  Given a one-dimensional weighted Dirac operator we can define a spectral
measure by virtue of singular Weyl-Titchmarsh-Kodaira theory. Using the theory
of de Branges spaces we show that the spectral measure uniquely determines the
Dirac operator up to a gauge transformation. Our result applies in particular
to radial Dirac operators and extends the classical results for Dirac operators
with one regular endpoint. Moreover, our result also improves the currently
known results for canonical (Hamiltonian) systems. If one endpoint is limit
circle case, we also establish corresponding two-spectra results.
