the pattern that is produced by the action of an optical system on the rays emitted by an object and that reproduces the contours and details of the object. The practical use of an optical image often entails a change in the scale of the images of the object and projection onto a surface (such as a screen, photographic film, or photocathode). The basis of the visual perception of an object is its optical image, as projected onto the retina of the eye.

Maximum correspondence of the image to the object is achieved when each point of the object is represented by a point. In other words, after all refractions and reflections in the optical system, the rays emitted by the light source should intersect at a single point. However, this is not possible for every location of an object with respect to the system. For example, in the case of systems that have an axis of symmetry (an optical axis), point optical images can be produced only for those points that lie at a slight angle to the axis, in the so-called paraxial region. The location of the optical image of any point of the paraxial region may be found by applying the laws of geometric optics; knowledge of the location of the cardinal points of the system is sufficient for this purpose.

The totality of points whose optical image can be produced by means of an optical system forms an object space, and the totality of the point images of these points forms the image space.

A distinction is made between real and virtual optical images. Real images are created by converging beams of rays at their points of intersection. The real optical image may be observed by placing a screen or photographic film in the plane of intersection of the rays. In other cases the rays emerging from an optical system diverge, but if they are mentally continued in the opposite direction they will intersect at a single point. This point is called the virtual image of a point object; it does not correspond to the intersection of real rays, and therefore a virtual optical image cannot be produced on a screen or recorded on film. However, a virtual optical image may play the role of an object with respect to another optical system (for example, the eye or a converging lens), which converts it into a real image.

An optical object is a set of points illuminated by its own or reflected light. If the way in which an optical system represents each point is known, it is easy to construct an image of the whole object.

The optical images of real objects in flat mirrors are always virtual (see Figure 1, a); in concave mirrors and converging lenses they may be either real or virtual images, depending on the distance of the objects from the mirror or lens (Figure 1, c and d). Convex mirrors and diverging lenses produce only virtual optical images of real objects (Figure 1, b and e). The location and dimensions of an optical image depend on the characteristics of the optical system and on the distance between it and the object. Only in the case of a flat mirror is an optical image always equal in size to the object.

If a point object does not lie in the paraxial region, then the rays that emerge from it and pass through the optical system are not collected at a single point but rather intersect the image plane at different points, forming an aberrational spot; the size of the spot depends on the location of the point object and on the design of the system. Only flat mirrors are nonaberrational (ideal) optical systems that produce a point image of a point. In the design of optical systems aberrations are corrected—that is, an effort is made to ensure that scattering aberrations do not deteriorate the image to noticeable degree; however, complete elimination of aberrations is impossible.

It should be noted that the above is strictly valid only within the framework of geometric optics, which, although quite satisfactory in many cases, nonetheless is only an approximate method of describing the phenomena that occur in optical systems. Only in geometric optics, where abstraction from the wave nature of light is used and, in particular, the phenomena of light diffraction are not taken into account, may the optical image of a luminous point be considered to be a point image. More detailed examination of the microstructure of an optical image, taking into account the wave nature of light, shows that a point image, even in an ideal (nonaberrational) system, is a complex diffraction pattern rather than a point.

Figure 1. Formation of optical images: (a) virtual image M’ of point M in a flat mirror, (b) virtual image M’ of point M in a convex spherical mirror, (c) virtual image M’ of point M and real image AB’ of point N in a concave spherical mirror, (d) real image A’B’ and virtual image M’N’ of objects AB and MN in a converging lens, (e) virtual image M’N’ of the object MN in a diverging lens; (i) and (j) angles of incidence of rays, (i’) and (j’) angles of reflection, (C) centers of spheres, (F) and (F’) foci of lenses

The light energy density distribution in the image is significant for the evaluation of the quality of an optical image, which has acquired great importance because of the development of photographic, television, and other methods. A special characteristic—the contrast k = (E_max— E_min)/(E_max— E_min) where the E_min and E_max are the least and greatest values of illumination of the optical image of a standard test object—is used for this purpose. A grid whose brightness varies sinusoidally with a frequency R (the number of periods of the grid per millimeter) is usually used as such a standard test object: k depends on R and the direction of the grid lines. The function k(R) is called the frequency-contrast characteristic. In ideal systems k = 0 when R = 2A’ /\\ or more, when A’ is the numerical aperture of the system in the image space and X is the wavelength of the light. The lower the k for a given R, the worse will be the quality of the optical image in the particular system.