The Rose model, revisited

In 1946 and 1948, three very important papers by Albert Rose J. Soc. Motion Pict. Eng. 47, 273 (1946); J. Opt. Soc. Am. 38, 196 (1948); L. Marton, ed. (Academic, New York, 1948) were published on the role that photon fluctuations have in setting fundamental performance limits for both human vision and electronic imaging systems. The papers were important because Rose demonstrated that the performance of imaging devices can be evaluated with an absolute scale (quantum efficiency). The analysis of human visual signal detection used in these papers (developed before the formal theory of signal detectability) was based on an approach that has come to be known as the Rose model. In spite of its simplicity, the Rose model is a very good approximation of a Bayesian ideal observer for the carefully and narrowly defined conditions that Rose considered. This simple model can be used effectively for back-of-the-envelope calculations, but it needs to be used with care because of its limited range of validity. One important conclusion arising from Rose's investigations is that pixel signal-to-noise ratio is not a good figure of merit for imaging systems or components, even though it is still occasionally used as such by some researchers. In the present study, (1) aspects of signal detection theory are presented, (2) Rose's model is described and discussed, (3) pixel signal-to-noise ratio is discussed, and (4) progress on modeling human noise-limited performance is summarized. This study is intended to be a tutorial with presentation of the main ideas and provision of references to the (dispersed) technical literature.