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# Object and Image Space

Author: the photonics expert

Definition: mathematical spaces for the description of optical elements and systems

In geometrical optics, extensive use is made of the concept of object and image spaces. In the simplest case, an object and image space is associated with a single optical element of zero longitudinal extension – for example, a plane or curved interface between two transparent optical media. In a first approach, one may consider the object space to be the space before that interface and the image space to lie after the interface; one sometimes finds drawings which suggest that. However, it is common practice to consider both object and image space to span the complete space. For example, one can extrapolate any rays on the object side to the image side – without taking into account any changes at the interface – to obtain those rays in the complete object space. Similarly, one can extrapolate back any rays on the image side. By extrapolating convergent rays, which meet in some point, one can obtain virtual points. For example, in image space one may have a virtual image of an object point.

Object space can thus contain real object points before the optical system and virtual object points behind it. Similarly, image space can contain real image points behind the system and virtual image points before it. For example, when using a photo camera, one deals with real object points in front of the camera, which are related to real image points on the film or image sensor.

Figure 1 shows a situation where a biconcave and thus defocusing (negative) lens modifies the appearance of a real object: on the image side, the rays appear to come from a virtual object position, and that is part of image space despite lying left of the lens. On the other hand, object space contains the rays coming from the object, not affected by the lens.

A similar situation would be found for a magnifying glass, where a focusing lens is used.

One can easily apply the concept of object and image space to extended optical systems, consisting of multiple optical elements.

In drawings, one often shows items of object and image space together (as in the top part of Figure 1). In order to avoid confusion in drawings or text, one may use some appropriate system of labeling. For example, one may indicate all points with capital letters, adding a prime for all points and image space only.

An optical imaging system will never be able to image all points of object space. It is not only that object space also comprises points behind the system, but also that there are limitations to the locations from which points before the system can be imaged. In particular, there is a limited field of view, and in addition there are usually limitations for sharp imaging; for example, one may not be able to focus a camera on very close objects.

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