The Ionospheric Connection Explorer - Prime Mission Review.

The two-year prime mission of the NASA Ionospheric Connection Explorer (ICON) is complete. The baseline operational and scientific objectives have been met and exceeded, as detailed in this report. In October of 2019, ICON was launched into an orbit that provides its instruments the capability to deliver near-continuous measurements of the densest plasma in Earth's space environment. Through collection of a key set of in-situ and remote sensing measurements that are, by virtue of a detailed mission design, uniquely synergistic, ICON enables completely new investigations of the mechanisms that control the behavior of the ionosphere-thermosphere system under both geomagnetically quiet and active conditions. In a two-year period that included a deep solar minimum, ICON has elucidated a number of remarkable effects in the ionosphere attributable to energetic inputs from the lower and middle atmosphere, and shown how these are transmitted from the edge of space to the peak of plasma density above. The observatory operated in a period of low activity for 2 years and then for a year with increasing solar activity, observing the changing balance of the impacts of lower and upper atmospheric drivers on the ionosphere.

Inferring Nighttime Ionospheric Parameters With the Far Ultraviolet Imager Onboard the Ionospheric Connection Explorer.

The Ionospheric Connection Explorer (ICON) Far Ultraviolet (FUV) imager, ICON FUV, will measure altitude profiles of OI 135.6 nm emissions to infer nighttime ionospheric parameters. Accurate estimation of the ionospheric state requires the development of a comprehensive radiative transfer model from first principles to quantify the effects of physical processes on the production and transport of the 135.6 nm photons in the ionosphere including the mutual neutralization contribution as well as the effect of resonant scattering by atomic oxygen and pure absorption by oxygen molecules. This forward model is then used in conjunction with a constrained optimization algorithm to invert the anticipated ICON FUV line-of-sight integrated measurements. In this paper, we describe the connection between ICON FUV measurements and the nighttime ionosphere, along with the approach to inverting the measured emission profiles to derive the associated O+ profiles from 150-450 km in the nighttime ionosphere that directly reflect the electron density in the F-region of the ionosphere.

Analytical Fresnel imaging models for photon sieves.

Photon sieves are a fairly new class of diffractive lenses that open unprecedented possibilities for high resolution imaging and spectroscopy, especially at short wavelengths such as UV and x-rays. In this paper, we model and analyze the image formation process of photon sieves using Fourier optics. We derive closed-form Fresnel imaging models that relate an input object to the image formed by a photon sieve system, both for coherent and incoherent illumination. These analytical models also provide a closed-form expression for the point-spread function of the system for both in-focus and out-of-focus cases. All the formulas are expressed in terms of Fourier transforms and convolutions, which enable easy interpretation as well as fast computation. The derived analytical models provide a unified framework to effectively develop new imaging modalities enabled by diffractive lenses and analyze their imaging capabilities for different design configurations, prior to physical production. To illustrate their utility and versatility, the derived formulas are applied to several important special cases such as photon sieves with circular holes and pixelated diffractive lenses generated by SLM-type devices. The analytical image formation models presented in this paper provide a generalizable and powerful means for effective analysis and simulation of any imaging system with a diffractive lens, including Fresnel zone plates, Fresnel phase plates, and other modified Fresnel lenses and mask-like patterns such as coded apertures.

Tactile soft-sparse mean fluid-flow imaging with a robotic whisker array.

An array of whiskers is critical to many mammals to survive in their environment. However, current engineered systems generally employ vision, radar or sonar to explore the surroundings, not having sufficiently benefited from tactile perception. Inspired by the whisking animals, we present here a novel tomography-based tactile fluid-flow imaging technique for the reconstruction of surroundings with an artificial whisker array. The moment sensed at the whisker base is the weighted integral of the drag force per length, which is proportional to the relative velocity squared on a whisker segment. We demonstrate that the 2D cross-sectional mean fluid-flow velocity-field can be successfully mapped out by collecting moment measurements at different angular positions with the whisker array. We use a regularized version of the FOCal underdetermined system solver algorithm with a smoothness constraint to obtain soft-sparse static estimates of the 2D cross-sectional velocity-squared distribution. This new proposed approach has the strong potential to be an alternative environmental sensing technology, particularly in dark or murky environments.

