Optical imaging systems in which the lens and sensor are free to rotate about independent pivots offer greater degrees of freedom for controlling and optimizing the process of image gathering. However, to benefit from the expanded possibilities, we need an imaging model that directly incorporates the essential parameters. In this work, we propose a model of imaging which can accurately predict the geometric properties of the image in such systems. Furthermore, we introduce a new method for synthesizing an omnifocus (all-in-focus) image from a sequence of images captured while rotating a lens. The crux of our approach lies in insights gained from the new model.