Frequency-modulated continuous-wave LiDAR compressive depth-mapping

We present an inexpensive architecture for converting a frequency-modulated continuous-wave LiDAR system into a compressive-sensing based depth-mapping camera. Instead of raster scanning to obtain depth-maps, compressive sensing is used to significantly reduce the number of measurements. Ideally, our approach requires two difference detectors. % but can operate with only one at the cost of doubling the number of measurments. Due to the large flux entering the detectors, the signal amplification from heterodyne detection, and the effects of background subtraction from compressive sensing, the system can obtain higher signal-to-noise ratios over detector-array based schemes while scanning a scene faster than is possible through raster-scanning. %Moreover, we show how a single total-variation minimization and two fast least-squares minimizations, instead of a single complex nonlinear minimization, can efficiently recover high-resolution depth-maps with minimal computational overhead. Moreover, by efficiently storing only $2m$ data points from $m<n$ measurements of an $n$ pixel scene, we can easily extract depths by solving only two linear equations with efficient convex-optimization methods

Fast Hadamard transforms for compressive sensing of joint systems: measurement of a 3.2 million-dimensional bi-photon probability distribution

We demonstrate how to efficiently implement extremely high-dimensional compressive imaging of a bi-photon probability distribution. Our method uses fast-Hadamard-transform Kronecker-based compressive sensing to acquire the joint space distribution. We list, in detail, the operations necessary to enable fast-transform-based matrix-vector operations in the joint space to reconstruct a 16.8 million-dimensional image in less than 10 minutes. Within a subspace of that image exists a 3.2 million-dimensional bi-photon probability distribution. In addition, we demonstrate how the marginal distributions can aid in the accuracy of joint space distribution reconstructions

Estimating moose population parameters from aerial surveys

Successful moose management depends on knowledge of population dynamics. The principal parameters required are size, rate of change, recruitment, sex composition, and mortality. Moose management in Alaska has been severely hampered by the lack of good estimates of these parameters, and unfortunately, this lack contributed to the decline of many Alaskan moose populations during the 1970s (e.g., Gasaway et al. 1983). The problems were: (1) population size not adequately estimated, (2) rapid rates of decline not acknowledged until populations were low, (3) meaningful recruitment rates were not available in the absence of good population estimates, and (4) calf and adult mortality rates were grossly underestimated. Frustration of moose managers working with inadequate data led to development of aerial survey procedures that yield minimally biased, sufficiently precise estimates of population parameters for most Alaskan moose management and research. This manual describes these procedures. Development of these procedures would have been impossible without the inspiration, support, advice, and criticism of many colleagues. We thank these colleagues for their contributions. Dale Haggstrom and Dave Kelleyhouse helped develop flight patterns, tested and improved early sampling designs, and as moose managers, put these procedures into routine use. Pilots Bill Lentsch and Pete Haggland were instrumental in developing and testing aerial surveying techniques. Their interest and dedication to improving moose management made them valuable allies. Statisticians Dana Thomas of the University of Alaska and W. Scott Overton of Oregon State University provided advice on variance approximations for the population estimator. Warren Ballard, Sterling Miller, SuzAnne Miller, Doug Larsen, and Wayne Kale tested procedures and provided valuable criticisms and suggestions. Jim Raymond initially programmed a portable calculator to make lengthy calculation simple, fast, and error-free. Angie Babcock, Lisa Ingalls, Vicky Leffingwell, and Laura McManus patiently typed several versions of this manual. John Coady and Oliver Burris provided continuous moral and financial support for a 3-year project that lasted 6 years. Joan Barnett, Rodney Boetje, Steven Peterson, and Wayne Regelin of the Alaska Department of Fish and Game provided helpful editorial suggestions in previous drafts. Finally, we thank referees David Anderson of the Utah Cooperative Wildlife Research Unit, Vincent Schultz of Washington State University, and James Peek, E. "Oz" Garton, and Mike Samuel of the University of Idaho whose comments and suggestions improved this manual. This project was funded by the Alaska Department of Fish and Game through Federal Aid in Wildlife Restoration Projects W-17-9 through W-22-1

