Abstract

The Badal principle¹ is that, if an eye is placed at the back focal point of a (Badal) lens, the angular size of the perceived object is independent of target position and the target vergence perceived by the eye is proportional to the distance of the target from the front focal point of the lens. The constancy of angular size can be appreciated from looking at Fig. 1. In this diagram, a ray is traced from the top of the target of height $\mathfrak{h}$ at $\mathcal{T}$ and parallel to the optical axis through the lens. It is refracted at the point $\mathcal{P}$ at the Badal lens of power F, and in the image space of the lens passes through the back focal point of the lens at $\mathcal{F}$. Regardless of target distance from the lens, the angle a subtended by the image is always $\mathfrak{h}$F. If the eye is placed here, the apparent angular size of the object must also be invariant.

© 1995 Optical Society of America