The degree to which hardware-in-the-loop tests can be used to replace more expensive flight tests is dependent on how well the tests resemble real flight tests. One of the most challenging problems associated with making realistic hardware-in-the-loop tests is the projection of realistic imagery to the seeker. Since a seeker is limited in its ability to `see' a real scene, projection systems do not have to perfectly replicate real scenes. They only have to produce scenes which appear the same as the real scenes when measured with spatial, spectral, and temporal resolutions that are at least as poor as those of the seekers to be tested. Unfortunately, this means that in order to determine the realism of a given test or class of tests, it is necessary to include in the analysis characteristics of the seekers as well as characteristics of both the real scenes and the projected scenes. For many reasons, the conventional Fourier transform techniques are not adequate for performing these analyses. In this paper, a formalism is given for analyzing spatial, spectral, and temporal effects in a hardware-in-the-loop system involving a pixelized projector and a passive imaging sensor. The fundamental equations are presented describing the measurement of either a real scene or a pixelized projector with a passive imaging sensor. The equations are kept in the space, wavelength, and time domains to avoid the unnecessary restrictions that are encountered when transforming to the Fourier domain. An example is given of an application of the formalism to evaluate the effects of projector pixel spacing and blur effects.