This PDF file contains the front matter associated with SPIE Proceedings Volume 13149, including the Title Page, Copyright information, Table of Contents, and Conference Committee information.

The development of low size, weight, and power (SWAP) long wave infrared (LWIR) hyperspectral imaging tools is challenging due to a need for either heterogenous integration of bandwidth limited pixels, dispersive filtering, or time varying spectral filtering (i.e. FTIR). Ideally, a high information yield, low SWAP imager should have high spatial resolution and temporal resolution as well as spectral sensitivity and require few hardware components. An imager composed of electrically tunable stacked graphene may be able to address many of these requirements. AB stacked bilayer graphene (BLG) exhibits bright exciton resonances at the 1s (P₁) and 2p (P₂) exciton states. These exciton resonances result in large peaks in the photocurrent, and previous works have shown that the location of these excitons can be tuned across the 10μm to 20μm spectral band by applying a vertical electric field across a gate/insulator/BLG/insulator/gate stack. An array of bilayer graphene infrared detectors can be individually gate-tuned to create a set of devices that each have a unique responsivity as a function of wavelength. Our work is the first to show via simulations based on experimentally measured, spectrally resolved bilayer graphene pixel responsivity data that complex spectral signatures can be reconstructed from 650cm^-1 to 750cm^-1 using fewer than 25 bilayer graphene detectors. Spectra reconstructions were performed using an Elastic Net algorithm that solves a least-squares minimization problem with additional L1 and L2 norm penalty terms. Then, we show for the first time that a single bilayer graphene pixel cooled to 80K can be used to detect the presence of atmospheric concentrations of CO₂ either by direct evaluation of the pixel’s photocurrent or through the Elastic Net reconstruction technique which relies on previous characterization of the detector’s responsivity as a function of gate voltage and wavelength.

Space Domain Awareness (SDA) is important for understanding the space environment to ensure safe operation of space missions. SDA activities include the detection, identification, tracking and characterizing of artificial satellites. SDA objectives rely greatly on the information that can be gained from ground-based sensors, such as optical telescopes. A space object may be detected by a telescope when it passes in front of a star. There have been studies of how the shadow cast to Earth from a star can be interpreted for important data, referred to as Shadow Imaging. Herein we discuss the usage of information theoretic methods to understand the limitations of stellar Shadow Imaging. These methods measure the information content in the irradiance pattern, as seen by a terrestrial observer, from the shadow cast by the geosynchronous space object passing in front of a stellar source.

Estimating the silhouette of large resident space objects through decreased intensity measurements is an established technique in astronomy. Synthetic Aperture Silhouette Imaging (SASI) applies these concepts using a North-South oriented linear array of hobby telescopes to detect decreased intensity from stars as satellites occult the stars. Within the past twenty years this technique has been expanded to satellites near Earth in mathematical and computer models as well as scaled laboratory demonstrations. Often this technique is discussed in relation to the geostationary (GEO) belt of satellites, but it could also be applied in other orbital regimes (where a linear North-South array configuration is likely non-optimal). Previous work has indicated that orbital ephemeris data may lack sufficient accuracy to reliably plan measurements of actual satellite occultations (using a single telescope). This paper discusses the progress of an initial field test using a single telescope equipped with a photon detector and astronomical camera. The goal is to measure intensity drops from stars when satellites are predicted to pass between the star and the telescope in a ground station. An 11-inch Celestron Rowe-Ackermann-Schmitt Astrograph is mounted on an Astro-Physics 1600GTO mount and equipped with a ThorLabs single photon counting module SPCM50A and ZWO ASI174 camera. The target is the International Space Station (ISS) in hopes that the larger area of the object’s silhouette will overcome uncertainties in the orbital data. This initial field test informs the design of an individual telescope in a SASI array by capturing challenges, limitations and potential solutions. Hardware issues like periodic error in the telescope mount, image focus, and USB overload led to hardware upgrades and substitutions. Environmental conditions impacted the performance of the telescope mount and camera due to the site location limitations. Ephemeris updates make long-term planning difficult, so occultation predictions need to be reassessed as close to the transit time as possible. These and other issues arose during the initial field test, highlighting challenges that need to be overcome to further develop SASI.

This work demonstrates the impact of sampling basis resolution on Single Pixel Imaging’s ability to accurately measure the amplitude and phase of an arbitrary complex light field. We observe that phase crosstalk occurs in the reconstructed amplitude when the sampling basis is coarser than the underlying phase distribution. To investigate this phenomenon, a spatial light modulator is employed to prepare the complex field—comprising both amplitude and phase—utilizing a phase-only hologram. The field is then sampled at various resolutions using the Hadamard basis on the same SLM with interferometric Single Pixel Imaging. Measurement of the field takes place on a single point through 3-step interferometry and a Mach-Zehnder interferometer. While the phase is correctly reconstructed for each resolution, our findings reveal distinctive attributes of the phase distribution in the reconstructed amplitude for coarser sampling resolutions.

Active imaging techniques such as continuous-wave (CW) illumination and laser range-gated (LRG) imagery can provide increased contrast-to-noise ratio over passively-illuminated systems under conditions with poor solar illumination and strong scattering. Additionally, the shortwave infrared (SWIR) and extended SWIR (eSWIR) bands have been shown to offer increased performance over VIS and NIR systems in these conditions. Our group at the University of Arizona has developed an active imaging testbed with capabilities in the SWIR and eSWIR in order to test and quantity these benefits in field imaging studies. We discuss the design of the testbed, and show imagery and performance calculations from our field collections.

Speckle noise is inherent to coherent imaging systems such as synthetic aperture radar (SAR), optical coherence tomography (OCT), and ultrasound imaging. However, its multiplicative nature makes it especially challenging to remove. Today the most effective speckle denoising methods average multiple identically distributed measurements—however, these approaches fail to reconstruct dynamic scenes. In this work we leverage implicit neural representations (INRs) to perform unsupervised speckle denoising of time-varying sequences. We optimize a maximum likelihood-based loss function to produce high-fidelity, speckle-free reconstructions. Our approach significantly outperforms existing techniques, achieving up to a 4dB improvement in peak signal-to-noise ratio (PSNR) for dynamic scenes with simulated speckle.

