Non-line-of-sight imaging using phasor-field virtual wave optics.

Non-line-of-sight imaging allows objects to be observed when partially or fully occluded from direct view, by analysing indirect diffuse reflections off a secondary relay surface. Despite many potential applications1-9, existing methods lack practical usability because of limitations including the assumption of single scattering only, ideal diffuse reflectance and lack of occlusions within the hidden scene. By contrast, line-of-sight imaging systems do not impose any assumptions about the imaged scene, despite relying on the mathematically simple processes of linear diffractive wave propagation. Here we show that the problem of non-line-of-sight imaging can also be formulated as one of diffractive wave propagation, by introducing a virtual wave field that we term the phasor field. Non-line-of-sight scenes can be imaged from raw time-of-flight data by applying the mathematical operators that model wave propagation in a conventional line-of-sight imaging system. Our method yields a new class of imaging algorithms that mimic the capabilities of line-of-sight cameras. To demonstrate our technique, we derive three imaging algorithms, modelled after three different line-of-sight systems. These algorithms rely on solving a wave diffraction integral, namely the Rayleigh-Sommerfeld diffraction integral. Fast solutions to Rayleigh-Sommerfeld diffraction and its approximations are readily available, benefiting our method. We demonstrate non-line-of-sight imaging of complex scenes with strong multiple scattering and ambient light, arbitrary materials, large depth range and occlusions. Our method handles these challenging cases without explicitly inverting a light-transport model. We believe that our approach will help to unlock the potential of non-line-of-sight imaging and promote the development of relevant applications not restricted to laboratory conditions.

Towards a more accurate light transport model for non-line-of-sight imaging.

Non-line-of-sight (NLOS) imaging systems involve the measurement of an optical signal at a diffuse surface. A forward model encodes the physics of these measurements mathematically and can be inverted to generate a reconstruction of the hidden scene. Some existing NLOS imaging techniques rely on illuminating the diffuse surface and measuring the photon time of flight (ToF) of multi-bounce light paths. Alternatively, some methods depend on measuring high-frequency variations caused by shadows cast by occluders in the hidden scene. While forward models for ToF-NLOS and Shadow-NLOS have been developed separately, there has been limited work on unifying these two imaging modalities. Dove et al introduced a unified mathematical framework capable of modeling both imaging techniques [Opt. Express27, 18016 (2019)10.1364/OE.27.018016]. The authors utilize this general forward model, known as the two frequency spatial Wigner distribution (TFSWD), to discuss the implications of reconstruction resolution for combining the two modalities but only when the occluder geometry is known a priori. In this work, we develop a graphical representation of the TFSWD forward model and apply it to novel experimental setups with potential applications in NLOS imaging. Furthermore, we use this unified framework to explore the potential of combining these two imaging modalities in situations where the occluder geometry is not known in advance.

How good are collimated Gaussian beams produced with engineered diffusers?

Collimating a Gaussian beam from an uncollimated laser source has been achieved via the deployment of engineered diffusers (EDs)-also referred to as light shaping diffusers. When compared to conventional pinhole-based optical collimation systems, this method of beam collimation ensures high optical transmission efficiency at the expense of the introduction of additional speckle and a resulting reduction in spatial coherence. Despite a lower collimation quality, these ED-produced collimated beams are attractive and promising in terms of their deployment in various benchtop or tabletop systems that involve shorter beam propagation distances of up to a few meters while requiring a high optical power throughput. This paper aims to further the understanding of collimation quality and propagation properties of ED-produced Gaussian collimated beams via carefully designed experiments and accompanying analysis. We measure and document the beam divergence, Rayleigh distance, and M 2 factor, as well as evolution of the wavefront radius of curvature (RoC), of these ED-generated beams over a few meters of propagation-a propagation distance which encapsulates a vast majority of optical systems. We further investigate the changes in the beam profile with the addition of a laser speckle reducer (SR) and compare the ED-produced beams with a near-ideal collimated beam produced with spatial filtering systems.

Measuring the radius of curvature of spherical surfaces with actively tunable Fizeau and Twyman-Green interferometers.

