Thomas C. Farrell

Phase screen simulations of laser propagation through non-Kolmogorov atmospheric turbulence

Phase Screen simulations for laser propagation through non-Kolmogorov turbulence are presented and the results for scintillation index and correlation functions for the intensity are compared with the theory at low turbulence levels at selected non-Kolmogorov exponents. Additional simulation results are presented the strong turbulence region. In particular, effects of transitioning from Kolmogorov to non-Kolmogorov turbulence using their spectral equivalence at the Fresnel scale (as suggested in the literature) on the scintillation index and correlation functions at the receiver are examined for two example paths.

Quantum limited performance of optical receivers

While the fundamental performance limit for traditional radio frequency (RF) communications is often set by background noise on the channel, the fundamental limit for optical communications is set by the quantum nature of light. Both types of systems are based on electro-magnetic waves, differing only in carrier frequency. It is, in fact, the frequency that determines which of these limits dominates. We explore this in the first part of this paper. This leads to a difference in methods of analysis of the two different types of systems. While equations predicting the probability of bit error for RF systems are usually based on the signal to background noise ratio, similar equations for optical systems are often based on the physics of the quantum limit and are simply a function of the detected signal energy received per bit. These equations are derived in the second part of this paper for several frequently used modulation schemes: On-off keying (OOK), pulse position modulation (PPM), and binary differential phase shift keying (DPSK). While these equations ignore the effects of background noise and non-quantum internal noise sources in the detector and receiver electronics, they provide a useful bound for obtainable performance of optical communication systems. For example, these equations may be used in initial link budgets to assess the feasibility of system architectures, even before specific receiver designs are considered.

The performance of Geiger mode avalanche photo-diodes in free space laser communication links

Geiger mode avalanche photo-diode (APD) arrays, when used as detectors in laser communication (lasercom) receivers, promise better performance at lower signal levels than APDs operated in the linear mode. In this paper, we describe the basic operation of the Geiger mode APD array as a lasercom detector, concentrating on aspects relevant to the link design engineer (rather than, for example, describing the details of the physics of the basic device operation itself). Equations are developed that describe the effects of defocus and hold-off time on the relation between the number of photons detected by the array and the output of photo-electron counts. We show how to incorporate these equations into a link budget. The resulting predictions are validated by comparison against simulation results. Finally, we compare the performance of linear mode APD based receivers and Geiger mode APD array based receivers. Results show the Geiger mode receivers yield better performance, in terms of probability of bit error, at lower signal levels, except on links where there is an exceptionally large amount of background noise. Under those conditions, not surprisingly, the hold-off time degrades performance.

Fast simulation of Strehl loss due to phase aberration for the sizing of adaptive optics in laser communications system design

An approximation is derived for the phase Strehl of an aberrated wavefront based on uncorrelated random variates. Eliminating the requirement to generate correlated variates offers an orders-of-magnitude improvement in simulation speed, while yielding accuracy that may be sufficient for the preliminary sizing of adaptive optics (AO) in laser communications system design. Examples are presented comparing the performance of several AO subsystem sizes when correcting a wavefront aberrated by Kolmogorov turbulence.

Predicting the performance of linear optical detectors in free space laser communication links

While the fundamental performance limit for optical communications is set by the quantum nature of light, in practical systems background light, dark current, and thermal noise of the electronics also degrade performance. In this paper, we derive a set of equations predicting the performance of PIN diodes and linear mode avalanche photo diodes (APDs) in the presence of such noise sources. Electrons generated by signal, background, and dark current shot noise are well modeled in PIN diodes as Poissonian statistical processes. In APDs, on the other hand, the amplifying effects of the device result in statistics that are distinctly non-Poissonian. Thermal noise is well modeled as Gaussian. In this paper, we appeal to the central limit theorem and treat both the variability of the signal and the sum of noise sources as Gaussian. Comparison against Monte-Carlo simulation of PIN diode performance (where we do model shot noise with draws from a Poissonian distribution) validates the legitimacy of this approximation. On-off keying, M-ary pulse position, and binary differential phase shift keying modulation are modeled. We conclude with examples showing how the equations may be used in a link budget to estimate the performance of optical links using linear receivers.

Sources of background light on space based laser communications links

We discuss the sources and levels of background light that should be expected on space based laser communication (lasercom) crosslinks and uplinks, as well as on downlinks to ground stations. The analyses are valid for both Earth orbiting satellites and inter-planetary links. Fundamental equations are derived suitable for first order system engineering analyses of potential lasercom systems. These divide sources of background light into two general categories: extended sources which fill the field of view of a receiver’s optics, and point sources which cannot be resolved by the optics. Specific sources of background light are discussed, and expected power levels are estimated. For uplinks, reflected sunlight and blackbody radiation from the Earth dominates. For crosslinks, depending on specific link geometry, sources of background light may include the Sun in the field of view (FOV), reflected sunlight and blackbody radiation from planets and other bodies in the solar system, individual bright stars in the FOV, the amalgam of dim stars in the FOV, zodiacal light, and reflected sunlight off of the transmitting spacecraft. For downlinks, all of these potentially come into play, and the effects of the atmosphere, including turbulence, scattering, and absorption contribute as well. Methods for accounting for each of these are presented. Specific examples are presented to illustrate the relative contributions of each source for various link geometries.

Understanding the physics of optical deep turbulence at the Earth's boundary layer

The Air Force Research Laboratory (AFRL) is developing and extending a model of the boundary layer that takes, as input, common atmospheric measurements and ground condition parameters, and predicts key parameters of optical turbulence such as strength and inner scale. In order to anchor the model, a field campaign is also being conducted. The campaign will include co-located meteorological instruments and an open loop Hartmann wavefront sensor. Here, a portion of the boundary layer model is discussed: that relevant for the daytime surface layer. A sensitivity analysis of input parameters is presented.

A Method for Developing Preliminary Adaptive Optics Designs for Lasercom Applications

There is a need for fast and intuitive methods for developing preliminary adaptive optics designs so that free space lasercom channels through the atmosphere meet performance requirements. We describe one.

Modifying the Inner Scale Equation of the Boundary Layer Turbulence Model to Account for Non-Kolmogorov Turbulence

Previously, we developed a model of the Earth’s boundary layer to predict optical turbulence characteristics from environmental parameters. This discusses a generalization made to the inner scale equation to account for non-Kolmogorov turbulence.

Characterizing Earth’s Boundary Layer (CEBL)—2014 Update

AFRL is developing a model of boundary layer turbulence. A field campaign, correlating meteorological conditions with measured turbulence, is being conducted to anchor the model. We present the 2014 update on the campaign.