Wave-front sensing with time-of-flight phase diversity.

We present a new way to sense atmospheric wave-front phase distortion. Short collimated pulses of laser light at $\sim 350 \text{nm}$ are projected from a small auxilliary telescope. Rayleigh scattering from each pulse is recorded over a wide range of height through the main telescope aperture in a continuous sequence of fast video frames by a detector conjugate to mid-height. Phase diversity is thus naturally introduced as the pulses approach and pass through focus. We show that an iterative algorithm can extract the phase structure from the recorded images and do so with a much higher signal-to-noise ratio than is possible with existing techniques. If the requirements for real-time data recording and reduction can be met, the new method will address the need for tomographic wave-front sensing at planned 30-m-class telescopes.