 Shack–Hartmann wavefront sensor

A Shack–Hartmann wavefront sensor divides an incoming beam among a regular array of small optical lenses, each forming a spot on a detector. A locally tilted wavefront displaces the corresponding spot relative to a reference measurement. For lens focal length $f$ and small local tilt $\alpha$, the displacement is approximately $f\alpha$.

If $W(x,y)$ denotes wavefront error as an optical path length in air, the measured displacements approximately give $\Delta x=f\partial W/\partial x$ and $\Delta y=f\partial W/\partial y$. Reconstructing $W$ from these slopes supports adaptive optics. A spatially constant offset in $W$ remains undetermined because it changes neither slope; overlapping or poorly sampled spots also limit reconstruction.