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Spectrophotometry

 

Spectrophotometer

In physics, spectrophotometry is the quantifiable study of electromagnetic spectra. It is more specific than the general term electromagnetic spectroscopy in that spectrophotometry deals with visible light, near-ultraviolet, and near-infrared. Also, the term does not cover time-resolved spectroscopic techniques.

Spectrophotometry involves the use of a spectrophotometer. A spectrophotometer is a photometer (a device for measuring light intensity) that can measure intensity as a function of the color, or more specifically, the wavelength of light. Important features of spectrophotometers are spectral bandwidth and linear range of absorption measurement.

Perhaps the most common application of spectrophotometers is the measurement of light absorption, but they can be designed to measure diffuse or specular reflectance.^{[clarification needed]} Strictly, even the emission half of a luminescence instrument is a kind of spectrophotometer.

The use of spectrophotometers is not limited to studies in physics. They are also commonly used in other scientific fields such as chemistry, biochemistry, and molecular biology.^[1] They are widely used in many industries including printing and forensic examination.

Contents   1 Design 2 UV and IR spectrophotometers 3 IR spectrophotometry 4 Spectroradiometers 5 See also 6 References 7 External links

 Design

There are two major classes of spectrophotometers; single beam and double beam. A double beam spectrophotometer compares the light intensity between two light paths, one path containing a reference sample and the other the test sample. A single beam spectrophotometer measures the relative light intensity of the beam before and after a test sample is inserted. Although comparison measurements from double beam instruments are easier and more stable, single beam instruments can have a larger dynamic range and are optically simpler and more compact.

Historically, spectrophotometers use a monochromator containing a diffraction grating to produce the analytical spectrum. There are also spectrophotometers that use arrays of photosensors. Especially for infrared spectrophotometers, there are spectrophotometers that use a Fourier transform technique to acquire the spectral information quicker in a technique called Fourier Transform InfraRed...

The spectrophotometer quantitatively compares the fraction of light that passes through a reference solution and a test solution. Light from the source lamp is passed through a monochromator, which difracts the light into a "rainbow" of wavelngths and outputs narrow bandwidths of this diffracted spectrum. Discrete frequencies are transmitted through the test sample. Then the intensity of the transmitted light is measured with a photodiode or other light sensor, and the transmittance value for this wavelength is then compared with the transmission through a reference sample.

In short, the sequence of events in a spectrophotometer is as follows:

1. The light source shines into a monochromator.
2. A particular output wavelength is selected and beamed at the sample.
3. The sample absorbs light.
4. The photodetector behind the sample responds to the light stimulus and outputs an analog electronic current which is converted to a usable format.
5. The numbers are either plotted straight away, or are fed to a computer to be manipulated (e.g. curve smoothing, baseline correction and coversion to absorbency, a log function of light transmittance through the sample)

Many spectrophotometers must be calibrated by a procedure known as "zeroing." The absorbency of a reference substance is set as a baseline value, so the absorbencies of all other substances are recorded relative to the initial "zeroed" substance. The spectrophotometer then displays % absorbency (the amount of light absorbed relative to the initial substance).^[1]

 UV and IR spectrophotometers

Main article: Ultraviolet-visible spectroscopy

The most common spectrophotometers are used in the UV and visible regions of the spectrum, and some of these instruments also operate into the near-infrared region as well.

Visible region 400-700 nm spectrophotometry is used extensively in colorimetry science. Ink manufacturers, printing companies, textiles vendors, and many more, need the data provided through colorimetry. They take readings in the region of every 10- 20 nanometers along the visible region, and produce a spectral reflectance curve or a data stream for alternative presentations. These curves can be used to test a new batch of colorant to check if it makes a match to specifications e.g., iso printing standards.

