Understanding Lens Aberrations and Lens Distortion
Gaspar van Elmbt
In the world of machine vision, achieving precise and reliable results depends heavily on capturing high-quality images. While industrial cameras and machine vision lighting play crucial roles, the machine vision lens is perhaps the most critical component for ensuring the image faithfully reproduces the object being inspected. However, the lenses are not perfect, and the way they refract and focus light can lead to various imperfections in the resulting image. These imperfections are known as lens aberrations and lens distortion. Understanding these phenomena is essential for machine vision systems designers and integrators to choose the right lens and optimize system performance, avoiding potentially wasted investment on unsuitable components.
Table of contents
What are Lens Aberrations and Lens Distortion?
Lens Aberrations are deviations from the ideal image formation by a machine vision lens, causing the image to be blurred, have color fringes, or exhibit other defects not present in the actual object. They occur because real lenses cannot perfectly focus all incoming light rays to a single point, even when perfectly manufactured. Aberrations are generally classified into two main types: monochromatic aberration and chromatic aberration. In 1857, five key types of monochromatic lens aberrations were defined: spherical aberration, coma, astigmatism, field curvature, and distortion. Axial and lateral chromatic aberrations were identified later, occurring with polychromatic light.
In an ideal world, a lens would focus all incoming light rays from a single point on an object to a single corresponding point on the image sensor, regardless of the light's color or where the ray passes through the lens. Lens aberrations represent deviations from this ideal behavior, causing light rays to converge improperly or shift position, leading to blurred or warped images.
Lens Distortion is a specific type of aberration where the magnification of the image varies across the field of view, causing straight lines in the object to appear curved in the image. In geometric distortion, image points are displaced radially from the optical axis, making straight lines appear curved. Unlike some other aberrations, distortion does not blur the image but changes its shape.
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Understanding Lens Distortion
Lens distortion, unlike these sharpness issues, is a geometrical phenomenon that displaces image points radially relative to the optical axis without necessarily blurring them. The position of a point in a slightly blurred image can still be measured as the center of the blurred point; however, if that measured position is inaccurate due to distortion, results depending on image coordinates will be erroneous. The most common types of distortion are radially symmetric. These radial distortions typically fall into two categories: barrel distortion and pincushion distortion.
Significant Lens Aberrations
While lens distortion is one type of lens aberration, it is distinct from others like spherical aberration, coma, astigmatism, and field curvature, which primarily impact image sharpness without changing the basic structure of the object in the image (a straight line remains straight, though potentially blurred). Distortion, however, can fundamentally alter the perceived shape of objects in the image.
Let's briefly touch upon some of the other aberrations to highlight this distinction:
Spherical Aberration
Commonly occurs in older or lower-quality lenses. It arises when light rays passing through the horizontal axis of a spherical lens converge at different points after passing through the lens, depending on whether they pass nearer the center or the periphery of the field of view. In a perfect lens, all rays would converge at the same focal point. The result of spherical aberration is a blurred image, as a single point in the object is imaged as a spot rather than a sharp point on the sensor. Many modern lenses employ aspherical lens elements, which have a curvature that varies from the edge to the center, specifically designed to correct light rays and guide them to a single focal point, thereby reducing spherical aberration.
Coma
Another aberration that affects off-axis points. Light rays passing through points further from the optical axis are refracted differently than those closer to the axis. This causes off-axis point sources to appear distorted with a characteristic teardrop or comet-like shape at the image plane, often larger than the rays passing through the axis. Coma, in combination with spherical aberration, contributes to irregular shapes and blurring in images.
Astigmatism
Occurs when a point object is far from the axis of a lens. Similar to field curvature as it impacts corner-to-corner sharpness, with sharper areas typically found in the center. However, astigmatism also affects magnification across the frame, often leading to less clarity in affected areas compared to field curvature alone. Astigmatism results in light rays oriented horizontally and vertically having different focal points. The difference between these focal lengths, known as the astigmatic distance, serves as a measure of the amount of astigmatism in the lens.
