{{Unsourced, date=September 2013
Optical spaces are mathematical
coordinate system
In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space. The order of the coordinates is sig ...
s that facilitate the modelling of optical systems as mathematical transformations. An optical space is a mathematical coordinate system such as a
Cartesian coordinate system
A Cartesian coordinate system (, ) in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in t ...
associated with a
refractive index
In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium.
The refractive index determines how much the path of light is bent, or ...
. The analysis of optical systems is greatly simplified by the use of optical spaces which enable designers to place the origin of a coordinate system at any of several convenient locations. In the design of optical systems two optical spaces, object space and image space, are always employed. Additional intermediate spaces are often used as well.
Optical spaces extend to infinity in all directions. The object space does not exist only on the "input" side of the system, nor the image space only on the "output" side. Spaces in this sense can be considered points of view. All optical spaces thus overlap completely to infinity in all directions. Typically, the origin and at least some of the coordinate axes of each space are different, providing different perspectives to the designer. It may not be possible to discern from an illustration to which space a point, ray, or plane belongs unless some convention is adopted. A common convention uses capital letters like X, Y, or Z to label points and lower case letters like a, b, and c to indicate distances. Unprimed letters like t or v indicate object space and primed letters like t′ or v′ indicate image space. Intermediate spaces are indicated by additional primes such as r″, z″, or q″. The same letter is used to indicate points or distances that share a
conjugate relationship. The only exception is the use of F and F′ to indicate respectively object and image space
focal points (which are not conjugate). The term "object point" does not necessarily refer to a point on a specific object but rather to a point in object space; similarly for "image point".
One may wonder how an object point can exist on the "output" side of an optical system or conversely how an image point could be located on the "input" side of an optical system. The answer in both cases is that the points are virtual; they do not physically exist. Optical spaces are divided into real and virtual parts. Thus, an object point on the "output" side of the system is in the virtual part of object space and is referred to as a ''virtual'' object point. Object points on the "input" side are in the real part of object space and are ''real'' object points. The situation is reversed for image points.
It is common practice to designate the horizontal axis of an optical space as the z-axis with the positive direction left to right. Similarly, the y-axis is vertical with the positive direction upward.
Geometrical optics