Lens Distortion is an optical change in image geometry introduced by a lens or optical imaging system. In its most specific sense, it occurs when the position or magnification of image points departs from the ideal geometrical projection expected from the corresponding camera or optical system.
The term is frequently used too broadly. Not every unusual shape, enlarged foreground, converging building, stretched edge or curved line in a photograph is caused by lens distortion. Some effects arise from the viewpoint; some from the Field of View; some from the geometrical form of the chosen projection; some from camera orientation; and others are genuine optical defects introduced by the lens.
The Perspective Research Centre therefore distinguishes optical lens distortion from the normal geometrical transformations of perspective. This distinction is essential for understanding camera and photographic perspective correctly.
Lens Distortion and Perspective Distortion Are Not the Same Thing
One of the most important distinctions is between lens distortion and more general perspective distortion.
Perspective changes can arise simply because an object is viewed from a particular position, distance and angle. Moving closer to an object changes the relative apparent sizes of its nearer and farther parts. Looking upwards at a building can cause vertical lines to converge. Representing an extremely wide angular field on a flat rectilinear image can stretch Forms near the edges.
None of these effects necessarily indicates a defective lens.
True optical lens distortion occurs when the lens itself causes the resulting image to depart from the geometry of the intended projection system.
The Dictionary Classification of Camera and Optical Distortion
Within its broader classification of Perspective of Lateral Distortion, the Dictionary separates five important photographic factors:
- 1. Viewpoint or Camera-Position Perspective
- 2. Focal Length and Field of View
- 3. Rectilinear Edge Stretching
- 4. Camera Tilt and Converging Verticals
- 5. Optical Lens Distortion
This division is extremely useful because all five can alter the appearance of a photograph, but their causes are different.
The Ideal Central-Projection Model
A useful reference for understanding lens distortion is the ideal pinhole camera or geometrical central-projection model.
Light rays from points within a spatial scene pass through a single aperture or projection centre and intersect an image plane. The geometry can therefore be modelled without the additional optical complications introduced by a real multi-element lens.
A real camera lens attempts to form a corresponding optical image while also collecting considerably more light, focusing it and controlling other image properties. Because a practical lens consists of refracting optical elements rather than one dimensionless aperture, its image can depart from the ideal geometrical model.
Those departures include optical aberrations and lens distortion.
Rectilinear Lens Projection
A rectilinear lens is designed so that straight lines in the spatial scene are ideally represented as straight lines in the photograph.
Its geometry corresponds broadly to central projection onto a flat image plane. This is closely related to the familiar geometry of linear perspective.
An ideal rectilinear lens can therefore produce a very wide-angle image in which straight architectural edges remain straight even far from the image centre.
However, preserving straightness over a very wide field produces another geometrical effect: Forms towards the outer regions can become progressively enlarged or stretched. This is a property of the rectilinear projection itself and is not necessarily lens distortion.
Optical Lens Distortion
The Dictionary identifies genuine optical lens distortion as a departure from the intended or ideal projection model.
The principal forms identified are:
- Barrel Distortion;
- Pincushion Distortion;
- Moustache or Wave Distortion; and
- Decentring or Tangential Distortion.
These should be distinguished from changes caused solely by camera position, perspective projection, viewing angle or Field of View.
Radial Distortion
Radial Distortion occurs when image magnification changes according to the distance of an image point from the optical axis or image centre.
The scale of the image is therefore not uniform across the whole field.
The two familiar radial forms are:
- Barrel Distortion: magnification decreases towards the image edge.
- Pincushion Distortion: magnification increases towards the image edge.
Because the magnification changes with field position, straight object lines that do not pass through the centre can become visibly curved.
Barrel Distortion
Barrel Distortion is a radial scale distortion in which magnification becomes lower towards the edges of the image.
Straight object-space lines that would remain straight under an ideal rectilinear projection can consequently bow outwards.
The resulting image can appear expanded around the centre and compressed towards its perimeter, producing the characteristic barrel-like curvature.
