Title: $q$-deformed quadrature operator and optical tomogram,
Abstract: In this letter, we define the homodyne $q$-deformed quadrature operator.
Analytic expression for the wavefunctions of $q$-deformed oscillator in the
quadrature basis are found. Furthermore, we compute the explicit analytical
expression for the tomogram of the $q$-deformed coherent states by finding the
eigenstates of the $q$-deformed quadrature operator.