Modulation effect of the atmosphere in a pyramid wave-front sensor.

The pyramid wave-front sensor in its original form works with a mechanical modulation that adapts the linear range of the sensor to seeing and sensing conditions. For adaptive optics systems working in an astronomical context, the way in which the aberrations produced by the atmospheric turbulence, which are not seen by the sensor owing to its limited temporal bandwidth, act as modulators is shown. These aberrations have the same effect of increasing the linear range and localizing the measurement as does mechanical modulation. The effect of residual wave-front aberrations is estimated for some example conditions of telescope diameter, system bandwidth, wind velocity, and Fried parameter.