Barrel Distortion is an optical departure from ideal rectilinear projection. It should not be confused with the legitimate enlargement or stretching of Forms towards the margins of a mathematically correct wide-angle rectilinear image.
Pincushion Distortion
Pincushion Distortion is the opposite radial tendency.
Image magnification increases towards the edge of the field. Straight lines that would ideally remain straight therefore bend inwards towards the image centre.
The resulting rectangular or grid-like image can acquire the characteristic inward-curving appearance associated with a pincushion.
Again, this is a genuine optical distortion rather than a normal consequence of camera viewpoint.
Moustache or Wave Distortion
Moustache Distortion, also called Wave Distortion, combines more than one radial distortion pattern within the same image.
The direction or strength of the curvature can therefore change as distance from the image centre increases rather than following one simple barrel or pincushion relationship across the complete field.
This produces a more complex wavy transformation of straight lines and is one reason why some lens distortions cannot be described adequately as purely barrel or purely pincushion.
Decentring or Tangential Distortion
Decentring or Tangential Distortion can arise when optical elements are imperfectly aligned within the lens system.
The resulting geometrical displacement is not necessarily centred symmetrically upon the optical axis in the way a simple radial distortion is.
The effect therefore represents another genuine optical departure from the ideal camera projection and can occur alongside radial distortion.
Scale Magnification Distortion
The Dictionary uses Scale Magnification Distortion for image distortion produced when an imaging system does not magnify uniformly across its Field of View.
This provides a useful general way of understanding barrel and pincushion distortion.
If magnification varies with image height or distance from the optical axis, the relationship between object-space geometry and image-space scale changes progressively across the picture.
The resulting distortion can alter both the position of image points and the apparent geometry of Forms.
Lens Distortion and Optical Aberration
Lens distortion belongs to the broader subject of optical aberration, but distortion should not be used as a synonym for every optical aberration.
The Dictionary identifies five principal optical-system aberration types:
- Spherical Aberration;
- Coma;
- Astigmatism;
- Field Curvature; and
- Distortion.
These phenomena affect images in different ways. Some primarily affect the formation, location or sharpness of image points, whereas geometrical distortion primarily alters the mapped shape or position of image Forms across the field.
Spherical Aberration
Spherical Aberration is an optical aberration involving variation of focus with aperture.
It primarily affects how rays are brought towards an image point rather than producing the systematic barrel- or pincushion-type bending of the complete image geometry.
It is therefore a lens aberration, but should be distinguished from lens distortion in the narrower geometrical sense.
Coma
Coma is another optical aberration and is associated in the Dictionary with variation of magnification with aperture.
Like spherical aberration, it is part of the wider family of optical image defects and must not automatically be classified as barrel or pincushion distortion.
Astigmatism
Astigmatism occurs when rays propagating in two perpendicular planes have different focal relationships.
Its principal effect concerns image formation and focus rather than the systematic radial bending of straight image lines.
It is therefore another example of why the general expression lens aberration is broader than lens distortion.
Field Curvature
Field Curvature occurs when the region of sharp image formation is naturally curved rather than coincident with a flat image surface.
The Dictionary notes that positive lenses can introduce inward image curvature and negative lenses outward curvature.
Field curvature should be distinguished carefully from the apparent curvature of straight object lines caused by barrel, pincushion or other geometrical distortion. The former concerns the shape of the focal region; the latter concerns the mapped geometry of the image.
Chromatic Aberration
Chromatic Aberration is a colour-related optical aberration caused when different wavelengths of light are not brought to precisely the same image location or focus by a refractive optical system.
It can produce visible colour fringing but should not be confused with geometrical Lens Distortion.
A lens may therefore exhibit chromatic aberration while having relatively low geometrical distortion, or vice versa.
Wide-Angle Perspective Is Not Automatically Lens Distortion
A particularly common error is to describe every unusual wide-angle photographic appearance as lens distortion.
The Dictionary explicitly distinguishes Wide-Angle Perspective from optical lens defects. A wide-angle image simply captures a larger Field of View than a normal lens used with the same image format.
