Non-ergodicity of neuronal dynamics from rapid ion channel gating through the membrane induces membrane displacement statistics that deviate from Brownian motion. The membrane dynamics from ion channel gating were imaged by phase-sensitive optical coherence microscopy. The distribution of optical displacements of the neuronal membrane showed a Lévy-like distribution and the memory effect of the membrane dynamics by the ionic gating was estimated. The alternation of the correlation time was observed when neurons were exposed to channel-blocking molecules. Non-invasive optophysiology by detecting the anomalous diffusion characteristics of dynamic images is demonstrated.