General Linear Cameras with Finite Aperture

A pinhole camera selects a two-dimensional set of rays from the four-dimensional light field. Pinhole cameras are a type of general linear camera, defined as planar 2D slices of the 4D light field. Cameras with finite apertures can be considered as the summation of a collection of pinhole cameras. In the limit they evaluate a two-dimensional integral of the four-dimensional light field. Hence a general linear camera with finite aperture factors the 4D light field into two integrated dimensions and two imaged dimensions. We present a simple framework for representing these slices and integral projections, based on certain eigenspaces in a two-plane parameterization of the light field. Our framework allows for easy analysis of focus and perspective, and it demonstrates their dual nature. Using our framework, we present analogous taxonomies of perspective and focus, placing within them the familiar perspective, orthographic, cross-slit, and bilinear cameras; astigmatic and anastigmatic focus; and several other varieties of perspective and focus.