  The knowledge of the dynamical state of galaxy clusters allows to alleviate
systematics when observational data from these objects are applied in
cosmological studies. Evidence of correlation between the state and the
morphology of the clusters is well studied. The morphology can be inferred by
images of the surface brightness in the X-ray band and of the thermal component
of the Sunyaev-Zel'dovich (tSZ) effect in the millimetre range. For this
purpose, we apply, for the first time, the Zernike polynomial decomposition, a
common analytic approach mostly used in adaptive optics to recover aberrated
radiation wavefronts at the telescopes pupil plane. With this novel way we
expect to correctly infer the morphology of clusters and so possibly, their
dynamical state. To verify the reliability of this new approach we use more
than 300 synthetic clusters selected in THE THREE HUNDRED project at different
redshifts ranging from 0 up to 1.03. Mock maps of the tSZ, quantified with the
Compton parameter, $y$-maps, are modelled with Zernike polynomials inside
$R_{500}$, the cluster reference radius. We verify that it is possible to
discriminate the morphology of each cluster by estimating the contribution of
the different polynomials to the fit of the map. The results of this new method
are correlated with those of a previous analysis made on the same catalogue,
using two parameters that combine either morphological or dynamical-state
probes. We underline that instrumental angular resolution of the maps has an
impact mainly when we extend this approach to high-redshift clusters.
