Optical filters are commonly used in photography (where some special effect filters are occasionally used as well as absorptive filters), in many optical instruments, and to colour stage lighting. In astronomy optical filters are used to restrict light passed to the spectral band of interest, e.g., to study infrared radiation without visible light which would affect film or sensors and overwhelm the desired infrared. Optical filters are also essential in fluorescence applications such as fluorescence microscopy and fluorescence spectroscopy.

The Iraqi mathematician Ibn Sahl discovered the full law of refraction in 984. Sahl showed that the angle of incidence is related to the angle of refraction using the law of sines.[4] Sahl couldn’t use this method to measure the actual speed of light, however, and could only determine the ratios.

Infrared-passing filters are used to block visible light but pass infrared; they are used, for example, in infrared photography.

↑ Lindberg, D. C., The Beginnings of Western Science: The European Scientific Tradition in Philosophical, Religious, and Institutional Context, Prehistory to A.D. 1450, University of Chicago Press, 2010.

Here v is velocity and n is the refractive index. n=c/v, where c is the speed of light in a vacuum, which is very close to its speed in air.

Long pass filterflow cytometry

The basic scientific instrument of this type is a Fabry–Pérot interferometer. It uses two mirrors to establish a resonating cavity. It passes wavelengths that are a multiple of the cavity's resonance frequency.

Infrared cut-off filters are designed to block or reflect infrared wavelengths but pass visible light. Mid-infrared filters are often used as heat-absorbing filters in devices with bright incandescent light bulbs (such as slide and overhead projectors) to prevent unwanted heating due to infrared radiation. There are also filters which are used in solid state video cameras to block IR due to the high sensitivity of many camera sensors to unwanted near-infrared light.

Long pass FilterThorlabs

An optical filter is a device that selectively transmits light of different wavelengths, usually implemented as a glass plane or plastic device in the optical path, which are either dyed in the bulk or have interference coatings. The optical properties of filters are completely described by their frequency response, which specifies how the magnitude and phase of each frequency component of an incoming signal is modified by the filter.[1]

Examples of band-pass filters are the Lyot filter and the Fabry–Pérot interferometer. Both of these filters can also be made tunable, such that the central wavelength can be chosen by the user. Band-pass filters are often used in astronomy when one wants to observe a certain process with specific associated spectral lines. The Dutch Open Telescope[5] and Swedish Solar Telescope[6] are examples where Lyot and Fabry–Pérot filters are being used.

A wedge filter is an optical filter so constructed that its thickness varies continuously or in steps in the shape of a wedge. The filter is used to modify the intensity distribution in a radiation beam. It is also known as linearly variable filter (LVF). It is used in various optical sensors where wavelength separation is required e.g. in hyperspectral sensors.[7]

↑ Yurkin, A. V., “New view on the diffraction discovered by Grimaldi and Gaussian beams”, arXiv preprint arXiv:1302.6287, 2013.

Shortpassvslong pass filter

The Ancient Greek mathematician Euclid described the law of reflection in about 300 BCE. This states that light travels in straight lines and reflects from a surface at the same angle at which it hit it.

Optical filters selectively transmit light in a particular range of wavelengths, that is, colours, while absorbing the remainder. They can usually pass long wavelengths only (longpass), short wavelengths only (shortpass), or a band of wavelengths, blocking both longer and shorter wavelengths (bandpass). The passband may be narrower or wider; the transition or cutoff between maximal and minimal transmission can be sharp or gradual. There are filters with more complex transmission characteristic, for example with two peaks rather than a single band;[2] these are more usually older designs traditionally used for photography; filters with more regular characteristics are used for scientific and technical work.[3]

Bandpass filter

Filters mostly belong to one of two categories. The simplest, physically, is the absorptive filter; then there are interference or dichroic filters. Many optical filters are used for optical imaging and are manufactured to be transparent; some used for light sources can be translucent.

Dichroic filters are particularly suited for precise scientific work, since their exact colour range can be controlled by the thickness and sequence of the coatings. They are usually much more expensive and delicate than absorption filters.

