Sensing optical phase distortion via beatnote detection of a dual probe beam encoded with orbital angular momentum.

Laser based optical applications such as imaging, ranging, and wireless communications are susceptible to environmental distortions. Inferring the strength of these optical distortions is crucial to obtaining information about the environment in which the system is operating. Our technique of inferring environmental distortion strength leverages the spreading of light's orbital angular momentum (OAM) spectrum combined with heterodyne detection. A laser encoded with OAM can be decomposed into a basis set of helical modes that spreads upon interaction with optical distortions. This mode spreading is quantified using the OAM spectrum that can be measured using mode projection or mode sorting techniques. This new technique, to the best of our knowledge, provides benefits compared to the latter two OAM detection methods such as: low-frequency noise rejection, a simpler optical receiver, lower noise floor, and an inherent optical phase component. Central to the method is the heterodyne detection of the zeroth-order OAM coefficient of a superimposed two-beam, two-frequency, probe. The measured heterodyne signal power is seen to be proportional to the coupling power of each beam's OAM spectra. To test the idea, wave-optic simulations and experiments using spatial light modulators are implemented using a simplified optical turbulence model to represent the environment. The experimental implementation agrees well with simulated and theoretical results.

Weak turbulence effects on different beams carrying orbital angular momentum.

The study of beams carrying orbital angular momentum (OAM) has been of interest for its use in free-space optical communications (FSOC), directed energy applications, and remote sensing (RS). For FSOC and RS, it is necessary to measure the wavefront of the beam to recover transmitted or environmental information, respectively. In this computational study, common OAM beams such as the Laguerre-Gaussian (LG), Bessel-Gaussian (BG), and Bessel beams are propagated through atmospheric turbulence and compared to their Gaussian beam counterpart. The turbulence is simulated using multiple phase screens within the framework of a split-step method. Beam metrics used to quantify beam propagation will include the spatial coherence radius, OAM spectrum, on-axis intensity, spot size, divergence, and on-axis scintillation. Atmospheric turbulence along the path is limited to the weak scintillation limit, where beam parameters can be predicted analytically using the Rytov approximation. The results show that BG beams and multiplexed BG beams retain more OAM information than their LG and Bessel beam counterparts. The LG beam on-axis intensity and on-axis scintillation are seen to be independent of OAM mode. The scintillation of the LG beam is less than a BG, Bessel, and Gaussian beam across low- and high-order OAM modes. Insight into these results is discussed through studying the beam divergence, while the initial spot sizes of the Gaussian, LG, and BG beams are limited to the same spatial extent.

Assisting target recognition through strong turbulence with the help of neural networks.

Imaging and target recognition through strong turbulence is regarded as one of the most challenging problems in modern turbulence research. As the aggregated turbulence distortion inevitably degrades remote targets and makes them less recognizable, both adaptive optics approaches and image correction methods will become less effective in retrieving correct attributes of the target. Meanwhile, machine learning (ML)-based algorithms have been proposed and studied using both hardware and software approaches to alleviate turbulence effects. In this work, we propose a straightforward approach that treats images with turbulence distortion as a data augmentation in the training set, and investigate the effectiveness of the ML-assisted recognition outcomes under different turbulence strengths. Retrospectively, we also apply the recognition outcomes to evaluate the turbulence strength through regression techniques. As a result, our study helps to build a deep connection between turbulence distortion and imaging effects through a standard perceptron neural network (NN), where mutual inference between turbulence levels and target recognition rates can be achieved.

Quadrant Fourier transform and its application in decoding OAM signals.

We present a new, to the best of our knowledge, concept of using quadrant Fourier transforms (QFTs) formed by microlens arrays (MLAs) to decode complex optical signals based on the optical intensity collected per quadrant area after the MLAs. From a computational optics viewpoint, we show the most promising use of the QFT in low-cost and passive decoding of laser signals carrying optical angular momenta (OAM) that are prevalent in research frontiers of optical communications, computation, and imaging. There are numerous ways of creating, adding, and combining OAM states in optical waves, while decoding or demultiplexing approaches often turn out to be complicated or expensive. The simple OAM decoder formed by a pair of identical MLAs, which are concatenated in the focal plane and transversely offset by half-pitch length, can accomplish the imaging task with four pixels per cell. By sorting the gradient curls of the optical wave into local quadrant cells, the decoder analyzes the intensity reallocation that is proportional to the gradients and computes the gradient curls accordingly. The low-cost, compactness, and simplicity of the proposed OAM sensor will further promote OAM-based applications, as well as many other applications that exploit the spatial complexity of optical signals.

Lossy wavefront sensing and correction of distorted laser beams.

