Perspective
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.
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