images of objects imbedded in or located behind turbid media from continuous-wave measurements of the scattered light transmitted through the media. In particular, we use a blind deconvolution imaging algorithm to determine both a deblurred image of the object and the depth of the object inside the turbid medium. Preliminary results indicate that blind deconvolution produces better reconstructions than can be obtained using backpropagation techniques. Moreover, it does so without requiring prior knowledge of the characteristics of the turbid medium or of what the blur-free target should look like: important advances over backpropagation.