Lens Distortion - Guillermo Algora - Visual Effects Compositor

Guillermo Algora
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Artists may embrace lens distortion creatively for specific effects, as it can add a sense of realism to computer generated imagery, and it is a must when compositing them into live-action, matching the distortion already present in the footage.
Table of Contents:
1. Optical Distortion:
1.1 Barrel.
1.2 Pincushion.
1.3 Mustache.
2. Perspective Distortion:
1. Optical Distortion:

Optical distortion refers to the bending or warping that occurs when light passes through a curved lens, often observed at the periphery of the frame, causing a geometric displacement of information that changes the shape of an image. It is "treated" monochromatically and simply encompasses the geometric distortion of the image field (change in magnification of an image across the field of view), separating it from any softness or wavelength dependence, which are considered separate aberrations. Almost all lenses exhibit optical distortion to some extent, although some exhibit more than others.

It is completely insensitive to aperture, but is intrinsically related to focal length, which (in common optical systems) is known as the distance between the lens and the focal plane, that conversely relates to the field of view (as illustrated in the diagram below). Under a theoretical approximation, any lens focal length that deviates from the diagonal of the film/sensor will create some form of optical distortion, i.e. because the field of view will be "squeezed in" or "stretched out" to fit it. Therefore, lens design aside, in general the further the focal length deviates from the diagonal ratio, the greater the optical distortion. In the full frame (35mm) format, the diagonal is 43mm (i.e. diagonal of 36mm x 24mm).

However, large field of views (wide-angle lenses, short focal lengths) generally tend to exhibit stronger amounts of distortion than smaller field of views (telephoto lenses, long focal lengths). This is because a wider field of view captures a larger part of the scene and, consequently, elements towards the periphery of the frame are physically further away from the the optical axis (center of the image), where light rays pass through without much deviation. As such, distortion generally increases away from optical axis. In contrast, telephoto lenses have a narrower field of view (capturing a smaller portion of the scene) and therefore elements towards the periphery of the frame are relatively closer to the center (optical axis) compared to wide-angle lenses.

Lens design greatly influences the amount of distortion. Zoom lenses (which cover a wide range of focal lengths), for example, often have more complex optical designs than prime lenses (which have a fixed focal length). This complexity can lead to greater distortion, as it becomes difficult for manufacturers to perfectly compensate for distortion over the entire zoom range. At the other end, for example, telecentric lenses are designed in a way that minimises distortion, maintaining a consistent perspective regardless of the distance from the element to the lens, which results in very little distortion.
Focal Length - Working Distance
Relationship Diagram
Focal Length - Field of View relation
Sensor Diagonal Diagram
Focal Lengths Comparison Diagram
Although distortion can be irregular or follow many patterns, the most commonly encountered distortions are radially symmetrical, or approximately so, arising from the symmetry of the lens. There are three main types of distortion patterns:

1.1 Barrel:

Image magnification decreases with distance from the optical axis, in other words, the image curves inwards in a barrel shape towards the periphery.

Commonly seen at short focal lengths (wide-angle lenses) since the field of view of the lens is much wider than the size of the film/sensor and therefore has to be "squeezed in" to fit. As a result, straight lines are visibly curved inwards, especially towards the extreme edges of the frame.

1.2 Pincushion:

Opposite of barrel distortion, image magnification increases with distance from the optical axis, i.e. the image curves outwards towards the periphery.

It is often seen at long focal lengths (telephoto lenses) because, this time, the field of view is smaller than the size of the film/sensor and "stretched out" to fit it. As a result, straight lines appear to be pulled upwards in the corners.

1.3 Mustache:

A mixture of barrel and pincushion, also sometimes referred as 'wavy' or 'complex' distortion, which is less common but not rare. It starts as barrel distortion close to the image center (optical axis) and gradually turns into pincushion towards the periphery.

Mustache distortion is observed particularly at the wide-end of zooms, with certain retrofocus lenses and more recently on large-range zooms. Most modern lenses are designed to minimize or eliminate mustache distortion and this type of distortion is more common in older lenses

It is worth noting that most zoom lenses going from wide-angle to standard or telephoto focal lengths tend to suffer from barrel distortion at the shorter focal lengths, which gradually transitions to pincushion towards the longer end.

The most common photographic lenses are rectilinear, which aim to reproduce straight lines in the scene with the least minimal distortion. Although not perfect, they are designed to minimise the bending of light rays and create a realistic representation. Curvilinear lenses, on the other hand, intentionally bend the light rays to create a curved image. A common example of it is fish-eye lenses, which produce a very wide field of view with a dramatic, bulbous image shape in which straight lines appear curved.
No Distortion
2. Perspective Distortion:

While optical distortion is caused by lens design, perspective distortion is entirely dependent on the distance between the camera and the subject and thus not an optical phenomenon, but a perceptional one.

Different focal lengths will require the camera to be positioned at different distances to the subject in order to capture the same framing and it is these distances what causes perspective distortion. In a nutshell, perspective distortion refers to how the distance of an object from the camera affects its apparent size and shape in the image, and therefore how different focal lengths result in different perspective distortion, due to the different distance required for a given framing.

Although perspective distortion cannot be technically corrected as the optical distortion, it is a phenomenon to be taken into account when composing our images, as it can definitely prevent an external element from appearing fully integrated within a live-action plate.
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