In coherent imaging systems like SAR and digital holography, speckle noise is effectively mitigated using the multilook or multishot approach. Utilizing maximum likelihood estimation (MLE), we recently theoretically and algorithmically showed the feasibility of effectively recovering a signal from multilook measurements, even when each look is severely under-determined . Our method leverages the "Deep Image Prior (DIP) hypothesis," which posits that images can be effectively represented within untrained neural networks with fewer parameters than the total pixel count, using i.i.d. noises as inputs. We also developed a computationally efficient algorithm inspired by projected gradient descent to solve the MLE optimization, incorporating a model bagged-DIP concept for the projection step. This paper explores the method's applicability to deblurring in coherent imaging, where the forward model involves a blurring kernel amidst speckle noise—a significant challenge with broad applications. We introduce a novel iterative algorithm to address these issues, enabling multi-look deblurring without simplifying or approximating the MLE cost function.

Active imaging techniques can provide increased signal-to-noise ratio over passive imaging approaches, particularly in the reflective infrared bands (NIR, SWIR, and eSWIR) where passive solar illumination is reduced relative to the visible band. However, providing sufficient illuminator power at long range can introduce severe SWaP tradeoffs for system designers, as the strength of the illumination for a resolved laser spot scales proportionally to the inverse square of the illuminator-to-target distance. Active systems must therefore use illuminator photons efficiently. Avalanche photodiodes (APDs) offer high gain in the electronic domain, allowing the detection of a small number of photons by boosting the signal above the floor imposed by read noise. We compare the contrast-to-noise ratio performance of a mercury-cadmium-telluride (MCT) APD camera and a COTS InGaAs SWIR camera with an illuminator at 1.645[um] as a function of illuminator power. Factors affecting performance are discussed.

Disturbances such as atmospheric turbulence and aero-optic effects lead to wavefront aberrations, which degrade performance in imaging and laser propagation applications. Adaptive optics (AO) provide a method to mitigate these effects by pre-compensating the wavefront before propagation. However, development and testing of AO systems requires wavefront aberration data, which is difficult and expensive to obtain. Simulation methods can be used to generate such data less expensively. For atmospheric turbulence, the Kolmogorov-Taylor model provides a well-defined power spectrum that can be combined with the well-known angular spectrum method to generate synthetic phase screens. However, as aero-optics cannot be similarly generalized, this process cannot be applied to aero-optically relevant phenomena. In this paper, we introduce ReVAR (Re-Whitened Vector Auto- Regression), a novel algorithm for data-driven aero-optic phase screen generation. ReVAR trains on an input time-series of spatially and temporally correlated wavefront images from experiment and then generates synthetic data that captures the statistics present in the experimental data. The first training step of ReVAR distills the input images to a set of prediction weights and residuals. A further step we call re-whitening uses a spatial principal component analysis (PCA) to whiten these residuals. ReVAR then uses a white noise generator and inverts the previous transformation to construct synthetic time-series of data. This algorithm is computationally efficient, able to generate arbitrarily long synthetic time-series, and produces high-quality results when tested on turbulent boundary layer (TBL) data measured from a wind tunnel experiment. Using measured data for training, the temporal power spectral density (TPSD) of data generated using ReVAR closely matches the TPSD of the experimental data.

The aero-optical distortions caused by supersonic mixing layers over a flat optical window are relevant to the performance of hypersonic vehicles. Such mixing layers are typically temperature-mismatched and gas speciesmismatched due to a need to efficiently cool the optical window. To investigate the effect of the mismatched properties across the mixing layer created by blowing a cool gas over a flat window, optical measurements of an M=2 freestream air flow with a cooling two-dimensional gas jet were taken using time-resolved Shack-Hartmann WFS and Schlieren photography. To complement the optical measurements, other non-intrusive techniques, specifically acetone-based PLIF and spatially-resolved infrared thermography techniques were implemented to extract relevant fluidic properties of the mixing layer. The cooling jet gas species were air, helium and carbon dioxide (CO2). To create the temperature mismatch, the total temperature of the freestream flow was varied from 295K to 750K, while the total temperature of the cooling jet was kept constant at 295K. Results of this experimental work will be presented and discussed. Based on experimental input, a scaling method proposed in previous work was implemented in order to predict aero-optical distortions, using the mixing-dominant assumption previously applied to the helium-air and air-CO2 case.

In previous work, we studied the effects of a supersonic shockwave on the performance of a Shack-Hartmann wavefront sensor (SHWFS). A shockwave is a sudden change in density which then cause a sharp gradient in the wavefront. This results in dots distorting in the SHWFS dot pattern which in turn affects the accuracy of wavefront reconstruction. We used higher order statistics, such as standard deviation, skewness and kurtosis to identify and eliminate these distorted dots in Shack-Hartmann wavefront sensors, improving the accuracy of the final reconstructed wavefront. However, this is contingent on accurate calculations of the centroid, standard deviation, skewness, and kurtosis of these dots. In the first part of this work, we look at the effect of the finite pixel size on the accuracy of the Shack-Hartmann wavefront sensor, specifically on the calculation of the centroid and higher order statistics of a pixelated dot. We simulate a dot and average the intensity distribution for different pixel sizes. We show that the error is significant if the ratio of the center Dot size/pixel size is less than 2. Past this ratio of 2, the centroid and statistics error of the dots drop to near zero. We also explain some striping artifacts observed in the statistics maps in experimental work. In the second part of this paper, we investigate the centroid error of a dot approaching the edge of the Area of Interest (AOI). In cases of large tilts in the wavefronts, the dot can be pushed into or past the edge of the AOI. We show that a large AOI size/Dot size ratio allows for the most tilt and range of movement. However, by squaring or cubing the intensity distribution, the error can be further reduced for a given system.

Airborne laser propagation systems requiring precise focus and pointing of a beam are subject to aero-optical wavefront aberrations, due to the time and space variations in the index of refraction of the air which is disturbed by the system. While these disturbances can be compensated with conventional adaptive optics (AO), in general their speed and magnitude require an extremely large AO system. Effective aero-dynamic design of the turret and aircraft can significantly mitigate these disturbances, but a ‘quasi-static’ lensing term often remains. A simple image sharpening metric (ISm) is evaluated using surrogate imagery aberrated by real world measured aero-optic wavefront data. This method is compared to a far field power-in-the-bucket beam quality metric (PIBm) for a simulated laser beam subject to the same disturbances and wavefront compensation. The convergence of these metrics are compared in order to gauge the suitability of using the image sharpness metric to compensate aero-lensing effects.

