Wide angle is not distortion
Photograph a group of people with a wide lens and the ones at the edges come out wrong. Faces are broadened, heads are stretched toward the corners, a round object becomes an egg. Everyone has seen it and the usual explanation is that the lens distorts.
The lens does not distort. A well-corrected wide-angle lens is a rectilinear projection — it maps straight lines to straight lines — and the stretching is what a rectilinear projection is obliged to do. The amount is exactly 1/cos θ at angle θ off the optical axis, it is computable before any photograph is taken, and it disappears completely if the picture is viewed from the point it was made for.
Why spheres
The demonstration uses spheres deliberately, because they remove the objection that the object might be at fault.
A sphere is the same shape from every direction. It has no orientation, no foreshortening of its own, and no aspect that could be said to be turned away. Whatever happens to its image across the frame is the projection’s doing.
And what happens is that a sphere off the optical axis does not image as a circle. It images as an ellipse, elongated radially — along the line from the centre of the frame outward. That is the fact that surprises people, because a sphere seems like the one thing that could not come out oval.
The reason: the sphere’s silhouette is a cone of rays from the eye, and a cone cut obliquely by a plane gives an ellipse. The picture plane cuts the cone squarely only for a sphere on the axis. Off axis the cut is oblique, and the further off axis, the more oblique.
The number
The elongation factor is 1/cos θ, where θ is the angle between the optical axis and the direction to the object.
| Field of view | θ at the frame edge | Stretch |
|---|---|---|
| 28° | 14° | 3% |
| 40° | 20° | 6% |
| 60° | 30° | 15% |
| 90° | 45° | 41% |
| 110° | 55° | 74% |
Measured from the drawn spheres in the figure, the outer one is 27% wider than the central one at 84° across, and it agrees with 1/cos θ at the measured angle off axis to within the sampling.
The cure, which nobody applies
The whole of the stretch vanishes when the picture is viewed from the correct distance.
The reason is exactly the reason it exists. The picture point at radius r represents a direction at angle arctan(r/f); an eye at distance f·(scale) from the picture sees that point at the same angle; so the angular shape presented to the eye is the angular shape the camera recorded, and a sphere that subtended a circular cone at the camera subtends a circular cone at the eye. It looks round.
Move the eye back and the correspondence breaks. The picture’s periphery now subtends a smaller angle than it should, and the compensation the eye would have applied is no longer appropriate, so the elongation shows.
For an 84° frame shown 160 mm wide, the correct distance is about 9 cm. Nobody looks at a photograph from 9 cm. So the stretch is always visible, always in the same direction, and never a lens fault.
What is a lens fault
There is a genuine lens defect with a similar name and it should not be confused with this.
Barrel and pincushion distortion are departures from the rectilinear ideal: straight lines in the world come out curved in the image. That is an aberration, it is a property of the particular lens design, it is measurable as a deviation from straightness, and it is corrected either in the optics or in software.
The two are distinguishable by a simple test. Photograph a straight line. If it comes out curved, that is distortion. If it comes out straight and objects near it are stretched, that is the projection.
Almost every complaint about “wide-angle distortion” of faces is the second, and correcting the first does nothing about it — which is why software distortion correction leaves the stretched faces exactly as they were.
The effect also has a proper name that avoids the confusion: volume anamorphosis, or perspective distortion. It applies to volumes rather than to lines, which is why the flat, straight-edged parts of a wide photograph look fine while the heads at the edges do not.
The trade nobody escapes
Something has to give when a wide field is put on a flat surface, and it is worth seeing that this is unavoidable rather than a choice made badly.
A flat picture plane at 1/cos θ stretch preserves straight lines exactly. That is the rectilinear projection and it is what architecture wants.
A cylindrical or spherical picture surface can be built to preserve angular size instead, keeping shapes right at the edge — and then straight world lines come out curved, which is what a panoramic projection does and why panoramas bend the horizon.
There is no surface that does both. A flat picture of a wide field either stretches shapes or bends lines; the choice is which, and both answers are correct answers to different questions. Fisheye lenses take the second option deliberately and are called distorting for it, which is the same misnaming in the other direction.
What to do about it in practice
The geometry gives three practical responses, and the first is the one that actually gets used.
Keep faces away from the corners. The stretch depends only on the angle off axis, so a face near the centre of a wide frame is fine and the same face in the corner is not. Group photographs are composed with this in mind whether or not the photographer could state the reason.
Use a longer lens and step back. This reduces the field of view and moves the correct viewing distance out toward where people actually look from. It changes the relationship between foreground and background as a side effect, which is a compositional decision rather than a free fix.
Accept the stretch as part of the look. A wide interior with stretched objects at the edges reads as spacious, and that reading is produced by the same geometry. Architectural and interior photography uses wide lenses constantly, and the stretch is visible in almost all of it and complained about almost never — because rooms are not faces, and viewers have no strong prior about the shape of a sofa.
The related effect that is genuinely about distance
One more confusion is worth clearing, because it is usually rolled into the same complaint and has a different cause.
A portrait taken from very close makes the nose large relative to the ears. That is not a lens effect at all — it is the ordinary consequence of the nose being substantially closer to the camera than the ears are, and it would happen with any lens from that distance.
