Salvatore J. Cusumano

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.

A first principles atmospheric propagation & characterization tool: the laser environmental effects definition and reference (LEEDR)

The Air Force Institute of Technology Center for Directed Energy (AFIT/CDE) has developed a first principles atmospheric propagation and characterization model called the Laser Environmental Effects Definition and Reference or LEEDR. This package enables the creation of profiles of temperature, pressure, water vapor content, optical turbulence, and atmospheric particulates and hydrometeors as they relate to line-by-line layer extinction coefficient magnitude at wavelengths from the UV to the RF. Worldwide seasonal, diurnal, and geographical variability in these parameters is accessed from probability density function (PDF) databases using a variety of recently available resources to include the Extreme and Percentile Environmental Reference Tables (ExPERT), the Master Database for Optical Turbulence Research in Support of the Airborne Laser, and the Global Aerosol Data Set (GADS). GADS provides aerosol constituent number densities on a 5° x 5° grid worldwide. ExPERT mapping software allows the LEEDR operator to choose from specific site or regional upper air data to characterize correlated molecular absorption, aerosol absorption and scattering by percentile. The integration of the Surface Marine Gridded Climatology database, the Advanced Navy Aerosol Model (ANAM), and the Navy Surface Layer Optical Turbulence (NSLOT) model provides worldwide coverage over all ocean regions on a 1° x 1° grid. Molecular scattering is computed based on Rayleigh theory. Molecular absorption effects are computed for the top 13 absorbing species using line strength information from the HITRAN 2004 database in conjunction with a community standard molecular absorption continuum code. Aerosol scattering and absorption are computed with the Wiscombe Mie model. Each atmospheric particulate/hydrometeor is evaluated based on its wavelength-dependent forward and off-axis scattering characteristics and absorption effects on laser energy delivered at any wavelength from 0.355 μm to 8.6 m. LEEDR can also produce correlated optical turbulence profiles in percentile format. In addition, probability of cloud free line of sight (CFLOS) for hundreds of land sites worldwide is available in LEEDR. Effects of layers of fog, several types of rain and several types of water droplet and ice clouds can also be considered. In addition to describing some of the underlying theory to the LEEDR calculations, this paper presents graphical results for several different scenarios. These generic scenarios are meant to exemplify how LEEDR enables the physically realistic data capture of atmospheric effects on electromagnetic propagation.

Physical optics solution for the scattering of a partially-coherent wave from a statistically rough material surface.

The scattering of a partially-coherent wave from a statistically rough material surface is investigated via derivation of the scattered field cross-spectral density function. Two forms of the cross-spectral density are derived using the physical optics approximation. The first is applicable to smooth-to-moderately rough surfaces and is a complicated expression of source and surface parameters. Physical insight is gleaned from its analytical form and presented in this work. The second form of the cross-spectral density function is applicable to very rough surfaces and is remarkably physical. Its form is discussed at length and closed-form expressions are derived for the angular spectral degree of coherence and spectral density radii. Furthermore, it is found that, under certain circumstances, the cross-spectral density function maintains a Gaussian Schell-model form. This is consistent with published results applicable only in the paraxial regime. Lastly, the closed-form cross-spectral density functions derived here are rigorously validated with scatterometer measurements and full-wave electromagnetic and physical optics simulations. Good agreement is noted between the analytical predictions and the measured and simulated results.

A Computational Tool for Evaluating THz Imaging Performance in Brownout Conditions at Land Sites Throughout the World