This work presents preliminary results on aero-mechanical jitter of a hemispherical optical turret. A simplified geometry with a hemispherical shell and optics-holding canister was designed to reduce degrees of freedom and provide better insight into fundamental physics. Modal analysis of the turret and mounting plate to the wind tunnel, performed using finite element analysis (FEA), revealed significant plate displacements in the lowest frequency modes. Three mounting plate thicknesses (1/4”, 1/2”, and 1”) were tested. Wind tunnel tests at the University of Notre Dame’s White Field Mach 0.6 wind tunnel assessed turret vibrations at speeds from Mach 0.2 to 0.5, using accelerometers and Shack-Hartmann tilt sensors. Two scenarios were tested: one with the turret inside the tunnel exposed to the flow, and another with the turret attached outside of the wind tunnel so that it is only excited by the base motion of the wind tunnel. The 1/4” plate showed tilt measurements ranging from 30 to 190 microradians when exposed to flow, compared to 10 to 50 microradians in the baseline case. The 1/2” and 1” plates exhibited lower tilts and less distinction between flow and baseline conditions. Overall, the simplified turret only had about three vibration modes affecting tilt, with strong spatial agreement between experimental and FEA modal patterns.

This paper explores the efficacy of employing machine learning, specifically an encoder-style convolutional neural network, to estimate the magnitude of an optical-phase discontinuity (|Δϕ|) that results in an aberrated, farfield irradiance pattern. The model receives a single 32×32 normalized irradiance pattern image and returns the estimated |Δϕ|. We train and validate the model using simulated data with varying values of Δϕ (from 0 to 2π radians), discontinuity locations within the aperture of the simulated system, and strengths of background noise. In exploring this trade space, we calculate the mean absolute errors of the model to be between 0.0603 and 0.475 radians. We also explore the model’s versatility using varying spot sizes to augment the transfer of this model across various systems where the focal length, aperture diameter, or light wavelength may differ, thereby influencing the number of pixels holding information across each irradiance pattern. Finally, this model is tested on experimentally collected data using a spatial light modulator, resulting in a mean absolute error of 0.909 radians. This research supports the development of a shock-wave-tolerant phase reconstruction algorithm for the Shack–Hartmann wavefront sensor. At large, robust shock-wave-tolerant phase reconstruction algorithms will improve wavefront sensing efforts where shock waves are present.

The objective of the research is to experimentally investigate multi-conjugate adaptive optics for compensating strong atmospheric turbulence in laser beam propagation. By using multiple wavefront sensors and deformable mirrors placed at multiple conjugate planes along the beam propagation path, multi-conjugate adaptive optics allows for the simultaneous compensation of both the amplitude and phase of the propagating laser beam. This paper provides a description of the laboratory multi-conjugate adaptive optics testbed developed at the Naval Postgraduate School and presents current experimental results on the compensation of laboratory-simulated atmospheric turbulence using multi-conjugate adaptive optics.

The MMT Adaptive optics exoPlanet characterization System (MAPS) is currently in its engineering phase, operating on sky at the MMT Telescope. The MAPS Adaptive Secondary Mirror’s actuators are controlled by a closed loop modified PID control law and an open loop feed forward law, which in combination allows for faster actuator response time. An essential element of achieving the secondary’s performance goals involves the process of PID gain tuning. To start, we briefly discuss the design of the MAPS ASM and its actuators. We then describe the actuator positional control system and control law. Next, we discuss a few of the issues that make ASM tuning difficult. We then outline our initial attempts at tuning the actuator controllers, and discuss the use of actuator positional power spectra for both tuning and determining the health and failure states of individual actuators. We conclude by presenting the results of our latest round of tuning configuration trials, which have been successful at decreasing mirror latency, increasing operational mirror modes and improving image PSF.

Using digital holographic (DH) sensors, coupled with iterative computational algorithms we can sense and correct the effects of distributed volume turbulence in DH imagery. These iterative methods minimize a non-convex cost function with respect to the wavefront phase function, modeled as discreet arrays. This approach leads to high-dimensional optimization problems plagued by local minima. The problem is amplified in the presence of challenging conditions, (e.g., high noise, strong turbulence, insufficient data). We investigate using implicit neural representations (INRs) to model atmospheric phase errors in DH data. INRs offer a low-dimensional functional representation, simplifying the optimization problem and allowing us to produce high-quality wavefront estimates and focused images, even in deep-turbulence conditions.

In this paper we explore the use of digital holography with a high-speed camera to sense and correct atmospheric turbulence. Deep turbulence, a type of atmospheric turbulence, degrades the performance of both imaging and directed-energy systems. Characterizing and correcting atmospheric turbulence requires knowledge of the induced phase errors on the wavefront. Digital holography provides the capability to measure phase errors in the most challenging atmospheric conditions. Previous laboratory experiments at the United States Air Force Academy have demonstrated both sensing and correction of simulated atmospheric turbulence at discrete planes using digital holography. In this work, we design and test a digital holography system capable of imaging in relevant atmospheric conditions. This paper expands the optical design of the existing laboratory-based digital holography system to be more capable of accurately measuring real-world turbulence because it uses a high-speed camera. Our results detail the performance of the digital holography system in a controlled test environment and provide data about the feasibility of integrating digital holography into future fielded systems.

Applications utilizing free space beam propagation over long distances in the atmosphere require active sensors and beam shaping. New wavefront sensor designs promise improved performance in deep turbulence, but comprehensive comparisons of modern wavefront sensor designs within Adaptive Optics (AO) loops have yet to reveal winning system-level designs for adaptive optics systems capable of correcting deep turbulence. Here, we attempt to shed light on the problem using a comprehensive wave optics model to evaluate a least-squares based and interferometric-based wavefront sensing techniques, namely the Shack-Hartmann wavefront sensor and pupil plane off-axis digital holography in combination with optimal and adaptive predictive control. The Shack Hartmann wavefront sensor has been an established wavefront sensor that provides a measurement of the wavefront through fast measurements of the wavefront gradient and least squares reconstruction. Interferometric techniques such as digital holography provide higher resolution wavefront reconstruction and improved performance with strong turbulence but with stricter laser requirements and larger computation time. For an optimal AO design in a given application, there is a trade-off between reconstructed wavefront resolution and speed. In this paper, we use wave-optics simulation to qualitatively discuss the upper bounds of AO in deep turbulence, spatial resolution limitations of Shack-Hartmann and Digital Holography wavefront sensors. We show preliminary results of closed-loop AO performance in dynamic deep turbulence, inclusive of wind and limited spatial resolution. Additionally, we show a preliminary analysis of using predictive control to improve the temporal performance of an AO loop and compensate for latencies due to hardware.

