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

Compressive Wavefront Sensing with Weak Values

We demonstrate a wavefront sensor based on the compressive sensing, single-pixel camera. Using a high-resolution spatial light modulator (SLM) as a variable waveplate, we weakly couple an optical field's transverse-position and polarization degrees of freedom. By placing random, binary patterns on the SLM, polarization serves as a meter for directly measuring random projections of the real and imaginary components of the wavefront. Compressive sensing techniques can then recover the wavefront. We acquire high quality, 256x256 pixel images of the wavefront from only 10,000 projections. Photon-counting detectors give sub-picowatt sensitivity

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

Moore’s Law and Space Exploration: New Insights and Next Steps

Understanding how technology changes over time is important for industry, science, and government policy. Empirical examination of the capability of technologies across various domains reveals that they often progress at an exponential rate. In addition, mathematical models of technological development have proven successful in deepening our understanding. One area that has not been shown to demonstrate exponential trends, until recently, has been space travel. This paper will present plots illustrating trends in the mean lifespan of satellites whose lifespans ended in a given year. Our study identifies both Wright’s law and Moore’s law regressions. For the Moore’s law regression, we found a doubling time of approximately 15 years. For Wright’s law we can see an approximate doubling of lifespan with every doubling of accumulated launches. We conclude by presenting a conundrum generated by the use of Moore’s law that is the subject of ongoing research

The effect of certain organic compounds on the time of set of silicic acid gels

When a sodium silicate solution and an acid are mixed, a gel is sooner or later formed. The spped of gelation is a variable, and it depends on a number of factors, of which there are four fundamental ones. There are as follows: (1) The concentration of water glass (2) The concentration of acid (3) Agitation (4) Temperature. In this investigation of time of set, these four elements were kept as constant as possible. There is a fifth factor of real importance. This is one that has to do with the addition of some impurity. Of course if the impurity added is acid or base, numbers (1) and (2) above enter in. The question arises, is it entirely due to neutralization of the acid, when for example, CH3NH3OH is the foreign matter added? In the first part of this work, the effect of CH3COOC2H5 and its products of hydrolosis was studied. This was followed by a more interesting group of compounds

Josh Daniel Howell in a Senior Baritone Recital

This is the program for the senior baritone recital of Josh Daniel Howell. Mr. Howell was accompanied on the piano by Kati Huryta. This recital took place on February 2, 2002, in the McBeth Recital Hall in the Mabee Fine Arts Center

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 $2\sqrt{2}$. 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