The reason it gets blamed on wide lenses is that a wide lens is what allows the photographer to be that close and still fit the head in the frame. The lens enables the distance; the distance produces the effect.
The two can be separated by an experiment: photograph a face from two metres with a wide lens and crop to the head. The proportions are correct, and if the head is at the frame edge the edge stretch is present as well, which is how the two effects can be seen to be independent.
That distinction matters for portraiture. The rule “use a longer lens for portraits” is really “stand further away”, and the lens is a means of doing so while keeping the framing.
The stretch is radial, which is the tell
One detail distinguishes this effect from everything else it gets confused with, and it is visible without measurement.
The elongation is radial — along the line from the frame’s centre outward. A face at the left edge is stretched horizontally; a face at the top edge is stretched vertically; a face in the top-left corner is stretched along the diagonal.
That is diagnostic. A lens aberration would not respect the frame’s centre in that way, and neither would a stretch introduced in processing. Any stretch that is radial, grows with distance from the centre, and follows 1/cos θ is the projection.
It also explains a compositional habit that predates any theory. Photographers keep faces away from corners of wide frames, and the corner is the worst place because it is furthest from the centre in both directions at once — the angle θ at a corner is larger than at either edge, so the stretch is larger than the horizontal or vertical figures suggest.
Correcting it, and what correction costs
Software exists to fix stretched faces in wide group photographs, and how it works says something about the geometry.
The correction cannot be a single reprojection, because reprojecting the whole frame to a shape-preserving surface would bend the straight lines — which is the trade no surface escapes. What the correction does instead is local: it identifies faces, applies a locally shape-preserving warp to those regions, and blends back into the rectilinear projection elsewhere.
The result is a picture that is a projection of nothing at all. Its faces come from one projection and its architecture from another, and there is no camera position and no surface for which it is correct.
That is a defensible engineering choice — the picture looks better and nobody was going to view it from 9 cm anyway — and it is worth being clear that it is a departure from projection rather than a repair of one. A picture corrected this way fails every consistency check this site is built on: its vanishing points no longer agree, its cross-ratios no longer survive, and a camera recovered from one part of it disagrees with a camera recovered from another.
The 50 mm question
A related piece of folklore: that a 50 mm lens on a 35 mm frame is “normal” because it matches human vision.
It does not match human vision in any interesting sense — the eye’s field is far wider, and its resolution is far from uniform across it. What a 50 mm lens does is produce a picture whose correct viewing distance is about the same as the comfortable viewing distance for a print of ordinary size.
The arithmetic is the same as everywhere on this site. A 50 mm lens on a 36 mm-wide frame, printed 250 mm wide, is a sevenfold enlargement, so the print is correct from 350 mm — which is about where a person holds a photograph.
So “normal” means correct from where it will actually be viewed, and the reason wider and longer lenses depart from normal is that their correct distances are respectively closer and further than that. Nothing about the eye enters. The convention encodes a fact about how prints are held.
Straight lines are the thing being protected
It is worth being explicit about what the flat picture plane is buying with the stretch, because otherwise the trade looks like a bad one.
A rectilinear projection maps every straight world line to a straight picture line, exactly. That is why a wide photograph of a building has straight edges, why a construction can be carried out on it with a straightedge, and why vanishing points exist and can be found from the drawn edges.
Give it up and none of that survives. A cylindrical projection keeps shapes at the edges and bends every straight line that does not pass through its axis, so the same building comes out bowed.
For architecture the choice is not close: bent buildings are unacceptable and stretched corners are tolerable. For a group portrait it goes the other way. That is the whole of the decision, and it is why both projections are offered by every panoramic tool and neither is the default for everything.
The rule of thumb
For anyone who wants one line to carry away: the stretch at the frame edge is 1/cos of half the field of view, and it is invisible below about 50° and unmistakable past about 80°.
Between those, keep faces away from the corners. Past 80°, either accept the look or change the projection — and if the projection changes, expect the straight lines to go.
Volume anamorphosis, which is the proper name
The effect has a technical name that avoids the confusion this essay is about, and it is worth using: volume anamorphosis.
The word is exact. It is anamorphosis — a picture correct from a stated viewpoint and wrong from anywhere else — applied to volumes rather than to a flat design. A sphere at the edge of a wide frame is drawn as an ellipse for the same reason a skull on a wall is drawn as a smear: both are correct projections onto their surfaces from their own centres, and both look wrong from the position anyone actually takes.
That framing also predicts which things are affected and which are not. Flat, straight-edged parts of a wide photograph look fine, because straightness is what a flat picture plane preserves and a rectangle at the frame edge is still a rectangle. Volumes look stretched, because a volume’s silhouette is a cone of rays and an oblique cut through a cone is an ellipse.
So a wide interior with a stretched sofa in the corner reads as spacious, and a wide group photograph with a stretched head in the corner reads as a mistake. The geometry is identical in both. What differs is that viewers hold a strong prior about the shape of a head and none at all about the shape of a sofa, which is a fact about perception rather than about projection — and one more place where the geometry stops and something else begins.