Three-geometry and reformulation of the Wheeler-DeWitt equation

A reformulation of the Wheeler-DeWitt equation which highlights the role of gauge-invariant three-geometry elements is presented. It is noted that the classical super-Hamiltonian of four-dimensional gravity as simplified by Ashtekar through the use of gauge potential and densitized triad variables can furthermore be succinctly expressed as a vanishing Poisson bracket involving three-geometry elements. This is discussed in the general setting of the Barbero extension of the theory with arbitrary non-vanishing value of the Immirzi parameter, and when a cosmological constant is also present. A proposed quantum constraint of density weight two which is polynomial in the basic conjugate variables is also demonstrated to correspond to a precise simple ordering of the operators, and may thus help to resolve the factor ordering ambiguity in the extrapolation from classical to quantum gravity. Alternative expression of a density weight one quantum constraint which may be more useful in the spin network context is also discussed, but this constraint is non-polynomial and is not motivated by factor ordering. The article also highlights the fact that while the volume operator has become a preeminient object in the current manifestation of loop quantum gravity, the volume element and the Chern-Simons functional can be of equal significance, and need not be mutually exclusive. Both these fundamental objects appear explicitly in the reformulation of the Wheeler-DeWitt constraint.Comment: 10 pages, LaTeX fil

SU(2) approach to the pseudogap phase of high-temperature superconductors: electronic spectral functions

We use an SU(2) mean-field theory approach with input from variational wavefunctions of the t-J model to study the electronic spectra in the pseudogap phase of cuprates. In our model, the high-temperature state of underdoped cuprates is realized by classical fluctuations of the order parameter between the d-wave superconductor and the staggered-flux state. Spectral functions of the intermediate and the averaged states are computed and analyzed. Our model predicts a photoemission spectrum with an asymmetric gap structure interpolating between the superconducting gap centered at the Fermi energy and the asymmetric staggered-flux gap. This asymmetry of the gap changes sign at the point where the Fermi surface crosses the diagonal (\pi,0)-(0,\pi).Comment: 7 pages, 10 figures; estimate of applicable temperature range corrected and refs. added, ref. to ARPES paper added; minor changes to published versio

Towards a closed differential aging formula in special relativity

It is well known that the Lorentzian length of a timelike curve in Minkowski spacetime is smaller than the Lorentzian length of the geodesic connecting its initial and final endpoints. The difference is known as the 'differential aging' and its calculation in terms of the proper acceleration history of the timelike curve would provide an important tool for the autonomous spacetime navigation of non-inertial observers. I give a solution in 3+1 dimensions which holds whenever the acceleration is decomposed with respect to a lightlike transported frame (lightlike transport will be defined), the analogous and more natural problem for a Fermi-Walker decomposition being still open.Comment: Latex2e, 6 pages, 1 figure, uses psfrag. Contribution to the Proceedings of The Spanish Relativity Meeting (ERE 2006), Palma de Mallorca, Spain September 4-8, 200

Compressive Direct Imaging of a Billion-Dimensional Optical Phase-Space

Optical phase-spaces represent fields of any spatial coherence, and are typically measured through phase-retrieval methods involving a computational inversion, interference, or a resolution-limiting lenslet array. Recently, a weak-values technique demonstrated that a beam's Dirac phase-space is proportional to the measurable complex weak-value, regardless of coherence. These direct measurements require scanning through all possible position-polarization couplings, limiting their dimensionality to less than 100,000. We circumvent these limitations using compressive sensing, a numerical protocol that allows us to undersample, yet efficiently measure high-dimensional phase-spaces. We also propose an improved technique that allows us to directly measure phase-spaces with high spatial resolution and scalable frequency resolution. With this method, we are able to easily measure a 1.07-billion-dimensional phase-space. The distributions are numerically propagated to an object placed in the beam path, with excellent agreement. This protocol has broad implications in signal processing and imaging, including recovery of Fourier amplitudes in any dimension with linear algorithmic solutions and ultra-high dimensional phase-space imaging.Comment: 7 pages, 5 figures. Added new larger dataset and fixed typo