An analysis of experimentally observed far-field irradiance statistics, suggesting an approach to calculating the probability distribution for intensity fluctuations of an optical wave in a turbulent medium and expressions for measuring important wave characteristics. Two theoretical treatments of probability distribution are investigated. Because none of the proposed theories can account for irradiance statistics in a consistent manner, it is suggested that a modified geometric optics approach would lead to an improved quantitative understanding of the phenomena. Expressions are derived for measuring wave phase structure function and modulation transfer function. Results are useful in determining the limited resolution obtainable in forming an image through a turbulent medium, as well as in calculating the signal-to-noise ratio of an optical heterodyne detection system.