When a rectilinear lens is used, straight scene lines can remain straight while Forms towards the margins become increasingly stretched.
This edge stretching is a geometrical consequence of representing a wide angular field on one flat rectilinear image plane. It can occur even with an optically perfect lens.
Rectilinear Edge Stretching
Rectilinear Edge Stretching, classified by the Dictionary under Graphical Lateral Distortion and Camera Perspective, becomes increasingly conspicuous as a wide Field of View is mapped onto a flat image plane.
Rounded objects, human heads, figures and other volumetric Forms near the image margins can appear elongated, enlarged or asymmetric.
Yet straight object lines remain straight.
This combination — straight lines but stretched marginal Forms — is a characteristic of wide rectilinear projection and should not be confused with barrel distortion, in which straight lines themselves bow outwards.
Why Wide Rectilinear Images Stretch at the Edges
A flat rectilinear projection converts changing angular direction into position upon a flat image surface.
As the represented visual angle moves farther from the central axis, the corresponding planar scale per degree increases. The outer parts of an extremely wide view therefore occupy progressively larger distances across the flat picture plane.
This maintains the rectilinearity of straight spatial lines but transforms the apparent shape and dimensions of Forms near the margins.
The effect belongs to the selected projection geometry rather than necessarily to the imperfections of the lens.
Fisheye Curvature Is Not Necessarily a Lens Defect
A fisheye lens deliberately employs a curvilinear rather than an ordinary rectilinear mapping in order to compress an extremely large Field of View onto a finite image.
Straight scene lines can consequently appear curved, especially away from particular principal directions.
This curvature should not automatically be classified as optical distortion in the sense of a defective lens. It can instead be the intended geometrical result of the chosen projection system.
Volume 1 specifically emphasises that fisheye curvature is a consequence of the projection mapping rather than merely a random optical defect.
Rectilinear and Curvilinear Lens Images
A useful distinction can therefore be made between two broad approaches to wide-field lens imaging:
- Rectilinear projection: preserves straight object lines as straight image lines but increasingly stretches Forms towards the margins as Field of View expands.
- Curvilinear or fisheye projection: redistributes a wide angular field differently and allows many straight spatial lines to become curved in the resulting image.
Neither mapping should automatically be labelled incorrect. They preserve and transform different image relationships.
Field of View and Lens Distortion
Field of View is closely associated with the appearance of lens and projection effects, but it is not itself a distortion.
For a given image or sensor format, a shorter focal length normally records a wider Field of View, while a longer focal length records a narrower one.
As the represented Field of View expands, peripheral image regions become increasingly important and both projection effects and optical lens departures may become more conspicuous.
Very wide-angle optical systems therefore present particularly demanding problems for lens design.
Focal Length Is Not the Same as Perspective
Another common source of confusion concerns focal length.
For a fixed sensor format, changing focal length changes Field of View, framing and image scale.
If the camera projection centre remains in the same physical position, a shorter focal length does not by itself change the fundamental near–far perspective relationships within the scene. A longer-focal-length image from the same location resembles a central crop and enlargement of the wider image, apart from differences introduced by the optical system, focus, resolution and related imaging properties.
The dramatic perspective commonly associated with wide-angle photography usually also involves a change of camera position.
Camera Position and Apparent Distortion
The camera position determines the relative spatial angles and apparent sizes of objects at different distances.
Moving the camera closer to a subject increases differences between nearer and farther Forms. Nearby features can become very large relative to more distant features.
Moving farther away reduces these relative differences.
This is a perspective effect produced by changing viewpoint. It should not be classified as an optical defect of the lens.
The So-Called Wide-Angle Distortion Effect
Photographers often use a short-focal-length lens and then move closer to the subject in order to fill the image frame.
The final photograph may show very large nearer Forms and much smaller distant ones. This appearance is frequently called wide-angle lens distortion.
However, the major near–far size transformation is principally produced by the closer camera position. The short focal length makes it possible to include the resulting broad scene within the frame.