The art of rectifying a laser beam carrying amplitude and phase distortions has been demonstrated through several competing methods. Both wavefront sensor and wavefront sensor-less approaches show that the closed-loop correction of a laser beam can be accomplished by exploiting high-resolution sampling of the beam distortion in its spatial or time domain, respectively. Moreover, machine-learning-based wavefront sensing has emerged recently, and uses training data on an arbitrary sensing architecture to map observed data to reasonable wavefront reconstructions. This offers additional options for beam correction and optical signal decoding in atmospheric or underwater propagation. Ideally, wavefront sensing can be achieved through any resolution in spatial samples, provided that more frequent sampling in the time domain can be achieved for a reduced number of spatial samples. However, such trade-offs have not been comprehensively studied or demonstrated experimentally. We present a fundamental study of lossy wavefront sensing that reduces the number of effective spatial samples to the number of actuators in a deformable mirror for a balanced performance of dynamic wavefront corrections. As a result, we show that lossy wavefront sensing can both simplify the design of wavefront sensors and remain effective for beam correction. In application, this concept provides ultimate freedom of hardware choices from sensor to sensorless approaches in wavefront reconstruction, which is beneficial to the frontier of study in free-space optical communication, lidar, and directed energy.

Light field camera study of near-ground turbulence anisotropy and observation of small outer-scales.

Understanding turbulence effects on laser beam propagation is critical to the emerging design, study, and test of many long-range free space optical (FSO) communication and directed energy systems. Conventional studies make the prevalent assumption of isotropic turbulence, while more recent results suggest anisotropic turbulence for atmospheric channels within a few meters elevation above the ground. As countless FSO systems have been and continue to be deployed in such channels, analysis of anisotropic modelings has become one of the fastest growing areas in FSO research. This in turn motivates new tools that can distinguish anisotropic characteristics to improve both modeling accuracy and physical interpretations. Wavefront sensors such as Shack-Hartmann sensors, interferometers, and plenoptic sensors have been devised and used in experiments; however, they all require rigid alignments that lack resilience against temperature gradient buildup and beam wander. We find that by using a light field camera (LFC) that extracts perturbation of individual light rays, the wave structure function of turbulence can be retrieved with high reliability. Furthermore, we find through experiments that the outer scales of near-ground turbulence tend to be a magnitude smaller than conventional theoretical assumptions, agreeing with new findings by others but being absent in current theoretical modelings. As a result, we believe that the LFC is an ideal candidate in the frontier of turbulence research; it is both commercially available and easy to adapt to turbulence experiments.

Measuring the turbulence profile in the lower atmospheric boundary layer.

Optical turbulence can have a severe effect on the propagation of laser beams through the atmosphere. In free space optics and directed energy applications, these laser beams quite often propagate along a slant or vertical path. In these cases, the refractive index structure function parameter cannot be assumed constant, since it varies with height. How it varies with height, especially in the first few meters above the ground, is not well behaved. Turbulence height profiles have been measured since the 1970s, mainly for astronomical observations. These profiles are usually measured for the atmospheric boundary layer (the layer of air from the ground up to approx. 1 km during day and 100 m during night) and some kilometers above it. We have measured the temperature fluctuations in the first few meters above ground level using a system containing eight resistance thermometer devices, mounted in a row at different spacings. Measurements were made flying this system under a tethered balloon or mounted on a telescoping mast. The temperature structure function parameter, CT2, can be estimated from the temperature fluctuations measured by the 28 different probe pairs and the unique distances between the two probes. Finally, Cn2 is estimated from this temperature structure function parameter and compared to values predicted by a turbulence profile model.

Using turbulence scintillation to assist object ranging from a single camera viewpoint.

Image distortions caused by atmospheric turbulence are often treated as unwanted noise or errors in many image processing studies. Our study, however, shows that in certain scenarios the turbulence distortion can be very helpful in enhancing image processing results. This paper describes a novel approach that uses the scintillation traits recorded on a video clip to perform object ranging with reasonable accuracy from a single camera viewpoint. Conventionally, a single camera would be confused by the perspective viewing problem, where a large object far away looks the same as a small object close by. When the atmospheric turbulence phenomenon is considered, the edge or texture pixels of an object tend to scintillate and vary more with increased distance. This turbulence induced signature can be quantitatively analyzed to achieve object ranging with reasonable accuracy. Despite the inevitable fact that turbulence will cause random blurring and deformation of imaging results, it also offers convenient solutions to some remote sensing and machine vision problems, which would otherwise be difficult.

Phase and amplitude beam shaping with two deformable mirrors implementing input plane and Fourier plane phase modifications.