For several decades, the Tyler frequency has provided the tracking community with a reliable estimate of the bandwidth required to track an object through turbulence consistently. Specifically, it determines a 3-dB bandwidth at which the expected one-axis/one-sigma residual G or Z tilt equals the diffraction angle of a given system. That analysis, however, arrives at tractable solutions by operating in continuous rather than discrete time. Furthermore, it assumes only a first-order lowpass filter as the dynamic controller model. This paper extends Tyler’s original treatment to address each of these potential limitations by analyzing digital rather than analog controllers and generalizing beyond a single-pole transfer function for higher-order control. It further identifies an additional bandwidth constraint from image-plane speckle noise associated with coherent illumination. At its most severe, speckle can reduce precision to the point of becoming stringent than turbulence as a limiting factor in tracking performance. Reducing the sample rate can then allow for speckle averaging, which in turn leads to improvements in track precision and ultimately buys back performance. This trade space poses an optimization problem, with proposed solutions in the form of modified bandwidth requirements that depend upon system diffraction angle, object angular velocity and speckle contrast ratio. Validation from wave-optics simulations and computer-aided control system design informs the analytical tools developed here and demonstrates their applicability to modern challenges in active tracking.

Free-space optical communications (FSOC) is emerging as a crucial alternative for high data rate networks. With the commercial availability of optical wide band super continuum lasers, there arises an opportunity to enhance the link availability in the presence of strong turbulence. This paper presents a comprehensive analysis of a terrestrial optical link, considering the compounding factor of exploiting the advantages of incoherent beam combining from spatial diverse laser sources. To assess the performance of the optical link, wave optics simulation and perturbation theory are employed and compared. The analysis focuses on exploring the reduction in fade statistics, which is critical for ensuring reliable and robust communication links in adverse atmospheric conditions. Analysis will be conducted over a variety of, ranges, aperture diameters, wavelengths, and levels of turbulence. By leveraging the capabilities of wide band super continuum lasers, the proposed study demonstrates the potential improvements in link availability, throughput, and stability in the presence of turbulent atmospheric conditions. Moreover, the benefits of harnessing incoherent beam combining from spatial diverse laser sources are also considered in the trade space analysis.

Wave optics simulations study the effect of beam propagation through the atmosphere; one notable method is the split-step beam propagation method. Current atmospheric propagation software utilizes an alternating series of Fresnel propagation and phase accumulation methods through screens which are statistically representative of the atmospheric turbulence along a line-of-sight path. From this assumption the scintillation parameter along the laser path relies on an atmospheric structure parameter, 𝐶_𝑛², and is typically measured using a path averaged scintillometer. While this works well for links established in static atmospheric conditions in harsher environments such as high precipitation rates, heavy fog, or clouds demand a more rigorous approach. Thus, current software typically over-predicts beam performance of links in harsh conditions. This work proposes a model in which scattering is computed from a “first principles” approach, i.e. the full Mie series is calculated at several locations along the simulated beam path. The scattering results are then combined with the traditional split-step beam propagation method through a correction factor to provide a model of attenuation on beam performance. Results show that the addition of the extinction efficiency factor reduced the overall intensity on target by a significant margin as compared to the traditional split-step beam propagation method. More work is needed to verify the utilization of the Mie scattering extinction along with the log-amplitude variance typically utilized to model the turbulence phase.

Optical tracking of extended targets poses significant challenges in system design and algorithm development. However, the collection of experimental data that can accurately represent these scenarios is often impractical due to cost constraints. To address this issue, this talk aims to present innovative methods that enable the generation of realistic synthetic imagery, which can be used for the purpose of tracker development. By leveraging these methods, researchers can overcome the limitations of relying solely on scarce real-world data. Synthetic imagery offers the advantage of being highly customizable, allowing for the creation of various scenarios that may not be easily accessible or feasible in real-life experiments. This flexibility provides a valuable tool for exploring different tracking algorithms and designing robust systems. However, it is essential to acknowledge the capabilities and limitations of using synthetic imagery for tracker development. While it can accurately represent certain aspects of extended target tracking, there may still exist discrepancies when compared to real-world scenarios. This talk aims to define the synthetic imagery capabilities and limitations while understanding its impact on system evaluation.

Wave optics simulations of speckle fields can be particularly prone to aliasing when using the angular spectrum propagator. We examined several methods of mitigating aliasing, which include larger guard bands, output plane windowing, absorbing boundaries, and an alternative propagator known as the sinc-basis propagator. We compared the angular spectrum propagator to the sinc-basis propagator and found that, while absorbing boundaries greatly assisted the angular spectrum propagator, the sinc-basis propagator always achieved lower root-mean-squared errors for a given array size due to the non-periodicity of the sinc basis. We examined the computation time as a function of the number of pixels and the root-mean-squared error associated with each of the propagators. Direct comparisons on same array size configurations primarily indicated that the relative wall clock time between the two methods depended highly on the core count of the machine. For all machines tested at the same pixel number, the sinc-basis propagator was generally faster up to a machine dependent pixel threshold, after which the angular spectrum propagator was faster. For machines with more parallelization, this threshold was higher and the speed-up of the sinc-basis propagator relative to the angular spectrum method was larger. It was found that the sinc-basis propagator usually has comparable to shorter computation times than the angular spectrum method to achieve the same threshold error in simulations on the computers tested.

