Laser-based applications leveraging coherent laser sources are subject to optical distortions created by random media containing random refractive index variations of various scale sizes. Refractive index fluctuations sizes comparable to the optical wavelength, due to small particles, create complex light-material interactions. Studying this particle interaction can be approached using statistical optics that model the coherence properties of the medium by the implementation of random phase screens. A phase screen represents a statistical realization of the optical phase shifts accumulated during propagation whose statistics are derived from a medium’s optical phase power spectrum. In this work, the phase power spectrum of a turbid medium is connected to the medium’s particle distribution by the medium’s volume scattering function by radiative transfer theory. This model is limited to small-angle forward scattering and small propagation geometries to prevent aliasing by high angle scattered light. Using this relationship, the statistics of the generated phase screens are studied and applied to the propagation of optical vortex beams through turbid water. Experimental orbital angular momentum mode spectrum measurements and intensity attenuation data are presented showing good agreement with the model. Furthermore, the validated phase screen model is shown to predict, as particle sizes increases, the effects of forward peaked scattering leading to vortex beam distortion.
Accurate measurement of laser light phase after propagation through underwater optical turbulence is crucial for defense and commercial applications like underwater communications and sensing. Traditional phase-measuring methods, like Shack-Hartmann wavefront sensors, have limited effectiveness in strong optical turbulence. The Gerchberg-Saxton (GS) method utilizes synchronized intensity images in the image and Fourier planes and retrieves the phase through an iterative algorithm. We evaluate the Gerchberg-Saxton algorithm's accuracy for laser light propagation through simulated Kolmogorov turbulence and experimentally generated Rayleigh-Bénard (RB) natural convection. The results of the phase retrieved from the experimental data recorded in pupil and focal planes are compared with the phase measurements from a Shack-Hartmann sensor. We tested the efficacy of the Gerchberg-Saxton algorithm to estimate the phase of laser light upon propagation through underwater optical turbulence.
In the ocean, underwater currents are driven by various natural effects attributed to heat transfer through water. The movement of heat subsequently affects light propagation due to changes in the water’s refractive index leading to optical phase distortions. Applications implementing laser beams containing structured phase profiles are prone to being distorted by this underwater optical turbulence. Typical distortions of these beams can include beam wander, intensity and phase variations, and beam spreading that can limit their effectiveness for applications including free-space optical communication, imaging, or sensing. Experimental and theoretical studies have shown optical vortices, a form of structured light, propagate differently through optical turbulence compared with Gaussian beams. Changes in propagation are observed by varying the amount of Orbital Angular Momentum (OAM) a vortex beam carries that increases the beam size as OAM increases. This experimental study intends to fairly compare Laguerre-Gaussian (LG) beams to Gaussian beams after propagation through underwater turbulence by normalizing the initial beam size using the RMS radius. The metrics chosen are the mean scintillation, on-axis intensity, and intensity correlation. Results show the scintillation and on-axis intensity, when chosen at locations along the LG beam annuli, are similar for different LG beams. When the initial beam waist is normalized, the speckle field correlation width and peak correlation energy decreases as RMS radius increases. These results show that structured light is not independent of the effects of beam size and divergence, similar to Gaussian beams, to determine propagation effectiveness or robustness.
Optical applications, such as imaging, communications, and sensing, can be severely limited by the effects of oceanic turbulence when the water is free of particulate matter. To study this phenomenon in a controlled environment, a Rayleigh B`enard tank, housed at the U.S. Naval Academy, was used to study heat driven convective turbulence in a systemic manner. A Gaussian laser beam was characterized though synchronized phase and intensity measurements obtained by a Shack-Hartmann wavefront sensor and high-speed camera, respectively. The beam’s instantaneous intensity and phase measurements were analyzed in space and time, and the synchronicity between the wavefront sensor and camera allows for the temporal statistics to be directly compared. Phase time series were analyzed to obtain an ensemble averaged power spectrum that was fit to a bounded Kolmogorov model. Wavelet analysis was leveraged to process the turbulence frequency rates at weak and moderate turbulence levels. Estimates for the turbulence turnover rates were obtained from the temporal statistics. Upon applying the same methods to the intensity time series, the statistics appeared subtly different compared to the phase statistics. It was shown within the wavefront frequency statistics that features changed on the time scale of seconds. However, intensity features changed on timescales of seconds to a tenth of a second.