Traditional visual region spectrophotometers cannot detect if a colorant or the base material has fluorescence. This can make it difficult to manage color issues if for example one or more of the printing inks is fluorescent. Where a colorant contains fluorescence, a bi-spectral fluorescent spectrophotometer is used. There are two major setups for visual spectrum spectrophotometers, d/8 (spherical) and 0/45. The names are due to the geometry of the light source, observer and interior of the measurement chamber. Scientists use this machine to measure the amount of compounds in a sample. If the compound is more concentrated more light will be absorbed by the sample; within small ranges, the Beer-Lambert law holds and the absorbance between samples vary with concentration linearly. In the case of printing measurements 2 alternative settings are commonly used- without/with uv filter to control better the effect of uv brighteners within the paper stock.

Samples are usually prepared in cuvettes; depending on the region of interest, they may be constructed of glass, plastic, or quartz.

 IR spectrophotometry

Main article: Infrared spectroscopy

Spectrophotometers designed for the main infrared region are quite different because of the technical requirements of measurement in that region. One major factor is the type of photosensors that are available for different spectral regions, but infrared measurement is also challenging because virtually everything emits IR light as thermal radiation, especially at wavelengths beyond about 5 μm.

Another complication is that quite a few materials such as glass and plastic absorb infrared light, making it incompatible as an optical medium. Ideal optical materials are salts, which do not absorb strongly. Samples for IR spectrophotometry may be smeared between two discs of potassium bromide or ground with potassium bromide and pressed into a pellet. Where aqueous solutions are to be measured, insoluble silver chloride is used to construct the cell.

 Spectroradiometers

Spectroradiometers, which operate almost like the visible region spectrophotometers, are designed to measure the spectral density of illuminants in order to evaluate and categorize lighting for sales by the manufacturer, or for the customers to confirm the lamp they decided to purchase is within their specifications. Components:

1. The light source shines onto or through the sample.
2. The sample transmits or reflects light.
3. The detector detects how much light was reflected from or transmitted through the sample.
4. The detector then converts how much light the sample transmitted or reflected into a number.

 See also

• Atomic Absorption Spectrophotometry
• Spectroradiometry

 References

1. ^ ^{a b} Rendina, George. Experimental Methods in Modern Biochemistry W. B. Saunders Company: Philadelphia, PA. 1976. pp. 46-55

 External links

• Optical systems using concave gratings

Photometer

In its widest sense, a photometer is an instrument for measuring light intensity or optical properties of solutions or surfaces. Photometers are used to measure:

• Illuminance
• Irradiance
• Light absorption
• Scattering of light by media
• Reflection of light
• Fluorescence
• Phosphorescence
• Luminescence

Contents   1 History 2 Principle of photometers 3 Photon counting 4 Photography 5 Visible light reflectance photometry 6 UV and visible light transmission photometry 7 Infrared light transmission photometry 8 Atomic absorption photometry 9 See also

 History

Before electronic light sensitive elements were developed, photometry was done by estimation by the eye. The relative luminous flux of a source was compared with a standard source. The photometer is placed such that the illuminance from the source being investigated is equal to that of the standard source as equal illuminance can be judged by the eye. The relative luminous fluxes can then be calculated as the illuminance decreases proportionally to the inverse square of distance. A well known such photometer consists of a paper with an oil spot, that makes the paper slightly more transparent – when the spot is not visible from either side the illuminance from the two sides is equal.

 Principle of photometers

Most photometers detect the light with photoresistors, photodiodes or photomultipliers. To analyze the light, the photometer may measure the light after it has passed through a filter or through a monochromator for determination at defined wavelengths or for analysis of the spectral distribution of the light.

 Photon counting

Some photometers measure light by counting individual photons rather than incoming flux. The operating principles are the same but the results are given in units such as photons/cm² or photons·cm⁻²·sr⁻¹ rather than W/cm² or W·cm⁻²·sr⁻¹.

Due to their individual photon counting nature, these instruments are limited to observations where the irradiance is low. The irradiance is limited by the time resolution of its associated detector readout electronics. With current technology this is in the megahertz range. The maximum irradiance is also limited by the throughput and gain parameters of the detector itself.

