Jim F. Riker

Analytical expressions for the log-amplitude correlation function for plane wave propagation in anisotropic non-Kolmogorov refractive turbulence

An analytical expression for the log-amplitude correlation function for plane wave propagation through anisotropic non-Kolmogorov turbulent atmosphere is derived. The closed-form analytic results are based on the Rytov approximation. These results agree well with wave optics simulation based on the more general Fresnel approximation as well as with numerical evaluations, for low-to-moderate strengths of turbulence. The new expression reduces correctly to the previously published analytic expressions for the cases of plane wave propagation through both nonisotropic Kolmogorov turbulence and isotropic non-Kolmogorov turbulence cases. These results are useful for understanding the potential impact of deviations from the standard isotropic Kolmogorov spectrum.

Deep turbulence effects compensation experiments with a cascaded adaptive optics system using a 3.63 m telescope

Compensation of extended (deep) turbulence effects is one of the most challenging problems in adaptive optics (AO). In the AO approach described, the deep turbulence wave propagation regime was achieved by imaging stars at low elevation angles when image quality improvement with conventional AO was poor. These experiments were conducted at the U.S. Air Force Maui Optical and Supercomputing Site (AMOS) by using the 3.63 m telescope located on Haleakala, Maui. To enhance compensation performance we used a cascaded AO system composed of a conventional AO system based on a Shack-Hartmann wavefront sensor and a deformable mirror with 941 actuators, and an AO system based on stochastic parallel gradient descent optimization with four deformable mirrors (75 control channels). This first-time field demonstration of a cascaded AO system achieved considerably improved performance of wavefront phase aberration compensation. Image quality was improved in a repeatable way in the presence of stressing atmospheric conditions obtained by using stars at elevation angles as low as 15 degrees.

Analytical expressions for the log-amplitude correlation function for spherical wave propagation through anisotropic non-Kolmogorov atmosphere

An analytical expression for the log-amplitude correlation function based on the Rytov approximation is derived for spherical wave propagation through an anisotropic non-Kolmogorov refractive turbulent atmosphere. The expression reduces correctly to the previously published analytic expressions for the case of spherical wave propagation through isotropic Kolmogorov turbulence. These results agree well with a wave-optics simulation based on the more general Fresnel approximation, as well as with numerical evaluations, for low-to-moderate strengths of turbulence. These results are useful for understanding the potential impact of deviations from the standard isotropic Kolmogorov spectrum.

Moment-matching method for extracting beam jitter and boresight in experiments with satellites of small physical cross section

The boresight and atmospheric jitter errors in a satellite tracking experiment are currently estimated by matching the probability density function (PDF) of the received signal counts with a set of PDFs of the signal for several combinations of jitter and boresight errors and then the best choice of jitter and boresight error is accepted via the chi-square test. Here a technique that can estimate atmospheric beam jitter and boresight error directly in a satellite active tracking experiment using the moments of the returns off the satellites is proposed. That is, we use the theoretical PDF for the signal return from a small target and compute the corresponding theoretical PDF moments. We can then form a few equations from these moments with only two unknowns, namely, the jitter and boresight. Solving for the unknowns is then unambiguous and very rapid. The method is valid for small physical cross-section targets and has been verified by using simulation and experimental data. Extending the case to asymmetric jitter and asymmetric boresight is possible.

Results from precision tracking tests against distant objects

In order to assess an object in space, in the air, or on the ground, it is first necessary to acquire and track it. In this paper, we will discuss distant object tracking, both passively and actively, and show some recent results from the Air Force Maui Optical and Supercomputing (AMOS) site and also from the Starfire Optical Range (SOR). In the past ten years, we have moved well beyond passive tracking on objects, to obtain the first-ever high-bandwidth closed loop tracks on skin satellites. But even passive tracking has developed further, with the advent of new sensor technology and also new beam control stabilization techniques. We will review some of our results here. In addition, a colleague and I have developed some new techniques to unambiguously estimate the active tracking jitter and boresight errors solely from the signal returned by the object being illuminated. We will review some of those results as well, and point the reader toward a more thorough published paper on that topic.

Active Tracking Lasers for Precision Target Stabilization

Lasers have historically been considered in the context of weapons, but recent progress has also permitted us to consider using lasers for more subtle applications such as designation, tracking, and discrimination. In this paper, we will review the state of the art of active tracking, including effects such as laser beam quality, diffraction, atmospheric turbulence, and other aspects of laser interactions with its propagation environment. We will present the theory for using lasers in these lower power applications.

