The high-order irradiance moments recently measured in turbulent air up to the fifth order in connection with the K distribution are compared with previous theory based on a cluster expansion of the irradiance moments mν = 〈Iν〉/〈I〉ν, ν = 1, 2, 3, …. Good agreement is confirmed over the entire observed range 0.1 ≲ σI2/〈I〉2 ≲ 6 of the normalized variance of irradiance σI2/〈I〉2, including the regions of both unsaturated and saturated scintillations. Also shown are the theoretical curves of the mean and the variance of the log-amplitude, and good consistency is found with values of previous experiments made exclusively in terms of the log-amplitude and also of recent experiments made simultaneously on both log-amplitude and irradiance. The K distribution fits the experimental results of the mν values well within the range σI2/〈I〉2 ≳ 2 but definitely fails to fit those of the mean and the variance of the log-amplitude.
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