The light sensing element in photon counting devises in NIR, visible and ultrviolet wavelengths is a photomultiplier to achieve sufficient sensitivity.

In airborne and space-based remote sensing such photon counters are used at the upper reaches of the electromagnetic spectrum such as the X-ray to far ultraviolet. This is usually due to the lower radiant intensity of the objects being measured as well as the difficulty of measuring light at higher energies using its particle-like nature as compared to the wavelike nature of light at lower frequencies. Conversely, radiometers are typically used for remote sensing from the visible, infrared though radio frequency range.

 Photography

Main article: Light meter

Photometers are used to determine the correct exposure in photography. In modern cameras, the photometer is usually built in. As the illumination of different parts of the picture varies, advanced photometers measure the light intensity in different parts of the potential picture and use an algorithm to determine the most suitable exposure for the final picture, adapting the algorithm to the type of picture intended(see Metering mode). Historically, a photometer was separate from the camera. The advanced photometers then could be used either to measure the light from the potential picture as a whole, to measure from elements of the picture to ascertain that the most important parts of the picture are optimally exposed, or to measure the incident light to the scene with an integrating adapter.

 Visible light reflectance photometry

A reflectance photometer measures the reflectance of a surface as a function of wavelength. The surface is illuminated with white light, and the reflected light is measured after passing through a monochromator. This type of measurement has mainly practical applications, for instance in the paint industry to characterize the colour of a surface objectively.

 UV and visible light transmission photometry

Main article: Absorption spectroscopy

These are optical instruments for measurement of the absorption of light of a given wavelength (or a given range of wavelengths) of coloured substances in solution. From the light absorption, Beer's law makes it possible to calculate the concentration of the coloured substance in the solution. Due to its wide range of application and its reliability and robustness, the photometer has become one of the principal instruments in biochemistry and analytical chemistry. Absorption photometers for work in aqueous solution work in the ultraviolet and visible ranges, from wavelength around 240 nm up to 750 nm.

The principle of spectrophotometers and filter photometers is that (as far as possible) monochromatic light is allowed to pass through a container (cell) with optically flat windows containing the solution. It then reaches a light detector, that measures the intensity of the light compared to the intensity after passing through an identical cell with the same solvent but without the coloured substance. From the ratio between the light intensities, knowing the capacity of the coloured substance to absorb light (the absorbancy of the coloured substance, or the photon cross section area of the molecules of the coloured substance at a given wavelength), it is possible to calculate the concentration of the substance using Beer's law.

Two types of photometers are used: spectrophotometer and filter photometer. In spectrophotometers a monochromator (with prism or with grating) is used to obtain monochromatic light of one defined wavelength. In filter photometers, optical filters are used to give the monochromatic light. Spectrophotometers can thus easily be set to measure the absorbance at different wavelengths, and they can also be used to scan the spectrum of the absorbing substance. They are in this way more flexible than filter photometers, also give a higher optical purity of the analyzing light, and therefore they are preferably used for research purposes. Filter photometers are cheaper, robuster and easier to use and therefore they are used for routine analysis. Photometers for microtiter plates are filter photometers.

 Infrared light transmission photometry

Main article: Infrared spectroscopy

Spectrophotometry in infrared light is mainly used to study structure of substances, as given groups give absorption at defined wavelengths. Measurement in aqueous solution is generally not possible, as water absorbs infrared light strongly in some wavelength ranges. Therefore, infrared spectroscopy is either performed in the gaseous phase (for volatile substances) or with the substances pressed into tablets together with salts that are transparent in the infrared range. Potassium bromide (KBr) is commonly used for this purpose. The substance to be tested is thoroughly mixed with specially purified KBr and pressed into a transparent tablet, that is placed in the beam of light. The analysis of the wavelength dependence is generally not done using a monochromator as it is in UV-Vis, but with the use of an interferometer. The interference pattern can be analyzed using a Fourier transform algorithm. In this way, the whole wavelength range can be analyzed simultaneously, saving time, and an interferometer is also less expensive than a monochromator. The light absorbed in the infrared region does not correspond to electronic excitation of the substance studied, but rather to different kinds of vibrational excitation. The vibrational excitations are characteristic of different groups in a molecule, that can in this way be identified. The infrared spectrum typically has very narrow absorption lines, which makes them unsuited for quantitative analysis but gives very detailed information about the molecules. The frequencies of the different modes of vibration varies with isotope, and therefore different isotopes give different peaks. This makes it possible also to study the isotopic composition of a sample with infrared spectrophotometry.