Signal-to-noise ratio limitations for intensity correlation imaging

Intensity correlation imaging (ICI) is a concept which has been considered for the task of providing images of satellites in geosynchronous orbit using ground-based equipment. This concept is based on the intensity interferometer principle first developed by Hanbury Brown and Twiss. It is the objective of this paper to establish that a sun-lit geosynchronous satellite is too faint a target object to allow intensity interferometry to be used in developing image information about it-at least not in a reasonable time and with a reasonable amount of equipment. An analytic treatment of the basic phenomena is presented. This is an analysis of one aspect of the statistics of the very high frequency random variations of a very narrow portion of the optical spectra of the incoherent (black-body like-actually reflected sunlight) radiation from the satellite, an analysis showing that the covariance of this radiation as measured by a pair of ground-based telescopes is directly proportional to the square of the magnitude of one component of the Fourier transform of the image of the satellite-the component being the one for a spatial frequency whose value is determined by the separation of the two telescopes. This analysis establishes the magnitude of the covariance. A second portion of the analysis considers shot-noise effects. It is shown that even with much less than one photodetection event (pde) per signal integration time an unbiased estimate of the covariance of the optical fields random variations can be developed. Also, a result is developed for the standard deviation to be associated with the estimated value of the covariance. From these results an expression is developed for what may be called the signal-to-noise ratio to be associated with an estimate of the covariance. This signal-to-noise ratio, it turns out, does not depend on the measurements integration time, Δt (in seconds), or on the optical spectral bandwidth, Δν (in Hertz), utilized-so long as ΔtΔν≫1, which condition it would be hard to violate. It is estimated that for a D=3.16 m diameter satellite, with a pair of D=1.0 m diameter telescopes (which value of D probably represents an upper limit on allowable aperture diameter since the telescope aperture must be much too small to even resolve the size of the satellite) at least N=2.55×10(16) separate pairs of (one integration time, pde count) measurement values must be collected to achieve just a 10 dB signal-to-noise ratio. Working with 10 pairs of telescopes (all with the same separation), and with 10 nearly adjacent and each very narrow spectral bands extracted from the light collected by each of the telescope-so that for each measurement integration time there would be 100 pairs of measurement values available-and with an integration time as short as Δt=1 ns, it would take T=2.55×10(5) s or about 71 h to collect the data for just a single spatial frequency component of the image of the satellite. It is on this basis that it is concluded that the ICI concept does not seem likely to be able to provide a timely responsive capability for the imaging of geosynchronous satellites.

Moment-matching method for extraction of asymmetric beam jitters and bore sight errors in simulations and experiments with actively illuminated satellites of small physical cross section

Optical returns from remote resident space-based objects such as satellites suffer from pointing and tracking errors. In a previously reported paper [Appl. Opt.46, 5608 (2007)APOPAI0003-693510.1364/AO.46.005608], we developed a moment-matching technique that used the statistics of time series of these optical returns to extract information about bore sight and symmetric beam jitter errors (symmetric here implies that the standard deviations of the jitter measured along two orthogonal axes, perpendicular to the line of sight, are equal). In this paper, we extend that method to cover the case of asymmetric beam jitter and bore sight. The asymmetric beam jitter may be due to the combination of symmetric atmospheric turbulence beam jitter and optical beam train jitter. In addition, if a tracking control system is operating, even the residual atmospheric tracking jitter could be asymmetric because the power spectrum is different for the slewing direction compared to the cross-track direction. Analysis of the problem has produced a set of nonlinear equations that can be reduced to a single but much higher-order nonlinear equation in terms of one of the jitter variances. After solving for that jitter, all the equations can be solved to extract all jitter and bore sight errors. The method has been verified by using simulations and then tested on experimental data. In order to develop this method, we derived analytical expressions for the probability density function and the moments of the received total intensity. The results reported here are valid for satellites of small physical cross section, or else those with retroreflectors that dominate the signal return. The results are, in general, applicable to the theory of noncircular Gaussian speckle with a coherent background.

Active tracking with moderate power lasers

Progress on active tracking at the Starfire Optical Range (SOR) has been significant in the years 2003-2004. We have obtained laser returns from a number of retro-reflector and also unaugmented satellite objects, and compared the signal returns to theories presented in previous SPIE papers (ref. 1-3). These results have concentrated on very low-power, sinusoidally-modulated lasers and a large-aperture, phase-sensitive detection receiver to discriminate the return signal from background and noise. This year, we have installed and used a much higher average power, high-repetition-rate pulsed laser in order to increase the signal-to-noise ratio. Results from these laser engagements will be presented along with simulation and theoretical comparisons. Techniques for diagnosing the laser uplink and the receiver systems will be discussed.

Long-range speckle imaging theory, simulation, and brassboard results

In the SPIE 2016 Unconventional Imaging session, the authors laid out a breakthrough new theory for active array imaging that exploits the speckle return to generate a high-resolution picture of the target. Since then, we have pursued that theory even in long-range (<1000-km) engagement scenarios and shown how we can obtain that high-resolution image of the target using only a few illuminators, or by using many illuminators. There is a trade of illuminators versus receivers, but many combinations provide the same synthetic aperture resolution. We will discuss that trade, along with the corresponding radiometric and speckle-imaging Signal-to-Noise Ratios (SNR) for geometries that can fit on relatively small aircraft, such as an Unmanned Aerial Vehicle (UAV). Furthermore, we have simulated the performance of the technique, and we have created a laboratory version of the approach that is able to obtain high-resolution speckle imagery. The principal results presented in this paper are the Signal to Noise Ratios (SNR) for both the radiometric and the speckle imaging portions of the problem, and the simulated results obtained for representative arrays.