Projector nonuniformity and spatial effects modeling

This paper presents mathematical models and measurements of the spatial noise a camera observes as it views a projection system with nonuniform emitter responses. The models account for the effects of the projector and camera spatial resolutions and of the alignment of the emitters with respect to the camera detectors. The models attempt to provide a better understanding of the spatial effects in a projection system and provide mathematical models for analyzing measurements and designing future hardware-in-the-loop tests. In previous work, one of the authors presented a model of the spatial, spectral, and temporal effects in a pixelized projector. In this paper, the previous model is simplified omitting the temporal effects (the scenes are assumed static). The model is then modified to describe random variations (noise) in the responses from one emitter to the next. This paper presents two different methods of modeling these effects. The first involves evaluating the spatial model directly. The second method involves performing a first order error propagation analysis on the spatial model and neglecting alignment effects. Measurements were performed to validate the models. The measurements are described in detail in a companion paper. In this paper, the spatial noise measurements are compared with model results. It was found that alignment effects were negligible, and the resulting predictions of the simplest model were in good agreement with the measured spatial noise.