 Atomic absorption photometry

Main article: Atomic absorption spectroscopy

Atomic absorption photometers are photometers that measure the light from a very hot flame. The solution to be analyzed is injected into the flame at a constant, known rate. Metals in the solution are present in atomic form in the flame. The monochromatic light in this type of photometer is generated by a discharge lamp where the discharge takes place in a gas with the metal to be determined. The discharge then emits light with wavelengths corresponding to the spectral lines of the metal. A filter may be used to isolate one of the main spectral lines of the metal to be analyzed. The light is absorbed by the metal in the flame, and the absorption is used to determine the concentration of the metal in the original solution.

 See also

• Radiometry
• Raman spectroscopy
• Photodetector – A transducer capable of accepting an optical signal and producing an electrical signal containing the same information as in the optical signal.

Article partly based on the corresponding article in Swedish Wikipedia

 

Photometry (optics)

Photopic (black) and scotopic [1] (green) luminosity functions. The photopic includes the CIE 1931 standard [2] (solid), the Judd-Vos 1978 modified data [3] (dashed), and the Sharpe, Stockman, Jagla & Jägle 2005 data [4] (dotted). The horizontal axis is wavelength in nm.

Photometry is the science of the measurement of light, in terms of its perceived brightness to the human eye. It is distinct from radiometry, which is the science of measurement of radiant energy (including light) in terms of absolute power; rather, in photometry, the radiant power at each wavelength is weighted by a luminosity function (a.k.a. visual sensitivity function) that models human brightness sensitivity. Typically, this weighting function is the photopic sensitivity function, although the scotopic function—and others—may also be applied in the same way.

Contents   1 Photometry and the eye 2 Photometric quantities 2.1 Photometric versus radiometric quantities 2.2 Watts versus lumens 3 Photometric measurement techniques 4 Non-SI photometry units 4.1 Luminance 4.2 Illuminance 5 See also 6 External links 6.1 Photometry diagrams and applets

 Photometry and the eye

The human eye is not equally sensitive to all wavelengths of visible light. Photometry attempts to account for this by weighting the measured power at each wavelength with a factor that represents how sensitive the eye is at that wavelength. The standardized model of the eye's response to light as a function of wavelength is given by the luminosity function. Note that the eye has different responses as a function of wavelength when it is adapted to light conditions (photopic vision) and dark conditions (scotopic vision). Photometry is typically based on the eye's photopic response, and so photometric measurements may not accurately indicate the perceived brightness of sources in dim lighting conditions where colors are not discernible, such as under just moonlight or starlight.

 Photometric quantities

Many different units of measure are used for photometric measurements. People sometimes ask why there need to be so many different units, or ask for conversions between units that can't be converted (lumens and candelas, for example). We are familiar with the idea that the adjective "heavy" can refer to weight or density, which are fundamentally different things. Similarly, the adjective "bright" can refer to a light source which delivers a high luminous flux (measured in lumens), or to a light source which concentrates the luminous flux it has into a very narrow beam (candelas), or to a light source that is seen against a dark background. Because of the ways in which light propagates through three-dimensional space — spreading out, becoming concentrated, reflecting off shiny or matte surfaces — and because light consists of many different wavelengths, the number of fundamentally different kinds of light measurement that can be made is large, and so are the numbers of quantities and units that represent them.