Atmospheric induced amplitude fluctuations, known as scintillation, impose limitations on active tracking and wavefront-sensing performance over near-horizontal propagation paths. These sensors typically use centroid tracking to estimate the aperture-averaged phase gradient (G-tilt). G-tilt, in practice, is a phase-only measurement, whereas centroid tracking includes both the phase and amplitude components. For a nonuniform beam, centroid tracking will measure the irradiance-weighted average phase gradient (C-tilt). In a closed-loop system, the angular position of the centroid is used to conjugate tilt and reduce system jitter. Of particular interest are the effects of scintillation on the estimation of G-tilt from the centroid angular position. Scintillation will cause an error in the estimation of the G-tilt, and this error can be quantified by the noise-equivalent angle (NEA). The two main objectives of this work are to formulate a closed-form expression for (1) the NEA due to scintillation, and (2) the difference between G-tilt and C-tilt in the weak-to-moderate scintillation regime. The derived solutions are based on the first-order Rytov approximation. As such, the difference will be quantified by deriving a mean-squared error between the desired measurement (G-tilt) and the estimator (C-tilt).

We review our recently developed computationally-efficient methods for optical propagation and phase screen generation, and apply these techniques to the split-step propagation through turbulence. Specifically, we demonstrate the sinc method for optical propagation and phase screen generation provides accurate results for a wide range of propagation distances without the restrictive sampling requirements of Fourier methods. Beyond phase screen generation, the sinc method for phase screen generation lends itself to an efficient extension algorithm that maintains ergodicity of the random fields - a crucial detail for dynamic simulations. We verify the performance of the sinc method for static and dynamic split-step propagation of a Gaussian beam through turbulence as modeled by a modified von Karman spectrum, and we compare it to propagation with the angular spectrum method (ASM). In particular we evaluate the accuracy and robustness of the sinc method for split-step simulations through computation of second and fourth order statistics of the propagated field wherein the ASM breaks down due to artificial periodicity at the same conditions.

Algorithms that correct for volume atmospheric turbulence in coherent imagery are computationally intensive, typically requiring several iterations to converge to a solution with a split-step model, where each iteration involves multiple optical propagation computations. We examine the sampling requirements for split-step modeling using phase-space optics and show that we can propagate fields accurately, using array sizes that are 2-4× smaller than the array sizes used in a typical split-step model. These smaller array sizes can be used when the aperture and field stops for the imaging system are used as intermediary planes for individual propagation steps. We evaluate the fidelity of vacuum split-step propagation results, describe split-step model adjustments needed to accommodate diffraction and turbulence effects, and illustrate how we use split-step models for analyzing the expected performance of turbulence-compensation algorithms.

Frodo is a new Differential Image Motion Monitor (DIMM) developed as a companion instrument to the Starfire Atmospheric Monitor (SAM). SAM is a Shack-Hartmann sensor that observes bright stars to provide atmospheric information above the Air Force Research Laboratory’s Starfire Optical Range (SOR). Frodo is designed to extend atmospheric characterization at the SOR into the day, estimating all of the atmospheric parameters that SAM currently provides. The optical train of Frodo has been reproduced on the Multiconjugate Adaptive Optics (MCAO) bench in the Atmospheric Simulation and Adaptive Optics Laboratory Testbed (ASALT) at SOR. The enhanced atmospheric turbulence simulator (ATS) on the MCAO bench generates turbulence conditions with as many as 10 phase screens. The atmospheric parameter estimates from data collected with the ASALT Frodo system are presented alongside the estimates made with the laboratory’s Shack-Hartmann wavefront sensor.

The interactions between Earth’s surface and atmosphere are crucial to understanding their impact on surface layer optical turbulence, specifically the temperature structure function (C_T²) and refractive index structure function (C_n²). The Energy Balance Bowen Ratio (EBBR) – the ratio of sensible heat flux to latent heat flux – has shown promising capabilities to calculate sensible heat flux, a key component for computing C_T² and C_n². Sensible heat as calculated via the Bowen Ratio inherently accounts for moisture content and evaporation as it apportions the balance of sensible heat to latent heat in the ratio. Thus it better permits the calculation of C_T² and C_n² via a single equation only dependent on temperature and sensible heat in any stability condition as compared to “ground truth” sonic anemometer turbulence values during daylight and nighttime hours at various land sites. The Bulk Aerodynamic method relies on standard meteorological observations but requires stability corrections based on underlying assumptions with this approach. Researchers have shown success of Bulk Aerodynamic methods and similarity theory to predict C_n² in the maritime surface layer, but many adjustments for weakness in stable conditions (air warmer than the water) are necessary. In this study, field data from a marine wave boundary layer test site allow for assessments of both the EBBR and Aerodynamic methods to quantify maritime surface layer turbulence, and the results compared to sonic anemometer and DELTA C_n² values.

MZA Associates has developed and tested multiple atmospheric profiling tools to determine the levels of turbulence within a given area. This includes using multiple sensors, include imaging systems, as well as wavefront sensor (WFS) based systems. These sensors have been set up to operate unattended, including weatherproofed and non-weatherproofed hardware configurations, and are all operated through a centralized processing software called the Module Atmospheric Sensor Suite (MASS). In order to support further development of atmospheric characterization techniques, MZA has also developed a Matlab based software suite called ProfilerTools. Utilizing this software suite allows for further testing and evaluation of WFS data collected from single or dual ended systems. This paper describes the ProfilerTools libraries and how it is used to process WFS data from MZA commercial equipment and experimental WFS systems.

There are many challenges in characterizing open-air laser propagation. Varying measurement methodologies with diverse instrumentation can provide contradictory results for both optical turbulence and extinction. This paper assesses instrumentation accuracy w.r.t. a propagating laser and explores the optimal experimental setup. Accordingly, an open-air experiment was conducted to characterize the atmosphere and high-energy laser (HEL) propagation with commonly deployed instrumentation. Presented here is a comparative evaluation of the instrumentation results to far-field HEL measurements. The differential image motion monitor (DIMM) and the wide angle tele-radiometric transmissometer (WATT) provided measurements with the lowest mean percent error for optical turbulence and extinction, respectively. This suggests that path-integrated dual-sided instrumentation outperforms nodal measurements. However, it is found that nodal measurements perform best near and at the laser’s aperture height if dual-sided instrumentation is not available. Additionally, a quality-control routine is outlined for all deployed instruments considered in the evaluation. The experimental results in this paper yield instrumentation performance for characterizing static laser propagation over land. Further research is recommended to assess instrumentation over longer optical paths both static and dynamic.

