Two spatial light modulator system for laboratory simulation of random beam propagation in random media: comment.

In a recent paper [Appl. Opt.55, 1112 (2016)APOPAI0003-693510.1364/AO.55.001112], the authors present a procedure for synthesizing Gaussian phase screens to generate Schell-model sources. Their synthesis method is analyzed, revealing interesting phenomena not fully described by the authors.

Two-dimensional simulation of optical wave propagation through atmospheric turbulence.

A methodology for the two-dimensional simulation of optical wave propagation through atmospheric turbulence is presented. The derivations of common statistical field moments in two dimensions, required for performing and validating simulations, are presented and compared with their traditional three-dimensional counterparts. Wave optics simulations are performed to validate the two-dimensional moments and to demonstrate the utility of performing two-dimensional wave optics simulations so that the results may be scaled to those of computationally prohibitive 3D scenarios. Discussions of the benefits and limitations of two-dimensional atmospheric turbulence simulations are provided throughout.

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.

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.

Fade statistics of a ground-to-satellite optical link in the presence of lead-ahead and aperture mismatch.

In a recent publication [J. Opt. Soc. Am. A25, 1594-1608 (2008).JOAOD60740-323210.1364/JOSAA.25.001594] we developed expressions for the tilt errors that arise from the effects of lead-ahead and aperture mismatch when transmitting a laser beam from the ground to a satellite. We extend these results to examine the fade statistics of the irradiance at the satellite due to these tilt errors and turbulence induced scintillation. The system concept is that the light from a beacon on the satellite is received by the ground station and a derived signal is used to drive a tracking/pointing system for the uplink beam. However, the beam must be pointed ahead along the satellite track to intercept the satellite (lead-ahead), and physical constraints may require that the beam transmit aperture is different in size or location than the aperture receiving the beacon signal (aperture mismatch). These two issues cause the light entering the receiving aperture (tracker) and the beam exiting the transmit aperture (pointer) to traverse somewhat different turbulence volumes, which limits the ability of the tracking/pointing system to place the maximum flux on the satellite.

Tracking in a ground-to-satellite optical link: effects due to lead-ahead and aperture mismatch, including temporal tracking response.

Establishing a link between a ground station and a geosynchronous orbiting satellite can be aided greatly with the use of a beacon on the satellite. A tracker, or even an adaptive optics system, can use the beacon during communication or tracking activities to correct beam pointing for atmospheric turbulence and mount jitter effects. However, the pointing lead-ahead required to illuminate the moving object and an aperture mismatch between the tracking and the pointing apertures can limit the effectiveness of the correction, as the sensed tilt will not be the same as the tilt required for optimal transmission to the satellite. We have developed an analytical model that addresses the combined impact of these tracking issues in a ground-to-satellite optical link. We present these results for different tracker/pointer configurations. By setting the low-pass cutoff frequency of the tracking servo properly, the tracking errors can be minimized. The analysis considers geosynchronous Earth orbit satellites as well as low Earth orbit satellites.

Maximum-likelihood estimation of a laser system pointing parameters by use of return photon counts.

A maximum-likelihood estimator used to determine boresight and jitter performance of a laser pointing system has been derived. The estimator is based on a Gaussian jitter model and uses a Gaussian far-field irradiance profile. The estimates are obtained using a set of return shots from the intended target. An experimental setup with a He-Ne laser and steering mirrors is used to study the performance of the proposed method. Both Monte Carlo simulations and experimental results demonstrate excellent performance of the estimator. Our study shows that boresight estimation is more challenging than jitter estimation when both quantities are estimated. Furthermore, their estimation performance improves with an increase in the number of shots. The experimental results are found to agree well with the simulation results.