Parameter dimension of turbulence-induced phase errors and its effects on estimation in phase diversity

The method of phase diversity has been used in the context of incoherent imaging to estimate jointly an object that is being imaged and phase aberrations induced by atmospheric turbulence. The method requires a parametric model for the phase-aberration function. Typically, the parameters are coefficients to a finite set of basis functions. Care must be taken in selecting a parameterization that properly balances accuracy in the representation of the phase-aberration function with stability in the estimates. It is well known that over parameterization can result in unstable estimates. Thus a certain amount of model mismatch is often desirable. We derive expressions that quantify the bias and variance in object and aberration estimates as a function of parameter dimension

Joint Estimation of Stokes Images and Aberrations from Phase-Diverse Polarimetric Measurements

The technique of phase diversity has been used in traditional incoherent imaging systems to jointly estimate an object and optical system aberrations. This paper extends the technique of phase diversity to polarimetric imaging systems. Specifically, we describe penalized-likelihood methods for jointly estimating Stokes images and optical system aberrations from measurements that contain phase diversity. Jointly estimating Stokes images and optical system aberrations involves a large parameter space. A closed-form expression for the estimate of the Stokes images in terms of the aberration parameters is derived and used in a formulation that reduces the dimensionality of the search space to the number of aberration parameters only. We compare the performance of the joint estimator under both quadratic and edge-preserving regularization; we also compare the performance of the reduced parameter search strategy to the full parameter search strategy under quadratic regularization. The joint estimator with edge-preserving regularization yields higher fidelity polarization estimates than with quadratic regularization. With the reduced parameter search strategy, accurate aberration estimates can be obtained without recourse to regularization “tuning.”Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85915/1/Fessler9.pd

Evaluation of phase-diversity techniques for solar-image restoration

Phase-diversity techniques provide a novel observational method for overcomming the effects of turbulence and instrument-induced aberrations in ground-based astronomy. Two implementations of phase-diversity techniques that differ with regard to noise model, estimator, optimization algorithm, method of regularization, and treatment of edge effects are described. Reconstructions of solar granulation derived by applying these two implementations to common data sets are shown to yield nearly identical images. For both implementations, reconstructions from phase-diverse speckle data (involving multiple realizations of turbulence) are shown to be superior to those derived from conventional phase-diversity data (involving a single realization). Phase-diverse speckle reconstructions are shown to achieve near diffraction-limited resolution and are validated by internal and external consistency tests, including a comparison with a reconstruction using a well-accepted speckle-imaging method

Space object identification using phase-diverse speckle

Space-object identification from ground-based telescopes is challenging because of the degradation in resolution arising from atmospheric turbulence. Phase-diverse speckle is a novel post-detection correction method that can be used to overcome turbulence-induced aberrations for telescopes with or without adaptive optics. We present a simulation study of phase-diverse speckle satellite reconstructions for the Air Force Maui Optical station 1.6-meter telescope. For a given turbulence strength, satellite reconstruction fidelity is evaluated as a function of quality and quantity of data. The credibility of this study is enhanced by reconstructions from actual compensated data collected with the 1.5-meter telescope at the Starfire Optical Range. Consistent details observed across a time series of reconstructions from a portion of a satellite pass enhance the authenticity of these features. We conclude that phase-diverse speckle can restore fine-resolution features not apparent in the raw aberrated images of space objects

Space object identification using phase-diverse speckle

Space-object identification from ground-based telescopes is challenging because of the degradation in resolution arising from atmospheric turbulence. Phase-diverse speckle is a novel post-detection correction method that can be used to overcome turbulence-induced aberrations for telescopes with or without adaptive optics. We present a simulation study of phase-diverse speckle satellite reconstructions for the Air Force Maui Optical station 1.6-meter telescope. For a given turbulence strength, satellite reconstruction fidelity is evaluated as a function of quality and quantity of data. The credibility of this study is enhanced by reconstructions from actual compensated data collected with the 1.5-meter telescope at the Starfire Optical Range. Consistent details observed across a time series of reconstructions from a portion of a satellite pass enhance the authenticity of these features. We conclude that phase-diverse speckle can restore fine-resolution features not apparent in the raw aberrated images of space objects

Multi-messenger observations of a binary neutron star merger

On 2017 August 17 a binary neutron star coalescence candidate (later designated GW170817) with merger time 12:41:04 UTC was observed through gravitational waves by the Advanced LIGO and Advanced Virgo detectors. The Fermi Gamma-ray Burst Monitor independently detected a gamma-ray burst (GRB 170817A) with a time delay of ~1.7 s with respect to the merger time. From the gravitational-wave signal, the source was initially localized to a sky region of 31 deg2 at a luminosity distance of 40+8-8 Mpc and with component masses consistent with neutron stars. The component masses were later measured to be in the range 0.86 to 2.26 Mo. An extensive observing campaign was launched across the electromagnetic spectrum leading to the discovery of a bright optical transient (SSS17a, now with the IAU identification of AT 2017gfo) in NGC 4993 (at ~40 Mpc) less than 11 hours after the merger by the One- Meter, Two Hemisphere (1M2H) team using the 1 m Swope Telescope. The optical transient was independently detected by multiple teams within an hour. Subsequent observations targeted the object and its environment. Early ultraviolet observations revealed a blue transient that faded within 48 hours. Optical and infrared observations showed a redward evolution over ~10 days. Following early non-detections, X-ray and radio emission were discovered at the transient’s position ~9 and ~16 days, respectively, after the merger. Both the X-ray and radio emission likely arise from a physical process that is distinct from the one that generates the UV/optical/near-infrared emission. No ultra-high-energy gamma-rays and no neutrino candidates consistent with the source were found in follow-up searches. These observations support the hypothesis that GW170817 was produced by the merger of two neutron stars in NGC4993 followed by a short gamma-ray burst (GRB 170817A) and a kilonova/macronova powered by the radioactive decay of r-process nuclei synthesized in the ejecta

Piston alignment for a segmented-aperture imaging system by using piston-sweep phasing

This Letter presents a novel method for aligning the piston settings for a segmented-aperture imaging system. By sweeping the piston setting for a reference segment, a stack of images can be acquired that encodes information about the relative piston alignment for all segments in the system. We also demonstrate how a matched-filter processing method can be used to estimate the relative piston settings to align the imaging system at its full resolution