I. Definition and Types of Distortion
Distortion is a highly unique geometric aberration. It does not affect the sharpness of the image, but it causes originally straight lines in the actual scene to bend, thereby altering the geometric similarity between the object and the image.

Distortion is a behavior of the chief ray. The actual lateral magnification varies across different fields, leading to different distortion phenomena.
Distortion can be classified into the following three types:
Pincushion distortion: Also known as positive distortion. It manifests as a larger lateral magnification at the image edges compared to the center, causing straight lines to bend inward, resembling a pincushion. This type of distortion is commonly seen in telephoto lenses.

(Telephoto lens image source: By WolfWings - Own work, Public Domain, https://commons.wikimedia.org/w/index.php?curid=1388853)

Barrel distortion: Also known as negative distortion. It manifests as a larger lateral magnification at the image center compared to the edges, causing straight lines to bulge outward, resembling a barrel. This distortion is particularly common in wide-angle lenses.

(Fisheye lens image source: By WolfWings - Own work, Public Domain, https://commons.wikimedia.org/w/index.php?curid=1388846)

Mustache distortion: It combines the characteristics of pincushion and barrel distortion, typically manifesting as barrel distortion in the central region of the image, gradually transitioning to pincushion distortion in the peripheral regions, forming complex curves resembling a mustache. This is a relatively rare type of distortion.

II. Causes of Distortion
An ideal lens has no distortion because the aperture stop, nodal points, and optical center coincide. When the chief ray passes through the optical center, its propagation direction remains unchanged, and the lateral magnification remains constant. However, actual lenses are composed of multiple lens elements. The fundamental cause of distortion is that the effective focal length (EFL) is not constant, causing the lateral magnification to vary with the angle of the incident rays (i.e., across different fields), ultimately resulting in a loss of geometric similarity between the image and the object.
Its evolution path is as follows: Aperture stop position (determines the path) → Aperture zone selection (determines the active region) → Effective focal length (EFL) fluctuation (fundamental root cause) → Spatial non-uniformity of lateral magnification → Distortion occurs.
So, why does the effective focal length (EFL) change? The answer is related to the position of the aperture stop.
The aperture stop is the “window” inside the lens that restricts the light beam. Its position determines which aperture zone of the lens the rays from different fields will pass through. The refractive power varies across different aperture zones of the lens (weaker refraction in the central region, stronger refraction in the edge region). Therefore, when rays from different fields pass through different aperture zones, the effective focal length (EFL) of the imaging system changes with the field position, leading to non-uniform lateral magnification and ultimately producing distortion.

Taking a single convex lens as an example (as shown in the figure above):
Aperture stop on the image side (behind the lens): The chief ray of the marginal field passes through the lens first. Due to the filtering effect of the aperture stop, only rays with a large exit slope can pass through, causing the actual marginal image height to be greater than the ideal image height, resulting in pincushion distortion (positive distortion).
Aperture stop on the object side (in front of the lens): The chief ray of the marginal field enters from the marginal aperture zone of the lens and is excessively deflected toward the optical axis, causing the actual marginal image height to be less than the ideal image height, resulting in barrel distortion (negative distortion).
Note: If the convex (positive) lens is replaced with a concave (negative) lens, the distortion phenomenon will be reversed.

III. Calculation Principle of TV Distortion
Traditional TV Distortion (ISO 9039/EBU Tech 3249)
Originating from the analog television era, it was initially used to quantify the visual impact of “straight lines becoming curved” at the image edges caused by cathode ray tube (CRT) displays or early camera lenses. It is defined by measuring the degree of curvature of lines at the image edges, with the calculation formula as follows:
$$D = \frac{\Delta H}{H} \cdot 100$$ Where: $\Delta H$ is the difference between the actual image height and the ideal image height, and $H$ is the image height of the ideal undistorted image.

SMIA TV Distortion
SMIA TV Distortion is an industry standard evolved from traditional TV distortion, and its numerical magnitude is typically about twice that of traditional TV distortion. The calculation process is as follows:
1. Feature extraction: Use a high-precision test chart (such as a checkerboard or dot grid) to extract the actual imaging coordinates $(x_{real}, y_{real})$ of the feature points in the image.
2. Model fitting: Combined with the nominal ideal coordinates, use the least squares method to fit the radial distortion model of the lens (typically using a third-order or fifth-order polynomial, such as $r_{\text{real}} = r_{\text{ideal}} \left(1 + k_1 r^2 + k_2 r^4\right)$).
3. Virtual frame mapping: Based on the fitted model, establish a virtual test frame at 98% of the image field height to ensure the calculation covers the vast majority of the field of view while avoiding invalid edge regions.
4. Numerical output: Calculate the “ideal height (B)” and “distorted actual height (A)” of the virtual frame under the model, respectively, and substitute them into the SMIA standard formula for calculation. The calculation formula is as follows:
$$ A = \frac{A_{1}+A_{2}}{2} $$ $$ SMIA= \frac{A-B}{B} \times100% $$ Where:
SMIA: corresponds to SMIA (%); $A_{1}$: distance from the top-left to the bottom-left of the grid points; $A_{2}$: distance from the top-right to the bottom-right of the grid points; B: distance between the midpoints of the topmost and bottommost grid points.
When SMIA TV Distortion > 0, it is pincushion distortion; when SMIA TV Distortion < 0, it is barrel distortion.

Frequently Asked Questions:
Q1: Does distortion cause edge blur?
A1: No. Distortion is “sharp deformation.” Edge blur is usually caused by field curvature (uneven image plane) or astigmatism. Although algorithmic distortion correction (stretching the image) may introduce secondary blur due to interpolation compensation, optical distortion itself does not impair image sharpness.
Q2: Is distortion unrelated to light color?
A2: Theoretically, distortion is a monochromatic aberration and is unrelated to the color of light. However, in actual optical systems, lens materials (glass) exhibit dispersion, meaning different wavelengths of light have different refractive indices. This causes the effective focal length (EFL) to vary slightly with wavelength, leading to slight differences in the degree of distortion for different colors of light, which manifests as magnification chromatic aberration in high-precision imaging systems. Therefore, while distortion is theoretically unrelated to light color, actual measurements will be affected by wavelength.

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iso_17850_畸变测试, Distortion Test