Analytic determination of optimal projector lens design requirements for pixilated projectors used to test pixilated imaging sensors

Abstract

A model is described for the problem of optimally projecting a pixellated light source onto a pixellated imaging sensor, in the context that the projected source is used for performance testing of the sensor. The model can be used, for example, to compute the paraxial design requirements of the projection lens, given that the parameters of all other subsystems in the problem are fixed. For remote sensing applications, where the performance of a sensor focused at infinity is to be tested, the projector lens becomes a collimator. For optimal projection when using the source for performance testing of the sensor, one then requires that the projector pixels are not spatially resolved by the imaging sensor, the entrance pupil of the sensor is overfilled without vignetting, and also, where feasible, the sensor field of view is overfilled. The model uses paraxial analytical ray tracing approximations to provide a set of equations that are used in an associated spreadsheet to determine the basic collimator requirements such as effective focal length, f/#, and relief distance, given the geometrical characteristics of the projector spatial light modulator and the sensor under test. Beyond this, the model provides a sense of intuition and guidance prior to detailed computerized ray tracing.