  The free expansion of a planar plasma surface is a fundamental
non-equilibrium process relevant for various fields but as-yet experimentally
still difficult to capture. The significance of the associated spatiotemporal
plasma motion ranges from astrophysics and controlled fusion to laser
machining, surface high-harmonic generation, plasma mirrors, and laser-particle
acceleration. Here, we show that x-ray coherent diffractive imaging can surpass
existing approaches and enables the quantitative real-time analysis of the
sudden free expansion of nanoplasmas. For laser-ionized SiO$_2$ nanospheres, we
resolve the formation of the emerging nearly self-similar plasma profile
evolution and expose the so far inaccessible shell-wise expansion dynamics
including the associated startup delay and rarefaction front velocity. Our
results establish time-resolved diffractive imaging as an accurate quantitative
diagnostic platform for tracing and characterizing plasma expansion and
indicate the possibility to resolve various laser-driven processes including
shock formation and wave-breaking phenomena with unprecedented resolution.
