Variation of magnification with focus

Applications of optical systems, including depth by focus and three-dimensional metrology, have been developed recently in which the image is characterized over a range of object depths simultaneously and in which the focus of the systems is also varied. Important to such applications is the variation of image magnification with focus. A general understanding of this phenomenon is developed, and two new and useful concepts associated with the variation of the magnification of an image are introduced. Errors and oversights in the existing literature are explained and corrected, and the requirements for an optical system to exhibit the magnification properties desired in such applications are identified. It is shown that not all telecentric systems have these properties and that there exist practical and attractive nontelecentric systems that do exhibit them.