When reading Griffiths' paper "Hermitian differential geometry, Chern classes and positive vector bundles", I found his definition of ampleness:
Let $X$ be a compact complex manifold, $E\to X$ a holomorphic vector bundle, $E$ is called ample if
The global section generate each fibre, so that we have $0\to F_z\to\Gamma(E)\to E_z\to 0$ for all $z\in X$.
The natural mapping $F_z\to E_z\otimes T_z^*$ is onto ($F_z=$ sections of $E$ vanishing at $z$, $T_z$ is the tangent bundle)
But from most of the definitions nowadays, ampleness of vector bundle is
$E$ is called ample if the line bundle $\mathscr{O}_{\mathbb{P}(E^*)}(1)$ is ample.
Since Griffiths claimed in his theorem A that ampleness implies Griffiths positivity, his ampleness here doesn't seems to coincide with our modern definition (Because Griffiths' conjecture is still open! And this conjecture says "ampleness implies Griffiths' positivity", this ampleness here is from the second definition.) So I wonder what Griffiths' ampleness is in modern language? Is there any reference for this ampleness? Thanks!