Stops

Stops and apertures

Two important aspects of any imaging system are the amount of radiation passed by the system and the extent of an object that is seen by the system. Stops and apertures limit the brightness of an image and the field of view of an optical system.

The aperture stop (AS) is defined to be the stop or lens ring, which physically limits the solid angle of rays passing through the system from an on-axis object point. The aperture stop limits the brightness of an image.

For system (a) in the figure above the aperture is the aperture stop, for system (b) the first lens is the aperture stop and for system (c) the second lens is the aperture stop.

The exit pupil is the image of the aperture stop formed by the light rays after they have passed through the optical system, i.e. it is the image of the aperture stop as seen through all the optics beyond the aperture stop. It can be a real or virtual image, depending on the location of the aperture stop.

The entrance pupil is the opening an observer would identify as the limitation on the solid angle of rays diverging from an on-axis object point, i.e. it is the image of the aperture stop in as seen through all the optics before the aperture stop. Again, it can be a real or virtual image, depending on the location of the aperture stop.

Entrance and exit pupils of two camera lenses
Source: Carl Zeiss AG

The following is simply a recipe for finding the aperture stop, entrance pupil, and exit pupil, given an optical system.

Image all optical elements in the system into object space.
Find the angle subtended by each element image at the on-axis position of the object.
The element image with the smallest angle is the entrance pupil.
The physical object corresponding to this image is the aperture stop.
The image of the aperture stop in image space is the exit pupil.

The diagrams below shows two thin lenses with focal lengths f = 1 unit and f = 0.5 units, respectively, placed two units apart. The on-axis object is located 1.5 units in front of the first lens.

Lens 1 is the aperture stop for the shown position of the object. It physically limits the solid angle of rays passing through the system.
The exit pupil is the image of lens 1 formed by lens 2. If the exit pupil is a real image, then all the light that is transmitted through the system, even from extended objects, will pass through the exit pupil. If you want to catch all this light with the smallest possible detector, you must place a detector that has the size of the exit pupil at the location of the exit pupil.
The entrance pupil is lens 1 itself, since there are no optical elements located in front of it.

In an optical system designed for visual observations, it is desirable to have the exit pupil approximately coincide with the pupil of the observer’s eye, since all the light from the object gathered by the optical system then enters the eye. This is the origin of the term "pupil".

Field stop

For an off-axis object, the chief ray (CR) is the ray that passes through the center of the aperture stop. Rays that pass through the edge of the aperture stop are marginal rays (MR).

The aperture stop determines the solid angle of the transmitted light cone for an on-axis object. It limits the brightness of an image. The field stop determines the solid angle formed by chief rays from off-axis objects. It limits the field of view of an optical instrument. The image of the field stop as seen through all the optics before the field stop is called the entrance window. The image as seen through all the optics after the field stop is called the exit window.

The following is simply a recipe for finding the field stop, entrance window, and exit window, given a an optical system.

Image all optical elements in the system into object space.
Find the angle subtended by each image at the on-axis position of the entrance pupil.
The element image with the smallest angle is the entrance window
The physical object corresponding to this image is the field stop.
The image of the field stop in image space is the exit window.

For the telescopic system shown below, the object is very far away and the aperture stop and the entrance pupil are lens 1.

The entrance window is the image of lens 2 formed by lens 1.
Lens 2 (the eyepiece) is the field stop and the exit window for very distant objects.

A cone of light rays from an off-axis object to the entrance pupil will not necessarily be transmitted in its entirety. It can be partially cut off by field stops or lens rims in the system. This is called vignetting.

Field of view

The angular field of view is the angle formed by the edges of the entrance window at the on-axis position of the entrance pupil. For the telescopic system shown above, we find the location of the entrance window by finding the location of the image of lens 2 formed by lens 1.
(1/4 + 1/x_i = 1/3, x_i = 12)
The entrance window is located 12 units to the left of lens 1. Since the magnification is M = -3, the diameter of the entrance window is three times the diameter of lens 2. The entrance pupil is lens 1 itself. The half angle θ for the field of view is given by tanθ = 3*(radius of lens 2)/12.

In a system with vignetting, the angular field of view may also be defined as the largest angle of an input chief ray with the optical axis.

AI Study Tip:

Example prompt: 'Explain why placing the aperture stop at different locations in a multi-lens system changes the field of view (FOV). Create a scenario where an improperly placed stop causes vignetting, and describe how I would identify the chief ray and marginal ray to fix it.'