317 research outputs found
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 data points from measurements of an
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
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
Position-Momentum Bell-Nonlocality with Entangled Photon Pairs
Witnessing continuous-variable Bell nonlocality is a challenging endeavor,
but Bell himself showed how one might demonstrate this nonlocality. Though Bell
nearly showed a violation using the CHSH inequality with sign-binned
position-momentum statistics of entangled pairs of particles measured at
different times, his demonstration is subject to approximations not realizable
in a laboratory setting. Moreover, he doesn't give a quantitative estimation of
the maximum achievable violation for the wavefunction he considers. In this
article, we show how his strategy can be reimagined using the transverse
positions and momenta of entangled photon pairs measured at different
propagation distances, and we find that the maximum achievable violation for
the state he considers is actually very small relative to the upper limit of
. Although Bell's wavefunction does not produce a large violation of
the CHSH inequality, other states may yet do so.Comment: 6 pages, 3 figure
Demonstrating Continuous Variable EPR Steering in spite of Finite Experimental Capabilities using Fano Steering Bounds
We show how one can demonstrate continuous-variable Einstein-Podolsky-Rosen
(EPR) steering without needing to characterize entire measurement probability
distributions. To do this, we develop a modified Fano inequality useful for
discrete measurements of continuous variables, and use it to bound the
conditional uncertainties in continuous-variable entropic EPR-steering
inequalities. With these bounds, we show how one can hedge against experimental
limitations including a finite detector size, dead space between pixels, and
any such factors that impose an incomplete sampling of the true measurement
probability distribution. Furthermore, we use experimental data from the
position and momentum statistics of entangled photon pairs in parametric
downconversion to show that this method is sufficiently sensitive for practical
use.Comment: 7 pages, 2 figure
Compressively characterizing high-dimensional entangled states with complementary, random filtering
The resources needed to conventionally characterize a quantum system are
overwhelmingly large for high- dimensional systems. This obstacle may be
overcome by abandoning traditional cornerstones of quantum measurement, such as
general quantum states, strong projective measurement, and assumption-free
characterization. Following this reasoning, we demonstrate an efficient
technique for characterizing high-dimensional, spatial entanglement with one
set of measurements. We recover sharp distributions with local, random
filtering of the same ensemble in momentum followed by position---something the
uncertainty principle forbids for projective measurements. Exploiting the
expectation that entangled signals are highly correlated, we use fewer than
5,000 measurements to characterize a 65, 536-dimensional state. Finally, we use
entropic inequalities to witness entanglement without a density matrix. Our
method represents the sea change unfolding in quantum measurement where methods
influenced by the information theory and signal-processing communities replace
unscalable, brute-force techniques---a progression previously followed by
classical sensing.Comment: 13 pages, 7 figure
Frequency Modulated Continuous Wave 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. 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, by efficiently storing only 2m data points from m \u3c n measurements of an n pixel scene, we can easily extract depths by solving only two linear equations with efficient convex-optimization methods
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. 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, by efficiently storing only 2m data points from m \u3c 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
Position-Momentum Bell Nonlocality with Entangled Photon Pairs
Witnessing continuous-variable Bell nonlocality is a challenging endeavor, but Bell himself showed how one might demonstrate this nonlocality. Although Bell nearly showed a violation using the Clauser-Horne-Shimony-Holt (CHSH) inequality with sign-binned position-momentum statistics of entangled pairs of particles measured at different times, his demonstration is subject to approximations not realizable in a laboratory setting. Moreover, he does not give a quantitative estimation of the maximum achievable violation for the wave function he considers. In this article, we show how his strategy can be reimagined using the transverse positions and momenta of entangled photon pairs measured at different propagation distances, and we find that the maximum achievable violation for the state he considers is actually very small relative to the upper limit of 2β2. Although Bell\u27s wave function does not produce a large violation of the CHSH inequality, other states may yet do so
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