  Quantum light is described not only by a quantum state but also by the shape
of the electromagnetic modes on which the state is defined. Optical precision
measurements often estimate a ``mode parameter'' that determines properties
such as frequency, temporal shape and the spatial distribution of the light
field. By deriving quantum precision limits, we establish the fundamental
bounds for mode parameter estimation. Our results reveal explicit mode-design
recipes that enable the estimation of any mode parameter with quantum enhanced
precision. Our approach provides practical methods for optimizing mode
parameter estimation with relevant applications, including spatial and temporal
positioning, spectroscopy, phase estimation, and superresolution imaging.