SI photometry units

v • d • e

Quantity	Symbol	SI unit	Abbr.	Notes
Luminous energy	Qv	lumen second	lm·s	units are sometimes called talbots
Luminous flux	F	lumen (= cd·sr)	lm	also called luminous power
Luminous intensity	Iv	candela (= lm/sr)	cd	an SI base unit
Luminance	Lv	candela per square metre	cd/m2	units are sometimes called "nits"
Illuminance	Ev	lux (= lm/m2)	lx	Used for light incident on a surface
Luminous emittance	Mv	lux (= lm/m2)	lx	Used for light emitted from a surface
Luminous efficacy		lumen per watt	lm/W	ratio of luminous flux to radiant flux
SI • Photometry

 Photometric versus radiometric quantities

There are two parallel systems of quantities known as photometric and radiometric quantities. Every quantity in one system has an analogous quantity in the other system. Some examples of parallel quantities include:

• Luminance (photometric) and radiance (radiometric)
• Luminous flux (photometric) and radiant flux (radiometric)
• Luminous intensity (photometric) and radiant intensity (radiometric)

See chart for more. (full page)

In photometric quantities every wavelength is weighted according to how sensitive the human eye is to it, while radiometric quantities use unweighted absolute power. For example, the eye responds much more strongly to green light than to red, so a green source will have greater luminous flux than a red source with the same radiant flux would. Radiant energy outside the visible spectrum does not contribute to photometric quantities at all, so for example a 1000 watt space heater may put out a great deal of radiant flux (1000 watts, in fact), but as a light source it puts out very few lumens (because most of the energy is in the infrared, leaving only a dim red glow in the visible).

SI radiometry units

Quantity	Symbol	SI unit	Abbr.	Notes
Radiant energy	Q	joule	J	energy
Radiant flux	Φ	watt	W	radiant energy per unit time, also called radiant power
Radiant intensity	I	watt per steradian	W·sr−1	power per unit solid angle
Radiance	L	watt per steradian per square metre	W·sr−1·m−2	power per unit solid angle per unit projected source area.   called intensity in some other fields of study.
Irradiance	E, I	watt per square metre	W·m−2	power incident on a surface.   sometimes confusingly called "intensity".
Radiant exitance / Radiant emittance	M	watt per square metre	W·m−2	power emitted from a surface.
Radiosity	J or Jλ	watt per square metre	W·m−2	emitted plus reflected power leaving a surface
Spectral radiance	Lλ or Lν	watt per steradian per metre3 or   watt per steradian per square metre per hertz	W·sr−1·m−3 or   W·sr−1·m−2·Hz−1	commonly measured in W·sr−1·m−2·nm−1
Spectral irradiance	Eλ or Eν	watt per metre3 or watt per square metre per hertz	W·m−3 or W·m−2·Hz−1	commonly measured in W·m−2·nm−1

 Watts versus lumens

Watts are units of radiant flux while lumens are units of luminous flux. A comparison of the watt and the lumen illustrates the distinction between radiometric and photometric units.

The watt is a unit of power. We are accustomed to thinking of light bulbs in terms of power in watts. This power is not a measure of the amount of light output, but rather indicates how much energy the bulb will use. Because incandescent bulbs sold for "general service" all have fairly similar characteristics (same spectral power distribution), power consumption provides a rough guide to the light output of incandescent bulbs.

Watts can also be a direct measure of output. In a radiometric sense, an incandescent light bulb is about 80% efficient: 20% of the energy is lost (e.g. by conduction through the lamp base). The remainder is emitted as radiation, mostly in the infrared. Thus, a 60 watt light bulb emits a total radiant flux of about 45 watts. Incandescent bulbs are, in fact, sometimes used as heat sources (as in a chick incubator), but usually they are used for the purpose of providing light. As such, they are very inefficient, because most of the radiant energy they emit is invisible infrared. A compact fluorescent lamp can provide light comparable to a 60 watt incandescent while consuming as little as 15 watts of electricity.