True barrel, pincushion or other lens distortion may also be present, but it is a separate phenomenon.
Telephoto Compression Is Primarily a Viewpoint Effect
The opposite confusion occurs with so-called telephoto compression.
A long-focal-length lens is commonly used from a greater camera distance in order to obtain the required framing. From this farther viewpoint, the relative difference between the distances of near and far objects is reduced.
They consequently appear closer together in scale and the scene may seem compressed in depth.
The major perspective change is therefore produced principally by the changed camera position rather than by the focal length alone.
Camera Tilt Is Not Lens Distortion
Converging verticals in architectural photographs are also frequently misidentified as wide-angle or lens distortion.
If a camera is tilted upwards, its image plane is no longer parallel to the vertical lines of the building. Those vertical directions then possess a finite vanishing point and converge within the image.
This is a geometrical consequence of camera and image-plane orientation.
A wide-angle lens may make the effect more conspicuous because a greater vertical Field of View is represented, but the lens itself is not the fundamental cause of the convergence.
Keystone Distortion
Keystone Distortion is a trapezoidal perspective transformation produced when an image plane is not parallel to the relevant subject plane, or when a projector is positioned obliquely relative to a screen.
It is therefore primarily a projective or orientation effect rather than radial lens distortion.
A photograph can, of course, contain both keystone transformation and genuine optical lens distortion simultaneously. Their causes should nevertheless be identified separately.
Oblique Views and Foreshortening Are Not Lens Distortion
An object viewed at an oblique angle can become compressed, skewed or foreshortened in the resulting image.
These changes can result from Aspect Perspective and Foreshortening and do not require any lens defect.
The Dictionary explicitly distinguishes such oblique compaction from camera tilt and optical lens distortion.
In an ideal rectilinear image, oblique viewing can radically transform apparent dimensions while straight object lines nevertheless remain straight.
Curved Lines: What Causes Them?
A curved line in a perspective photograph can arise for several quite different reasons.
It may be:
- the image of a genuinely curved line in object space;
- the image of a straight line intentionally transformed by a curvilinear, cylindrical, spherical or fisheye projection;
- a straight line bent by barrel, pincushion, moustache or other optical lens distortion; or
- a curve introduced through later image processing or digital transformation.
In an ideal rectilinear central projection, a straight spatial line remains straight.
Lens Design and Perspective Image Geometry
Different camera lenses are designed to produce different combinations of focal length, Field of View, image scale, resolution and optical performance.
A practical lens normally contains several optical elements arranged so as to form a useful image while controlling aberrations.
The Dictionary emphasises that different lens classes and individual lens designs can produce slightly or substantially different image geometries and levels of optical distortion.
Lens designers therefore attempt to reduce unwanted aberrations while achieving the required Field of View and projection characteristics.
Wide-Angle Lens Design
Wide-angle lenses present an especially important perspective problem because they must represent a large angular field within a finite image.
A designer may seek a rectilinear image in which straight object lines remain straight across a large Field of View. Alternatively, a fisheye design may deliberately employ curvilinear projection in order to compress a still wider angular field.
Volume 1 notes that very wide-angle lenses can sometimes introduce curvilinear aberrations, but also stresses that wide-angle lenses do not necessarily produce curvilinear distortion. The result depends upon the optical design and projection geometry.
Normal, Wide-Angle and Telephoto Lenses
The Dictionary distinguishes broad camera-lens classes according to focal length and image format:
- Normal Lens;
- Wide-Angle or Short-Focal-Length Lens;
- Telephoto or Long-Focal-Length Lens; and
- Zoom or Variable-Focal-Length Lens.
These categories primarily describe focal-length and Field-of-View relationships. None is synonymous with a particular lens distortion.
A wide-angle lens may be highly corrected for barrel distortion, while another lens of a different focal length may exhibit noticeable optical distortion. The specific optical design matters.
Lens Distortion and Image Format
Focal length cannot be considered independently of the size of the image or sensor format when discussing Field of View.
A given focal length used with a smaller sensor records a smaller central portion of the available image than the same focal length used with a larger sensor.