Accurate and repeatable measurement of the radius of curvature (RoC) of spherical sample surfaces is of great importance in optics. This importance lies in the ubiquitous use of spherical optical elements such as curved mirrors and lenses. Due to a high measurement sensitivity, interferometric techniques are often deployed for accurate characterization of the sample surface RoC. One method by which a typical commercial Fizeau or Twyman-Green (TG) interferometer measures surface RoC is via scanning between two principal retroreflective optical configurations-namely, the confocal and catseye configurations. Switching between these two configurations is typically achieved by moving an optical head along the axis of the propagating laser beam and the RoC is estimated by measuring the magnitude of mechanical motion to switch between the two principal configurations. In this paper, we propose a motion-free catseye/confocal-imaging-based sample RoC measurement system. The necessity of bulk motion to switch between the two configurations is circumvented via the use of an actively controlled varifocal lens. We demonstrate the usefulness of the proposed innovation in RoC measurements with either the TG or the Fizeau interferometer. Furthermore, we convert a commercial motion-based Zygo RoC measurement system into a motion-free one by introducing a tunable lens inside the apparatus and using it to accurately characterize the RoC of different test samples. We also compute the wavefront aberrations for all spherical sample surfaces from the recorded measurement data.

Low-loss tunable beam collimator and expander assembly with no moving parts using an engineered diffuser and varifocal lenses.

In this paper, we present a novel design for a tunable beam collimator. A variable collimator assists in achieving an adaptive size of an output collimated beam. Alternatively, it can also provide an adjustable output beam divergence angle for a noncollimated beam output. Tunable collimators are highly desirable for various applications in testing, engineering, and measurements. Such devices are also useful in providing tunable illumination of samples or targets in microscopes and emulating different target distances for characterizing the performance of camera systems in laboratory settings. The proposed collimator has two distinct advantages: it is light-efficient compared with pinhole-based collimator designs, and it delivers a large range of output beam sizes without involving the mechanical motion of bulk components. These attributes are achieved via the use of an engineered diffuser (in the place of a pinhole) and a pair of large aperture tunable focus lenses, which deliver a tunable magnification to the output collimated beam. In laboratory experiments, we achieve an optical transmission efficiency of 90% for the proposed tunable collimator.

Simultaneous thickness and phase index measurements with a motion-free actively tunable Twyman-Green interferometer.

In this paper, we present a scheme to simultaneously measure the thickness and refractive index of parallel plate samples, involving no bulk mechanical motion, by deploying an electronically tunable Twyman-Green interferometer configuration. The active electronic control with no bulk mechanical motion is realized via the introduction of a tunable focus lens within the classical motion-based Twyman-Green interferometer configuration. The resulting interferometer is repeatable and delivers accurate estimates of the thickness and refractive index of a sample under test. Elimination of bulk motion also promises a potential for miniaturization. We develop a theoretical model for estimating sample thickness and index values using this reconfigurable interferometer setup and present detailed experimental results that demonstrate the working principle of the proposed interferometer.

Phasor field waves: experimental demonstrations of wave-like properties.

Time-of-flight (ToF) non-line-of-sight (NLoS) imaging reconstructs images of scenes with light that have undergone diffuse reflections. While, in the past, ToF light propagation and reconstruction methods have been described using their own inverse methods, it has recently been shown that ToF light transport can be described as the propagation of a wave, allowing it to be modeled by the same methods that are applied for direct imaging with electromagnetic or sound waves. This wave of fluctuating optical irradiance is called the phasor field (P-field) wave. Here, we perform a series of experiments to show the wave-like behavior of this P-field wave. We design a P-field source and detector and use them to demonstrate interference of P-field waves in a double slit experiment, as well as mutually-independent focusing and imaging of P-field waves and their optical carrier. Besides establishing the properties of P-field waves, our work demonstrates that imaging of ToF signals is possible without any computation enabling fast and energy-efficient NLoS imaging systems.

Phasor field waves: A Huygens-like light transport model for non-line-of-sight imaging applications.

Non-line-of-sight (NLOS) imaging has recently attracted a lot of interest from the scientific community. The goal of this paper is to provide the basis for a comprehensive mathematical framework for NLOS imaging that is directly derived from physical concepts. We introduce the irradiance phasor field (P-field) as an abstract quantity for irradiance fluctuations, akin to the complex envelope of the Electrical field (E-field) that is used to describe propagation of electromagnetic energy. We demonstrate that the P-field propagator is analogous to the Huygens-Fresnel propagator that describes the propagation of other waves and show that NLOS light transport can be described with the processing methods that are available for LOS imaging. We perform simulations to demonstrate the accuracy and validity of the P-field formulation and provide experimental results to demonstrate a Huygens-like P-field summation behavior.

