When measuring atmospheric turbulence along the propagation path to an extended non-cooperative target, a wavefront sensor normally suffers from severe noise due to speckle. In this work, we quantify the benefits of speckle mitigation via polychromatic illumination for a Shack–Hartmann wavefront sensor. We obtain results over a wide range of conditions by using the spectral-slicing approach to polychromatic wave-optics simulations. To quantify speckle noise, even when turbulence is present, we introduce a metric involving racetrack-mode strength in slope-discrepancy space. The results show that polychromatic illumination greatly reduces speckle noise under realistic conditions. Even with near worst-case conditions, 15 coherence lengths per resolution cell reduce the wavefront-measurement error by 56%
