  The measurement process is considered for quantum field theory on curved
spacetimes. Measurements are carried out on one QFT, the "system", using
another, the "probe" via a dynamical coupling of "system" and "probe" in a
bounded spacetime region. The resulting "coupled theory" determines a
scattering map on the uncoupled combination of the "system" and "probe" by
reference to natural "in" and "out" spacetime regions. No specific interaction
is assumed and all constructions are local and covariant.
  Given any initial probe state in the "in" region, the scattering map
determines a completely positive map from "probe" observables in the "out"
region to "induced system observables", thus providing a measurement scheme for
the latter. It is shown that the induced system observables may be localized in
the causal hull of the interaction coupling region and are typically less sharp
than the probe observable, but more sharp than the actual measurement on the
coupled theory. Post-selected states conditioned on measurement outcomes are
obtained using Davies-Lewis instruments. Composite measurements involving
causally ordered coupling regions are also considered. Provided that the
scattering map obeys a causal factorization property, the causally ordered
composition of the individual instruments coincides with the composite
instrument; in particular, the instruments may be combined in either order if
the coupling regions are causally disjoint. This is the central consistency
property of the proposed framework.
  The general concepts and results are illustrated by an example in which both
"system" and "probe" are quantized linear scalar fields, coupled by a quadratic
interaction term with compact spacetime support. System observables induced by
simple probe observables are calculated exactly, for sufficiently weak
coupling, and compared with first order perturbation theory.