To see sunlight that has passed through a raindrop, there needs to be an angle of about 40°-42° between you, the raindrop, and the Sun. The set of all the raindrops that can be seen from this angle at once forms a cone pointing towards the Sun. Coloured light is not visible from any other angle, and so when you move, the rainbow moves with you. This is why you will never be able to reach the end of a rainbow.

The term "infrared filter" can be ambiguous, as it may be applied to filters to pass infrared (blocking other wavelengths) or to block infrared (only).

Also in general, light which is not transmitted is absorbed; for intense light, that can cause significant heating of the filter. However, the optical term absorbance refers to the attenuation of the incident light, regardless of the mechanism by which it is attenuated. Some filters, like mirrors, interference filters, or metal meshes, reflect or scatter much of the non-transmitted light.

UVlong pass filter

They can be used in devices such as the dichroic prism of a camera to separate a beam of light into different coloured components.

A relatively new class of filters introduced around 1990. These filters are normally filters in reflection, that is they are notch filters in transmission. They consist in their most basic form of a substrate waveguide and a subwavelength grating or 2D hole array. Such filters are normally transparent, but when a leaky guided mode of the waveguide is excited they become highly reflective (a record of over 99% experimentally) for a particular polarization, angular orientations, and wavelength range. The parameters of the filters are designed by proper choice of the grating parameters. The advantage of such filters are the few layers needed for ultra-narrow bandwidth filters (in contrast to dichroic filters), and the potential decoupling between spectral bandwidth and angular tolerance when more than 1 mode is excited.

Grimaldi’s findings were published in 1665, two years after his death.[15] Diffraction is now understood in terms of the superposition principle (discussed in Chapter 5).

An arc source puts out visible, infrared and ultraviolet light that may be harmful to human eyes. Therefore, optical filters on welding helmets must meet ANSI Z87:1 (a safety glasses specification) in order to protect human vision.

Al-Haytham experimented with the laws of reflection and refraction using different shaped mirrors and lenses, and he accurately described how the eye functions as an optical instrument. He likened it to a camera obscura, a pinhole camera, and so suggested that images must also be inverted in the eye. This led him to suggest that vision occurs in the brain, rather than the eyes and that it is, therefore, subjective.[11]

A shortpass (SP) Filter is an optical interference or coloured glass filter that attenuates longer wavelengths and transmits (passes) shorter wavelengths over the active range of the target spectrum (usually the ultraviolet and visible region). In fluorescence microscopy, shortpass filters are frequently employed in dichromatic mirrors and excitation filters.

Ultraviolet (UV) filters block ultraviolet radiation, but let visible light through. Because photographic film and digital sensors are sensitive to ultraviolet (which is abundant in skylight) but the human eye is not, such light would, if not filtered out, make photographs look different from the scene visible to people, for example making images of distant mountains appear unnaturally hazy. An ultraviolet-blocking filter renders images closer to the visual appearance of the scene.

Photographic filters are a particular case of optical filters, and much of the material here applies. Photographic filters do not need the accurately controlled optical properties and precisely defined transmission curves of filters designed for scientific work, and sell in larger quantities at correspondingly lower prices than many laboratory filters. Some photographic effect filters, such as star effect filters, are not relevant to scientific work.

Shortpass filter

The (dimensionless) Optical Density of a filter at a particular wavelength of light is defined as − log 10 ⁡ T {\displaystyle -\log _{10}T} where T is the (dimensionless) transmittance of the filter at that wavelength.

Some examples of filters that would provide this kind of filtering would be earth elements embedded or coated on glass, but practically speaking it is not possible to do perfect filtering. A perfect filter would remove particular wavelengths and leave plenty of light so a worker can see what he/she is working on.

↑ Pontrjagin, L. S., Learning Higher Mathematics: Part I: The Method of Coordinates Part II: Analysis of the Infinitely Small, Springer Science & Business Media, 2013.

