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.
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).
KEYWORDS: Speckle, Sampling rates, Tunable filters, Turbulence, Adaptive optics, Digital signal processing, Control systems, Motion blur, Linear filtering, Optical tracking
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.
Direct measurement of F-number presents a known challenge in characterizing electro-optical and infrared imaging systems. Conventional methods typically require the sensor to be evaluated separately from the lens, indirectly calculating F-number from measurements of effective focal length and entrance-pupil diameter. When a focal plane array is positioned behind the optics and cannot be removed, some potential options could be to quantify signal-to-noise ratio or depth of field using incoherent light. In either of these cases, the result is subject to extraneous camera parameters and sensitive to noise, aberrations, etc. To address these issues, we propose an alternative measurement routine that utilizes a coherent point source at the focus of an off-axis Newtonian collimator to generate collimated light. This allows us to place the system under test at optical infinity, where retroreflections from its focal plane depend solely on angle of incidence, wavelength of illumination and F-number. Thus by measuring retroreflected power as a function of incidence angle, we can back out the system’s F-number with a high degree of confidence. We demonstrate this concept through numerical simulation and laboratory testing, along with an unconventional knife-edge technique for gauging the entrance-pupil diameter in situ. Together these two measurements enable us to calculate effective focal length (and in turn pixel pitch by measuring instantaneous field of view) for a comprehensive system description. We further show that a working F-number and effective image distance are attainable through this method for finite-conjugate systems. These tools improve our ability to update existing system models with objective measurements.
The sensitivity of active targeting systems in the shortwave infrared band is currently limited by high read noise associated with conventional readout integrated circuitry. This limit imposes a barrier to leveraging other performance trades, such as source power, illumination wavelength, and temporal coherence. Introducing gain in the charge domain prior to signal readout can reduce the impact of read noise, to the point that it no longer limits performance. In preparation for a series of planned active-imaging field tests, we demonstrate improved system performance on a modeling basis with two different charge-domain gain cameras: the electron bombarded active pixel sensor (EBAPS) and the mercury cadmium telluride avalanche photodiode sensor. We find that both solutions mitigate read noise to make either one suitable for laser range gating, but the high dark current associated with EBAPS may make it unsuitable for continuous-wave imaging in some scenarios. These results aid in our understanding of expected performance in field testing of charge-domain gain systems.
Active imaging systems can provide increased contrast-to-noise ratio (CNR) and targeting performance over passive systems in low-light and long-range applications. We use both a radiometric model and the Night Vision Integrated Performance Model to compare the performance of active continuous-wave (CW) and laser range-gated (LRG) imaging systems with laser illumination at 1.6 and 2.1 μm, corresponding to the shortwave infrared (SWIR) and extended SWIR (eSWIR) bands, respectively. The imager performance is characterized by CNR as a function of range, as well as pixels-on-target. The modeling results demonstrate increased performance in the eSWIR band over the SWIR band in the majority of cases and increased performance for LRG systems over CW systems in all cases. The in-progress design of an active imaging testbed to confirm these modeling results with field imagery is discussed.
KEYWORDS: Clouds, Light sources and illumination, Short wave infrared radiation, Near infrared, Cameras, Sun, Atmospheric modeling, Multiple scattering, Signal to noise ratio, Sensors
Daytime low light conditions such as overcast, dawn, and dusk pose a challenge for object discrimination in the reflective bands, where the majority of illumination comes from reflected solar light. In reduced illumination conditions, sensor signal-to-noise ratio can suffer, inhibiting range performance for recognizing and identifying objects of interest. This performance reduction is more apparent in the longer wavelengths where there is less solar light. Range performance models show a strong dependence on cloud type, thickness, and time of day across all wavebands. Through an experimental and theoretical analysis of a passive sensitivity and resolution matched testbed, we compare Vis (0.4-0.7μm), NIR (0.7-1μm), SWIR (1-1.7μm), and eSWIR (2-2.5μm) to assess the limiting cases in which reduced illumination inhibits range performance.
KEYWORDS: Single photon avalanche diodes, Electrons, Histograms, Photons, Systems modeling, Imaging systems, Signal detection, LIDAR, Dark current, Cameras
Single Photon Avalanche Diodes (SPAD) have shown great promise for use in Lidar and low light applications. Although staring arrays were initially developed for medical applications, recent Lidar sensor solution demands have fueled the development of large count staring sensors with quantum efficiencies extending in the NIR/SWIR and with exotic readout circuits. The same technology also enables low light systems with sensitivity below conventional CMOS. As the name implies, SPAD detectors are sensitive to single photons, behave as stochastic devices, and require special treatment for signal interpretation. In this paper, we describe a signal and noise model for both active and passive SPAD based imaging systems that includes the generation of readout events based on the SPAD detector stochastic model. The model presented here allows the evaluation of SPAD based systems under specific illumination conditions and enables the evaluation of SPAD and sensor parameter system sensitivity.
KEYWORDS: Signal to noise ratio, Speckle, Diffraction, Monte Carlo methods, Imaging systems, Modulation transfer functions, Phase measurement, Optical transfer functions, Reticles, Laser irradiation
This paper seeks to address whether active or passive tracking is preferable in terms of centroid-track error. Active tracking has the advantage of allowing for SWaP-limited source control to scale SNR. With coherent illumination, however, speckle noise gives rise to a fundamental limit in tracking precision. On the other hand, passive tracking relies on incoherent illumination with speckle-free return. The drawback in this case is that SNR itself is inherently limited, thus limiting precision with respect to tracking measurements. In our analysis, we first present the theory that drives limiting factors of both active and passive tracking schemes. From these limitations we then estimate Strehl ratio at various SNRs for direct comparison of active and passive performance. We consider objects of various shapes and sizes, study both well-resolved and unresolved objects, and anchor our findings to first-order simulation results that demonstrate significance in the design of tracking systems.
This effort characterizes proper sampling of laser speckle in wave-optics simulations, with an emphasis on active imagers in outdoor environments. Modeling of performance degradations induced by speckle is critical in the design of such devices. We expose tradeoffs between sampling conditions in multiple planes of interest, namely the object, pupil and focal planes of an imaging system. The goal of our analysis is to develop an optimized numerical tradespace that models the underlying physics of speckle and turbulence with high fidelity. We begin by showing that speckle statistics are relatively straightforward to produce in the case of vacuum propagation. Then by propagating through different strengths of turbulence, we demonstrate how sampling requirements can become much more difficult to satisfy. We pay particular attention to the problem of sufficiently sampling a target object without subjecting it to anisoplanatism. As a way of overcoming such challenges, we propose and test an optimization routine that defines acceptable simulation parameters based on user-defined physical parameters. Successful implementation of this approach streamlines the design process for applications that involve active target tracking and coherent imaging through turbulence.
In this study, we use a series of computational-wave-optics experiments to address the statistics associated with image-plane speckle fields resulting from a tilted flat plate that is rough compared to the wavelength of uniform illumination. To quantify the strength of simulated speckle, we make use of the focal ratio a.k.a. f number. This parameter provides a gauge for the size of speckles appearing across the image of a target. Our goal throughout is to show that, frame to frame, the analysis can appropriately simulate correlated speckle fields in an image plane. Our results show that the speckle fields we simulate are properly correlated from one frame to the next, relative to closed-form expressions. This outcome leads to the ability to perform closed-loop-tracking studies, which are becoming increasingly important for applications that involve imaging through turbulence.
In this study we use a series of computational-wave-optics experiments to look at the statistics associated with speckle fields resulting from a tilted flat plate (i.e. one that is optically rough compared to the wavelength of plane-wave illumination). To help quantify the strength of the simulated speckle, we make use of the target Fresnel number. This parameter gives a gauge for the number of speckles across the receiver. The goal throughout is to show that, frame to frame, the analysis can appropriately simulate correlated speckle fields in terms of the magnitude of the complex degree of coherence as a function of tilt. The results show that the simulated speckle fields are properly correlated from frame to frame, and this outcome leads to the ability to perform closed-loop-phase-compensation studies in the presence of extended beacons. Such studies are becoming increasingly important for applications that involve imaging through turbulence.
This study evaluates the effects of beacon-wavelength mismatch on phase-compensation performance. In general,
beacon-wavelength mismatch occurs at the system level because the beacon-illuminator laser (BIL) and high-energy
laser (HEL) are often at different wavelengths. Such is the case, for example, when using an aperture sharing element to
isolate the beam-control sensor suite from the blinding nature of the HEL. With that said, this study uses the WavePlex
Toolbox in MATLAB® to model ideal spherical wave propagation through various atmospheric-turbulence conditions.
To quantify phase-compensation performance, we also model a nominal adaptive-optics (AO) system. We achieve
correction from a Shack-Hartmann wavefront sensor and continuous-face-sheet deformable mirror using a least-squares
phase reconstruction algorithm in the Fried geometry and a leaky integrator control law. To this end, we plot the power
in the bucket metric as a function of BIL-HEL wavelength difference. Our initial results show that positive BIL-HEL
wavelength differences achieve better phase compensation performance compared to negative BIL-HEL wavelength
differences (i.e., red BILs outperform blue BILs). This outcome is consistent with past results.
KEYWORDS: Diffusers, Free space optics, Atmospheric optics, Radio optics, Wireless communications, Atmospheric turbulence, Speckle, Signal to noise ratio, Binary data, Data modeling
Wireless communication systems that employ free-space optical links in place of radio/microwave technologies carry substantial benefits in terms of data throughput, network security and design efficiency. Along with these advantages comes the challenge of counteracting signal degradation caused by atmospheric turbulence in free-space environments. A fully coherent laser source experiences random phase delays along its traversing path in turbulent conditions forming a speckle pattern and lowering the received signal-to-noise ratio upon detection. Preliminary research has shown that receiver-side speckle contrast may be significantly reduced and signal-to-noise ratio increased accordingly through the use of a partially coherent light source. While dynamic diffusers and adaptive optics solutions have been proven effective, they also add expense and complexity to a system that relies on accessibility and robustness for successful implementation. A custom Hadamard diffractive matrix design is used to statically induce partial coherence in a transmitted beam to increase signal-to-noise ratio for experimental turbulence scenarios. Atmospheric phase screens are generated using an open-source software package and subsequently loaded into a spatial light modulator using nematic liquid crystals to modulate the phase.
Waveguide (WG) photonic-bridge taper modules are designed for symmetric planar coupling between silicon WGs and single-mode fibers (SMFs) to minimize photonic chip and packaging footprint requirements with improving broadband functionality. Micromachined fabrication and evaluation of polymer WG tapers utilizing high-resolution focused ion beam (FIB) milling is performed and presented. Polymer etch rates utilizing the FIB and optimal methods for milling polymer tapers are identified for three-dimensional patterning. Polymer WG tapers with low sidewall roughness are manufactured utilizing FIB milling and optically tested for fabrication loss. FIB platforms utilize a focused beam of ions (Ga+) to etch submicron patterns into substrates. Fabricating low-loss polymer WG taper prototypes with the FIB before moving on to mass-production techniques provides theoretical understanding of the polymer taper and its feasibility for connectorization devices between silicon WGs and SMFs.
Polymer waveguides (PWGs) are used within photonic interconnects as inexpensive and versatile substitutes for traditional optical fibers. The PWGs are typically aligned to silica-based optical fibers for coupling. An epoxide elastomer is then applied and cured at the interface for index matching and rigid attachment. Self-written waveguides (SWWs) are proposed as an alternative to further reduce connection insertion loss (IL) and alleviate marginal misalignment issues. Elastomer material is deposited after the initial alignment, and SWWs are formed by injecting ultraviolet (UV) light into the fiber or waveguide. The coupled UV light cures a channel between the two differing structures. A suitable cladding layer can be applied after development. Such factors as longitudinal gap distance, UV cure time, input power level, polymer material selection and choice of solvent affect the resulting SWWs. Experimental data are compared between purely index-matched samples and those with SWWs at the fiber-PWG interface. It is shown that < 1 dB IL per connection can be achieved by either method and results indicate lowest potential losses associated with a fine-tuned self-writing process. Successfully fabricated SWWs reduce overall processing time and enable an effectively continuous low-loss rigid interconnect.
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