A dynamic model of IR missile engagements must combine the output of signature models into a scene of given resolution with a changing viewpoint and moving targets against some background. Some signature prediction models are stand-alone software packages, which currently cannot be dynamically interfaced to a running engagement model. They can be used to conveniently provide an image of an IR target at high resolution at a single viewpoint. An algorithm to solve the radiance map composition problem and combine target, sea, and sky signatures can be thought of intuitively as an idealized imaging radiometer model. We present the derivation of such a model from physical and signal processing considerations and its practical implementation; show that under reasonable assumptions, the radiance integral takes the form of a particularly simple computation; and demonstrate that the model behaves reasonably with translucent targets. The derived methodology provides very high radiometric accuracy with a rigorously controlled error and smooth integration of objects moving through the scene.