Optics in the context of Etendue

An image or picture is a visual representation. An image can be two-dimensional, such as a drawing, painting, or photograph, or three-dimensional, such as a carving or sculpture. Images may be displayed through other media, including a projection on a surface, activation of electronic signals, or digital displays; they can also be reproduced through mechanical means, such as photography, printmaking, or photocopying. Images can also be animated through digital or physical processes.

In the context of signal processing, an image is a distributed amplitude of color(s). In optics, the term image (or optical image) refers specifically to the reproduction of an object formed by light waves coming from the object.

A lens is a transmissive optical device that focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (elements), usually arranged along a common axis. Lenses are made from materials such as glass or plastic and are ground, polished, or molded to the required shape. A lens can focus light to form an image, unlike a prism, which refracts light without focusing. Devices that similarly focus or disperse waves and radiation other than visible light are also called "lenses", such as microwave lenses, electron lenses, acoustic lenses, or explosive lenses.

Lenses are used in various imaging devices such as telescopes, binoculars, and cameras. They are also used as visual aids in glasses to correct defects of vision such as myopia and hypermetropia.

A laser guide star is an artificial star image created for use in astronomical adaptive optics systems, which are employed in large telescopes in order to correct atmospheric distortion of light (called astronomical seeing). Adaptive optics (AO) systems require a wavefront reference source of light called a guide star. Natural stars can serve as point sources for this purpose, but sufficiently bright stars are not available in all parts of the sky, which greatly limits the usefulness of natural guide star adaptive optics. Instead, one can create an artificial guide star by shining a laser into the atmosphere. Light from the beam is reflected by components in the upper atmosphere back into the telescope. This star can be positioned anywhere the telescope desires to point, opening up much greater amounts of the sky to adaptive optics.

Because the laser beam is deflected by astronomical seeing on the way up, the returning laser light does not move around in the sky as astronomical sources do. In order to keep astronomical images steady, a natural star nearby in the sky must be monitored in order that the motion of the laser guide star can be subtracted using a tip-tilt mirror. However, this star can be much fainter than is required for natural guide star adaptive optics because it is used to measure only tip and tilt, and all higher-order distortions are measured with the laser guide star. This means that many more stars are suitable, and a correspondingly larger fraction of the sky is accessible.

Abū Yūsuf Yaʻqūb ibn ʼIsḥāq aṣ-Ṣabbāḥ al-Kindī (/ælˈkɪndi/; Arabic: أبو يوسف يعقوب بن إسحاق الصبّاح الكندي; Latin: Alkindus; c. 801–873 AD) was an Arab Muslim polymath active as a philosopher, mathematician, physician, and music theorist. Al-Kindi was the first of the Islamic peripatetic philosophers, and is hailed as the "father of Arab philosophy".

Al-Kindi was born in Kufa and educated in Baghdad. He became a prominent figure in the House of Wisdom, and a number of Abbasid Caliphs appointed him to oversee the translation of Greek scientific and philosophical texts into the Arabic language. This contact with "the philosophy of the ancients" (as Hellenistic philosophy was often referred to by Muslim scholars) had a profound effect on him, as he synthesized, adapted and promoted Hellenistic and Peripatetic philosophy in the Muslim world. He subsequently wrote hundreds of original treatises of his own on a range of subjects ranging from metaphysics, ethics, logic and psychology, to medicine, pharmacology, mathematics, astronomy, astrology and optics, and further afield to more practical topics like perfumes, swords, jewels, glass, dyes, zoology, tides, mirrors, meteorology and earthquakes.