The lumen is the photometric unit of light output. Although most consumers still think of light in terms of power consumed by the bulb, in the U.S. it has been a trade requirement for several decades that light bulb packaging give the output in lumens. The package of a 60 watt incandescent bulb indicates that it provides about 900 lumens, as does the package of the 15 watt compact fluorescent.

The lumen is defined as amount of light given into one steradian by a point source of one candela strength; while the candela, a base SI unit, is defined as the luminous intensity of a source of monochromatic radiation, of frequency 540 terahertz, and a radiant intensity of 1/683 watts per steradian. (540 THz corresponds to about 555 nanometres, the wavelength, in the green, to which the human eye is most sensitive. The number 1/683 was chosen to make the candela about equal to the standard candle, the unit which it superseded).

Combining these definitions, we see that 1/683 watt of 555 nanometre green light provides one lumen.

The relation between watts and lumens is not just a simple scaling factor. We know this already, because the 60 watt incandescent bulb and the 15 watt compact fluorescent can both provide 900 lumens.

The definition tells us that 1 watt of pure green 555 nm light is "worth" 683 lumens. It does not say anything about other wavelengths. Because lumens are photometric units, their relationship to watts depends on the wavelength according to how visible the wavelength is. Infrared and ultraviolet radiation, for example, are invisible and do not count. One watt of infrared radiation (which is where most of the radiation from an incandescent bulb falls) is worth zero lumens. Within the visible spectrum, wavelengths of light are weighted according to a function called the "photopic spectral luminous efficiency." According to this function, 700 nm red light is only about 4% as efficient as 555 nm green light. Thus, one watt of 700 nm red light is "worth" only 27 lumens.

Because of the summation over the visual portion of the EM spectrum that is part of this weighting, the unit of "lumen" is color-blind: there is no way to tell what color a lumen will appear. This is equivalent to evaluating groceries by number of bags: there is no information about the specific content, just a number that refers to the total weighted quantity.

 Photometric measurement techniques

Photometric measurement is based on photodetectors, devices (of several types) that produce an electric signal when exposed to light. Simple applications of this technology include switching luminaires on and off based on ambient light conditions, and light meters, used to measure the total amount of light incident on a point.

More complex forms of photometric measurement are used frequently within the lighting industry. Spherical photometers can be used to measure the directional luminous flux produced by lamps, and consist of a large-diameter globe with a lamp mounted at its center. A photocell rotates about the lamp in three axes, measuring the output of the lamp from all sides.

Luminaires (known to laypersons simply as light fixtures) are tested using goniophotometers and rotating mirror photometers, which keep the photocell stationary at a sufficient distance that the luminaire can be considered a point source. Rotating mirror photometers use a motorized system of mirrors to reflect light emanating from the luminaire in all directions to the distant photocell; goniophotometers use a rotating 2-axis table to change the orientation of the luminaire with respect to the photocell. In either case, luminous intensity is tabulated from this data and used in lighting design.

 Non-SI photometry units

 Luminance

• Footlambert
• Millilambert
• Stilb

 Illuminance

• Foot-candle
• Phot

 See also

• Reflectivity
• List of light sources
• Spectrometer
• Radiometer

 External links

• Realization of the Candela, the Lumen, and Other Photometric Units (nist.gov)

• Radiometry and photometry FAQ Professor Jim Palmer's Radiometry FAQ page (University of Arizona).

 Photometry diagrams and applets

• Diagram of relation between SI photometry units (anees.com)

• Diagrams and formulas for photometry and optics — A good-quality collection. (anees.com)

• Photometric demo (at page bottom) — 10/07: "coming soon" — (University of Barcelona)
• Visualization and calculation of photometric quantities — Java applet

Spectrum

The spectrum in a rainbow

A spectrum (plural spectra or spectrums^[1]) is a condition that is not limited to a specific set of values but can vary infinitely within a continuum. The word saw its first scientific use within the field of optics to describe the rainbow of colors in visible light when separated using a prism; it has since been applied by analogy to many fields other than 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.