The Reflective Atmospheric Turbulence Simulator (RATS) in the Air Force Research Laboratory’s Beam Control Laboratory is used to impart realistic distortions to a propagating wavefront for testing in the advancement of adaptive optical technologies. Here RATS is being used to simulate turbulence conditions over which the Small Mobile Atmospheric Sensing Hartmann (SMASH) system has typically operated. An optical clone of the SMASH system installed on the optical bench behind RATS measures the imparted optical disturbance and makes an estimate of the turbulence profile. The results are compared with the profile calculated based on the configuration of the RATS system.

Recent studies have shown that incorporating phase information alongside registered intensity distribution enhances Deep Neural Networks (DNNs) based predictions of refractive index structure function, C_n², which characterizes turbulence strength. In this study, we conducted numerical simulations to analyze the impact of received phase information on C_n² recovery error depending on properties of the used sensor and atmospheric conditions. We examined the size and number of lenses required to form an intensity pattern in the focal plane and its impact on C_n² predictions. We also considered the impact of presence of localized turbulence layer on accuracy of DNN-based C_n² predictions, ways to eliminate this impact, and locate the layer. We used wave-optics numerical simulations to generate datasets of short-exposure intensity distributions. The atmospheric propagation of a collimated Gaussian beam over the considered distance was simulated using the split-step method. The atmospheric turbulence followed von Karman’s power spectrum and was represented by a set of phase screens. These datasets were then used for training, validating, and testing the DNN models. The DNN architecture consisted of feature extracting blocks each containing three convolutional and max-pooling layers, and a single perceptron layer with 20 neurons. The model featured 16 feature extracting blocks with identical topology and weights, simultaneously receiving sequential frames from the dataset.

Branch points are seen in many adaptive optical experiments where the sensed beam has propagated over an extended path, through sufficiently strong turbulence. It has been shown that branch points provide information on how the turbulence responsible for their formation is distributed and moving along the path. Shack-Hartmann wave front sensors have previously been somewhat limited in their ability to fully capture the branch points present within their measurements. A new technique for the detection of branch points based on the second moment statistics of the individual spots in images created with a Shack-Hartmann wave front sensor system is examined. Data collected by Small Mobile Atmospheric Sensing Hartmann (SMASH) units are used to test the method under a range of turbulence conditions. The results of the second moment technique are compared with the standard elementary circulation method.

This work presents a comprehensive characterization of a benchtop optical-turbulence simulator system using a Shack—Hartmann (SH) wavefront sensor, an off-axis digital holography (DH) wavefront sensor, and a far-field imaging camera. The system employs two spatial-light modulators (SLMs) to impose turbulent phase screens with prescribed statistics onto a laser beam, simulating atmospheric turbulence. We conduct tests to compare the system’s performance against wave-optics simulations by varying turbulence strength, varying the modeled propagation distance, and using both SLMs to model beam propagation. The results show that the DH wavefront measurements have a root mean square error (RMSE) of 0.02–0.03 µm compared to the simulated wavefronts, while the SH measurements have a RMSE of 0.02–0.05 µm compared to the DH wavefront measurements. We also assess the system’s ability to model beam propagation. Here, we find that the extent of phase disagreement increases with increasing propagation distances. Overall, the results of a Monte–Carlo simulation that models a 25 cm beam along a 1 km path reveal that DH measurements closely match the known turbulence parameters whereas the SH measurements generally underestimate turbulence strength. At large, this work informs system designers of how different wavefront sensors perform in varying optical-turbulence conditions.

The Reflective Atmospheric Turbulence Simulator (RATS) is an instrument used to simulate the propagation of light through atmospheric turbulence. RATS can simulate up to six layers of atmospheric turbulence using reflective phase wheels with many configurations that can simulate a broad range of atmospheric turbulence conditions. Two ShackHartmann wavefront sensors are integrated with RATS. One of these Shack-Hartmann wavefront sensors has an effective aperture size of 40cm, and the other has an effective aperture size of 6.75cm. We simulated propagation through atmospheric turbulence using RATS and made measurements of turbulence parameters using the two Shack-Hartmann wavefront sensors. In this paper, we compare the measurements of turbulence parameters from both Shack-Hartmann wavefront sensors to each other as well as to the theoretical values for atmosphere turbulence simulated by RATS.

Event-based sensors (EBSs) consist of a pixelated focal plane array in which each pixel is an independent asynchronous change detector. The analog asynchronous array is read by a synchronous digital readout and written to disk. As a result, EBS pixels consume minimal power and bandwidth unless the scene changes. Furthermore, the change detectors have a very large dynamic range (~120 dB) and rapid response time (~20 us). A framing camera with comparable speed requires ~3 orders of magnitude more power and ~2 orders of magnitude higher bandwidth. Remote sensing deployed in the field requires low power, low bandwidth, and low complexity algorithms. An EBS inherently allows for low power and low bandwidth, but there is a lack of mature image analysis algorithms. While analysis of conventional imagers draws from decades of image processing algorithms, EBS data is a fundamentally different format; a series of x, y, asynchronous time, and polarization change (increase/decrease) as opposed to x, y, and intensity at a regularly sampled framerate. Our team has worked to develop and refine image processing algorithms that use EBS data directly.

Event-based vision sensor (EVS) technology has expanded the CMOS image sensor design space of low-SWaP sensors with high-dynamic range operation and ability, under certain conditions, to efficiently capture scene information at a temporal resolution beyond that achievable by a typical sensor operating near a 1 kHz frame rate. Fundamental differences between EVS and framing sensors necessitate development of new characterization techniques and sensor models to evaluate hardware performance and the camera architecture trade-space. Laboratory characterization techniques reported previously include noise level as a function of static scene light level (background activity), contrast responses referred to as S-curves, refractory period characterization using the mean minimum interspike interval, and a novel approach to pixel bandwidth measurement using a static scene. Here we present pre-launch characterization results for the two Falcon ODIN (Optical Defense and Intelligence through Neuromorphics) event-based cameras (EBCs) scheduled for launch to the International Space Station (ISS). Falcon ODIN is a follow-on experiment to Falcon Neuro previously installed and operated onboard the ISS. Our characterization of the two ODIN EBCs includes high-dynamic range background activity, contrast response S-curves, and low-light cutoff measurements. Separately, we report evaluation of the IMX636 sensor functionality get_illumination which gives an auxiliary measurement of on-chip illuminance (irradiance) and can provide high dynamic range sensing of sky brightness (background light level).

