When observing the human eye, a dark circular opening known as the pupil can be seen, through which incident light enters the eye. Physiologically, the pupil is the aperture located at the center of the iris. However, the visible pupil is not the physical opening itself, but the image of the pupil formed by the refractive structures in front of it, such as the cornea and aqueous humor.

A similar phenomenon occurs in photographic lenses. When a camera lens is viewed from the front under illumination, a bright circular region can be observed. This region is the image of the aperture stop, formed by the lens elements located in front of the stop, and is referred to as the entrance pupil.

In optical engineering and camera imaging systems, the entrance pupil is an important optical concept. It plays a central role in the definition and analysis of parameters such as f-number, field angle, field of view, illumination distribution, and imaging geometry.

Concept
The optical principle underlying modern cameras originates from the camera obscura, in which a small aperture serves as the common entrance for all imaging rays. In geometrical optics, this aperture is referred to as the aperture stop. For an object point, the size of the aperture stop limits the solid angle of the imaging beam and therefore determines the amount of radiant flux that can reach the image plane.

One of the main differences between modern camera lenses and pinhole imaging systems is the size of the aperture stop. A sufficiently large aperture is required to provide practical image brightness. In photographic lenses, the aperture stop is typically located inside the lens assembly.

The aperture stop limits the imaging bundle, but determining this limitation usually requires ray tracing and detailed optical data. A simpler and more intuitive representation is provided by the entrance pupil. The entrance pupil is the image of the aperture stop formed by the optical system in front of the stop, as shown in Figure 3.

For a luminous object point, the aperture stop that it “sees” is not the physical stop itself, but its image. According to the principle of optical reversibility, the limitation imposed by the aperture stop on the incident beam may therefore be regarded as being imposed by the entrance pupil.

In photographic lenses, the entrance pupil is generally a virtual image of the aperture stop, and is therefore upright and magnified. In Figure 3, the images of the upper and lower edges of the aperture stop formed by the lens correspond respectively to the upper and lower edges of the entrance pupil. In other words, a ray emitted from an object point toward the edge of the entrance pupil also passes through the corresponding edge of the aperture stop.

Once the position and size of the entrance pupil are known, the solid angle of the imaging bundle can be determined without knowledge of the actual lens structure or the use of ray tracing and numerical calculation.

If the aperture stop is reduced to a small opening such that only rays passing through its center can form an image, these rays are called chief rays. A chief ray defines the propagation direction of the imaging bundle emitted from an object point. In addition, the intersections of chief rays with optical surfaces are closely related to optical aberrations and are important in aberration correction.

Ideally, the chief rays from different object points intersect at the center of the aperture stop. Consequently, the chief rays, or their extensions, also intersect at the center of the entrance pupil. In contrast to the chief ray, a ray passing through the edge of the aperture stop or entrance pupil is called a marginal ray.

The definition of the entrance pupil provided above is based on the assumption of an ideal system, in which all rays are paraxial and the entrance pupil is free of distortion.

First, image-plane illuminance is inversely proportional to the square of the f-number. For an ideal Lambertian object, the luminous flux admitted by the entrance pupil is proportional to the pupil area, whereas the image area is proportional to the square of the focal length. Since illuminance is the ratio of flux to area, the image illuminance varies inversely with (N^2), where (N) is the f-number. Consequently, image brightness depends not only on the entrance pupil diameter but also on the focal length.

Second, the diameter of the Airy disk is proportional to the f-number. For an object at infinity, diffraction by the circular aperture stop produces an Airy pattern in the image plane, whose central bright region (the Airy disk) increases in size with increasing f-number. Because diffraction blur directly affects the modulation transfer function (MTF) and cutoff spatial frequency, the f-number is closely associated with image quality.

Third, the f-number is inversely related to the aperture angle. The aperture angle, defined by the marginal rays of the imaging beam, increases with larger entrance pupils and shorter focal lengths, both corresponding to smaller f-numbers. Certain imaging devices impose constraints on the aperture angle and therefore on the minimum usable f-number. For example, color-separation prisms used in television cameras have limits on the acceptable beam angle. Likewise, image sensors commonly employ microlenses above the pixels, whose geometry and alignment also impose requirements on the incident ray angle and effective f-number.

Applications of the angle of view and field of view
The angle of view is an important parameter that describes the maximum extent of a scene captured by a camera. In photographic imaging systems, this range is primarily determined by the size of the image sensor. If the effective sensor area is reduced, for example by masking the sensor edges, the observable scene correspondingly becomes smaller.

In geometrical optics, the aperture that limits the image field is called the field stop. The image of the field stop formed by the optical system toward object space is known as the entrance window. In most cameras, the image sensor itself serves as the field stop. By object–image conjugation, the entrance window is located in object space and determines the observable region of the scene, referred to as the field of view. The angle subtended by the entrance window at the center of the entrance pupil is called the angle of view.

One traditional method for measuring the angle of view employs a calibration target containing a regular grid or dot pattern large enough to cover the entire field of view. From the extent of the target visible in the captured image, the physical dimensions of the observable scene can be determined. If the distance between the camera and the target is known, the angle of view can then be calculated from the arctangent of the corresponding geometric ratio.

For accurate measurement, the distance (d) between the camera and the target should be referenced from the plane of the entrance pupil; otherwise, systematic error may be introduced into the calculated angle of view.

In automotive camera testing, fixed-focus cameras with very long design object distances and ultra-wide-angle (fisheye) lenses are commonly encountered. Performance parameters such as spatial frequency response, distortion, angle of view, chromatic aberration, and stray light are typically evaluated using a collimator that projects a virtual test target at the specified object distance and field position.

Two common test configurations are used. The first employs multiple collimators to generate virtual targets simultaneously at different field positions. In this arrangement, the optical axes of all collimators should intersect at the center of the entrance pupil of the camera under test. The second configuration uses a single collimator, while either the collimator or the camera is rotated about the center of the entrance pupil.

If the rotation center does not coincide with the entrance pupil center, but is located in front of or behind it, errors are introduced in angle-of-view measurements. When the virtual target is effectively located at infinity, corresponding to a plane wave emitted by the collimator, the measurement is theoretically unaffected as long as the emitted beam enters the entrance pupil. However, when the virtual target is at a finite distance, corresponding to a diverging spherical wave, the maximum rotation angle no longer equals the true angle of view.

Specifically, if the rotation center is located in front of the entrance pupil, the measured angle of view becomes larger than the true value. Conversely, if the rotation center is behind the entrance pupil, the measured value becomes smaller, as illustrated in Figure 8.

For example, in the RFT integrated camera test system, the camera position can be adjusted according to the entrance pupil location specified in the lens datasheet, ensuring that the collimator rotation center coincides with the entrance pupil center of the lens under test, as shown in Figure 9.