Characterization of the optical turbulence of complex media is important to designing resilient free-space optical communication systems. Previous studies have used machine learning algorithms to characterize optical turbulence in the atmospheric environment, but we propose to extend this concept to the underwater medium. Our experimental design propagates a Gaussian beam ~1.25 meters through a Rayleigh-Bénard (RB) turbulence tank, which creates realistic optical turbulence that is fully controllable and repeatable. The intensity and phase distortions of the Gaussian beam after propagation will be collected and used to train a convolutional neural network (CNN), for the purpose of the underwater optical turbulence characterization. The CNN will be trained to classify turbulence levels based on both intensity and phase measurements in varied levels of optical turbulence.
In the underwater environment, scattering due to optical turbulence can degrade radio frequency (RF) information encoded on a laser beam’s intensity profile and can limit the effectiveness of free-space optical communications. However, for sensing applications, changes in the RF subcarrier due to turbulence could be used to characterize the underwater environment. An alternative form of modulation can be created through heterodyne detection by interfering two co-propagating beams with different optical frequencies on an optical detector. This form of modulation was used to sense spatial properties of optical turbulence using beams carrying orbital angular momentum (OAM). Upon detection, each modulation method results in an oscillating photocurrent; however, it is not clear if the photocurrent produced by each modulation method responds differently to the effects of turbulence. To address how these modulation schemes may be affected by turbulence, a series of experiments are conducted. The results are analyzed to identify the impact of different charges of OAM relative to a Gaussian beam.
We consider the design and generation of spatially partially coherent (SPC) beams carrying orbital angular momentum (OAM) propagating through complex random media. It has been theoretically shown that spatial coherence can be controlled through a prescribed linear superposition of Laguerre-Gaussian (LG) modes. Experimentally the SPC beams are obtained by randomly cycling the phase screens of the coherent modes, with each mode contributing a weight that is proportional to its eigenvalue in the coherent mode decomposition equation. The spectral degree of coherence, ξ , theoretically varies from 0 (fully coherent) to 1 (incoherent). Experimentally, it is suggested that we can reach the highest level of incoherence when the modes are combined where LG mode orders are of equal weights. Preliminary measurements indicate a reduced coherence corresponding to increasing ξ. Our experimental design imposes turbulence on the beam to examine the effects of its spatial partial coherence on the scintillation index (SI). It has been shown that benefits to communication system performance, specifically underwater, can be achieved through the control of spatial coherence properties of laser light propagation.
Remote sensing modalities can utilize the effects of laser scattering from particulate matter to infer information about environmental conditions present in the optical path. Light contains many degrees of freedom that can be manipulated for sensing. In this work the spatial phase distribution is leveraged through the use of light's orbital angular momentum (OAM). Our sensing method, called optical heterodyne detection of orthogonal OAM modes (OHDOOM), uses the distortion of the optical signal to determine the presence of environmental disturbances. OAM beams are sensitive to optical disturbances that induce phase variations, in turn, spreading power among other OAM modes. A set of experiments are performed using different solutions of particulate matter to create a turbid medium. The experimental results showed that OHDOOM is most likely sensitive to a turbid medium containing particles larger than the wavelength.
Structured laser beam propagation through inhomogeneous media is of interest for remote sensing and spatial division multiplexed free-space optical communications. The structured light of interest contains orbital angular momentum (OAM) that inherently forms an orthogonal basis set. The decomposition of an optical wavefront into OAM modes is analogous to an azimuthal Fourier transform that provides angular information. When a wavefront propagates through an imperfect optical system or an inhomogeneous medium, the inhomogeneities manifest themselves as phase distortions along the optical wavefront. This study aims to understand how phaseonly distortions shape a beam’s OAM spectrum. The azimuthal information of the distortions will be explored using the Fourier duality between the angular position and azimuthal frequency. To present this perspective, the example of an azimuthal aperture will be used to display the angular uncertainty principle. This concept will be further discussed using an example of a phase-only distortion represented by a common lens aberration using Zernike polynomials and then to the more complicated scenario of a random medium. It is found that the Fourier duality can be used to calculate the OAM spectrum of a random phase distortion. For the case of a finite beam incident on the distortion, it is found that the beam size and spatial structure play a role in spreading the beam’s OAM spectrum. It is seen that a beam’s OAM spectrum spread is independent of the mode if the beam size is taken into account.