This study quantifies terahertz (THz) or sub-millimeter imaging performance during simulated rotary-wing brownout or whiteout environments based on geographic location and recent/current atmospheric weather conditions. The atmospheric conditions are defined through the Air Force Institute of Technology Center for Directed Energy (AFIT/CDE) Laser Environmental Effects Definition and Reference or LEEDR model. This model enables the creation of vertical profiles of temperature, pressure, water vapor content, optical turbulence, and atmospheric particulates and hydrometeors as they relate to line-by-line layer extinction coefficient magnitude at wavelengths from the UV to the RF. Optical properties and realistic particle size distributions for the brownout and whiteout particulates have been developed for and incorporated into LEEDR for this study. The expected imaging performance is assessed primarily at a wavelength of 454 μm (0.66 THz) in brownout conditions at selected geographically diverse land sites throughout the world. Seasonal and boundary layer variations (summer and winter) and time of day variations for a range of relative humidity percentile conditions are considered to determine optimum employment techniques to exploit or defeat the environmental conditions. Each atmospheric particulate/hydrometeor is evaluated based on its wavelength-dependent forward and off-axis scattering characteristics and absorption effects on the imaging environment. In addition to realistic vertical profiles of molecular and aerosol absorption and scattering, correlated optical turbulence profiles in probabilistic (percentile) format are used. Most evaluated scenarios are brownout environments over ranges up to 50 meters. At submillimeter wavelengths and the short ranges studied, preliminary results indicate the main source of image degradation in brownout conditions is water vapor content, even with visibility less than 10 m and strong optical turbulence.

A worldwide physics-based high spectral resolution atmospheric characterization and propagation package for UV to RF wavelengths

The Air Force Institute of Technologys Center for Directed Energy (AFIT/CDE) developed the High Energy Laser End-to-End Operational Simulation (HELEEOS) model in part to quantify the performance variance in laser propagation created by the natural environment during dynamic engagements. As such, HELEEOS includes a fast-calculating, first principles, worldwide surface-to-100 km, atmospheric propagation and characterization package. This package enables the creation of profiles of temperature, pressure, water vapor content, optical turbulence, atmospheric particulates and hydrometeors as they relate to line-by-line layer transmission, path and background radiance at wavelengths from the ultraviolet to radio frequencies. Physics-based cloud and precipitation characterizations are coupled with a probability of cloud free line-of-sight algorithm for all possible look angles. HELEEOS was developed under the sponsorship of the High Energy Laser Joint Technology Office. In the current paper an example of a unique high fidelity simulation of a bi-static, time-varying five band multispectral remote observation of laser energy delivered on a test object is presented. The multispectral example emphasizes atmospheric effects using HELEEOS, the interaction of the laser on target and the observed reflectance and subsequent hot spot generated. A model of a sensor suite located on the surface is included to collect the diffuse reflected in-band laser radiation and the emitted radiance of the hot spot in four separate and spatially offset MWIR and LWIR bands. Particular care is taken in modeling the bidirectional reflectivity distribution function (BRDF) of the laser/target interaction to account for both the coupling of energy into the target body and the changes in reflectance as a function of temperature. The architecture supports any platform-target-observer geometry, geographic location, season, and time of day; and it provides for correct contributions of the sky-earth background. The simulation accurately models the thermal response, kinetics, turbulence, base disturbance, diffraction, and signal-to-noise ratios.

Examining the validity of using a Gaussian Schell-model source to model the scattering of a fully coherent Gaussian beam from a rough impedance surface

Abstract. Military applications that use adaptive optics (AO) often require a point source beacon at the target to measure and correct for wavefront aberrations introduced by atmospheric turbulence. However, turbulence prevents the formation of such a point beacon. The extended beacons that are created instead have finite spatial extents and exhibit varying degrees of spatial coherence. Modeling these extended beacons using a Gaussian Schell-model (GSM) form for the autocorrelation function would be a convenient approach due to the analytical tractability of Gaussian functions. We examine the validity of using such a model by evaluating the field scattered from a rough impedance surface using a full-wave computational technique called the method of moments (MoM). The MoM improves the fidelity of the analysis since it captures all the physics of the laser-target interaction, such as masking, shadowing, multiple reflections, etc. Two rough-surface targets with different roughness statistics are analyzed. The simulation results are verified with experimental bidirectional reflectance distribution function measurements. It is seen that for rough surfaces, in general, the scattered-field autocorrelation function is not of a GSM form. However, under certain conditions, modeling an extended beacon as a GSM source is legitimate. This analysis will aid in understanding the behavior of extended beacons and how they affect the overall performance of an AO system.