Field Curvature
A very common issue where the target object appears sharp only in certain parts of the image frame, rather than being uniformly sharp across the entire field of view. Typically, the center of the image might be sharper and display better contrast than the edges, which appear blurred or out of focus. This happens because the depth of field itself is curved, and the lens images a flat object onto a curved surface. Since digital cameras have flat image sensors, capturing this curved image results in a blur towards the periphery. Most, if not all, lenses will produce some degree of field curvature, with higher quality lenses generally showing less. In real-world lenses with multiple elements, field curvature can sometimes appear 'wavy', meaning the image might be sharp in the center and corners but less sharp at intermediate points.
Chromatic Aberration
Occurs when imaging with polychromatic (color) light. It happens because the refractive index of the lens material varies slightly depending on the wavelength (color) of light. Since the refractive index is different for different colors (e.g., larger for blue light than red light), different wavelengths are focused differently. There are two types:
- Axial chromatic aberration occurs because different wavelengths are focused on different points along the optical axis. This leads to clouded colors both in front of and behind the ideal focus position. This variation in focal points for different colors is more noticeable at the edges and corners of the image where brightness might be higher.
- Lateral chromatic aberration happens because different wavelengths are magnified to different degrees. This results in color fringes appearing around high-contrast details in the image. These fringes might appear as fine details being blurred with opposing colors (e.g., red and cyan fringing) on either side. Lateral chromatic aberration is often seen at the edges and corners of frames, particularly with wide-aperture lenses. It's important to note that this aberration is caused by the lens, not the camera sensor.
Methods for Minimizing or Eliminating Lens Distortion
- Lens Design: While achieving a "perfect" lens is impossible, lens designers use techniques to reduce distortion and other aberrations. Using multiple lens elements or incorporating aspherical surfaces can help. Designing lenses of suitable shapes and materials can minimize aberrations like coma.
- Aperture: Placing an aperture can help minimize spherical aberration. Apertures can also be used to minimize or eliminate distortion. Positioning an aperture symmetrically between two lenses can help compensate for opposing types of distortion (e.g., barrel by one lens and pincushion by the other). Reducing the aperture size can decrease the amount of light passing through the outer edges of spherical lenses, thus reducing the potential for aberrations and distortion, though this impacts exposure and contrast.
- Selecting Appropriate Lenses: Choosing lenses known for low distortion is a direct way to avoid the problem. For tasks involving measurements, using a macro lens designed for close-up shooting, which is often well-corrected for distortion, can be beneficial. Using a focal length less prone to distortion for the specific lens, such as the 35-55mm range on some cameras, can also help.
- Software Correction: This is a powerful and widely used method, especially in digital photography and computer vision. Software correction requires performing camera calibration to determine the distortion coefficients of the lens. This involves using calibration targets (like checkerboards) with known 3D points and their corresponding image projections (For checking the distortion of your lens, we recommend using our checkerboard pattern chart, which can be downloaded here, Free Test Chart) Once calibrated, the distortion parameters are used to correct the image. Software can be calibrated (using pre-existing lens profiles) or allow for manual adjustment of parameters. Libraries like OpenCV provide functions for camera calibration and undistorting images. The process generally involves performing calibration to get intrinsic parameters (including distortion parameters), refining the camera matrix to optimize the undistorted image, and then applying the undistortion process. Some camera systems perform automatic distortion correction using parameters stored in the lens firmware.
For accurate machine vision and computer vision applications, addressing lens distortion is essential. While selecting well-designed lenses can minimize the issue upfront, camera calibration and software correction are often necessary, particularly for quantitative tasks. Understanding the nature of different distortion types and the limitations of the models used for correction is important for ensuring the reliability of image analysis results.
Concluding Lens Aberrations and Lens Distortion
Lens aberrations and distortion are inherent optical phenomena that can significantly impact image quality in machine vision applications. From the warping effects of barrel and pincushion distortion to the blurring caused by spherical aberration, coma, and astigmatism, and the color fringing from chromatic aberration, each type presents unique challenges. Field curvature affects uniform sharpness across the frame. By understanding these effects, how they are caused by the lens design, and how they can be minimized through lens selection and system configuration (like adjusting aperture), designers and integrators can make informed decisions to ensure the chosen lens is optimized for the specific camera and application requirements.