We find that ideas in optical image encryption can be very useful for adaptive optics in achieving simultaneous phase and amplitude shaping of a laser beam. An adaptive optics system with simultaneous phase and amplitude shaping ability is very desirable for atmospheric turbulence compensation. Atmospheric turbulence-induced beam distortions can jeopardize the effectiveness of optical power delivery for directed-energy systems and optical information delivery for free-space optical communication systems. In this paper, a prototype adaptive optics system is proposed based on a famous image encryption structure. The major change is to replace the two random phase plates at the input plane and Fourier plane of the encryption system, respectively, with two deformable mirrors that perform on-demand phase modulations. A Gaussian beam is used as an input to replace the conventional image input. We show through theory, simulation, and experiments that the slightly modified image encryption system can be used to achieve arbitrary phase and amplitude beam shaping within the limits of stroke range and influence function of the deformable mirrors. In application, the proposed technique can be used to perform mode conversion between optical beams, generate structured light signals for imaging and scanning, and compensate atmospheric turbulence-induced phase and amplitude beam distortions.

Multi-aperture laser transmissometer system for long-path aerosol extinction rate measurement.

We present the theory, design, simulation, and experimental evaluations of a new laser transmissometer system for aerosol extinction rate measurement over long paths. The transmitter emits an ON/OFF modulated Gaussian beam that does not require strict collimation. The receiver uses multiple point detectors to sample the sub-aperture irradiance of the arriving beam. The sparse detector arrangement makes our transmissometer system immune to turbulence-induced beam distortion and beam wander caused by the atmospheric channel. Turbulence effects often cause spatial discrepancies in beam propagation and lead to miscalculation of true power loss when using the conventional approach of measuring the total beam power directly with a large-aperture optical concentrator. Our transmissometer system, on the other hand, combines the readouts from distributed detectors to rule out turbulence-induced temporal power fluctuations. As a result, we show through both simulation and field experiments that our transmissometer system works accurately with turbulence strength Cn2 up to 10-12 m-2/3 over a typical 1-km atmospheric channel. In application, our turbulence- and weather-resistant laser transmissometer system has significant advantages for the measurement and study of aerosol concentration, absorption, and scattering properties, which are crucial for directed energy systems, ground-level free-space optical communication systems, environmental monitoring, and weather forecasting.

Comparison of the plenoptic sensor and the Shack-Hartmann sensor.

Adaptive optics has been successfully used for decades in the field of astronomy to correct for atmospheric turbulence. A well-developed example involves sensing the slightly distorted wavefronts with a Shack-Hartmann sensor and then correcting them with a phase conjugate device. While the Shack-Hartmann sensor has proven effective for astronomical purposes, it has been less successful for use in deep turbulence conditions often found in ground-to-ground-based optical systems. We have studied an alternative way to sense and correct distorted wavefronts using a plenoptic sensor. We review the design of the plenoptic sensor and directly compare it with the well-known Shack-Hartmann sensor. An experimental comparison of the plenoptic sensor and the Shack-Hartmann sensor is performed to highlight their differences in real-world atmospheric turbulence conditions.

Imaging through strong turbulence with a light field approach.

Under strong turbulence conditions, object's images can be severely distorted and become unrecognizable throughout the observing time. Conventional image restoring algorithms do not perform effectively in these circumstances due to the loss of good references on the object. We propose the use a plenoptic sensor as a light field camera to map a conventional camera image onto a cell image array in the image's sub-angular spaces. Accordingly, each cell image on the plenoptic sensor is equivalent to the image acquired by a sub-aperture of the imaging lens. The wavefront distortion over the lens aperture can be analyzed by comparing cell images in the plenoptic sensor. By using a modified "Laplacian" metric, we can identify a good cell image in a plenoptic image sequence. The good cell image corresponds with the time and sub-aperture area on the imaging lens where wavefront distortion becomes relatively and momentarily "flat". As a result, it will reveal the fundamental truths of the object that would be severely distorted on normal cameras. In this paper, we will introduce the underlying physics principles and mechanisms of our approach and experimentally demonstrate its effectiveness under strong turbulence conditions. In application, our approach can be used to provide a good reference for conventional image restoring approaches under strong turbulence conditions. This approach can also be used as an independent device to perform object recognition tasks through severe turbulence distortions.

Using a plenoptic sensor to reconstruct vortex phase structures.

A branch point problem and its solution commonly involve recognizing and reconstructing a vortex phase structure around a singular point. In laser beam propagation through random media, the destructive phase contributions from various parts of a vortex phase structure will cause a dark area in the center of the beam's intensity profile. This null of intensity can, in turn, prevent the vortex phase structure from being recognized. In this Letter, we show how to use a plenoptic sensor to transform the light field of a vortex beam so that a simple and direct reconstruction algorithm can be applied to reveal the vortex phase structure. As a result, we show that the plenoptic sensor is effective in detecting branch points and can be used to reconstruct phase distortion in a beam in a wide sense.

Omnidirectional beacon-localization using a catadioptric system.