↑ Cloud, R. R., Aristotle’s journey to Europe: A synthetic history of the role played by the Islamic Empire in the transmission of Western educational philosophy sources from the fall of Rome through the medieval period, ProQuest, 2007.

Dichroic filters use the principle of interference. Their layers form a sequential series of reflective cavities that resonate with the desired wavelengths. Other wavelengths destructively cancel or reflect as the peaks and troughs of the waves overlap.

A longpass (LP) Filter is an optical interference or coloured glass filter that attenuates shorter wavelengths and transmits (passes) longer wavelengths over the active range of the target spectrum (ultraviolet, visible, or infrared). Longpass filters, which can have a very sharp slope (referred to as edge filters), are described by the cut-on wavelength at 50 percent of peak transmission. In fluorescence microscopy, longpass filters are frequently utilized in dichroic mirrors and barrier (emission) filters. Use of the older term 'low pass' to describe longpass filters has become uncommon; filters are usually described in terms of wavelength rather than frequency, and a "low pass filter", without qualification, would be understood to be an electronic filter.

In the case of a double rainbow, secondary bows are caused by double reflection inside the raindrop. This causes the colours to be reversed and produces visible light at about 52°-54°.

There are now many absorptive filters made from glass to which various inorganic or organic compounds[citation needed] have been added. Colored glass optical filters, although harder to make to precise transmittance specifications, are more durable and stable once manufactured.[citation needed]

Optical filtering was first done with liquid-filled, glass-walled cells;[citation needed] they are still used for special purposes. The widest range of color-selection is now available as colored-film filters, originally made from animal gelatin but now usually a thermoplastic such as acetate, acrylic, polycarbonate, or polyester depending upon the application. They were standardized for photographic use by Wratten in the early 20th century, and also by color gel manufacturers for theater use.

Etalons are another variation: transparent cubes or fibers whose polished ends form mirrors tuned to resonate with specific wavelengths. These are often used to separate channels in telecommunications networks that use wavelength division multiplexing on long-haul optic fibers.

The Dutch mathematician Willebrord Snellius rediscovered the sine law of refraction in 1621. Snellius’ theory was not published in his lifetime and, in 1637, the French natural philosopher Rene Descartes rediscovered the law again, independently.[5]

Theodoric did this by experimenting with spherical flasks, which he filled with water to represent raindrops. Theodoric showed that the light of the Sun is refracted, and then internally reflected, inside each drop.[7]

As with infrared filters there is a potential ambiguity between UV-blocking and UV-passing filters; the latter are much less common, and more usually known explicitly as UV pass filters and UV bandpass filters.[4]

The Roman astronomer Ptolemy first tried to experimentally derive the law of refraction in the 2nd century CE.[2] Refraction explains how a ray of light changes direction when it travels between different mediums. This is either because it slows down or because it speeds up. Refraction occurs when light hits the surface of water or travels through the atmosphere, and it’s atmospheric refraction that causes the stars to ‘twinkle’.

The German philosopher Theodoric of Freiberg (also known as Dietrich of Freiberg) explained how rainbows are formed in about 1307.

Alternately, dichroic filters (also called "reflective" or "thin film" or "interference" filters) can be made by coating a glass substrate with a series of optical coatings. Dichroic filters usually reflect the unwanted portion of the light and transmit the remainder.

In general, a given optical filter transmits a certain percentage of the incoming light as the wavelength changes. This is measured by a spectrophotometer. As a linear material, the absorption for each wavelength is independent of the presence of other wavelengths. A very few materials are non-linear, and the transmittance depends on the intensity and the combination of wavelengths of the incident light. Transparent fluorescent materials can work as an optical filter, with an absorption spectrum, and also as a light source, with an emission spectrum.