Falcon ODIN is a technology demonstration science payload being designed for delivery to the International Space Station (ISS) in late 2024. Falcon ODIN contains two event based cameras (EBC) and two traditional framing cameras along with mirrors mounted on azimuth elevation rotation stages which allow the field of regard of the EBCs to move. We discuss the mission design and objectives for Falcon ODIN along with ground-based testing of all four cameras.

We present a novel deep learning-based framework for event-based Shack-Hartmann wavefront sensing. This approach leverages a convolutional neural network (CNN) to directly reconstruct high-resolution wavefronts from event-based sensor data. Traditional wavefront sensors, such as the Shack-Hartmann sensor, face challenges such as measurement artifacts and limited bandwidth. By integrating event-based cameras—which offer high temporal resolution and data efficiency—with CNN-based reconstruction—which can learn strong spatiotemporal priors— our method addresses these limitations while simultaneously improving the quality of reconstruction. We evaluate our framework on simulated high-speed turbulence data, demonstrating a 73% improvement in reconstruction fidelity compared to existing methods. Additionally, our framework is capable of predictive wavefront sensing to reduce compensation latency and increase overall system bandwidth.

Nuclear Scene Data Fusion (SDF) integrates radiation data and other contextual sensor measurements to enable free-moving localization and mapping of nuclear radiation from person or robot-borne sensor systems referred to as Localization and Mapping Platforms (LAMPs). The LAMP sensor suite typically utilizes lidar to create high-fidelity 3D point clouds representing the measurement scene. The high precision and accuracy of lidar has been essential to SDF, but its larger size, weight, power, and cost (SWaP-C) requirements limit its use in lightweight, portable applications, such as drones or handheld systems for remote field operations. In these cases, automotive millimeter-Wave radar presents a cost-effective, lightweight, and energy-efficient alternative, albeit with a significant compromise in spatial resolution and accuracy. We consider utilizing 2D radar point clouds to create occupancy maps of the scene. One method explored generates radar occupancy grids refined by a lidar-trained Pix2Pix conditional Generative Adversarial Network (cGAN) to approach lidar occupancy grid accuracy. We utilize these radar point occupancy grids to locate and quantify a gamma-ray point source in an environment never-before-seen by our lidar-trained Pix2Pix model, and we compare the results to those generated using standard lidar occupancy grids to assess the feasibility of using radar in place of lidar in some situations and environments.

The contemporary telecommunications system heavily depends on extensively spread optical fiber networks, which form its fundamental basis. Mechanical forces stemming from diverse ambient vibrations, including human activities and seismic movements, induce strains in these fibers. As a consequence, the light passing through the fibers experiences phase shifts. Consequently, these phase shifts can be detected throughout the entire fiber, offering insights into the original vibration occurrences. This characteristic renders them exceptionally suitable for distributed seismic sensing.

The United States Air Force Academy (USAFA) has developed techniques to characterize and identify satellites since 2014 using a 16-inch telescope on campus, as well as off-campus telescopes which comprise the Falcon Telescope Network. USAFA is upgrading its Falcon telescopes with new dual filter wheels and cameras. This will require updated calibrations for the new equipment along with a new capability to combine hyperspectral and polarimetric observations. For polarization calibration, highly accurate star fields are used. Emission and absorption stars will be used to calibrate the hyperspectral observations. Once the calibrations are updated, the combined observations with the new dual filter wheels will be used to make observations of geosynchronous satellites. This effort focuses on these combined hyperspectral-polarimetric observations, characterizing differences observed between satellites, and development of techniques to exploit these differences for the identification or discrimination of satellites.

I experimentally investigated and modeled a proposed frequency-domain method for detecting and tracking cislunar spacecraft and near-earth asteroids using heliostat fields at night. Unlike imaging, which detects spacecraft and asteroids by their streak in star-fixed long-exposure photographs, the proposed detection method oscillates the orientation of heliostats concentrating light from the stellar field and measures the light’s photocurrent power spectrum at sub-milliHertz resolution. If heliostat oscillation repetitively traces out a closed loop fixed to the stars, light from spacecraft or asteroids moving along that loop produce photocurrent at a frequency slightly shifted from starlight. The frequency shift is proportional to the spacecraft or asteroid’s apparent angular rate relative to sidereal. Relative phase corresponds to relative angular position, enabling tracking. Since heliostats are inexpensive compared to an astronomical observatory and otherwise unused at night, the proposed method may cost-effectively augment observatory systems such as NASA’s Asteroid Terrestrial-impact Last Alert System (ATLAS).

The vision through scattering media is of great importance for many application fields such as driver assistance systems or medical diagnosis. By correlating the speckle pattern of two different illumination modalities, we are able to retrieve object information through scattering media, as long as the two illumination wavefronts are within the memory effect range of the medium. This relaxes the requirements for the object's position and dimension, which often exist in other memory effect protocols. For instance, with our method, we are able to extract information about objects embedded in extended multiply scattering media in a single shot.

Performance metric standardization has eluded free space optical communications systems, generating comparison and assessment inconsistencies. The authors hope to incite discourse within the community, with the goal of establishing standards, while introducing an example metric.

Small angle scattering by relatively large atmospheric cloud/fog water droplets and ice crystals can cause significant contrast reduction and blurring of imagery. While this effect is quite well explained and verified in field experiments and sensor models, the extent to which aerosols, especially those of quite prevalent anthropogenic fine/ultra-fine/coarse mode play a role in image degradation remains to this date, a controversial topic. In this work, the contribution of aerosols to image blur is revisited but with special focus on field data collected with a relatively large variety of ambient aerosol characterization and optical instrumentation. Ambient particulate/aerosol morphology and optical properties and trends are correlated with collected imagery using instruments including nano-class condensation particle counters, and a nephelometer. Images were captured by a visible camera at different times of the day over a 450 m path. We quantified the blurring in these images through evaluation of the Modulation Transfer Function (MTF). The MTF of the imaging system was characterized through a short-range experiment in the laboratory and turbulence MTF was computed independently from the turbulence-induced motion of features in the images. The aerosol MTF was extracted by dividing the overall MTF by the turbulence and imager MTFs.

