Three-dimensional Scheimpflug principle and its application to full-focus positioning

The Scheimpflug principle specifies the relationship between the object, lens, and image planes, providing conditions for focusing the entire image plane even for tilted objects. This classical principle is confined to unidirectional tilting and has not been extended to camera systems with two-axis tilts. Herein, we present an extension of the Scheimpflug principle to three dimensions, demonstrating that images can be decomposed and focused independently in the vertical and horizontal directions. This simplifies focusing on the overall image, which requires a two-dimensional search, into a combination of one-dimensional searches. The proposed theory was validated through practical experimentation using cameras.