  This paper deals with a non-parametric problem coming from physics, namely
quantum tomography. That consists in determining the quantum state of a mode of
light through a homodyne measurement. We apply several model selection
procedures: penalized projection estimators, where we may use pattern functions
or wavelets, and penalized maximum likelihood estimators. In all these cases,
we get oracle inequalities. In the former we also have a polynomial rate of
convergence for the non-parametric problem. We finish the paper with
applications of similar ideas to the calibration of a photocounter, a
measurement apparatus counting the number of photons in a beam. Here the
mathematical problem reduces similarly to a non-parametric missing data
problem. We again get oracle inequalities, and better speed if the photocounter
is good.