Scalar wave solution for the scattering of a partially coherent beam from a statistically rough metallic surface

The scattering of a spatially partially coherent wave from a one-dimensional statistically rough metallic surface is investigated. Assuming a Gaussian Schell-model form for the incident field autocorrelation function, a closed-form expression for the scattered field autocorrelation function is derived using the physical optics approximation (Kirchhoff approximation). Two forms of the solution are derived—one applicable to very rough surfaces and the other applicable to moderately rough surfaces. It is shown that for very rough surfaces, the solution, under certain circumstances, remains Gaussian Schell model as has been previously reported. As such, closed-form expressions for the angular coherence radius and angular scattering radius are derived. These expressions are, in general, complicated functions of both the source (size and coherence properties) and surface parameters (surface height standard deviation and correlation length). It is demonstrated that for many scenarios of interest, the angular coherence radius can be safely approximated as a function of just the source parameters and the angular scattering radius can be simplified to a function of just the surface parameters. For the moderately rough surface solution, the scattered field autocorrelation function is, in general, not Gaussian Schell model and it is therefore not possible to derive analytical forms for the angular coherence radius or angular scattering radius. Nonetheless, the form of the autocorrelation function is physically intuitive and is discussed in this work. To verify the presented theoretical analysis, wave optics simulation results are presented and compared to the predictions of the analytical models. This analysis is concluded with a discussion of future work.

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.

Impact of spatial resolution on thermal blooming phase compensation instability

Phase compensation instability (PCI) is the time-dependent development of spatial perturbations that occur within thermally bloomed high-energy laser (HEL) beams. These types of spatial perturbations act as local hot spots that create small negative lenses within the HEL beam. Closed-loop adaptive optics (AO) corrects for these spatial perturbations by applying small positive-lens phase compensations, which only increases the strength of the local hot spots and leads to runaway in the adaptive-optics servo. This study uses a straightforward wave-optics code to model horizontal propagation with the effects of thermal blooming for a focused Gaussian beam. The strength of the thermal blooming effects is characterized using the classic dimensionless distortion number. A nominal AO system is used to mitigate phase distortions accumulated from thermal blooming. Parameters within the AO system, such as the number of actuators on the deformable mirror and the resolution of the wavefront sensor, are varied to determine the impact of spatial resolution in the development of the PCI. A discussion is given on the potential use of control theory to diminish the effects of the PCI.

Worldwide estimates and uncertainty assessments of laser propagation for diverse geometries for paths in the altitude regime of 3 km and below at wavelengths 0.355 μm to 10.6 μm

The directed energy modeling and simulation community can make important direct contributions to the joint warfighting community by establishing clear and fully integrated future program requirements. These requirements are best determined via analysis of the expected variability/uncertainty in system performance arising from spatial, spectral and temporal variations in operating conditions. In this study of atmospheric effects on HEL systems, the parameter space is explored using the Air Force Institute of Technology Center for Directed Energys (AFIT/CDE) High Energy Laser End-to-End Operational Simulation (HELEEOS) parametric one-on-one engagement level model. HELEEOS is anchored to respected wave optics codes and all significant degradation effects-including optical turbulence and molecular, aerosol, and liquid water drop/droplet absorption and scattering-are represented in the model. Beam spread effects due to thermal blooming caused by the various absorbers are considered when appropriate. Power delivered in a 5 cm diameter circular area normalized by the total transmitted power is the primary performance metric used in the study, with results presented in the form of histograms. The expected performance of laser systems operating at both low and high powers is assessed at 24 wavelengths between 0.355 &mgr;m and 10.6 &mgr;m for a number of widely dispersed land and maritime locations worldwide. Scenarios evaluated include both up and down looking generally oblique engagement geometries over ranges up to 6000 meters in which anticipated clear air aerosols and thin layers of fog, and very light rain are simulated. Seasonal and boundary layer variations (summer and winter) for nighttime conditions for a range of relative humidity percentile conditions are considered to determine optimum employment techniques to exploit or defeat the environmental conditions. Each atmospheric particulate/obscurant is evaluated based on its wavelength-dependent forward and off-axis scattering characteristics and absorption effects on laser energy delivered. In addition to realistic vertical profiles of molecular and aerosol absorption and scattering, correlated optical turbulence profiles in probabilistic (percentile) format are used, a feature unique to HELEEOS.