Stops

The limiting effect on the imaging process by the size of the unobstructed clear diameter in an optical system depends upon the location of that "stop", or limiting diameter. The limiting diameter which determines the amount of light which reaches the imaging area is called the aperture stop, typified by the adjustable diaphragm near the front of a compound camera lens. The limiting diameter which controls the size object which can be imaged is called the field stop.

Adjustable stops are commonly created from thin metallic leaf structures to determine the amount of light which reaches a film or CCD detector. Shown at left is a laboratory stop which determines the amount of light that reaches an adjustable slit for diffraction studies. It was used to produce the single slit diffraction patterns shown to demonstrate the diffraction phenomenon. Such structures are also used in cameras to set the f-stops for exposure adjustment.

Apertures and f-stops

An adjustable metallic leaf structure is typically used behind the first few elements of a compound camera lens to control the amount of light which reaches the film or CCD detector. It is common practices to denote the size of the opening in this aperture stop in terms of the "f-stop" or "f-number". The f-stop is defined by It is evident from this relationship that a higher f-number implies a smaller diameter stop for a given focal-length lens. Since a circular stop has area A = πr2, doubling the aperture diameter and therefore halving the f-number will admit four times as much light into the system. The usual practice is to designate a stop whose diameter D is half the focal length f as f/2. The illustration shows that f/4 at left has half the diameter of f/2, and therefore admits 1/4 as much light. For cameras, you have set "stops" that progress so that "1 stop" wider will admit twice as much light, and that requires a diameter increase by a factor of 1.414 or the square root of 2. That gives the typical number sequence seen on camera lenses: f/2 2.8 4 5.6 8 11 16

Increasing the f-number of a camera lens decreases the amount of light entering a camera by decreasing the aperture size. Increasing by one f-stop halves the light and therefore requires double the exposure time (half the shutter speed). Increasing the f-number has the benefit of increasing the "depth of field" of the image, so photographers must continually judge the proper balance between shutter speed and f-number to minimize motion-blur for the image while achieving acceptable depth of field.

Since the opening up of the aperture by one f-stop or increasing the exposure time by a factor of two would both double the light collection, it is common practice to refer to both of these as increasing the exposure by 1 "stop".

f-stops and Depth of Field

Increasing the f-stop by one stop has the disadvantage of requiring you to slow down the shutter speed to one-half, but has the advantage of increasing the depth of field of the formed image. By "depth of field" we practically mean the depth of the image where it appears to be sharply focused. While "sharpness of focus" is a relative term, there is a practical depth over which the image appears to be in focus. That depth of field increases with f-number.

f/2.8

At f/2.8 you can shoot at a faster shutter speed, but with very shallow depth of field. There are times when you would deliberately choose this condition, for example to shoot a picture of a rose where the leaves behind it soften progressively in focus.

f/16

At f/16 you get much greater depth of field, but it is five stops up in f-number, each of which costs you a factor of two in light. So the shutter speed has to be 25 = 32 times longer for this view. The practical depth of field diminishes with increasing focal length, so that long telephoto shots tend to have shallow depth of field. It is good to use as high an f-number as practicable for telephoto shots to increase that depth of field.

Close-up photography is quite demanding in terms of depth of field. The objects of interest (e.g., flowers, butterflies) have greater depth compared the distance to the object than most more distant objects. It is therefore desirable to use high f-numbers for closeup photography.

There is a limit to how high you can make the effective f-number. If the aperture becomes too small, then aperture diffraction will begin to affect the image sharpness. Particularly with small CCD detectors, one has to experiment to find out the optimum f-number for sharpness. For too high an f-number, the resolution may be diffraction limited.

Aperture Stops

An aperture stop is the opening which limits the amount of light which passes through an optical system. For example, the adjustable diaphragm near the front of a compound camera lens is the aperture stop for the lens. The amount of light admitted is controlled by the diameter of the diaphragm opening which is indicated on the camera by the "f number" or "f-stop number". Making the aperture smaller reduces the light, but increases the depth of focus.

Adjustable stops are commonly created from thin metallic leaf structures to determine the amount of light which reaches a film, CCD detector, or whatever plays the role of the final image plane.

Field Stops

The element that limits the size or angular breadth of an object that can be imaged by the system is called the field stop. For cameras, the size of the film or CCD detector determines the maximum image size and serves as the field stop.

Pupils

The idea of a pupil is that the effective size of a stop may be larger or smaller than its physical size because of the refractive action of a lens. Formally, a pupil is an image of the aperture stop. The entrance pupil is defined as the image of the aperture stop as seen from an axial point on the object through those elements of the lens which precede the stop. The exit pupil is the image of the aperture stop as seen from an axial point in the image plane. This discussion follows the treatment in Hecht.

Entrance Pupil

The entrance pupil of a system is the image of the aperture stop as seen from a point on the optic axis in the object plane.

In the illustration, the physical aperture is behind the lens. You can see that more light will get through the physical aperture behind the lens than would have if the lens were not present. The extreme ray is one that is refracted by the lens so that it just passes through the aperture. Tracing the projected path of that extreme ray without the lens, you can see that the entrance pupil is the size aperture that would be required to pass that extreme ray in the absence of the lens.

In this example, the physical aperture is the exit pupil because there is no intervening lens between the image and the aperture.

The images of the same laboratory aperture above were taken from the same object point. The image on the left is of the aperture directly, the middle image is through a single lens, and the right image was taken through a two-lens system. This shows a case where the same aperture can have three different sized pupils.

Exit Pupil

The exit pupil of a system is the image of the aperture stop as seen from a point on the optic axis in the image plane.

In this case where the physical aperture stop is in front of the lens, the exit pupil is the image of that aperture stop as seen from the optic axis in the image plane, looking back through the lens. In this case the entrance pupil is just the physical aperture since there is no lens intervening from the standpoint of the object.