  In the framework of quantum optics, we study the problem of goodness-of-fit
testing in a severely ill-posed inverse problem. A novel testing procedure is
introduced and its rates of convergence are investigated under various
smoothness assumptions. The procedure is derived from a projection-type
estimator, where the projection is done in $\mathbb{L}_2$ distance on some
suitably chosen pattern functions. The proposed methodology is illustrated with
simulated data sets.