Low-cost Gaussian beam profiling with circular irises and apertures.

The fundamental Gaussian TEM00 mode is the most common mode of propagation within various optical devices, modules, and systems. Beam profilers are widely used in accurately ascertaining the cross-sectional irradiance profile of a TEM00 mode for free-space optical communication systems as well as tracking beam evolution when propagating within optical submodules. We demonstrate beam profiling methods that use low-cost, off-the-shelf, widely available circular apertures such as circular irises and spatial filters. In order to demonstrate beam profiling with any circular aperture, we first derive exact analytical expressions for power transmittance of the TEM00 mode through a decentered circular aperture and then use this mathematical derivation to estimate the irradiance profile of a Gaussian beam by 1) fixing the location of a circular aperture and changing its radius, and 2) scanning the entire area of the beam profile by translating a circular aperture of a fixed radius across the region of interest. This method is fast and easily reproducible and simply puts to use circular irises/circular spatial filters, which are commonly available in most optical laboratories. Consequently, the proposed method provides cheap and convenient means to estimate the profile of a Gaussian beam with simple optical components. Our experimental results demonstrate a performance that is comparable to a standard knife-edge-based estimate of beam profile. Moreover, a strong agreement with presented theory validates the analytical expressions derived in this paper.

Robust motion-free and error-correcting method of estimating the focal length of a lens.

This paper presents a motion-free technique to characterize the focal length of any spherical convex or concave lens. The measurement test-bench uses a Gaussian laser beam, an electronically controlled variable focus lens (ECVFL), a digital micro-mirror device (DMD), and a standard photo-detector (PD). The method requires measuring beam spot sizes for different focal length settings of the ECVFL and using the measurement data to obtain a focal length estimate through an iterative least-squares-based curve-fitting algorithm. The method is also shown to overcome potential measurement errors that arise due to inaccurate placement of optical components on the test-bench as well as unknown principal plane locations of asymmetric lens samples such as plano-convex lenses. Contrary to the commercially deployed and other proposed methods of focal length characterization, this method does not involve any bulk mechanical motion of optical elements. This approach eliminates measurement errors due to gradual mechanical wear and tear and improves measurement repeatability by minimizing mechanical hysteresis. The compact and fully automated method delivers fast, repeatable, and reliable measurements, which we believe makes it ideal for deployment in industrial lens production units and characterizing lenses used in sensitive imaging systems and various other optical experiments and systems. Measured focal lengths are within the 1% manufacturer-provided tolerance values showing excellent agreement between theory and experiments. We also demonstrate measurement robustness by rectifying discrepancies between known and actual separation distances on the measurement test bench.

Improved laser-based triangulation sensor with enhanced range and resolution through adaptive optics-based active beam control.

Various existing target ranging techniques are limited in terms of the dynamic range of operation and measurement resolution. These limitations arise as a result of a particular measurement methodology, the finite processing capability of the hardware components deployed within the sensor module, and the medium through which the target is viewed. Generally, improving the sensor range adversely affects its resolution and vice versa. Often, a distance sensor is designed for an optimal range/resolution setting depending on its intended application. Optical triangulation is broadly classified as a spatial-signal-processing-based ranging technique and measures target distance from the location of the reflected spot on a position sensitive detector (PSD). In most triangulation sensors that use lasers as a light source, beam divergence-which severely affects sensor measurement range-is often ignored in calculations. In this paper, we first discuss in detail the limitations to ranging imposed by beam divergence, which, in effect, sets the sensor dynamic range. Next, we show how the resolution of laser-based triangulation sensors is limited by the interpixel pitch of a finite-sized PSD. In this paper, through the use of tunable focus lenses (TFLs), we propose a novel design of a triangulation-based optical rangefinder that improves both the sensor resolution and its dynamic range through adaptive electronic control of beam propagation parameters. We present the theory and operation of the proposed sensor and clearly demonstrate a range and resolution improvement with the use of TFLs. Experimental results in support of our claims are shown to be in strong agreement with theory.

Nonbulk motion system for simultaneously measuring the refractive index and thickness of a sample using tunable optics and spatial signal processing-based Gaussian beam imaging.