Christiaan Huygens, Lord of Zeelhem, FRS (/ˈhaɪɡənz/ HY-gənz, US also /ˈhɔɪɡənz/ HOY-gənz; Dutch: [ˈkrɪstijaːn ˈɦœyɣə(n)s] ; also spelled Huyghens; Latin: Hugenius; 14 April 1629 – 8 July 1695) was a Dutch mathematician, physicist, engineer, astronomer, and inventor who is regarded as a key figure in the Scientific Revolution. In physics, Huygens made seminal contributions to optics and mechanics, while as an astronomer he studied the rings of Saturn and discovered its largest moon, Titan. As an engineer and inventor, he improved the design of telescopes and invented the pendulum clock, the most accurate timekeeper for almost 300 years. A talented mathematician and physicist, his works contain the first idealization of a physical problem by a set of mathematical parameters, and the first mathematical and mechanistic explanation of an unobservable physical phenomenon.

Huygens first identified the correct laws of elastic collision in his work De Motu Corporum ex Percussione, completed in 1656 but published posthumously in 1703. In 1659, Huygens derived geometrically the formula in classical mechanics for the centrifugal force in his work De vi Centrifuga, a decade before Isaac Newton. In optics, he is best known for his wave theory of light, which he described in his Traité de la Lumière (1690). His theory of light was initially rejected in favour of Newton's corpuscular theory of light, until Augustin-Jean Fresnel adapted Huygens's principle to give a complete explanation of the rectilinear propagation and diffraction effects of light in 1821. Today this principle is known as the Huygens–Fresnel principle.

Sir Isaac Newton (/ˈnjuːtən/ ; 4 January [O.S. 25 December] 1643 – 31 March [O.S. 20 March] 1727) was an English polymath active as a mathematician, physicist, astronomer, alchemist, theologian, author, and inventor. He was a key figure in the Scientific Revolution and the Enlightenment that followed. His book Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), first published in 1687, achieved the first great unification in physics and established classical mechanics. Newton also made seminal contributions to optics, and shares credit with German mathematician Gottfried Wilhelm Leibniz for formulating infinitesimal calculus, though he developed calculus years before Leibniz. Newton contributed to and refined the scientific method, and his work is considered the most influential in bringing forth modern science.

In the Principia, Newton formulated the laws of motion and universal gravitation that formed the dominant scientific viewpoint for centuries until it was superseded by the theory of relativity. He used his mathematical description of gravity to derive Kepler's laws of planetary motion, account for tides, the trajectories of comets, the precession of the equinoxes and other phenomena, eradicating doubt about the Solar System's heliocentricity. Newton solved the two-body problem and introduced the three-body problem. He demonstrated that the motion of objects on Earth and celestial bodies could be accounted for by the same principles. Newton's inference that the Earth is an oblate spheroid was later confirmed by the geodetic measurements of Alexis Clairaut, Charles Marie de La Condamine, and others, convincing most European scientists of the superiority of Newtonian mechanics over earlier systems. He was also the first to calculate the age of Earth by experiment, and described a precursor to the modern wind tunnel. Further, he was the first to provide a quantitative estimate of the solar mass.

A point source of pollution is a single identifiable source of air, water, thermal, noise or light pollution. A point source has negligible extent, distinguishing it from other pollution source geometrics (such as nonpoint source or area source). The sources are called point sources because in mathematical modeling, they can be approximated as a mathematical point to simplify analysis. Pollution point sources are identical to other physics, engineering, optics, and chemistry point sources and include:

• Air pollution from an industrial source (rather than an airport or a road, considered a line source, or a forest fire, which is considered an area source, or volume source)
• Water pollution from factories, power plants, municipal sewage treatment plants and some farms (see concentrated animal feeding operation). The U.S. Clean Water Act also defines municipal separate storm sewer systems and industrial stormwater discharges (such as construction sites) as point sources.
  • Man-made, natural, and groundwater reservoirs can all be contaminated by point source pollution which can threaten human health and safety.
• Noise pollution from a jet engine
• Disruptive seismic vibration from a localized seismic study
• Light pollution from an intrusive street light
• Radio emissions from an interference-producing electrical device

Pierre de Fermat (/fɜːrˈmɑː/; French: [pjɛʁ də fɛʁma]; 17 August 1601 – 12 January 1665) was a French magistrate, polymath, and above all mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality. In particular, he is recognized for his discovery of an original method of finding the greatest and the smallest ordinates of curved lines, which is analogous to that of differential calculus, then unknown, and his research into number theory. He made notable contributions to analytic geometry, probability, and optics. He is best known for his Fermat's principle for light propagation and his Fermat's Last Theorem in number theory, which he described in a note at the margin of a copy of Diophantus' Arithmetica. He was also a lawyer at the parlement of Toulouse, France, a poet, a skilled Latinist, and a Hellenist.

