  Given a generic ray of Higgs bundles $(\overline{\partial}_E, t\varphi)$, we
describe the corresponding family of hermitian metrics $h_t$ solving Hitchin's
equations via gluing methods. In the process, we construct a family of
approximate solutions $h_t^{\mathrm{app}}$ which differ from the actual
harmonic metrics $h_t$ by error terms of size $\mathrm{e}^{-\delta t}$. Such
families of explicit approximate solutions have already proved useful for
answering finer questions about the asymptotic geometry of the Hitchin moduli
space.
