Perspective is the way of rendering an image of a three-dimensional subject on a two‑dimensional surface so as to convey an impression of depth or distance. This impression is created by several factors, each of which contributes to the illusion of three-dimensional reality:

• The relative size of objects depicted in the image: just as in reality, nearer objects appear relatively larger than more distant objects;
• The convergence of parallel lines (such as rail tracks) as they recede into the distance - this is a special and obvious case of the relative size of objects, just mentioned;
• The apparent distortion of recognizable shapes, such as nearby spheres and cubes, when viewed at an angle - this is yet another manifestation of the 'relative size' phenomenon;
• The overlapping or partial hiding of more distant objects by nearer objects;
• The relative haziness of distant objects that is often caused by atmospheric conditions, known as aerial perspective. This can appear as reduced color saturation, a bluish cast or a slight loss of sharpness, or a combination of any of these factors.

In art and mathematics there are numerous different types of perspective, or ways of mapping points in three-dimensional space onto a flat surface. In photography, there are just two varieties that we need to understand: rectilinear perspective and spherical perspective.

We should really call them rectilinear and spherical projections, as mathematicians do, but there is little hope of changing the terminology already established among photographers, so let's just accept it. As we shall see near the end of this article ("Managing perspective"), the projection used to render a two-dimensional image of a three-dimensional object has no significant effect on the factors that contribute to the impression of depth listed above - the relative size of objects, overlapping of distant objects by nearer objects or aerial perspective effects. What does affect these factors? Read on ...

Rectilinear perspective

Rectilinear means 'in a straight line'.

The pin-hole camera makes images using rectilinear perspective: straight-line rays of light from the subject pass through the pin-hole to the flat film surface at the rear of the camera. Straight (3-D) lines in nature are rendered as straight (2-D) lines in the image.

Rectilinear perspective looks quite similar to classical artistic perspective, and is the design goal of 'normal' photographic lenses. When a lens fails to translate straight lines in the subject into straight lines in the image, we regard this as a defect or 'aberration' of the lens, which generally manifests itself as either 'pincushion distortion' (in which off-axis lines are rendered as curves that are bowed in towards the centre of the image) or 'barrel distortion' (in which off-axis lines are rendered as curves bowed out towards the edge of the image).

However, even with a pin-hole camera or well-corrected lens, rectilinear images of subjects near the edges of wide-angle views appear noticeably elongated in the radial direction from the image centre out towards the edge. This happens because you are usually viewing the image from a distance that is much greater than one which would give the same angle of view as the original scene. If you move closer to the image, increasing your angle of view until you are close to that of the original photograph, this elongation of objects out near the edges will no longer be visible. They will seem to revert to their normal shape (if you can get them in focus at all, out of the corner of your eye). Keep your eye in line with the centre of the photo.

This apparent distortion of images made with wide-angle lenses is sometimes called 'perspective distortion', but it's a bad name, because it's not really a distortion at all, but an accurate rectilinear projection of the subject onto the plane of the image. Also, to describe this phenomenon as perspective distortion can give the impression that perspective effects depend on the angle of view, and therefore on the focal length of your lens. This is simply not true. By switching to a wide-angle lens, you increase the angle of view: you are making a different image. In wide-angle views, the effect of perspective is more noticeable, especially near the edges of the frame, but if you compare the centre of a wide-angle view to a normal or telephoto shot of the same subject taken from the same place, you will find they are identical (except for the lower resolution of the wide-angle view which will need greater magnification to make it the same size as the narrow-angle view). There will be no difference in the relative size of objects, in the overlapping of more distant objects by nearer objects, or in the effects of aerial perspective. There is, therefore, no difference in perspective.

In the 35mm film format, rectilinear wide-angle lenses are available in focal lengths down to about 12mm.

Spherical perspective

If you had a pin-hole camera in which the film was spread on a hollow hemispherical camera back, and then somehow managed to flatten your image while stretching its edges so that the distance of points from its centre remained directly proportional to their angle off the lens axis, then you would have a spherical projection. A similar (but inverted) effect can be seen in the reflection off a shiny spherical surface.

Such spherical perspective is achieved in practice by using a fish-eye lens. Fish-eye lenses can cover an angle of view of up to 180° in all directions, thus giving circular images. More generally useful fish-eye lenses give an angle of view of 180° on the diagonal, and thus provide an image in the usual rectangular format.

In the 35mm film format, the first type of fish-eye lens typically has a nominal focal length of about 8mm, while the 'diagonal fish-eye' will have a nominal focal length of about 15mm.

Managing perspective

We saw above that perspective cannot be controlled by switching between lenses to change the angle of view, because this does not affect the relative size of objects, the overlapping of distant objects by nearer objects, or aerial perspective effects.

The only way you can influence these factors is by moving the camera.

If you move closer to your subject, you will increase the apparent size of everything in the scene, but closer objects will increase in size faster than more distant objects.

You will also change the relative placement (overlapping) of objects, except for those in the very centre of your image.

You will also (in extreme cases) increase the aerial perspective effect. If you are very far distant, everything in your scene may be more or less hazy. As you move closer, nearer objects may come into sharper focus, have more saturated colors, or lose their bluish tinge. Distant objects will be affected little or not at all.

To increase or exaggerate the effects of perspective, therefore, move closer to your subject. To emphasize height, for example, move close to the bottom of your subject. To emphasize distance or length, move close to the nearest point of your subject, while keeping its distant parts in view. This increases the relative size difference between its two ends.

You can control the angle of view with a zoom lens, or by changing between lenses of different focal length, but you can only control perspective with your feet.