  We establish a unconditional and optimal strong convergence rate of
Wong--Zakai type approximations in Banach space norm for a parabolic stochastic
partial differential equation with monotone drift, including the stochastic
Allen--Cahn equation, driven by an additive Brownian sheet. The key ingredient
in the analysis is the fully use of additive nature of the noise and
monotonicity of the drift to derive a priori estimation for the solution of
this equation, in combination with the factorization method and stochastic
calculus in martingale type 2 Banach spaces applied to deduce sharp error
estimation between the exact and approximate Ornstein--Uhlenbeck processes, in
Banach space norm.
