Penalized least-squares for imaging with hypertelescopes.

Practical considerations such as cost constrain the aperture size of conventional telescopes, which, combined with atmospheric turbulence effects, even in the presence of adaptive optics, limit achievable angular resolution. Sparse aperture telescopes represent a viable alternative for achieving improved angular resolution by combining light collected from small apertures distributed over a wide spatial area either using amplitude interferometry or a direct imaging approach to beam-combining. The so-called densified hypertelescope imaging concept in particular provides a methodology for direct image formation from large sparse aperture arrays. The densification system suppresses wide-angle side lobes and concentrates that energy in the center of the focal plane, significantly improving the signal-to-noise ratio of the measurement. Even with densification, an inevitable consequence of sparse aperture sampling is that the point-spread function associated with the direct image contains an additional structure not present in full aperture imaging systems. Postdetection image reconstruction is performed here to compute a high-fidelity estimate of the measured object in the presence of noise. In this paper, we describe a penalized least-squares object-estimation approach and compare the results with the classical Richardson-Lucy deconvolution algorithm as it is applied to hypertelescope image formation. The parameters of the algorithm are selected based on a comprehensive simulation study using the structure similarity metric to assess reconstruction performance. We find that the penalized least-squares formulation with optimized parameters provides significantly improved reconstructions compared with the conventional Richardson-Lucy algorithm.

Atmospheric turbulence characterization through multiframe blind deconvolution.

Characterization of turbulence in the atmosphere and mitigation of its effects in optical systems are important capabilities in both commercial and military applications. We present an image processing approach that jointly characterizes the magnitude of turbulence in the atmosphere and mitigates the adverse effects imposed on optical imaging systems. The magnitude of turbulence is measured indirectly through a series of image frames in terms of the atmospheric coherence length. We believe the results demonstrate the utility of the approach on both simulated and experimental data.

Target Localization and Tracking by Fusing Doppler Differentials from Cellular Emanations with a Multi-Spectral Video Tracker.

We present an algorithm for fusing data from a constellation of RF sensors detecting cellular emanations with the output of a multi-spectral video tracker to localize and track a target with a specific cell phone. The RF sensors measure the Doppler shift caused by the moving cellular emanation and then Doppler differentials between all sensor pairs are calculated. The multi-spectral video tracker uses a Gaussian mixture model to detect foreground targets and SIFT features to track targets through the video sequence. The data is fused by associating the Doppler differential from the RF sensors with the theoretical Doppler differential computed from the multi-spectral tracker output. The absolute difference and the root-mean-square difference are computed to associate the Doppler differentials from the two sensor systems. Performance of the algorithm was evaluated using synthetically generated datasets of an urban scene with multiple moving vehicles. The presented fusion algorithm correctly associates the cellular emanation with the corresponding video target for low measurement uncertainty and in the presence of favorable motion patterns. For nearly all objects the fusion algorithm has high confidence in associating the emanation with the correct multi-spectral target from the most probable background target.

Multi-spectral image shift-estimation error calculations using simulated phenomenology.

Registration of multi-spectral imagery is a critical pre-processing step for applications such as image fusion, but phenomenological differences between spectral bands can lead to significant estimation errors. To develop credible requirements for multi-spectral imaging systems, it is critical to characterize errors, both algorithmic and fundamental, associated with estimating registration parameters; however, attempting to quantify error using archival data sets poses a number of problems. In this paper, we demonstrate the use of commercially available graphics software and available optical property measurements to create fully synthetic, multi-spectral imagery with high-fidelity representations of emissive and reflective phenomenology. We discuss and demonstrate techniques needed to quantify error for both area- and feature-based algorithms. We further show that such synthetic data sets can be used to quantify both the Fisher information and sample errors associated with estimation of the shift between images acquired in different spectral bands and, by extension, estimation of registration model parameters. With the flexibility offered by synthetic data, such characterization can be obtained for robust domains of image brightness, sensor parameters, and differences in image phenomenology.

Anisotropic non-Kolmogorov turbulence phase screens with variable orientation.

We describe a modification to fast Fourier transform (FFT)-based, subharmonic, phase screen generation techniques that accounts for non-Kolmogorov and anisotropic turbulence. Our model also allows for the angle of anisotropy to vary in the plane orthogonal to the direction of propagation. In addition, turbulence strength in our model is specified via a characteristic length equivalent to the Fried parameter in isotropic, Kolmogorov turbulence. Incorporating this feature enables comparison between propagating scenarios with differing anisotropies and power-law exponents to the standard Kolmogorov, isotropic model. We show that the accuracy of this technique is comparable to other FFT-based subharmonic methods up to three-dimensional spectral power-law exponents around 3.9.