A parametric estimation approach to instantaneous spectral imaging.

Spectral imaging, the simultaneous imaging and spectroscopy of a radiating scene, is a fundamental diagnostic technique in the physical sciences with widespread application. Due to the intrinsic limitation of two-dimensional (2D) detectors in capturing inherently three-dimensional (3D) data, spectral imaging techniques conventionally rely on a spatial or spectral scanning process, which renders them unsuitable for dynamic scenes. In this paper, we present a nonscanning (instantaneous) spectral imaging technique that estimates the physical parameters of interest by combining measurements with a parametric model and solving the resultant inverse problem computationally. The associated inverse problem, which can be viewed as a multiframe semiblind deblurring problem (with shift-variant blur), is formulated as a maximum a posteriori (MAP) estimation problem since in many such experiments prior statistical knowledge of the physical parameters can be well estimated. Subsequently, an efficient dynamic programming algorithm is developed to find the global optimum of the nonconvex MAP problem. Finally, the algorithm and the effectiveness of the spectral imaging technique are illustrated for an application in solar spectral imaging. Numerical simulation results indicate that the physical parameters can be estimated with the same order of accuracy as state-of-the-art slit spectroscopy but with the added benefit of an instantaneous, 2D field-of-view. This technique will be particularly useful for studying the spectra of dynamic scenes encountered in space remote sensing.

Uncertainties in extracted parameters of a Gaussian emission line profile with continuum background.

We derive analytical equations for uncertainties in parameters extracted by nonlinear least-squares fitting of a Gaussian emission function with an unknown continuum background component in the presence of additive white Gaussian noise. The derivation is based on the inversion of the full curvature matrix (equivalent to Fisher information matrix) of the least-squares error, chi(2), in a four-variable fitting parameter space. The derived uncertainty formulas (equivalent to Cramer-Rao error bounds) are found to be in good agreement with the numerically computed uncertainties from a large ensemble of simulated measurements. The derived formulas can be used for estimating minimum achievable errors for a given signal-to-noise ratio and for investigating some aspects of measurement setup trade-offs and optimization. While the intended application is Fabry-Perot spectroscopy for wind and temperature measurements in the upper atmosphere, the derivation is generic and applicable to other spectroscopy problems with a Gaussian line shape.

Tomographic imaging of dynamic objects with the ensemble Kalman filter.

We address the image formation of a dynamic object from projections by formulating it as a state estimation problem. The problem is solved with the ensemble Kalman filter (EnKF), a Monte Carlo algorithm that is computationally tractable when the state dimension is large. In this paper, we first rigorously address the convergence of the EnKF. Then, the effectiveness of the EnKF is demonstrated in a numerical experiment where a highly variable object is reconstructed from its projections, an imaging modality not yet explored with the EnKF. The results show that the EnKF can yield estimates of almost equal quality as the optimal Kalman filter but at a fraction of the computational effort. Further experiments explore the rate of convergence of the EnKF, its performance relative to an idealized particle filter, and implications of modeling the system dynamics as a random walk.

Tomographic imaging of airglow from airborne spectroscopic measurements.

A description is given of the methodology based on a single, aircraft-mounted spectroscopic imager to tomographically reconstruct airglow perturbations induced by atmospheric gravity waves. In this configuration, the imager passes under the airglow structure to gather multiple-angle views of the wave structure in a relatively short amount of time. Under the assumption that the airglow structure does not change significantly during the acquisition interval, the data can be tomographically inverted to estimate the 2D (horizontal-vertical) airglow structure. We develop an inversion strategy for this image formation task and illustrate its applicability by inverting time-sequential imaging data taken from different vantage points during the ALOHA-93 campaign to reconstruct atmospheric gravity wave structures.

Optimal sensor array configuration in remote image formation.