We present a catadioptric beacon localization system that can provide mobile network nodes with omnidirectional situational awareness of neighboring nodes. In this system, a receiver composed of a hyperboloidal mirror and camera is used to estimate the azimuth, elevation, and range of an LED beacon. We provide a general framework for understanding the propagation of error in the angle-of-arrival estimation and then present an experimental realization of such a system. The situational awareness provided by the proposed system can enable the alignment of communication nodes in an optical wireless network, which may be particularly useful in addressing RF-denied environments.

Plenoptic mapping for imaging and retrieval of the complex field amplitude of a laser beam.

The plenoptic sensor has been developed to sample complicated beam distortions produced by turbulence in the low atmosphere (deep turbulence or strong turbulence) with high density data samples. In contrast with the conventional Shack-Hartmann wavefront sensor, which utilizes all the pixels under each lenslet of a micro-lens array (MLA) to obtain one data sample indicating sub-aperture phase gradient and photon intensity, the plenoptic sensor uses each illuminated pixel (with significant pixel value) under each MLA lenslet as a data point for local phase gradient and intensity. To characterize the working principle of a plenoptic sensor, we propose the concept of plenoptic mapping and its inverse mapping to describe the imaging and reconstruction process respectively. As a result, we show that the plenoptic mapping is an efficient method to image and reconstruct the complex field amplitude of an incident beam with just one image. With a proof of concept experiment, we show that adaptive optics (AO) phase correction can be instantaneously achieved without going through a phase reconstruction process under the concept of plenoptic mapping. The plenoptic mapping technology has high potential for applications in imaging, free space optical (FSO) communication and directed energy (DE) where atmospheric turbulence distortion needs to be compensated.

Determining the phase and amplitude distortion of a wavefront using a plenoptic sensor.

We have designed a plenoptic sensor to retrieve phase and amplitude changes resulting from a laser beam's propagation through atmospheric turbulence. Compared with the commonly restricted domain of (-π,π) in phase reconstruction by interferometers, the reconstructed phase obtained by the plenoptic sensors can be continuous up to a multiple of 2π. When compared with conventional Shack-Hartmann sensors, ambiguities caused by interference or low intensity, such as branch points and branch cuts, are less likely to happen and can be adaptively avoided by our reconstruction algorithm. In the design of our plenoptic sensor, we modified the fundamental structure of a light field camera into a mini Keplerian telescope array by accurately cascading the back focal plane of its object lens with a microlens array's front focal plane and matching the numerical aperture of both components. Unlike light field cameras designed for incoherent imaging purposes, our plenoptic sensor operates on the complex amplitude of the incident beam and distributes it into a matrix of images that are simpler and less subject to interference than a global image of the beam. Then, with the proposed reconstruction algorithms, the plenoptic sensor is able to reconstruct the wavefront and a phase screen at an appropriate depth in the field that causes the equivalent distortion on the beam. The reconstructed results can be used to guide adaptive optics systems in directing beam propagation through atmospheric turbulence. In this paper, we will show the theoretical analysis and experimental results obtained with the plenoptic sensor and its reconstruction algorithms.

Long-range vibration detection system using heterodyne interferometry.

We present the design and performance of an extremely sensitive coherent remote vibration detection system using optical heterodyne vibration of phase shifts produced by laser light scattered off a remote target. The resulting phase-modulated intermediate RF of 200 MHz, which carries the vibrational motion of the target, is demodulated down to baseband using an RF in-phase and quadrature demodulator. Acquisition and calculation of the target phase angle is carried out on a custom-made control board which utilizes high-resolution A/D converters, variable gain amplifiers, and a Spartan-6 field programmable gate array.

Design of dual-link (wide- and narrow-beam) LED communication systems.

We explore the design of an LED-based communication system comprising two free space optical links: one narrow-beam (primary) link for bulk data transmission and one wide-beam (beacon) link for alignment and support of the narrow-beam link. Such a system combines the high throughput of a highly directional link with the robust insensitivity to pointing errors of a wider-beam link. We develop a modeling framework for this dual-link configuration and then use this framework to explore system tradeoffs in power, range, and achievable rates. The proposed design presents a low-cost, compact, robust means of communication at short- to medium-ranges, and calculations show that data rates on the order of Mb/s are achievable at hundreds of meters with only a few LEDs.

Spectral LADAR: active range-resolved three-dimensional imaging spectroscopy.

We present the concept and experimental results for Spectral LADAR, an augmented LADAR imager combining three-dimensional (3D) time-of-flight ranging with active multispectral sensing in the shortwave infrared (1080-1620 nm). The demonstrated technique is based on a nanosecond regime pulsed supercontinuum transmitter and spectrally multiplexed receiver that computes a high-resolution range value for each of 25 spectral bands. A low frame-rate prototype unit is described. Results demonstrating 3D imaging and material type classification of objects, especially those obscured by camouflage, are shown at effective stand-off ranges exceeding 40 m. These capabilities and the highly eye safe wavelengths at which the system operates make it suitable for applications in military imaging and robotic perception.