This paper presents a novel approach to simultaneously measuring the thickness and refractive index of a sample. The design uses an electronically controlled tunable lens (ECTL) and a microelectromechanical-system-based digital micromirror device (DMD). The method achieves the desired results by using the DMD to characterize the spatial profile of a Gaussian laser beam at different focal length settings of the ECTL. The ECTL achieves tunable lensing through minimal motion of liquid inside a transparent casing, whereas the DMD contains an array of movable micromirrors, which make it a reflective spatial light modulator. As the proposed system uses an ECTL, a DMD, and other fixed optical components, it measures the thickness and refractive index without requiring any motion of bulk components such as translational and rotational stages. A motion-free system improves measurement repeatability and reliability. Moreover, the measurement of sample thickness and refractive index can be completely automated because the ECTL and DMD are controlled through digital signals. We develop and discuss the theory in detail to explain the measurement methodology of the proposed system and present results from experiments performed to verify the working principle of the method. Refractive index measurement accuracies of 0.22% and 0.2% were achieved for two BK-7 glass samples used, and the thicknesses of the two samples were measured with a 0.1 mm accuracy for each sample, corresponding to a 0.39% and 0.78% measurement error, respectively, for the aforementioned samples.

Toward the design of a motion-free tunable coupling module for varying spatial beam profiles: foundations of optimal coupling of a Gaussian mode into a fiber collimator with a dynamic two-lens system.

In this paper, we present analytical expressions for the coupling of the fundamental Gaussian mode into a fiber collimator (FC) using a two-lens system. For this two-lens system, we also derive the limiting condition imposed on the focal lengths of the two individual lenses and their mutual separation for near-to-perfect mode coupling into the FC. Variations in the spatial mode profile of a Gaussian beam may occur due to various reasons. These include controlled changes in the beam profile inside mode-division multiplexed systems, and undesired spatial profile variations in beams that pass through turbulent media. The necessity of a dynamic mode-coupling module is dictated by the need to optimally couple Gaussian beams with dynamically changing spatial profiles. Using the analytical expressions derived for mode-coupling efficiency and the resulting lens separation condition that is imposed on a two-lens coupling system, we propose the design of a dynamic two-lens mode-coupling system with a pair of electronically controlled tunable lenses. The proposed dynamic coupling module is motion free and involves the movement of bulk components in order to achieve optimal coupling. The experimental results are also presented to verify the theoretical claims and the working principle of a two-lens mode-coupling system. The results of the experiments are discussed in detail and an excellent agreement is demonstrated between the proposed theoretical framework and the experimental results.

Robust, motion-free optical characterization of samples using actively-tunable Twyman-Green interferometry.

Optical interferometry-based techniques are ubiquitous in various measurement, imaging, calibration, metrological, and astronomical applications. Repeatability, simplicity, and reliability of measurements have ensured that interferometry in its various forms remains popular-and in fact continues to grow-in almost every branch of measurement science. In this paper, we propose a novel actively-controlled optical interferometer in the Twyman-Green configuration. The active beam control within the interferometer is a result of using an actively-controlled tunable focus lens in the sample arm of the interferometer. This innovation allows us to characterize transparent samples cut in the cubical geometry without the need for bulk mechanical motion within the interferometer. Unlike thickness/refractive index measurements with conventional Twyman-Green interferometers, the actively-tunable interferometer enables bulk-motion free thickness or refractive index sample measurements. With experimental demonstrations, we show excellent results for various samples that we characterized. The elimination of bulk motion from the measurement process promises to enable miniaturization of actively-tunable Twyman-Green interferometers for various applications.

Smart agile lens remote optical sensor for three-dimensional object shape measurements.

We demonstrate what is, to the best of our knowledge, the first electronically controlled variable focus lens (ECVFL)-based sensor for remote object shape sensing. Using a target illuminating laser, the axial depths of the shape features on a given object are measured by observing the intensity profile of the optical beam falling on the object surface and tuning the ECVFL focal length to form a minimum beam spot. Using a lens focal length control calibration table, the object feature depths are computed. Transverse measurement of the dimensions of each object feature is done using a surface-flooding technique that completely illuminates a given feature. Alternately, transverse measurements can also be made by the variable spatial sampling scan technique, where, depending upon the feature sizes, the spatial sampling spot beam size is controlled using the ECVFL. A proof-of-concept sensor is demonstrated using an optical beam from a laser source operating at a power of 10 mW and a wavelength of 633 nm. A three-dimensional (3D) test object constructed from LEGO building blocks forms has three mini-skyscraper structures labeled A, B, and C. The (x, y, z) dimensions for A, B, and C are (8 mm, 8 mm, 124.84 mm), (24.2 mm, 24.2 mm, 38.5 mm), and (15.86 mm, 15.86 mm, 86.74 mm), respectively. The smart sensor experimentally measured (x,y,z) dimensions for A, B, C are (7.95 mm, 7.95 mm, 120 mm), (24.1 mm, 24.1 mm, 37 mm), and (15.8 mm, 15.8 mm, 85 mm), respectively. The average shape sensor transverse measurement percentage errors for A, B, and C are +/-0.625%, +/-0.41%, and +/-0.38%, respectively. The average shape sensor axial measurement percentage errors for A, B, and C are +/-4.03%, +/-3.9%, and +/-2.01%, respectively. Applications for the proposed shape sensor include machine parts inspection, 3D object reconstruction, and animation.

