Focus (optics)

Lore & Background

In geometrical optics, a focus is defined as a point where light rays from an object point converge. However, physical limitations such as aberrations and diffraction cause the focus to have a spatial extent known as the blur circle. The smallest possible blur circle, even without aberrations, is the Airy disc caused by diffraction from the optical system's aperture. Aberrations tend to worsen as aperture diameter increases, while the Airy circle is smallest for large apertures.

Reader's Guide

The concept of focus is fundamental to optical imaging, defining whether an image is in focus (light converged almost as much as possible) or out of focus. A principal focus or focal point is a special case: for lenses and spherical or parabolic mirrors, it is where collimated light parallel to the axis converges. Lenses have two focal points, one on each side, with the distance to the focus called focal length. Elliptical mirrors have two foci such that light passing through one reflects through the other. Hyperbolic mirrors have two foci with reflective properties used in designs like the Cassegrain telescope. Diverging lenses and convex mirrors do not focus collimated light to a real point; instead, the focus is the apparent origin of diverging rays. The border between in-focus and out-of-focus is sometimes defined using a circle of confusion criterion.

Did You Know?

• The smallest possible blur circle is the Airy disc, caused by diffraction from the optical system's aperture.
• Aberrations tend to worsen as aperture diameter increases, while the Airy circle is smallest for large apertures.
• A lens has two focal points, one on each side, because light can pass through it in either direction.
• Elliptical mirrors have two focal points such that light passing through one before striking the mirror is reflected through the other.

Core Philosophy: Transfer Over Image Formation

Nonimaging optics, sometimes called anidolic optics, represents a fundamentally different philosophy from traditional imaging optics. Rather than attempting to project a sharp picture of a light source onto a target, this branch of optics is entirely concerned with how efficiently and effectively radiation can be moved from where it originates to where it is needed. The goal is an optimized system for radiative transfer, not an optimized image. Designers working in this field must simultaneously manage several variables at the target—total radiant flux, the angular spread of the radiation, and its spatial distribution—while also accounting for how well the system collects light at the source. This dual optimization distinguishes nonimaging design from conventional approaches. The discipline excels in two problem domains where imaging optics falls short: concentrating solar energy onto receivers and controlling the distribution of light for illumination tasks. In both cases, the priority is getting the right amount of energy to the right place, not reproducing a visual representation of the source.

Concentrating the Sun's Power

When it comes to solar energy concentration, nonimaging optics offers advantages that imaging-based approaches like parabolic reflectors or Fresnel lenses simply cannot match. The most significant benefit is a dramatically wider acceptance angle, which translates into far greater tolerance for real-world imperfections: less precise sun tracking, manufacturing deviations, assembly misalignments, wind-induced movement, structural flexing, and material aging. This tolerance means higher effective efficiencies in deployed systems. Beyond tolerance, nonimaging designs enable higher concentration ratios, smaller solar cells in photovoltaic applications, higher operating temperatures and lower thermal losses in thermal systems, and the potential to power applications like solar lasers. They also allow uniform illumination of the receiver and offer design flexibility, since different geometries can be tailored to specific needs. For low-concentration scenarios, the wide acceptance angles can eliminate the need for continuous tracking entirely, reducing it to just a few adjustments per year. The one acknowledged drawback is an extra optical surface at high concentrations, which slightly reduces efficiency—but this penalty is largely theoretical, since real systems rarely aim perfectly at the Sun.

Shaping Light for the Modern World

In illumination engineering, nonimaging optics has become the design language behind countless everyday products. The toolkit includes optical light guides, nonimaging reflectors, nonimaging lenses, and combinations of these elements. Modern implementations span automotive headlamps, LCD backlights, illuminated instrument panels, fiber-optic illumination devices, LED-based lighting, projection display systems, and general luminaires. Compared to traditional design methods, nonimaging approaches handle extended light sources more gracefully, produce more compact optical assemblies, enable color mixing, allow a single source to be split and directed to multiple locations, and are particularly well suited to the increasingly dominant LED light sources. They also tolerate variations in the relative positioning of the source and the optic, a practical advantage in manufacturing. A notable solar-powered application is anidolic lighting, also known as solar pipes, which channels daylight into interior spaces. The field is also expanding into nanoscale territory through nonimaging metaoptics, which employs metalenses and metamirrors to manage light transfer in compact, lightweight, and wearable optical systems.

From Edge Rays to Metaoptics: The Design Toolbox

The simplest design approach, known as the method of strings, rests on the edge-ray principle. Starting in the early 1990s, more sophisticated methods emerged to handle extended sources more effectively, driven largely by the design challenges of solid-state automobile headlamps and complex illumination systems. Among these, the Simultaneous Multiple Surface (SMS) design method stands out; its two-dimensional formulation was patented (U.S. Some design methods have even crossed back into imaging territory, finding use in ultra-high-numerical-aperture imaging devices.

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