Non-Gaussian quantum states whose Wigner functions can take negative values are important both for fundamental tests of quantum physics and for the quantum information technologies that have been under active development recently. A typical example of a non-Gaussian state is the so-called Schrödinger's cat state. Its very interesting feature is that its 'classical' part (two Gaussian maxima) is geometrically separated from the 'nonclassical' part (interference fringes). In this paper, several methodological issues related to these fringes are considered.