Electronically controlled agile lens-based broadband variable photonic delay line for photonic and radio frequency signal processing.

To the best of our knowledge, proposed for the first time is the design of an optically broadband variable photonic delay line (VPDL) using an electronically controlled variable focus lens (ECVFL), mirror motion, and beam-conditioned free-space laser beam propagation. This loss-minimized fiber-coupled VPDL design using micro-optic components has the ability to simultaneously provide optical attenuation controls and analog-mode high-resolution (subpicoseconds) continuous delays over a moderate (e.g., <5 ns) range of time delays. An example VPDL design using a liquid-based ECVFL demonstrates up to a 1 ns time-delay range with >10 dB optical attenuation controls. The proposed VPDL is deployed to demonstrate a two-tap RF notch filter with tuned notches at 854.04 and 855.19 MHz with 22.6 dB notch depth control via VPDL attenuation control operations. The proposed VPDL is useful in signal conditioning applications requiring fiber-coupled broadband light time delay and attenuation controls.

Noncontact distance sensor using spatial signal processing.

To the best of our knowledge, proposed is the first distance-measurement sensor using direct spatial signal processing. The sensor is implemented using a laser beam engaged in target-dependent spatial beam processing using an electronically controlled variable focus lens (ECVFL). Specifically, the target-reflected beam is observed by an optical detector while electronically scanning the focal length of the ECVFL in the path of the laser beam. A received-beam minimum spatial size corresponds to a specific ECVFL focal length that in turn is used to compute the sensed target distance. Experiments have been conducted using a 633 nm He-Ne laser and a liquid ECVFL, giving target distance measurements from 6to109 cm with a <1.7% sensor resolution. Various noncontact applications for the sensor include sensing of object measurement parameters of distance, motion displacement, three-dimensional structure, spatial profile, and levels.

High-dynamic-range hybrid analog-digital control broadband optical spectral processor using micromirror and acousto-optic devices.

For the first time, to the best of our knowledge, the design and demonstration of a programmable spectral filtering processor is presented that simultaneously engages the power of an analog-mode optical device such as an acousto-optic tunable filter and a digital-mode optical device such as the digital micromirror device. The demonstrated processor allows a high 50 dB attenuation dynamic range across the chosen 1530-1565 nm (~C band). The hybrid analog-digital spectral control mechanism enables the processor to operate with greater versatility when compared to analog- or digital-only processor designs. Such a processor can be useful both as a test instrument in biomedical applications and as an equalizer in fiber communication networks.

Smart value-added fiber-optic modules using spatially multiplexed processing.

Intelligent fiber-optic value-added modules (VAMs) are proposed using what we believe to be a novel spatially multiplexed processing technique implemented with both reconfigurable and nonreconfigurable predesigned pixels per impinging beam that enables desired optical power split states needed for realizing a two state reconfigurable VAM. The preferred design uses broadband micromirrors such as ones fabricated via optical microelectromechanical systems technology. The basic VAM design uses two broadband micromirror pixels, where each pixel has its specific location and area and only one of these pixels is electrically driven to adjust its small tilt angle. The areas of the pixels are chosen to obtain the desired tap power. A proof-of-concept VAM with 100% digital repeatability is demonstrated using a Texas Instruments Digital Micromirror Device (DMD) where several micromirrors per beam are used to produce the dual-pixel effect. Example tap ratios experimentally implemented at 1550 nm include 10:90, 20:80, 66.66:33.33, 50:50, 30:70, and 25:75. DMD multipixel diffraction limits output port optical losses to 3.2 and 3.6 dB. The proposed VAM can have an impact in both digital electronic and analog RF optically implemented systems.