  We introduce a self-consistent tomography for arbitrary quantum
non-demolition (QND) detectors. Based on this, we build a complete physical
characterization of the detector, including the measurement processes and a
quantification of the fidelity, ideality, and back-action of the measurement.
This framework is a diagnostic tool for the dynamics of QND detectors, allowing
us to identify errors, and to improve their calibration and design. We
illustrate this on a realistic Jaynes-Cummings simulation of superconducting
qubit readout. We characterize non-dispersive errors, quantify the back-action
introduced by the readout cavity, and calibrate the optimal measurement point.