Atmospheric fogs create degraded visual environments, making it difficult to recover optical information from our surroundings. We have developed a low-SWaP technique which characterizes these environments using an f-theta lens to capture the angular scattering profile of a pencil beam passed through a fog. These measurements are then compared to data taken in tandem by conventional characterization techniques (optical transmission, bulk scattering coefficient, etc.). We present this angular scattering measurement as a low-SWaP alternative to current degraded visual environment characterization techniques to provide real-time data for implementation with signal recovery algorithms.

This paper will demonstrate an 18 aperture Digital Adaptive Optics system imaging through laboratory-controlled turbulence. Comparisons to a standard imaging system, with data that was captured simultaneously under the exact same conditions, will be shown. System performance relative to increasing turbulence strength will be quantified using QR codes as an imaging metric.

In this paper, we use wave-optics simulations to explore laser propagation system performance. We accomplish this by creating a trade space where we vary turbulence conditions as well as beacon size from a point-source beacon to an extended-source beacon with an object Fresnel number, Nobj, of 20. We explore performance when we employ no compensation, perfect phase compensation, and perfect full-phase compensation. The results of this trade space allow us to arrive at three main conclusions. First, if we have either a point-source beacon or a very small extended-source beacon and turbulence is strong, we get a significant improvement in performance using full-phase compensation compared to least-squares compensation and no compensation. If turbulence is weak, we see similar performance with least-squares and full-phase compensation, however, both are significantly improved over the no compensation case. Second, in strong turbulence conditions, there will be a very large number of turbulence-induced branch points. If left uncompensated, these turbulence-induced branch points will result in a major reduction in performance. Lastly, when the extended-source beacon is large, the associated rough-surface-scattering-induced phase aberrations will corrupt the compensation to the point where the drawbacks of compensating for surface-roughness-induced aberrations significantly outweigh the benefits of compensating for turbulence-induced aberrations. These results (1) inform researchers looking to conduct extended-source-beacon adaptive optics and (2) motivate research to explore methods for speckle mitigation in adaptive-optics systems.

The estimation of a phase aberration by observing a point spread function (PSF), known as wavefront estimation, is a critical problem in adaptive optics. Analogous to phase retrieval, wavefront estimation suffers from multiple ambiguous solutions. Many prior works require multiple structured measurements to overcome this fundamental challenge. In this paper, we use an asymmetric pupil to make what would otherwise be an impossible inverse problem to be possible. We combine this with an efficient machine learning algorithm to overcome remaining non-convexity. We empirically observe asymmetric pupils tend to outperform symmetric pupils.

Point-source transient events (PSTEs) – optical events that are both extremely fast and extremely small – pose several challenges to an imaging system. Due to their speed, accurately characterizing such events often requires detectors with very high frame rates. Due to their size, accurately detecting such events requires maintaining coverage over an extended field-of-view, often through the use of imaging focal plane arrays (FPA) with a global shutter readout. Traditional imaging systems that meet these requirements are costly in terms of price, size, weight, power consumption, and data bandwidth, and there is a need for cheaper solutions with adequate temporal and spatial coverage. To address these issues, we develop a novel compressed sensing algorithm adapted to the rolling shutter readout of an imaging system. This approach enables reconstruction of a PSTE signature at the sampling rate of the rolling shutter, offering a 1 to 2 order of magnitude temporal speedup and a proportional reduction in data bandwidth. We present empirical results demonstrating accurate recovery of PSTEs using measurements that are spatially under-sampled by a factor of 25, and our simulations show that, relative to other compressed sensing algorithms, our algorithm is both faster and yields higher quality reconstructions. We also present theoretical results characterizing our algorithm and corroborating simulations. The potential impact of our work includes the development of much faster, cheaper sensor solutions for PSTE detection and characterization.

In the present work, we propose a novel reference-less wavefront sensing method in a grating array-based wavefront sensor (GAWS). The proposed sensing method utilizes both +1 and -1 diffraction orders. The key idea is that when there is a local tilt in the wavefront, the array of +1 and -1 diffracted spots move in opposite directions due to their optical phase conjugate relationship but share a common reference position. By determining the displacement of these spots, the reference position can be precisely determined, and the local slope can be extracted from which the incident wavefront can be estimated. The proposed sensing method facilitates wavefront estimation using a single camera frame and is compatible with standard wavefront estimation algorithms. This proposed method proves particularly advantageous in scenarios where a highquality wavefront is unavailable as a reference. We have validated the effectiveness of our proposed method through simulation results.

Minnaert resonance analysis combined with Poincaré maps of optical fiber-based distributed acoustic sensor data is demonstrated for detecting gas bubbles in a 5163-ft-deep wellbore. This novel approach can improve drilling safety and prevent blowout incidents.

Transient events exhibit strong UV radiation, but transient activity is not well studied in the UV. Ground-based telescopes have an untapped potential to support space-based UV observations of transients, down to the atmospheric cutoff of roughly 320nm. The Super-LOTIS (Livermore Optical Transient Imaging System) telescope is the first ground-based optical telescope that is being converted for NUV transient science. It will follow up on transient targets identified by the Swift/UVOT instrument, ground-based robotic transient finders, and future space-based missions. It will also have the capacity to conduct its own observations. The development of the Super-LOTIS telescope will provide a model for future ground-based UV surveys. In this paper, we report on the progress to modify the existing camera optics to use a new NUV sensitive camera and filter system.

Optical synthesis aperture telescope technology can be used to get more rich astronomical information. Interference fringe scanning method is commonly used to eliminate optical path difference between different optical delayed lines, but due to the polarization difference between the interference arms will lead to interference fringe contrast degradation especially in interference type instrument. Especially when observing faint, more distant targets, it is more necessary to consider the polarization effects caused by the instrument itself. In this paper, the Fizeau-type Y-4 prototype developing by Shanghai Astronomical Observatory, Chinese Academy of Sciences is introduced first of all. Based on the principle of the vector-wave superposition, this paper focuses on fringe contrast degradation caused by polarization effects and the changes of polarization states caused by coating of different material. The simulation results show that the interference fringe contrast is sensitive to the polarization effects. Similarly, the changes of polarization state of the beam caused by the coating needs to be considered when designing the optical interferometer. Finally, a polarization compensator is proposed to compensate the polarization difference.