Detailed effects of scattering and absorption by haze and aerosols in the atmosphere on the average point spread function of an imaging system.

The Earth's atmosphere has significant effects on the propagation of electromagnetic (EM) radiation and accordingly degrades the performance of electro-optical systems. These effects are attributed to atmospheric turbulence and to absorption and scattering of EM waves by atmospheric molecules and aerosols. In this paper we develop a detailed model of the effects of absorption and scattering on the optical radiation propagating from the object plane to an imaging system based on the classical theory of EM scattering. Scattering has the effect of de-correlating the light leaving the target from the unscattered light reaching the imaging system, and scattering has the effect of broadening the angle at which the scattered light arrives at the receiver compared to the unscattered light. Absorption has the effect of reducing the amount of power available for the image. Both of these effects depend upon the atmospheric species present, their EM properties, and wavelength. We use this detailed model to compute the average point spread function (PSF) of an imaging system that properly accounts for the effects of the diffraction and scattering, and the appropriate optical power level of both the unscattered and the scattered radiation arriving at the pupil of the imaging system. Since the scattered radiation is temporally and spatially de-correlated from the unscattered radiation, we model the effects of the unscattered radiation and the radiation scattered from the various species as additive in the image plane. The key result of this study is the significant effect of atmospheric scattering on the contrast and spatial resolution of images acquired by imaging systems, due to the increased level of the scattered radiation PSF and the reduced level of the direct radiation PSF, upon increasing the atmospheric optical depth.

Monitoring the statistics of turbulence: Fried parameter estimation from the wavefront sensor measurements.

Near-the-ground laser communication systems must operate in the presence of strong atmospheric turbulence. The effects of atmospheric turbulence on the laser beam that are relevant to optical communications are a broadening of the laser footprint, random jitter of the laser beam, and high spatial frequency intensity fluctuations referred to as scintillation. The overall goal of our program is to improve the performance and extend the range of optical communications systems by exploring the use of adaptive optics and channel coding. Knowledge of the turbulence conditions and the ability to describe its properties are the key aspects to make these improvements effective. The developed multiphase approach is directed to statistically describe atmospheric turbulence based on results derived from experimentally collected data. Statistics of Fried parameter r(0) is derived from 6 TB of data collected over 50 days, and under various day and night atmospheric conditions. Significant fluctuations of r(0) are found with the values ranging from 2 mm and up to 15 cm, corresponding to the significant structure function Cn2 fluctuations from 7.4×10(-14) to 8.1×10(-16).

Probability density of aperture-averaged irradiance fluctuations for long range free space optical communication links.

The probability density function (PDF) of aperture-averaged irradiance fluctuations is calculated from wave-optics simulations of a laser after propagating through atmospheric turbulence to investigate the evolution of the distribution as the aperture diameter is increased. The simulation data distribution is compared to theoretical gamma-gamma and lognormal PDF models under a variety of scintillation regimes from weak to strong. Results show that under weak scintillation conditions both the gamma-gamma and lognormal PDF models provide a good fit to the simulation data for all aperture sizes studied. Our results indicate that in moderate scintillation the gamma-gamma PDF provides a better fit to the simulation data than the lognormal PDF for all aperture sizes studied. In the strong scintillation regime, the simulation data distribution is gamma gamma for aperture sizes much smaller than the coherence radius rho0 and lognormal for aperture sizes on the order of rho0 and larger. Examples of how these results affect the bit-error rate of an on-off keyed free space optical communication link are presented.

Digital simulation of scalar optical diffraction: revisiting chirp function sampling criteria and consequences.

Accurate simulation of scalar optical diffraction requires consideration of the sampling requirement for the phase chirp function that appears in the Fresnel diffraction expression. We describe three sampling regimes for FFT-based propagation approaches: ideally sampled, oversampled, and undersampled. Ideal sampling, where the chirp and its FFT both have values that match analytic chirp expressions, usually provides the most accurate results but can be difficult to realize in practical simulations. Under- or oversampling leads to a reduction in the available source plane support size, the available source bandwidth, or the available observation support size, depending on the approach and simulation scenario. We discuss three Fresnel propagation approaches: the impulse response/transfer function (angular spectrum) method, the single FFT (direct) method, and the two-step method. With illustrations and simulation examples we show the form of the sampled chirp functions and their discrete transforms, common relationships between the three methods under ideal sampling conditions, and define conditions and consequences to be considered when using nonideal sampling. The analysis is extended to describe the sampling limitations for the more exact Rayleigh-Sommerfeld diffraction solution.

Bootstrap beacon creation for overcoming the effects of beacon anisoplanatism in a laser beam projection system.

