We report experiments on the full space- and time-resolved
statistics of capillary wave turbulence at the air-water
interface. The three-dimensional shape of the free interface is
measured as a function of time by using the optical method of
diffusing light photography associated with a fast camera.
Linear and nonlinear dispersion relations are extracted from the
spatiotemporal power spectrum of wave amplitude. When wave
turbulence regime is reached, we observe power-law spectra both
in frequency and in wave number whose exponents are found to
agree with the predictions of capillary wave turbulence theory.
Finally, the temporal dynamics of the spatial energy spectrum
highlight the occurrence of stochastic bursts transferring wave
energy through the spatial scales.