Jack E. McCrae

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.

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.

Estimation of turbulence from time-lapse imagery

Abstract. Atmospheric turbulence parameters are estimated for an imaging path based on time-lapse imaging results. Atmospheric turbulence causes frame-to-frame shifts of the entire image as well as parts of the image. The statistics of these shifts encode information about the turbulence strength (as characterized by Cn2, the refractive index structure function constant) along the optical path. The shift variance observed is simply proportional to the variance of the tilt of the optical field averaged over the area being tracked and averaged over the camera aperture. By presuming this turbulence follows the Kolmogorov spectrum, weighting functions, which relate the turbulence strength along the path to the shifts measured, are derived. These weighting functions peak at the camera and fall to zero at the object. The larger the area observed, the more quickly the weighting function decays. One parameter we would like to estimate is r0 (the Fried parameter or atmospheric coherence diameter.) The weighting functions derived for pixel sized or larger parts of the image all fall faster than the weighting function appropriate for estimating the spherical wave r0. If we were to presume that Cn2 is constant along the path, then an estimate for r0 could be obtained for each area tracked, but since the weighting function for r0 differs substantially from that for every realizable tracked area, it can be expected that this approach would yield a poor estimate. Instead, the weighting functions for a number of different patch sizes can be combined through the Moore–Penrose pseudoinverse to create a weighting function that yields the least-squares optimal linear combination of measurements for the estimation of r0. This approach is carried out for one example and is shown to give noisy results. A modified version of this approach that creates larger patches by averaging several smaller patches together solves this noise issue. This approach can also work to estimate other atmospheric parameters.

Scattering from a rough surface in presence of atmospheric turbulence

A Gaussian Schell Model (GSM) might be a convenient way to model extended beacons created on diffuse targets. Earlier, we used a full wave computational technique called the Method of Moments (MoM) to evaluate the scattered field from a rough impedance surface in vacuum. The MoM model showed several deviations from GSM. The present work uses a simulation approach based on physical optics approximation to study the scattering behavior in presence of atmospheric turbulence. A fully coherent beam is propagated through weak turbulence and is incident on the rough surface. The light scattered from the rough surface is again propagated through turbulence back to the source plane and the properties of the scattered radiation are studied through numerical simulations. The simulation results are compared with a GSM.

Comparison of atmospheric refractive index gradient variations derived from time-lapse imagery and mesoscale modeling

An imaging experiment was conducted to measure the temporal variability of atmospheric refractive index gradient. The refractive index gradient changes inferred from image motion correspond well with those derived from a coupled mesoscale model and ray tracing framework.

Estimation of the path-averaged atmospheric refractive index structure constant from time-lapse imagery

A time-lapse imaging experiment was conducted to monitor the effects of the atmosphere over some period of time. A tripod-mounted digital camera captured images of a distant building every minute. Correlation techniques were used to calculate the position shifts between the images. Two factors causing shifts between the images are: atmospheric turbulence, causing the images to move randomly and quickly, plus changes in the average refractive index gradient along the path which cause the images to move vertically, more slowly and perhaps in noticeable correlation with solar heating and other weather conditions. A technique for estimating the path-averaged C 2n from the random component of the image motion is presented here. The technique uses a derived set of weighting functions that depend on the size of the imaging aperture and the patch size in the image whose motion is being tracked. Since this technique is phase based, it can be applied to strong turbulence paths where traditional irradiance based techniques suffer from saturation effects.

Estimation of atmospheric parameters from time-lapse imagery

A time-lapse imaging experiment was conducted to estimate various atmospheric parameters for the imaging path. Atmospheric turbulence caused frame-to-frame shifts of the entire image as well as parts of the image. The statistics of these shifts encode information about the turbulence strength (as characterized by Cn2, the refractive index structure function constant) along the optical path. The shift variance observed is simply proportional to the variance of the tilt of the optical field averaged over the area being tracked. By presuming this turbulence follows the Kolmogorov spectrum, weighting functions can be derived which relate the turbulence strength along the path to the shifts measured. These weighting functions peak at the camera and fall to zero at the object. The larger the area observed, the more quickly the weighting function decays. One parameter we would like to estimate is r0 (the Fried parameter, or atmospheric coherence diameter.) The weighting functions derived for pixel sized or larger parts of the image all fall faster than the weighting function appropriate for estimating the spherical wave r0. If we presume Cn2 is constant along the path, then an estimate for r0 can be obtained for each area tracked, but since the weighting function for r0 differs substantially from that for every realizable tracked area, it can be expected this approach would yield a poor estimator. Instead, the weighting functions for a number of different patch sizes can be combined through the Moore-Penrose pseudo-inverse to create a new weighting function which yields the least-squares optimal linear combination of measurements for estimation of r0. This approach is carried out, and it is observed that this approach is somewhat noisy because the pseudo-inverse assigns weights much greater than one to many of the observations.

Low cost digital photography approach to monitoring optical bending and guiding in the atmosphere

A low-cost system consisting of a commercial DSLR camera and a long focal length zoom lens is introduced for the purpose of recording the guiding and bending phenomena caused by atmospheric refraction in the planetary boundary layer. A significant advantage of this system is that long duration monitoring (weeks or months) is possible with the camera operated in a time-lapse mode. Recent experiments were performed with this type of system over a 12.8 km path in Dayton, OH and a 15.3 km path in Las Cruces, NM. The measured downward vertical drift of the target images in daytime (10 to 50 pixels) are roughly consistent with an approximate theory outlined in this paper.

Simulation of deep turbulence compensation for a laser phased array

The performance of a 127 element phased array laser system is simulated for the case of an extended target in the presence of strong atmospheric turbulence. The phases of the individual sub-apertures of a phased array laser system can be controlled to compensate for the beam quality degradation caused by atmospheric turbulence. This is done by setting the phases of the sub-apertures to the conjugate of the phase received from a beacon located at the target. As the level of turbulence increases, the ability of an adaptive optics system to correct for turbulence decreases; the quality of this compensation decreases due to increases in both scintillation and fitting error. In the case where the laser system itself is used to create the beacon on an extended target, the quality of the beacon produced is also degraded by this atmospheric turbulence and this further impacts the quality of the compensation. This study simulates a 10 km tactical engagement to quantify the performance impacts due to turbulence, and the portion of this impact due to the inability of the system to form a perfect beacon in these conditions. Performance is measured by both Strehl ratio and power delivered within a near diffraction limited circle. Results are presented comparing uncompensated, compensated with a perfect beacon, and compensated with simulated beacon cases as the level of turbulence increases.