The captured Field of View therefore changes even though the physical focal length of the lens remains unchanged.
This distinction is important because Field of View, wide-field edge effects and optical distortion are related but separate properties of the complete camera system.
Lens Distortion and Image Processing
Visible image distortion does not always originate in the lens.
Digital image processing can warp, rescale, rectify or otherwise transform image geometry after capture.
A photograph can therefore contain geometrical changes introduced at several different stages:
- during spatial viewing and projection;
- within the physical camera lens;
- at the image or sensor plane;
- through digital processing or correction; and
- during subsequent display and viewing.
Correct analysis requires identifying which stage has produced the observed transformation.
Lens Distortion in the Optical Image Chain
Volume 1 treats camera imaging as part of a wider optical image chain.
Spatial reality is transformed into an instrument image by the camera and lens, after which the image may be processed, displayed, projected and finally observed by the human visual system.
A geometrically valid central projection can preserve the intended projection geometry while losing some spatial information, whereas a physical lens may additionally introduce optical distortion.
The final viewed image can therefore contain several layers of perspective transformation that should not be conflated.
Lens Distortion and Photogrammetry
Lens distortion becomes especially significant when photographs are used not merely for visual representation but for measurement.
Photogrammetric analysis derives spatial information from photographs taken from one or more positions. Camera position, object coordinates and lens distortion therefore need to be considered in the reconstruction process.
A small geometrical displacement that might be visually unobtrusive can become important when the purpose of the image is precise spatial measurement rather than ordinary pictorial viewing.
Correcting Optical Lens Distortion
Optical lens distortion can be corrected or reduced by applying a calibrated transformation to the captured image.
The Dictionary identifies lens-profile correction for:
- Barrel Distortion;
- Pincushion Distortion;
- Moustache or Wave Distortion; and
- Tangential Distortion.
The purpose is to restore the image more closely to the intended projection model.
Such correction should not be described as removing perspective. Perspective relationships created by the viewpoint remain. What is corrected is the optical departure of the lens from the intended projection geometry.
Perspective Correction Is Different from Lens Correction
Lens correction and perspective correction solve different problems.
Lens correction can compensate for barrel, pincushion, moustache and tangential optical distortion.
Perspective correction or projective warping can instead alter geometrical effects such as converging verticals caused by camera orientation.
The second operation changes the represented projective geometry and may require cropping, resampling or alteration of image proportions. It is not equivalent to correcting an imperfect lens.
Perspective-Control and Shift Lenses
A Perspective-Control or Shift Lens can alter the framing of a scene while helping maintain a desired relationship between the camera image plane and subject geometry.
For architectural photography, lens or camera shift can allow more of a tall building to enter the image while keeping the image plane parallel to the building’s vertical directions.
This controls converging verticals without treating them as an optical lens defect.
Lens shift and optical distortion correction therefore solve fundamentally different problems.
Alternative Wide-Field Projections
Some apparent wide-field distortions cannot simply be eliminated because they arise from the fundamental problem of mapping a large angular environment onto a limited image surface.
The Dictionary identifies several alternative approaches:
- Rectilinear Projection preserves straight lines but produces increasing marginal stretching.
- Cylindrical Projection can reduce some horizontal edge stretching while preserving vertical straightness.
- Spherical Projection distributes the surrounding directional field over spherical geometry.
- Fisheye or Curvilinear Projection can represent an extremely wide field while curving many straight scene lines.
- Multi-Perspective and Computationally Warped Images can distribute geometrical transformation selectively across the image.
These are alternative projection strategies rather than simply different forms of defective imaging.
The Wide-Field Mapping Problem
There is a more fundamental problem behind many discussions of photographic distortion: an extremely wide three-dimensional directional field cannot be transferred onto a flat two-dimensional image while preserving every possible geometrical property simultaneously.
Different projection systems prioritise different properties.
Rectilinear projection prioritises straightness of spatial lines. Curvilinear and fisheye mappings distribute angular information differently. Cylindrical and spherical methods use other geometrical organisations again.
