The maximum tolerable spot displacement of the Shack-Hartmann wave-front sensor is named dynamic range

and it is limited by the f-number of the micro-lens. It is well known that there is a trade-off between the sensitivity and the dynamic range

if the f-number is relatively short

a high dynamic range is achieved

but the corresponding sensitivity is degraded. Extrapolation method could overcome the trade-off; since the extrapolation method is a simple algorithm that does not change the measurement configuration

there is no requirement for extra hardware

multiple measurements

or complicated algorithms. In this paper

we not only present the theory but also actually implement measurement of a highly aerated wave-front.