We derive a useful formula for the normal ordering of two-mode operator by the technique of integration within an ordered product (IWOP) of operators. Furthermore, we also calculate the Radon transformations for the coherent state, special squeezed coherent state, intermediary entangled state in the view of the quantum mechanics. Based on the results above, the Mexican hat's mother wavelet function is selected to analyse Ridgelet transformations of these three quantum optical states.