The resulting differences should not all be classified as lens distortion. Some are fundamental consequences of the selected projection itself.
Lens Distortion and Correct Viewing Position
The appearance of a perspective photograph also depends upon how the completed image is subsequently viewed.
A central-perspective image has an intended geometrical relationship to its original centre of projection and viewing distance.
A very wide-angle image generally corresponds to a relatively close viewing position if the angular field subtended by the displayed image is to reproduce the original camera field.
Viewing the picture from a substantially different location introduces another stage of perspective transformation. Such a viewing discrepancy should again be distinguished from distortion introduced by the camera lens itself.
Visual, Graphical and Optical Lateral Distortion
The Dictionary’s broader Perspective of Lateral Distortion classification is useful because apparent distortion can arise in different kinds of perspective space.
- Visual Lateral Diminution concerns the appearance of Forms in human Visual Perspective Type 2.
- Perspective-Window or Rectilinear Projection concerns the geometry of projection from a fixed centre onto a flat plane.
- Graphical Lateral Distortion concerns marginal enlargement and stretching within wide flat rectilinear representations.
- Camera Perspective and Optical Distortion distinguishes viewpoint, focal length, rectilinear stretching, camera tilt and actual lens distortion.
- Control and Correction concerns the different methods needed to deal with these different causes.
The central lesson is that there is no single phenomenon called simply “perspective distortion” that can be corrected in one universal way.
Common Misconceptions about Lens Distortion
Several common assumptions should therefore be avoided:
- Not every unusual photographic appearance is lens distortion. Viewpoint, projection geometry and camera orientation can transform the image without any optical defect.
- A wide-angle lens does not automatically distort perspective. Its shorter focal length principally provides a wider Field of View for a given image format.
- Large noses or enlarged foreground Forms in close wide-angle portraits are primarily viewpoint effects. Moving the camera close increases near–far size differences.
- Telephoto compression is principally associated with the more distant viewpoint normally used with a long lens.
- Converging verticals are not normally caused by barrel distortion. They result principally from camera and image-plane orientation.
- Rectilinear edge stretching is not necessarily a lens defect. It is inherent in mapping a very wide angular field onto a flat rectilinear plane.
- Curved lines in a fisheye image are not necessarily optical errors. They can be the intended result of curvilinear projection.
- Barrel Distortion is genuine lens distortion. Magnification decreases towards the image edge and straight lines can bow outwards.
- Pincushion Distortion is genuine lens distortion. Magnification increases towards the image edge and straight lines can bend inwards.
- Moustache Distortion combines multiple radial patterns.
- Tangential Distortion can result from imperfect alignment of lens elements.
- Optical aberration is broader than geometrical Lens Distortion. Spherical aberration, coma, astigmatism, Field Curvature and chromatic aberration are related but different optical effects.
- Lens correction does not remove perspective. It corrects departures from the intended optical projection model.
- Perspective correction and lens correction are different operations.
Why Lens Distortion Matters
Lens Distortion matters because a photographic perspective image is produced by a combination of spatial geometry, viewpoint, Field of View, projection geometry, camera orientation, lens design and image processing.
Without separating these factors, ordinary and correct perspective effects can easily be mistaken for optical defects, while genuine lens distortion can be wrongly attributed to perspective itself.
The crucial distinction is that perspective describes the transformation produced by the viewing and projection relationship, whereas Lens Distortion describes an additional optical departure from the intended lens or projection geometry.
Understanding Lens Distortion therefore provides a foundation for understanding Camera Perspective, Photographic Perspective, Instrument Perspective, optical aberration, Barrel Distortion, Pincushion Distortion, Moustache Distortion, Tangential Distortion, Radial Distortion, Rectilinear Perspective, Curvilinear Perspective, fisheye projection, Wide-Angle Perspective, Field of View, focal length, camera position, camera tilt, keystone distortion, Graphical Lateral Distortion, perspective correction, lens calibration and the broader Perspective of Lateral Distortion.