  Given a density operator $\hat \rho$ the optical tomography map defines a
one-parameter set of probability distributions $w_{\hat \rho}(X,\phi),\ \phi
\in [0,2\pi),$ on the real line allowing to reconstruct $\hat \rho $. We
introduce a dual map from the special class $\mathcal A$ of quantum observables
$\hat a$ to a special class of generalized functions $a(X,\phi)$ such that the
mean value $<\hat a>_{\hat \rho} =Tr(\hat \rho\hat a)$ is given by the formula
$<\hat a>_{\hat \rho}= \int \limits_{0}^{2\pi}\int
\limits_{-\infty}^{+\infty}w_{\hat \rho}(X,\phi)a(X,\phi)dXd\phi$. The class
$\mathcal A$ includes all the symmetrized polynomials of canonical variables
$\hat q$ and $\hat p$.
