On the determination of pure quantum states by the homodyne detection

The methods of reconstruction of the wave function of a pure state of a quantum system by quadrature distribution measured experimentally by the homodyne detection are considered. Such distribution is called optical tomogram of a state and containes one parameter $\theta$. Wave function of a state is determined exactly by its optical tomogram if last one is known for all $\theta$. But one can obtain optical tomogram from experiment of homodyne detection only for discrete number of $\theta$. We introduce some approximate methods of reconstructing the state by such information about its optical tomogram.