In optics, the aperture of an optical system (including a system consisting of a single lens) is the hole or opening that primarily limits light propagated through the system. The aperture defines a bundle of rays from each point on an object that will come to a focus in the image plane.

An optical system typically has many structures that limit ray bundles (ray bundles are also known as pencils of light). These structures may be the edge of a lens or mirror, or a ring or other fixture that holds an optical element in place or may be a special element such as a diaphragm placed in the optical path to limit the light admitted by the system. These structures are called stops, and the aperture stop is the stop that primarily determines the cone of rays that an optical system accepts (see entrance pupil). As a result, it also determines the ray cone angle and brightness at the image point (see exit pupil). Optical systems are typically designed for a particular stop to be the aperture stop, but it is possible for different stops to serve as the aperture stop for objects at different distances. Some rays from object points away from the optical axis may clip on surfaces other than the aperture stop. This is called vignetting. The aperture stop is not necessarily the smallest stop in the system. Magnification and demagnification by lenses and other elements can cause a relatively large stop to be the aperture stop for the system.

The angular diameter, angular width, angular size, apparent diameter, or apparent size is an angular separation (in units of angle) describing how large a sphere or circle appears from a given point of view. In the vision sciences, it is called the visual angle, and in optics, it is the angular aperture (of a lens). The angular diameter can alternatively be thought of as the angular displacement through which an eye or camera must rotate to look from one side of an apparent circle to the opposite side.

A person can resolve with their naked eyes diameters down to about 1 arcminute (approximately 0.017° or 0.0003 radians). This corresponds to 0.3 m at a 1 km distance, or to perceiving Venus as a disk under optimal conditions.

In philosophy, practical reason is the use of reason to decide how to act. It contrasts with theoretical reason, often called speculative reason, the use of reason to decide what to believe. For example, agents use practical reason to decide whether to build a telescope, but theoretical reason to decide which of two theories of light and optics is the best.

The visual system is the physiological basis of visual perception (the ability to detect and process light). The system detects, transduces and interprets information concerning light within the visible range to construct an image and build a mental model of the surrounding environment. The visual system is associated with the eye and functionally divided into the optical system (including cornea and lens) and the neural system (including the retina and visual cortex).

The visual system performs a number of complex tasks based on the image forming functionality of the eye, including the formation of monocular images, the neural mechanisms underlying stereopsis and assessment of distances to (depth perception) and between objects, motion perception, pattern recognition, accurate motor coordination under visual guidance, and colour vision. Together, these facilitate higher order tasks, such as object identification. The neuropsychological side of visual information processing is known as visual perception, an abnormality of which is called visual impairment, and a complete absence of which is called blindness. The visual system also has several non-image forming visual functions, independent of visual perception, including the pupillary light reflex and circadian photoentrainment.

Glass is an amorphous (non-crystalline) solid. Because it is often transparent and chemically inert, glass has found widespread practical, technological, and decorative use in window panes, tableware, and optics. Some common objects made of glass are named after the material, e.g., a "glass" for drinking, "glasses" for vision correction, and a "magnifying glass".

Glass is most often formed by rapid cooling (quenching) of the molten form. Some glasses such as volcanic glass are naturally occurring, and obsidian has been used to make arrowheads and knives since the Stone Age. Archaeological evidence suggests glassmaking dates back to at least 3600 BC in Mesopotamia, Egypt, or Syria. The earliest known glass objects were beads, perhaps created accidentally during metalworking or the production of faience, which is a form of pottery using lead glazes.

