Statistics of the received power for free space optical channels

Free space optical (FSO) communication links can experience extreme signal degradation due to atmospheric turbulence induced spatial and temporal irradiance fuctuations (scintillation) in the laser wavefront. In addition, turbulence can cause the laser beam centroid to wander resulting in power fading, and sometimes complete loss of the signal. Spreading of the laser beam and jitter are also artifacts of atmospheric turbulence. To accurately predict the signal fading that occurs in a laser communication system and to get a true picture of how this affects crucial performance parameters like bit error rate (BER) it is important to analyze the probability density function (PDF) of the integrated irradiance fuctuations at the receiver. In addition, it is desirable to find a theoretical distribution that accurately models these ?uctuations under all propagation conditions. The PDF of integrated irradiance fuctuations is calculated from numerical wave-optic simulations of a laser after propagating through atmospheric turbulence to investigate the evolution of the distribution as the aperture diameter is increased. The simulation data distribution is compared to theoretical gamma-gamma and lognormal PDF models under a variety of scintillation regimes from weak to very strong. Our results show that the gamma-gamma PDF provides a good fit to the simulated data distribution for all aperture sizes studied from weak through moderate scintillation. In strong scintillation, the gamma-gamma PDF is a better fit to the distribution for point-like apertures and the lognormal PDF is a better fit for apertures the size of the atmospheric spatial coherence radius ρ0 or larger. In addition, the PDF of received power from a Gaussian laser beam, which has been adaptively compensated at the transmitter before propagation to the receiver of a FSO link in the moderate scintillation regime is investigated. The complexity of the adaptive optics (AO) system is increased in order to investigate the changes in the distribution of the received power and how this affects the BER. For the 10 km link, due to the non-reciprocal nature of the propagation path the optimal beam to transmit is unknown. These results show that a low-order level of complexity in the AO provides a better estimate for the optimal beam to transmit than a higher order for non-reciprocal paths. For the 20 km link distance it was found that, although minimal, all AO complexity levels provided an equivalent improvement in BER and that no AO complexity provided the correction needed for the optimal beam to transmit. Finally, the temporal power spectral density of received power from a FSO communication link is investigated. Simulated and experimental results for the coherence time calculated from the temporal correlation function are presented. Results for both simulation and experimental data show that the coherence time increases as the receiving aperture diameter increases. For finite apertures the coherence time increases as the communication link distance is increased. We conjecture that this is due to the increasing speckle size within the pupil plane of the receiving aperture for an increasing link distance.

"Brethren upon the same level" : membership and class in Calumet's Masonic Lodge

The Keweenaw Peninsula of Upper Michigan was a ethnic conglomerate of cultures and ideas, with people attracted to the area by the mineral wealth found along the Copper Range. The center of copper mining from the mid 1860s to 1968 was in the vicinity of Calumet Township, home to the world-famous Calumet and Hecla Mining Company. The township depended on the mines and the company’s president Agassiz’s strove to make the area a “model community,” that included groups such as the Free and Accepted Masons. Men from myriad backgrounds arrived in Calumet from the British Isles, Germany, Finland, Eastern and Southern Europe and the Eastern United States. As in other communities from the time period these men formed common interest groups like Masonic Lodge 271, which received its charter in 1870. Gentlemen joined with merchants and craftsmen. They became “brethren upon the same level,” and were elevated to the status of Master Mason. This symbolic transformation within the Lodge removed the men from the “profane world” outside the sanctity of Masonry, and in the ritualistic transformation of the meeting they were reborn into Masonry’s sacred mysteries. Masonry acted as a means of moral guidance to men and gave them access to a larger social and economic community through a common connection of brotherhood. As the candidates moved through the three Blue Lodge degrees of Entered Apprentice, Fellowcraft, and Master Mason they saw each other as “brethren upon the same level” – all economic classes equal within the Masonic Lodge. To examine equality within Lodge 271, this study sorted workers into classes to allow a comparison of Lodge 271’s membership. Possibly a comparison between other lodges can be drawn from the membership. The Union Building in Calumet, MI will be examined for its role in the ritualistic transformation of Masonry as it housed Masonic activities and transformations. This transformation brought men into the lodge of brothers. While Masonry professed equality between members however, to what extent did the membership of the lodge reflect this between the brethren? To what extent did economic class determine who was made “brethren upon the same level? 1 Arthur Thurner, Calumet Copper and People: History of a Michigan Mining Community, 1864-1970 (Hancock, MI: Book Concern, 1974), 122.