Randomness is far from a disturbing disorder in nature. Rather, it underlies many processes and functions. Randomness can be used to improve the efficacy of development and of systems under certain conditions. Moreover, valid unpredictable random-number generators are needed for secure communication, rendering predictable pseudorandom strings unsuitable. This paper reviews methods of generating randomness in various fields. The potential use of these methods is also discussed. It is suggested that by disordering a “false order,” an effective disorder can be generated to improve the function of systems.

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Generating randomness: making the most out of disordering a false order into a real one.

Non-line-of-sight (NLOS) imaging enables monitoring around corners and is promising for diverse applications. The resolution of transient NLOS imaging is limited to a centimeter scale, mainly by the temporal resolution of the detectors. Here, we construct an up-conversion single-photon detector with a high temporal resolution of ∼1.4  ps and a low noise count rate of 5 counts per second (cps). Notably, the detector operates at room temperature, near-infrared wavelength. Using this detector, we demonstrate high-resolution and low-noise NLOS imaging. Our system can provide a 180  μm axial resolution and a 2 mm lateral resolution, which is more than 1 order of magnitude better than that in previous experiments. These results open avenues for high-resolution NLOS imaging techniques in relevant applications.

Non-Line-of-Sight Imaging with Picosecond Temporal Resolution.

Single-photon lidar (SPL) is a promising technology for depth measurement at long range or from weak reflectors because of the sensitivity to extremely low light levels. However, constraints on the timing resolution of existing arrays of single-photon avalanche diode (SPAD) detectors limit the precision of resulting depth estimates. In this work, we describe an implementation of subtractively-dithered SPL that can recover high-resolution depth estimates despite the coarse resolution of the detector. Subtractively-dithered measurement is achieved by adding programmable delays into the photon timing circuitry that introduce relative time shifts between the illumination and detection that are shorter than the time bin duration. Careful modeling of the temporal instrument response function leads to an estimator that outperforms the sample mean and results in depth estimates with up to 13 times lower root mean-squared error than if dither were not used. The simple implementation and estimation suggest that globally dithered SPAD arrays could be used for high spatial- and temporal-resolution depth sensing.

Dithered depth imaging.

We propose and demonstrate a photon-efficient optical classifier to overcome the Rayleigh limit in spatial resolution. It utilizes mode-selective sum-frequency generation and single-pixel photon detection to resolve closely spaced incoherent sources based on photon counting statistics. Super-resolving and photon efficient, this technique can find applications in microscopy, light detection and ranging, and astrophysics.

Super-resolution optical classifier with high photon efficiency.

Non-invasive optical imaging through opaque and multi-scattering media remains highly desirable across many application domains. The random scattering and diffusion of light in such media inflict exponential decay and aberration, prohibiting diffraction-limited imaging. By non-interferometric few picoseconds optical gating of backscattered photons, we demonstrate single photon sensitive non-invasive 3D imaging of targets occluded by strongly scattering media with optical thicknesses reaching 9.5ls (19ls round trip). It achieves diffraction-limited imaging of a target placed 130 cm away through the opaque media, with millimeter lateral and depth resolution while requiring only one photon detection out of 50,000 probe pulses. Our single photon sensitive imaging technique does not require wavefront shaping nor computationally-intensive image reconstruction algorithms, promising practical solutions for diffraction-limited imaging through highly opaque and diffusive media with low illumination power.

Non-invasive single photon imaging through strongly scattering media

Active imagers capable of reconstructing 3-dimensional (3D) scenes in the presence of strong background noise are highly desirable for many sensing and imaging applications. A key to this capability is the time-resolving photon detection that distinguishes true signal photons from the noise. To this end, quantum parametric mode sorting (QPMS) can achieve signal to noise exceeding by far what is possible with typical linear optics filters, with outstanding performance in isolating temporally and spectrally overlapping noise. Here, we report a QPMS-based 3D imager with exceptional detection sensitivity and noise tolerance. With only 0.0006 detected signal photons per pulse, we reliably reconstruct the 3D profile of an obscured scene, despite 34-fold spectral-temporally overlapping noise photons, within the 6 ps detection window (amounting to 113,000 times noise per 20 ns detection period). Our results highlight a viable approach to suppress background noise and measurement errors of single photon imager operation in high-noise environments. Imagers capable of reconstructing three-dimensional scenes in the presence of strong background noise are desirable for many remote sensing and imaging applications. Here, the authors report an imager operating in photon-starved and noise-polluted environments through quantum parametric mode sorting.

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Noise-tolerant single photon sensitive three-dimensional imager.

We demonstrate a viable source of unbiased quantum random numbers whose statistical properties can be arbitrarily programmed without the need for any postprocessing such as randomness distillation or distribution transformation It is based on measuring the arrival time of single photons in shaped temporal modes that are tailored with an electro-optical modulator We show that quantum random numbers can be created directly in customized probability distributions and pass all randomness tests of the NIST and Dieharder test suites without any randomness extraction The min-entropies of such generated random numbers are measured close to the theoretical limits, indicating their near-ideal statistics and ultrahigh purity Easy to implement and arbitrarily programmable, this technique can find versatile uses in a multitude of data analysis areas

Programmable quantum random number generator without postprocessing.

Non-line-of-sight (NLOS) optical imaging and sensing of objects imply new capabilities valuable to autonomous technology, machine vision, and other applications, in which case very few informative photons are buried in strong background counts. Here, we introduce a new approach to NLOS imaging and sensing using the picosecond-gated single photon detection generated by nonlinear frequency conversion. With exceptional signal isolation, this approach can reliably achieve imaging and position retrieval of obscured objects around the corner, in which case only 4 × 10−3 photons are needed to be detected per pulse for each pixel with high temporal resolution. Furthermore, the vibration frequencies of different objects can be resolved by analyzing the photon number fluctuation received within a ten-picosecond window, allowing NLOS acoustic sensing. Our results highlight the prospect of photon efficient NLOS imaging and sensing for real-world applications.

Single photon imaging and sensing of highly obscured objects around the corner

We propose and demonstrate a single-photon sensitive technique for optical vibrometry. It uses high speed photon counting to sample the modulated backscattering from a vibrating target. Designed for remote vibration sensing with ultralow photon flux, we show that this technique can detect small displacements down to 110 nm and resolve vibration frequencies from DC up to several kilohertz, with ≤0.01 detected photons per pulse. This single-photon sensitive optical vibrometry may find important applications in acousto-optic sensing and imaging, especially in photon-starved environments.

Patrick Rehain

Papers

Noise-tolerant single photon sensitive three-dimensional imager.

Programmable quantum random number generator without postprocessing.

Non-invasive single photon imaging through strongly scattering media

Single photon imaging and sensing of highly obscured objects around the corner

Single-photon vibrometry