In recent years the study of structured light, specifically orbital angular momentum (OAM), for remote sensing and free-space optical communications has gained great interest. Laser beams propagating through the atmosphere are susceptible to optical turbulence, which leads to beam distortions in the form of scintillation, beam wander, increased beam spreading, and loss of temporal and spatial coherence. One method that has been predicted to reduce scintillation is the use of partially coherent beams that can be propagated via their coherent mode representation (CMR). For the case of communications this is of great importance as scintillation reduction can lead to improved link effectiveness. For a spatially division multiplexed system employing OAM, reduction of the beam’s spatial coherence will possibly impede on the ability to separate the spatial modes on the output. A partially coherent beam carrying OAM through its CMR is the Im Bessel beam that recently has been experimentally realized. To expand upon the possible uses of the Im-Bessel beam, this paper intends to take a first step at simulating and quantifying the beam’s CMR through time-correlated optical turbulence. In this way, traditional beam metrics such as scintillation, beam spreading, spatial coherence, and OAM spectrum can be quantified. New degrees of freedom, such as CMR cycling rate and detector sampling rate relative to the turbulence, will also be explored.
Laser beams carrying orbital angular momentum (OAM) in underwater environments have been a topic of research for underwater communications and remote sensing applications. When a laser beam propagates through turbid water, the dominant form of attenuation and spatial dispersion is scattering due to small particles. The goal of this experimental study is to measure the transmitted OAM mode and its intermodal crosstalk via measurements of the OAM spectrum after propagation through turbid water. An initial beam is encoded with a single OAM state using a spiral phase hologram displayed on a high-resolution spatial light modulator. The optical receiver performs a phase cancellation measurement to decode the OAM on the incident beam. After recording images of the phase canceled beam, the OAM spectrum is found in post-processing. Three methods of post-processing are presented and compared to account for beam wander and an astigmatism in the experiment. After determining which method of post-processing gives the most accurate results, our results are compared to those in the literature. Our results show that an OAM beam maintains mode purity up to an optical depth (OD) of 12, whereas previous literature saw a loss of mode purity at an OD of 6. This is attributed to differences in receiver field of view, scattering volume, scattering length, and beam size.
The study of light carrying complex phase profiles, specifically orbital angular momentum (OAM), has been of interest for its use in free-space optical communications and remote sensing systems. Each of these applications requires a beam to propagate through the atmosphere, where optical turbulence is the main distorter of the beam. In this computational study, coherent Laguerre-Gaussian (LG) beams and partially coherent Im Bessel beams are propagated through atmospheric turbulence. The LG beams are propagated through turbulence using a split-step method for solving the Fresnel diffraction integral. Whereas for the the Im Bessel beams, the coherent mode representation is used, where each eigenmode is individually propagated through turbulence. The split-step algorithm is then modified to simulate optical turbulence by the use of phase screens. Beam metrics, in the form of intensity, scintillation, spot size, and OAM spectrum, are then calculated over a number of turbulence realizations. Three turbulence regimes are simulated that include the weak, moderate, and strong turbulence regimes along with two different initial beam sizes. The Im Bessel beam is simulated using three values of overall coherence ξ. The results for the metrics are plotted against propagation distance and OAM mode l. The resulting beam metrics show a strong dependence on turbulence strength, a weak dependence on OAM mode due to LG modes expanding with an extra prefactor of ι + 1, and no strong dependence on the overall coherence ξ.
