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We prove the existence and regularity of the isochron map for stableinvariant manifolds of a large class of evolution equations. Our results applyin particular to the isochron map of reaction-diffusion equations and neuralfield equations. Using the regularity properties proven here, we are able toobtain a strong It\^o formula for the isochronal phase of stochasticallyperturbed travelling waves, spiral waves, and other patterns appearing in SPDEsdriven by white noise, even for SPDEs that only admit mild solutions.

Existence, Regularity, and a Strong It\^o Formula for the Isochronal Phase of SPDE