Atmospheric effects on normalized stellar irradiance fluctuations for the weak fluctuation regime are examined. Both monochromatic and polychromatic effects are considered. Calculations are performed using a Rytov theory which explicitly includes refractive effects arising from the polychromatic stellar source. The atmospheric turbulence along the path is specified in a spherical shell or `onion- skin' model using a vertical profile specified by either the Clear 1 model or actual thermosonde measurements. Finite optical bandwidth, receiver aperture size, and variable turbulent inner scale are also included. Good agreement is found between ground-based measurements and model results in the weak scintillation regime. It is also shown that refraction effects can significantly alter the wavelength dependence of scintillation as well as produce a leveling off and decrease of scintillation with increasing zenith angle that could be misinterpreted as saturation.