The prolate spheroidal wave function is a set of complete orthogonal functions set in both the finite and infinite space domain, which is suitable to analyze the practical optical systems with finite aperture size .The linear canonical transform is a kind of important time-frequency analysis tool, and the Fresnel transform is a special case of linear canonical transform. So, the linear canonical transform can model optical system. The offset linear canonical transform of prolate spheroidal wave functions in finite space domain and frequency domain is instituted, and the offset linear canonical transform models a two-dimension optical system. Using the spheroidal wave functions as signal functions, the signal′s energy loss after passing through the system is analyzed. Based on prolate spheroidal wave functions′ eigenvalue property, the eigenvalue reflects the energy-preservation ratio. The numerical calculation result suggests that the signal function′s energy ratio after passing through the system is consistent with the energy ratio′s estimation value gained by the function′s eigenvalue, which indicates the validity of this method.