E. Keith Hege

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.

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.

Triple-correlation subplane reconstruction of photon-address stellar images

The performance of a photon-address, subplane implementation of the triple-correlation (TC) algorithm is evaluated for application to near-real-time, stellar speckle imaging at low-light levels. A simple least-squares relaxation algorithm for recovering object phase from the bispectrum is proposed and found to be consistently better than the usual recursive method. Photon-address speckle data from six simulated objects of different degrees of complexity, and from the binary stars β Del and μ Ori, were used in this study. For real-time applications for which computational efficiency is critical, the relaxed two-plane TC algorithm offers excellent performance and rugged-ness with respect to object complexity.

Multiple mirror telescope as a phased array telescope

By adjusting the optical path lengths of its individual beams, it is possible to make the multiple mirror telescope (MMT) into a phased array with a 6.86-m base line. A coherent phased focus can be achieved with tilted focal planes if the tilt angle is chosen so that the internal phase differences exactly compensate the external phase differences. This amounts to a slight change in configuration so that the beams are brought together at f/8.39 rather than the originally designed f/9. We summarize experiments which have used the MMT subapertures as a phased array and as a coherent phased telescope and present a simple analysis of the titled focal plane geometry for coherent observation. The phased operation of the MMT is important not only for obtaining high angular resolution but also for obtaining the higher detection sensitivity which results from the better discrimination against the sky emission background for IR diffraction-limited images. Full-aperture (six-beam) diffraction-limited results for the unresolved source Gama Orionis, the well-known close binary Capella, and the resolved red supergiant Betelgeuse (including a diffraction-limited differential speckle image of the latter) are presented as preliminary demonstration of the potential capabilities of this configuration.

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.

Stretched membrane with electrostatic curvature (SMEC): a new technology for ultralightweight space telescopes

Very large space telescopes with primary mirrors made of flat segments have been recently proposed. The segments would be extremely lightweight, made like pellicles from stretched, reflective membranes. Here we consider the use of such membrane primary mirrors in which slight concave curvature is induced by electrostatic force, by application of a potential difference between the membrane and a control electrode behind. In this way segmented spherical or paraboloidal primaries of long focal length can be made directly, eliminating the correction optics needed when flat segments are used. The electric potential would be spatially and temporally controlled to obtain uniform curvature despite non-uniformity in membrane tension, to create slight asphericity if needed and to provide active damping of vibrations. We report the operation of a small prototype telescope with a SEMC primary.

Self-calibrating shift-and-add technique for speckle imaging

An image-reconstruction technique for astronomical speckle interferometric data is described. This variant of the shift-and-add algorithm originally developed by Lynds et al. [ Astrophys. J.207, 174 ( 1976)] utilizes a weighted impulse distribution of speckle positions to extract an average speckle for a data set. This is done by means of a weighted deconvolution procedure, similar in form to a Weiner filter, which deconvolves the specklegram by the impulse distribution. Results show that this method appears to be self-calibrating for seeing effects. It yields point-spread functions, for observations of an unresolved star, that compare quantitatively with computed Airy patterns for both simple apertures and the fully phased multiple mirror telescope array. Images of the resolved object Alpha Orionis show evidence of an extended stellar envelope.

Wave-front sensing with time-of-flight phase diversity.

We present a new way to sense atmospheric wave-front phase distortion. Short collimated pulses of laser light at ~350nm are projected from a small auxilliary telescope. Rayleigh scattering from each pulse is recorded over a wide range of height through the main telescope aperture in a continuous sequence of fast video frames by a detector conjugate to mid-height. Phase diversity is thus naturally introduced as the pulses approach and pass through focus. We show that an iterative algorithm can extract the phase structure from the recorded images and do so with a much higher signal-to-noise ratio than is possible with existing techniques. If the requirements for real-time data recording and reduction can be met, the new method will address the need for tomographic wave-front sensing at planned 30-m-class telescopes.

Evaluations of classification and spectral unmixing algorithms using ground based satellite imaging

Abundances of material components in objects are usually computed using techniques such as linear spectral unmixing on individual pixels captured on hyperspectral imaging devices. However, algorithms such as unmixing have many flaws, some due to implementation, and others due to improper choices of the spectral library used in the unmixing (as well as classification). There may exist other methods for extraction of this hyperspectral abundance information. We propose the development of spatial ground truth data from which various unmixing algorithm analyses can be evaluated. This may be done by implementing a three-dimensional hyperpspectral discrete wavelet transform (HSDWT) with a low-complexity lifting method using the Haar basis. Spectral unmixing, or similar algorithms can then be evaluated, and their effectiveness can be measured by how well or poorly the spatial and spectral characteristics of the target are reproduced at full resolution (which becomes single object classification by pixel).

Speckle deconvolution imaging using an iterative algorithm

We present an application of an iterative deconvolution algorithm to speckle interferometric data. This blind deconvolution algorithm permits the recovery of the target distribution when the point spread function is either unknown or poorly known. The algorithm is applied to specklegrams of the multiple star systems, and the results for (zetz) UMa are compared to shift-and-add results for the same data. The linearity of the algorithm is demonstrated and the signal-to-noise ratio of the reconstruction is shown to grow as the square root of the number of specklegrams used. This algorithm does not require the use of an unresolved target for point spread function calibration.