The creation and detection of light carrying orbital angular momentum (OAM) has been of great interest for applications that require a beam to propagate through atmospheric turbulence such as for free-space optical communications and remote sensing. In this experiment, Laguerre-Gaussian (LG) beams are created using a high-resolution deformable micromirror device (DMD) and then propagated through two artificial turbulence strengths. To measure the OAM encoded on the LG beams, the wavefront is decomposed into an orthogonal basis set denoted as the OAM spectrum. The OAM spectrum is measured using two forms of Mach-Zehnder interferometers (MZI). The first interferometer is a modified MZI that is used to measures the OAM spectrum by first measuring the angular correlation function with a single interferogram. The second interferometer is a traditional MZI used to record an interferogram that can then be processed to extract the phase of the LG beam. The measured phase is then used to find the OAM spectrum by applying modal decomposition. To improve the OAM spectrum measurement, a singularity tracking algorithm is used to correct for the turbulence distortions. Each interferometric technique is compared with and without the presence of artificial turbulence. Both interferometric methods were significantly affected by turbulence, but the traditional MZI was able to measure the spreading of the OAM spectrum well with the support of a singularity tracking algorithm.
In recent years the study of the orbital angular momentum (OAM) of light has gained traction for applications of remote sensing in underwater environments. When a laser beam propagates through turbid water, the dominant form of attenuation is scattering by large particles relative to visible wavelengths. The volume scattering function (VSF) describes the intensity distribution of light versus angle from an infinitesimal volume of scatterers. Recent computational studies have suggested that the distribution of scattered light due to a single scattering particle differs depending on whether the light is encoded with OAM or not. Other computational studies suggest that these differences are minimized when a volume of particles is illuminated. However, none of these computational projects provide experimental evidence to validate their predictions. This paper sets out to determine the experimental behavior of the VSF in the single scattering regime with and without OAM encoding on the transmitted beam. The experimental results are directly compared to Mie theory and a mixed numerical and analytical method.
Optical countermeasures are widely used nowadays and quite often a laser is used as the optical source. Unfortunately such a laser beam can become severely distorted by optical turbulence when propagating through the atmosphere, resulting in effects such as beam spreading, beam wander, irradiance fluctuations, and loss of spatial coherence. These effects can be (partially) overcome using knowledge of the atmospheric conditions, as well as techniques to correct for amplitude and phase distortions. Our research focuses on the characterization of the atmospheric conditions, using adaptive optics, an in-house developed multi-aperture transmissometer, as well as a plenoptic sensor using phase distortion algorithms to compensate for effects caused by (strong) turbulence conditions.
Laser beams used in many open space applications, such as in defense, optical communication, and remote sensing, will subject to turbulence distortions that disrupt the intended beam profiles at the end of propagation. To guide the transmitted beam properly through an open space channel, adaptive optics (AO) are often used to implement beam corrections based on the reciprocity principles. In specific, if wave distortion from a remote spot can be determined and field conjugated at the site of the transmitter, the transmitted light will focus to the same spot at the receiver. Many experiments have demonstrated such a principle using a cooperative laser guide star on the target plane. However, finding or creating a well-defined guide star is impractical in real-world applications. The second best beacon choice is temporal glint signals that are relatively refined in geometry and brighter than ambient target illumination. To date, the best approach to extract information from arbitrary glint signals to instruct AO correction is still unknown. We propose the plenoptic sensor technique to extract phase distortion information from glint signals with minimum loss of information. In addition, as the addressed turbulence channel is typically a lateral path near the ground, we also validate the function of the plenoptic sensor in revealing the anisotropic state of turbulence.
Atmospheric aerosols, containing water, constitute most of the air during non-ideal weather conditions including fog, haze, and mist, and are present in a lower volume density during ideal weather conditions. These aerosols cause light to be attenuated while propagating through the atmosphere, which can be described by Lambert-Beer’s law. The extinction coefficient is dependent on the cross-sectional geometry of the scattering volume which can be found using Mie theory. In the case of a real environment a distribution of particle sizes must be considered where the particles present are described by a weighted value relative to the number density and distribution function of particle radii chosen. We have built a point visibility meter, which measures the amount of scattered light at a specific forward scattering angle under the assumption that the scattered light is linearly related to the extinction coefficient of different weather conditions. To validate our design, it will be compared against a commercial visibility meter.
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