Long pass filterfluorescence

Another kind of optical filter is a polarizer or polarization filter, which blocks or transmits light according to its polarization. They are often made of materials such as Polaroid and are used for sunglasses and photography. Reflections, especially from water and wet road surfaces, are partially polarized, and polarized sunglasses will block some of this reflected light, allowing an angler to better view below the surface of the water and better vision for a driver. Light from a clear blue sky is also polarized, and adjustable filters are used in colour photography to darken the appearance of the sky without introducing colours to other objects, and in both colour and black-and-white photography to control specular reflections from objects and water. Much older than g.m.r.f (just above) these first (and some still) use fine mesh integrated in the lens.

The sine of 90° is 1 because the opposite length will also be the longest, the hypotenuse. In the triangle above, sin(C) would equal length c / length c, which equals 1.

The sine function shows how the angle inside a triangle changes as the lengths of its sides change. The sine of an angle (θ) equals the ratio of two lengths - the length opposite the angle, and the longest length, the hypotenuse.

Band-pass filters only transmit a certain wavelength band, and block others. The width of such a filter is expressed in the wavelength range it lets through and can be anything from much less than an Ångström to a few hundred nanometers. Such a filter can be made by combining an LP- and an SP filter.

Filters for sub-millimeter and near infrared wavelengths in astronomy are metal mesh grids that are stacked together to form LP, BP, and SP filters for these wavelengths.

Polarized filters are also used to view certain types of stereograms, so that each eye will see a distinct image from a single source.

Long pass filterprice

Light is reflected in the same way that a ball would bounce off of a frictionless surface, and so Euclid claimed that light travels in rays that are discrete, like atoms, not continuous, like waves. This may mean that some of the objects in our visual field will always remain unilluminated, and therefore undetected. Unlike Aristotle, Euclid thought that light is emitted in rays from the eye.[1]

Neutral density (ND) filters have a constant attenuation across the range of visible wavelengths, and are used to reduce the intensity of light by reflecting or absorbing a portion of it. They are specified by the optical density (OD) of the filter, which is the negative of the common logarithm of the transmission coefficient. They are useful for making photographic exposures longer. A practical example is making a waterfall look blurry when it is photographed in bright light. Alternatively, the photographer might want to use a larger aperture (so as to limit the depth of field); adding an ND filter permits this. ND filters can be reflective (in which case they look like partially reflective mirrors) or absorptive (appearing grey or black).

The Italian natural philosopher Francesco Grimaldi discovered and coined the term ‘diffraction’ in 1660.[14] Grimaldi showed that a single beam of light spreads out, creating an interference pattern, if it’s shone through very small slits. Water and sound waves act the same way, and so this was an important finding for those that advocated for a wave theory of light. Before this, people had argued that the sharp boundaries created by shadows meant that light could not bend around corners in the same way that water or sound waves can.

The ancient Greek astronomer Hipparchus created the first documented table of sine functions before 125 BCE.[6] Hipparchus’ work was referenced by Ptolemy over 250 years later, and so it’s not known why he didn’t derive the sine law of refraction himself.[7][8]

The Iraqi mathematician Ibn al-Haytham (also known as Alhazen) was the first person to correctly describe how perception occurs in about 1021 when he proved that light enters, but is not emitted by, the eye.[10] Al-Haytham stated that light consists of tiny particles of energy that travel in straight lines and emanate from the Sun at a large but finite velocity. Vision occurs when the Sun’s rays are reflected from objects and into our eyes.

Science began to progress again in Europe after the Renaissance of the 12th century. This was mainly due to increased contact with the Islamic world.[12] The English philosopher Roger Bacon, who was one of the earliest European advocates of experimental science, reviewed Al-Haytham’s Book of Optics in 1267, and it was translated into Latin shortly after.[13]

Ptolemy measured the angle that a beam of light hits a boundary, the angle of incidence, and the angle at which it leaves, the angle of refraction, through different mediums. He discovered that the angle of incidence is proportional to the angle of refraction, but could not derive the full equation. Like Euclid, Ptolemy thought that light is emitted in rays from the eye.[3]

Sin, cos, and tan waves could not be represented graphically until after the invention of the Cartesian coordinate system by Descartes and the French mathematician Pierre de Fermat in 1637.[9]