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Abbe number

 A numerical value indicating the dispersion of optical glass, using the Greek symbol n. Also called the optical constant. The Abbe number is determined by the following formula using the index of refraction for three Fraunhofer’s lines: F (blue), d (yellow) and c (red). Abbe number = nd = nd — 1/nF — nc


The image formed by an ideal photographic lens would have the following characteristics:

a) A point would be formed as a point.
b) A plane (such as a wall) perpendicular to the optical axis would be formed as a plane.
c) The image formed by the lens would have the same shape as the subject.
Also, from the standpoint of image expression, a lens should exhibit true colour reproduction. If only light rays entering the lens close to the optical axis are used and the light is monochromatic (one specific wavelength), it is possible to realise virtually ideal lens performance. With real photographic lenses, however, where a large aperture is used to obtain sufficient brightness and the lens must converge light not only from near the optical axis but from all areas of the image, it is extremely difficult to satisfy the above-mentioned ideal conditions due to the existence of the following obstructive factors:

  • Since most lenses are constructed solely of lens elements with spherical surfaces, light rays from a single subject point are not formed in the image as a perfect point. (A problem unavoidable with spherical surfaces.)
  • The focal point position differs for different types (i.e., different wavelengths) of light.
  • There are many requirements related to changes in angle of view (especially with wide-angle, zoom and telephoto lenses).

    The general term used to describe the difference between an ideal image and the actual image affected by the above factors is “aberration.” Thus, to design a high-performance lens, aberration must be extremely small, with the ultimate objective being to obtain an image as close as possible to the ideal image.

A lens which corrects chromatic aberration for two wavelengths of light. When referring to a photographic lens, the two corrected wavelengths are in the blueviolet range and yellow range.

Actual photographic lenses

When looking at the enlarged image of an object through a magnifying glass, it is common for the edges of the image to be distorted or discoloured even if the center is clear. As this indicates, a single-element lens suffers from many types of aberrations and cannot reproduce an image which is clearly defined from corner to corner. Because of this, photographic lenses are constructed of several lens elements having different shapes and characteristics in order to obtain a sharp image over the entire picture area. The basic construction of a lens is listed in the specifications section of brochures and instruction manual in terms of elements and groups. Figure 33 shows an example of the EF 85mm f/1.2L II USM, constructed of 8 elements in 7 groups.

Air lens

The air spaces between the glass lens elements making up a photographic lens can be thought of as lenses made of glass having the same index of refraction as air (1.0). An air space designed from the beginning with this concept in mind is called an air lens. Since the refraction of an air lens is opposite that of a glass lens, a convex shape acts as a concave lens and a concave shape acts as a convex lens. This principle was first propounded in 1898 by a man named Emil von Hoegh working for the German company Goerz.

Angle of view

The area of a scene, expressed as an angle, which can be reproduced by the lens as a sharp image. The nominal diagonal angle of view is defined as the angle formed by imaginary lines connecting the lens’ second principal point with both ends of the image diagonal (43.2mm). Lens data for EF lenses generally includes the horizontal (36mm) angle of view and vertical (24mm) angle of view in addition to the diagonal angle of view.

Angular aperture

The angle between the subject point on the optical axis and the diameter of the entrance pupil, or the angle between the image point on the optical axis and the diameter of the exit pupil.

Aperture/effective aperture

The aperture of a lens is related to the diameter of the group of light rays passing through the lens and determines the brightness of the subject image formed on the focal plane. The optical aperture (also called the effective aperture) differs from the real aperture of the lens in that it depends on the diameter of the group of light rays passing through the lens rather than the actual lens diameter. When a parallel pencil of rays enters a lens and a group of these rays passes through the diaphragm opening, the diameter of this group of light rays when it enters the front lens surface is the effective aperture of the lens.

Aperture ratio

A value used to express image brightness, calculated by dividing the lens’ effective aperture (D) by its focal length (f). Since the value calculated from D/f is almost always a small decimal value less than 1 and therefore difficult to use practically, it is common to express the aperture ratio on the lens barrel as the ratio of the effective aperture to the focal length, with the effective aperture set equal to 1. (For example, the EF 85mm f/1.2L II USM lens barrel is imprinted with 1: 1.2, indicating that the focal length is 1.2 times the effective aperture when the effective aperture is equal to 1.) The brightness of an image produced by a lens is proportional to the square of the aperture ratio. In general, lens brightness is expressed as an F number, which is the inverse of the aperture ratio (f/D).


Since all lenses contain a certain amount of spherical aberration and astigmatism, they cannot perfectly converge rays from a subject point to form a true image point (i.e., an infinitely small dot with zero area). In other words, images are formed from a composite of dots (not points) having a certain area, or size. Since the image becomes less sharp as the size of these dots increases, the dots are called "circles of confusion." Thus, one way of indicating the quality of a lens is by the smallest dot it can form, or its "minimum circle of confusion." The maximum allowable dot size in an image is called the "permissible circle of confusion."

Aspherical lens

Photographic lenses are generally constructed of several single lens elements, all of which, unless otherwise specified, have spherical surfaces. Because all surfaces are spherical, it becomes especially difficult to correct spherical aberration in large-aperture lenses and distortion in super-wide-angle lenses. A special lens element with a surface curved with the ideal shape to correct these aberrations, i.e., a lens having a free-curved surface which is not spherical, is called an aspherical lens. The theory and usefulness of aspherical lenses. have been known since the early days of lens making, but due to the extreme difficulty of actually processing and accurately measuring aspherical surfaces, practical aspherical lens manufacturing methods were not realised until fairly recently. The first SLR photographic lens to incorporate a large diameter aspherical lens was Canon’s FD 55mm f/1.2AL released in March 1971. Due to revolutionary advances in production technology since that time, Canon’s current EF lens group makes abundant use of various aspherical lens types such as ground and polished glass aspherical lens elements, ultra-precision glass molded (GMo) aspherical lens elements, composite aspherical lens elements and replica aspherical lens elements.


With a lens corrected for spherical and comatic aberration, a subject point on the optical axis will be correctly reproduced as a point in the image, but an off-axis subject point will not appear as a point in the image, but rather as an ellipse or line. This type of aberration is called astigmatism. It is possible to observe this phenomenon near the edges of the image by slightly shifting the lens focus to a position where the subject point is sharply imaged as a line oriented in a direction radiating from the image enter, and again to another position.


The eye condition in which astigmatism exists on the eye’s visual axis.

Automatic diaphragm

The general diaphragm operation system used in SLR cameras, referring to a type of diaphragm mechanism which remains fully open during focusing and composition to provide a bright viewfinder image, but automatically closes down to the aperture setting necessary for correct exposure when the shutter button is pressed and automatically opens up again when the exposure is completed. Although conventional lenses use mechanical linkages for controlling this automatic diaphragm operation, EF lenses use electronic signals for more precise control. You can observe this instantaneous aperture stop-down operation by looking into the front of the lens when the shutter is released.