An F/1.2 infrared optical system that involves two aspheric BD-2 lenses and an aspheric diffractive surface was designed over $8-14{mu}m$ with a field angle of $15.2^{circ}$. The system may be used in uncooled cameras and is analyzed using beam synthesis propagation (BSP). The diffractive surface is modeled as a physical surface with a given thickness, and results are compared with those obtained by conventional methods, such as the exit-pupil method and a method which superposes diffraction orders.