# Entrance pupil

In an optical system, the entrance pupil is the optical image of the physical aperture stop, as 'seen' through the optical elements in front of the stop. The corresponding image of the aperture stop as seen through the optical elements behind it is called the exit pupil. The entrance pupil defines the cone of rays that can enter and pass through the optical system. Rays that fall outside of the entrance pupil will not pass through the system.
If there is no lens in front of the aperture (as in a pinhole camera), the entrance pupil's location and size are identical to those of the aperture. Optical elements in front of the aperture will produce a magnified or diminished image of the aperture that is displaced from the aperture location. The entrance pupil is usually a virtual image: it lies behind the first optical surface of the system.
The entrance pupil is a useful concept for determining the size of the cone of rays that an optical system will accept. Once the size and the location of the entrance pupil of an optical system is determined, the maximum cone of rays that the system will accept from a given object plane is determined solely by the size of the entrance pupil and its distance from the object plane, without any need to consider ray refraction by the optics.
In photography, the size of the entrance pupil (rather than the size of the physical aperture stop) is used to calibrate the opening and closing of the diaphragm aperture. The f-number (also called the 'relative aperture'), N, is defined by N = f / E$_N$, where f is the focal length and E$_N$ is the diameter of the entrance pupil. Increasing the focal length of a lens (i.e., zooming in) will usually cause the f-number to increase, and the entrance pupil location to move further back along the optical axis.
The center of the entrance pupil is the vertex of a camera's angle of view and consequently its center of perspective, perspective point, view point, projection center or no-parallax point. This point is important in panoramic photography without digital image processing, because the camera must be rotated around the center of the entrance pupil to avoid parallax errors in the final, stitched panorama. Panoramic photographers often incorrectly refer to the entrance pupil as a nodal point, which is a different concept. Depending on the lens design, the entrance pupil location on the optical axis may be behind, within or in front of the lens system; and even at infinite distance from the lens in the case of telecentric systems.
The entrance pupil of the human eye, which is not quite the same as the physical pupil, is typically about 4 mm in diameter. It can range from 2 mm (f/8.3) in a very brightly lit place to 8 mm (f/2.1) in the dark.
An optical system is typically designed with a single aperture stop, and therefore has a single entrance pupil at designed working conditions. In general, though, the determination of which element is the aperture stop depends on the object distance, so a system may have different entrance pupils for different object planes. Similarly, vignetting can cause different lateral locations at a given object plane to have different aperture stops, and therefore different entrance pupils.