For infrared optical systems a point spread function is calculated in terms of the spot diagram obtained through geometrical ray trace or the theory of Kirchhoff diffraction. Also is calculated the ratio T of the energy passing through the system onto the exit window, to the total energy radiated from a plane target into the entrance pupil. Formulas are derived separately for the following different cases: a circular or rectangular ring diffraction pupil, a blur of equivalent intensity distribution or a Gaussian blur, and a circular or rectangular field stop. In certain casses T values are given through digital calculation. This method of T calculation is useful for any infrared optical systems. The table of T values can be applied to the system layout design of infrared instruments and T function used as the merit function of optical systems. The calculation of T is very important for diffraction limited systems.