In optics, a dispersive prism is an optical prism that is used to disperse light, that is, to separate light into its spectral components (the colors of the rainbow). Different wavelengths (colors) of light will be deflected by the prism at different angles. This is a result of the prism material's index of refraction varying with wavelength (dispersion). Generally, longer wavelengths (red) undergo a smaller deviation than shorter wavelengths (blue). The dispersion of white light into colors by a prism led Sir Isaac Newton to conclude that white light consisted of a mixture of different colors.

Triangular prisms are the most common type of dispersive prism. Other types of dispersive prism exist that have more than two optical interfaces; some of them combine refraction with total internal reflection.

Dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency. Sometimes the term chromatic dispersion is used to refer to optics specifically, as opposed to wave propagation in general. A medium having this common property may be termed a dispersive medium.

Although the term is used in the field of optics to describe light and other electromagnetic waves, dispersion in the same sense can apply to any sort of wave motion such as acoustic dispersion in the case of sound and seismic waves, and in gravity waves (ocean waves). Within optics, dispersion is a property of telecommunication signals along transmission lines (such as microwaves in coaxial cable) or the pulses of light in optical fiber.

The human eye is a sensory organ in the visual system that reacts to visible light allowing eyesight. Other functions include maintaining the circadian rhythm, and keeping balance.

The eye can be considered as a living optical device. It is approximately spherical in shape, with its outer layers, such as the outermost, white part of the eye (the sclera) and one of its inner layers (the pigmented choroid) keeping the eye essentially light tight except on the eye's optic axis. In order, along the optic axis, the optical components consist of a first lens (the cornea—the clear part of the eye) that accounts for most of the optical power of the eye and accomplishes most of the focusing of light from the outside world; then an aperture (the pupil) in a diaphragm (the iris—the coloured part of the eye), which controls the amount of light entering the interior of the eye; then another lens (the crystalline lens) that accomplishes the remaining focusing of light into images; and finally a light-sensitive part of the eye (the retina), where the images fall and are processed. The retina makes a connection to the brain via the optic nerve. The remaining components of the eye keep it in its required shape, nourish and maintain it, and protect it.

Optical radiation is the part of the electromagnetic spectrum with wavelengths between 100 nm and 1 mm. This range includes visible light, infrared light, and part of the ultraviolet spectrum. Optical radiation is non-ionizing, and can be focused with lenses and manipulated by other optical elements. Optics is the study of how to manipulate optical radiation.

A spectrum (pl.: spectra or spectrums) is a set of related ideas, objects, or properties whose features overlap such that they blend to form a continuum. The word spectrum was first used scientifically in optics to describe the rainbow of colors in visible light after passing through a prism. In the optical spectrum, light wavelength is viewed as continuous, and spectral colors are seen to blend into one another smoothly when organized in order of their corresponding wavelengths. As scientific understanding of light advanced, the term came to apply to the entire electromagnetic spectrum, including radiation not visible to the human eye.

Spectrum has since been applied by analogy to topics outside optics. Thus, one might talk about the "spectrum of political opinion", or the "spectrum of activity" of a drug, or the "autism spectrum". In these uses, values within a spectrum may not be associated with precisely quantifiable numbers or definitions. Such uses imply a broad range of conditions or behaviors grouped together and studied under a single title for ease of discussion. Nonscientific uses of the term spectrum are sometimes misleading. For instance, a single left–right spectrum of political opinion does not capture the full range of people's political beliefs. Political scientists use a variety of biaxial and multiaxial systems to more accurately characterize political opinion.

Geometrical optics, or ray optics, is a model of optics that describes light propagation in terms of rays. The ray in geometrical optics is an abstraction useful for approximating the paths along which light propagates under certain circumstances.

The simplifying assumptions of geometrical optics include that light rays: