Noah R. Van Zandt

Comparison of coherent and incoherent laser beam combination for tactical engagements

Abstract. The performance of a multibeam laser system is evaluated for coherent and incoherent beam combination under tactical scenarios. For direct comparison, identical aperture geometries are used for both, coherent or incoherent, combination methods. The analysis assumes a multilaser source coupled with a conventional 0.32 m diameter, on-axis, beam director. Parametric analysis includes variations over residual errors, beam quality, atmospheric effects, and scenario geometry. Analytical solutions from previous results are used to evaluate performance for the vacuum case, providing an upper bound on performance and a backdrop for organizing the multitude of effects as they are analyzed. Wave optics simulations are used for total system performance. Each laser in the array has a wavelength of 1.07 μm, 10 kW (25 kW) output power, and Gaussian exitance profile. Both tracking and full-aperture adaptive optics are modeled. Three tactical engagement geometries, air to surface, surface to air, and surface to surface, are evaluated for slant ranges from 2.5 to 10 km. Two near-median atmospheric profiles were selected based upon worldwide climatological data. The performance metric used is beam propagation efficiency for circular target diameters of 5 and 10 cm.

Enhanced, fast-running scaling law model of thermal blooming and turbulence effects on high energy laser propagation

A new scaling law model is presented to rapidly simulate thermal blooming and turbulence effects on high energy laser propagation, producing results approaching the quality normally only available using wave-optics code, but at much faster speed. The model convolves irradiance patterns originating from two distinct scaling law models, one with a proficiency in thermal blooming effects and the other in turbulence. To underscore the power of the new model, results are verified for typical, realistic scenarios by direct comparison with wave optics simulation.

Modeled and measured image-plane polychromatic speckle contrast

Abstract. The statistical properties of speckle relevant to short- to medium-range (tactical) active tracking involving polychromatic illumination are investigated. A numerical model is developed to allow rapid simulation of speckled images including the speckle contrast reduction effects of illuminator bandwidth, surface slope, and roughness, and the polarization properties of both the source and the reflection. Regarding surface slope (relative orientation of the surface normal and illumination/observation directions), Huntley’s theory for speckle contrast, which employs geometrical approximations to decrease computation time, is modified to increase accuracy by incorporation of a geometrical correction factor and better treatment of roughness and polarization. The resulting model shows excellent agreement with more exact theory over a wide range. An experiment is conducted to validate both the numerical model developed here and existing theory. A diode laser source with coherence length of 259±7  μm is reflected off of a silver-coated diffuse surface. Speckle data are gathered for 16 surface slope angles corresponding to speckle contrast between about 0.55 and 1. Taking the measured data as truth, both equations show error mean and standard deviation of less than 3%. Thus, the theory is validated over the range of this experiment.

Simulation of Atmospheric Turbulence Compensation through Piston- only Phase Control of a Laser Phased Array

Beam propagation from a laser phased array system through the turbulent atmosphere is simulated and the ability of such a system to compensate for the atmosphere via piston-only phase control of the sub-apertures is evaluated. Directed energy (DE) applications demand more power than most lasers can produce, consequently many schemes for high power involve combining the beams from many smaller lasers into one. When many smaller lasers are combined into a phased array, phase control of the individual sub-apertures will be necessary to create a high-quality beam. Phase control of these sub-apertures could then be used to do more, such as focus, steer, and compensate for atmospheric turbulence. Atmospheric turbulence is well known to degrade the performance of both imaging systems and laser systems. Adaptive optics can be used to mitigate this degradation. Adaptive optics ordinarily involves a deformable mirror, but with phase control on each sub-aperture the need for a deformable mirror is eliminated. The simulation conducted here evaluates performance gain for a 127 element phased array in a hexagonal pattern with piston-only phase control on each element over an uncompensated array for varying levels of atmospheric turbulence. While most simulations were carried out against a 10 km tactical scenario, the turbulence profile was adjusted so performance could be evaluated as a function of the Fried Parameter (r0) and the log-amplitude variance somewhat independently. This approach is demonstrated to be generally effective with the largest percentage improvement occurring when r0 is close to the sub-aperture diameter.

Comparison of polychromatic wave-optics models

Polychromatic laser light can reduce speckle contrast in wavefront-sensing and imaging applications that use direct detection schemes. To help quantify the associated reduction in speckle contrast, this study investigates the accuracy and numerical efficiency of three separate wave-optics models that simulate the active illumination of extended objects with polychromatic laser light. The three separate models use spectral slicing, Monte Carlo averaging, and depth slicing, respectively, to simulate the laser-target interaction. The sampling requirements of all three models are discussed. Comparisons to analytical solutions and experimental data are made when possible. In general, the experiments and theory compare favorably with the models.

Wave-optics comparisons to a scaling-law formulation

This study investigates the use of a recently published generalized scaling law [J. Opt. Soc. Am. A 33(12), 2477-2484 (2016)]. In practice, the generalized scaling law accurately predicts the diffraction-limited peak irradiance in the far-field given the beam power, wavelength, propagation distance, field-effective area, and field-out-coupling factor. After reviewing this scaling-law formulation, we compare the far-zone predictions for peak irradiance and Gaussian beam spread to wave-optics simulations. Overall, the results show that this scaling-law formulation does not predict the correct peak irradiance, nor the correct Gaussian beam spread for horizontal-path scenarios with varying levels of atmospheric turbulence.

Wave-optics simulation of correlated speckle fields for use in closed-loop-phase-compensation studies

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.

Polychromatic speckle mitigation for improved adaptive-optics system performance

Adaptive-optics (AO) systems correct the distortions caused by atmospheric turbulence for imaging and laser transmission applications. Given an extended, uncooperative object, the AO system must create a reference wave for wavefront measurement. It does so by focusing a laser beam onto the object; therefore, creating a beacon. Unfortunately, the extended size of the beacon after propagation gives rise to speckle, causing noise in the wavefront measurements which degrades the AO system’s correction of the turbulence effects. In this paper, we use polychromatic illumination to create the reference wave, which results in an associated reduction in the speckle noise. To quantify the benefits, we use split-step wave-optics simulations with the spectral-slicing method for polychromatic light. We assume that the AO system uses a Shack Hartmann wavefront sensor. Furthermore, we assume that the speckle decorrelates over short periods of time corresponding to reasonable object motions. We consider a range of conditions for the object size (i.e. the object Fresnel number), object motion, and illuminator coherence length. The results show a reduction in the speckle-induced error with polychromatic light, especially when the object is large. This finding indicates that polychromatic illumination can improve the performance of AO systems when the object is both uncooperative and extended.

Simulating time-evolving non-cross-spectrally pure schell-model sources

Investigating the time-evolution of partially-coherent sources is necessary for certain optical coherence effects. Several simulation approaches have been developed, many of which can only treat cross-spectrally pure sources. However, some significant source types are not cross-spectrally pure. This paper reviews two methods for the synthesis of time-evolving sources which need not be pure. Both involve filtering matrices of uncorrelated Gaussian random numbers. One method requires control of both amplitude and phase, while the other only requires phase control. The utility of the methods for non-cross-spectrally pure sources is demonstrated for the first time. The source is generated by passing coherent light through two different diffusers which move at the same speed but in opposite directions. Simulation results for the time-evolving field are shown. Further, the coherence functions of the synthesized field are compared to theory for validation.

PITBUL: a physics-based modeling package for imaging and tracking of airborne targets for HEL applications including active illumination

Aimpoint acquisition and maintenance is critical to high energy laser (HEL) system performance. This study demonstrates the development by the AFIT/CDE of a physics-based modeling package, PITBUL, for tracking airborne targets for HEL applications, including atmospheric and sensor effects and active illumination, which is a focus of this work. High-resolution simulated imagery of the 3D airborne target in-flight as seen from the laser position is generated using the HELSEEM model, and includes solar illumination, laser illumination, and thermal emission. Both CW and pulsed laser illumination are modeled, including the effects of illuminator scintillation, atmospheric backscatter, and speckle, which are treated at a first-principles level. Realistic vertical profiles of molecular and aerosol absorption and scattering, as well as optical turbulence, are generated using AFIT/CDE’s Laser Environmental Effects Definition and Reference (LEEDR) model. The spatially and temporally varying effects of turbulence are calculated and applied via a fast-running wave optical method known as light tunneling. Sensor effects, for example blur, sampling, read-out noise, and random photon arrival, are applied to the imagery. Track algorithms, including centroid and Fitts correlation, as a part of a closed loop tracker are applied to the degraded imagery and scored, to provide an estimate of overall system performance. To gauge performance of a laser system against a UAV target, tracking results are presented as a function of signal to noise ratio. Additionally, validation efforts to date involving comparisons between simulated and experimental tracking of UAVs are presented.