Determination of optimal sensor configuration is an important issue in many remote imaging modalities, such as tomographic and interferometric imaging. In this paper, a statistical optimality criterion is defined and a search is performed over the space of candidate sensor locations to determine the configuration that optimizes the criterion over all candidates. To make the search process computationally feasible, a modified version of a previously proposed suboptimal backward greedy algorithm is used. A statistical framework is developed which allows for inclusion of several widely used image constraints. Computational complexity of the proposed algorithm is discussed and a fast implementation is described. Furthermore, upper bounds on the sum of the squared error of the proposed algorithm are derived. Connections of the method to the deterministic backward greedy algorithm for the subset selection problem are presented, and two application examples are described. Five compelling optimality criteria are considered, and their performance is investigated through numerical experiments for a tomographic imaging scenario. In all cases, it is verified that the configuration designed by the proposed algorithm performs better than wisely chosen alternatives.

A regularized inverse approach to ultrasonic pulse-echo imaging.

An inverse-theoretic approach to ultrasonic pulse-echo imaging based on nonquadratic regularization is presented, and its effectiveness is investigated computationally by: 1) evaluating the quality of the reconstruction of speckle-based images as a function of the transmit-receive bandwidth and focal number of the transducer; 2) comparing the reconstructed images with those obtained by using conventional B-mode imaging. The L-curve and the generalized cross-validation methods were evaluated as automatic regularization parameter selection techniques. The inversion using regularization produced better results than conventional B-mode imaging for high signal-to-noise ratios (SNRs). A lower bound of 30 dB for the SNR was found for this study, below which several of the image features were lost during the reconstruction process in order to control the distortion due to the noise.

Asymptotically optimal blind estimation of multichannel images.

Optimal estimation of a two-dimensional (2-D) multichannel signal ideally decorrelates the data in both channel and space and weights the resulting coefficients according to their SNR. Many scenarios exist where the required second-order signal and noise statistics are not known in which the decorrelation is difficult or expensive to calculate. An asymptotically optimal estimation scheme proposed here uses a 2-D discrete wavelet transform to approximately decorrelate the signal in space and the discrete Fourier transform to decorrelate between channels. The coefficient weighting is replaced with a wavelet-domain thresholding operation to result in an efficient estimation scheme for both stationary and nonstationary signals. In contrast to optimal estimation, this new scheme does not require second-order signal statistics, making it well suited to many applications. In addition to providing vastly improved visual quality, the new estimator typically yields signal-to-noise ratio gains 12 dB or higher for hyperspectral imagery and functional magnetic resonance images.

Deconvolution methods for mitigation of transverse blurring in optical coherence tomography.

Imaging resolution in optical coherence tomography (OCT) is a key determinant for acquiring clinically useful optical biopsies of tissues. In contrast to light or confocal microscopy, the axial and transverse resolutions in OCT are independent and each can be analyzed individually. A method for mitigating transverse blurring and the apparent loss of transverse resolution in OCT by means of Gaussian beam deconvolution is presented. Such a method provides better representation of a specimen by using known physical parameters of a lens. To implement this method, deconvolution algorithms based on a focal-dependent kernel are investigated. First, the direct inverse problem is investigated using two types of regularization, truncated singular value decomposition, and Tikhonov. Second, an iterative expectation maximization algorithm, the Richardson-Lucy algorithm, with a beam-width-dependent iteration scheme is developed. A dynamically iterative Richardson-Lucy algorithm can reduce transverse blurring by providing an improvement in the transverse point-spread-function for sparse scattering samples in regions up to two times larger than the confocal region of the lens. These deblurring improvements inside and outside of the confocal region, which are validated experimentally, are possible without introducing new optical imaging hardware or acquiring multiple images of the same specimen. Implementation of this method in sparse scattering specimens, such as engineered tissues, has the potential to improve cellular detection and categorization.

Comparative performance analysis of time-frequency distributions for spectroscopic optical coherence tomography.

The analysis of spectroscopic optical coherence tomography (SOCT) signals suffers the trade-off between time resolution and frequency resolution. Various joint time-frequency distributions (TFDs) can optimize this trade-off. Synthesized signals were generated and experimentally acquired data were obtained to compare and validate several different TFDs under different SOCT imaging schemes. Specific criteria were designed to quantify the TFD performance. We found that different SOCT imaging schemes require different optimal TFDs. Cohen's class TFDs generate the most compact time-frequency (TF) analysis, while linear TFDs offer the most reliable TF analysis. In both cases, if some prior information is known, model-based TF analysis can improve the performance.