Under weak turbulence theory, we will use the random thin phase screen model and the Kolmogorov power-law spectrum to derive approximate models for the scintillation index, covariance function of irradiance fluctuations, and temporal spectrum of irradiance fluctuations for collimated beams. In addition, we will provide an expression for the quasi-frequency of a collimated beam and investigate the relationship between the quasi-frequency and the maximum width of the normalized temporal spectrum of irradiance for a collimated beam.