Estimation of Temporal Variations in Path-averaged Atmospheric Refractive Index Gradient from Time-lapse Imagery

The sea level vertical refractive index gradient in the U.S. Standard Atmosphere model is −2.7×10−8  m−1 at 500 nm. At any particular location, the actual refractive index gradient varies due to turbulence and local weather conditions. An imaging experiment was conducted to measure the temporal variability of this gradient. A tripod mounted digital camera captured images of a distant building every minute. Atmospheric turbulence caused the images to wander quickly, randomly, and statistically isotropically and changes in the average refractive index gradient along the path caused the images to move vertically and more slowly. The temporal variations of the refractive index gradient were estimated from the slow, vertical motion of the building over a period of several days. Comparisons with observational data showed the gradient variations derived from the time-lapse imagery correlated well with solar heating and other weather conditions. The time-lapse imaging approach has the potential to be used as a validation tool for numerical weather models. These validations will benefit directed energy simulation tools and applications

Experimentally Generating Any Desired Partially Coherent Schell-model Source Using Phase-only Control

A technique is presented to produce any desired partially coherent Schell-model source using a single phase-only liquid-crystal spatial light modulator (SLM). Existing methods use SLMs in combination with amplitude filters to manipulate the phase and amplitude of an initially coherent source. The technique presented here controls both the phase and amplitude using a single SLM, thereby making the amplitude filters unnecessary. This simplifies the optical setup and significantly increases the utility and flexibility of the resulting system. The analytical development of the technique is presented and discussed. To validate the proposed approach, experimental results of three partially coherent Schell-model sources are presented and analyzed. A brief discussion of possible applications is provided in closing

Generating Partially Coherent Schell-Model Sources Using a Modified Phase Screen Approach

A significant improvement to the recently introduced complex screen (CS) method for generating partially coherent Schell-model sources is presented. The method, called the modified phase screen (MPS) technique, applies a deterministic amplitude and the phase portion of a CS to an initially coherent light source using a single phase-only spatial light modulator. The MPS technique, unlike the CS approach from which it is derived, does not produce a fully developed speckle pattern in the source plane, and therefore converges faster and more uniformly to the desired partially coherent source. The analytical development of the MPS method is presented. Experimental results of a Bessel-Gaussian-correlated Schell-model source, generated using the CS and MPS approaches, are compared to demonstrate the validity and utility of the MPS technique

Computational Approaches for Generating Electromagnetic Gaussian Schell-model Sources

Two different methodologies for generating an electromagnetic Gaussian-Schell model source are discussed. One approach uses a sequence of random phase screens at the source plane and the other uses a sequence of random complex transmittance screens. The relationships between the screen parameters and the desired electromagnetic Gaussian-Schell model source parameters are derived. The approaches are verified by comparing numerical simulation results with published theory. This work enables one to design an electromagnetic Gaussian-Schell model source with pre-defined characteristics for wave optics simulations or laboratory experiments. © 2014 Optical Society of Americ

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. © 2013 Optical Society of Americ

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

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

Comparison of Coherent and Incoherent Laser Beam Combination for Tactical Engagements

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.Abstract © SPI