We address the problem of using adaptive optics to deliver power from an airborne laser platform to a ground target through atmospheric turbulence under conditions of strong scintillation and anisoplanatism. We explore three options for creating a beacon for use in adaptive optics beam control: scattering laser energy from the target, using a single uncompensated Rayleigh beacon, and using a series of compensated Rayleigh beacons. We demonstrate that using a series of compensated Rayleigh beacons distributed along the path provides the best beam compensation.

Approach for reconstructing anisoplanatic adaptive optics images.

Atmospheric turbulence corrupts astronomical images formed by ground-based telescopes. Adaptive optics systems allow the effects of turbulence-induced aberrations to be reduced for a narrow field of view corresponding approximately to the isoplanatic angle theta(0). For field angles larger than theta(0), the point spread function (PSF) gradually degrades as the field angle increases. We present a technique to estimate the PSF of an adaptive optics telescope as function of the field angle, and use this information in a space-varying image reconstruction technique. Simulated anisoplanatic intensity images of a star field are reconstructed by means of a block-processing method using the predicted local PSF. Two methods for image recovery are used: matrix inversion with Tikhonov regularization, and the Lucy-Richardson algorithm. Image reconstruction results obtained using the space-varying predicted PSF are compared to space invariant deconvolution results obtained using the on-axis PSF. The anisoplanatic reconstruction technique using the predicted PSF provides a significant improvement of the mean squared error between the reconstructed image and the object compared to the deconvolution performed using the on-axis PSF.

Performance study of Kalman filter controller for multiconjugate adaptive optics.

We compare the performance of the Kalman filter (KF)-based and the minimum variance (MV) control algorithms for a zonal adaptive optics with a phase temporal prediction step included for effective compensation of the errors attributable to latencies in the system. The main goal is to evaluate the performance achievable by the computationally more expensive KF approach, which explicitly accounts for the atmospheric turbulence temporal behavior through a first-order autoregressive evolution model, and the simpler MV algorithm, with and without temporal prediction. For a representative example, the Gemini-South 8 m telescope multiconjugate adaptive optics system performance of the KF and the MV controllers has been compared with respect to their turbulence compensation capability. We show that the KF algorithm, as expected, shows superior performance to that of the MV algorithm, especially for extremely low sampling rates and large control latencies. We also show that for moderate control latencies the MV algorithm with a temporal prediction step added to it approaches the performance of the KF technique.

Experimental estimation of the spatial statistics of turbulence-induced index of refraction fluctuations in the upper atmosphere.

We present results from an experiment to estimate the parameters of homogeneous, isotropic optical turbulence in the upper atmosphere. The balloon-borne experiment made high-resolution temperature measurements at seven points on a hexagonal grid for altitudes from 12,000 to 18,000 m. From the temperature data, we obtained index of refraction fluctuations that can be used to compute a sample-based estimate for a parameterized description of the spatial autocorrelation of the turbulence. The three parameters of interest were a proportionality constant Pc, the power-law parameter alpha, and the outer scale L0. The results obtained for Pc are within the expected range and agree well with independent measurements made from a standard rising thermosonde measurement made approximately simultaneously with the data collection. Values for a were in the range 1.52 < or = alpha < or = 1.73 were observed, which are significantly less than the power law used in the Kolmogorov and von Karman models, alpha = 1.833. Values observed for L0 were in the range 5 < or = L0 < or = 19 m. Evidence that alpha may be consistently less than that used in the Kolmogorov and von Karman models likely has the most significant implications for systems that must work in or through the tropopause.

Measurement and data processing approach for detecting anisotropic spatial statistics of the turbulence-induced index of refraction fluctuations in the upper atmosphere.

We discuss a method of data reduction and analysis that has been developed for a novel experiment to detect anisotropic turbulence in the tropopause and to measure the spatial statistics of these flows. The experimental concept is to make measurements of temperature at 15 points on a hexagonal grid for altitudes from 12,000 to 18,000 m while suspended from a balloon performing a controlled descent. From the temperature data, we estimate the index of refraction and study the spatial statistics of the turbulence-induced index of refraction fluctuations. We present and evaluate the performance of a processing approach to estimate the parameters of an anisotropic model for the spatial power spectrum of the turbulence-induced index of refraction fluctuations. A Gaussian correlation model and a least-squares optimization routine are used to estimate the parameters of the model from the measurements. In addition, we implemented a quick-look algorithm to have a computationally nonintensive way of viewing the autocorrelation function of the index fluctuations. The autocorrelation of the index of refraction fluctuations is binned and interpolated onto a uniform grid from the sparse points that exist in our experiment. This allows the autocorrelation to be viewed with a three-dimensional plot to determine whether anisotropy exists in a specific data slab. Simulation results presented here show that, in the presence of the anticipated levels of measurement noise, the least-squares estimation technique allows turbulence parameters to be estimated with low rms error.