In most modern usages of spectrum there is a unifying theme between extremes at either end. Some older usages of the word did not have a unifying theme, but they led to modern ones through a sequence of events set out below. Modern usages in mathematics did evolve from a unifying theme, but this may be difficult to recognize.

Contents   1 Origins 2 Modern meaning in the physical sciences 3 See also 3.1 Physical science 3.2 Social and medical sciences 3.3 Mathematics 4 References

 Origins

In Latin spectrum means "image" or "apparition", including the meaning "spectre". Spectral evidence is testimony about what was done by spectres of persons not present physically, or hearsay evidence about what ghosts or apparitions of Satan said. It was used to convict a number of persons of witchcraft at Salem, Massachusetts in the late 17th century.

 Modern meaning in the physical sciences

The spectrum of a star of spectral type K4III

In the 17th century the word spectrum was introduced into optics, referring to the range of colors observed when white light was dispersed through a prism. Soon the term referred to a plot of light intensity or power as a function of frequency or wavelength, also known as a spectral density.

The term spectrum was soon applied to other waves, such as sound waves, and now applies to any signal that can be decomposed into frequency components. A spectrum is a usually 2-dimensional plot, of a compound signal, depicting the components by another measure. Sometimes, the word spectrum refers to the compound signal itself, such as the "spectrum of visible light", a reference to those electromagnetic waves which are visible to the human eye. Looking at light through a prism separates visible light into its colors according to wavelength. It separates them according to its dispersion relation and a grating separates according to the grating equation and if massive particles are measured often their speed is measured. To get a spectrum, the measured function has to be transformed in their independent variable to frequencies and the dependent variable has to be reduced in regions, where the independent variable is stretched. For this imagine that the spectrum of pulse with a finite number of particles is measured on a film or a CCD. Assuming no particles are lost, any nonlinearity (compared to frequency) on the spectral separation concentrates particles at some points of the film. The same is true for taking a spectrum by scanning a monochromator with a fixed slit width. Violet at one end has the shortest wavelength and red at the other end has the longest wavelength of visible light. The colors in order are violet, blue, green, yellow, orange, red. As the wavelengths get bigger below the red visible light they become infrared, microwave, and radio. As the wavelengths get smaller above violet light, they become ultra-violet, x-ray, and gamma ray.

 See also

 Physical science

• Electromagnetic spectrum
  • Visible spectrum or optical spectrum, a subset of the electromagnetic spectrum
  • Emission spectrum observed in light
  • Absorption spectrum observed in light
• Energy spectrum of a collection of particles (particle physics)
• Frequency spectrum of a signal
• Mass spectrum chemical analysis of atoms and molecules
• Power spectrum of a signal
• Spectrogram
• Spectrometer

 Social and medical sciences

• Economic spectrum
• Political spectrum of opinion
• Spectrum disorder, in psychiatry

 Mathematics

• Spectrum (homotopy theory)
• Spectrum of a matrix, in linear algebra
• Spectrum of an operator, in functional analysis (a generalisation of the spectrum of a matrix)
• Spectrum of a ring, in commutative algebra
• Spectrum of a C*-algebra
• Spectrum of a theory, in mathematical logic
• Stone space of Boolean algebra

 References

1. ^ Dictionary.com. The American Heritage Dictionary of the English Language, Fourth Edition. Houghton Mifflin Company, 2004. (accessed: January 25, 2008).

Spectroscopy

Animation of the dispersion of light as it travels through a triangular prism

Spectroscopy was originally the study of the interaction between radiation and matter as a function of wavelength (λ). In fact, historically, spectroscopy referred to the use of visible light dispersed according to its wavelength, e.g. by a prism. Later the concept was expanded greatly to comprise any measurement of a quantity as function of either wavelength or frequency. Thus it also can refer to a response to an alternating field or varying frequency (ν). A further extension of the scope of the definition added energy (E) as a variable, once the very close relationship E = hν for photons was realized (h is the Planck constant). A plot of the response as a function of wavelength—or more commonly frequency—is referred to as a spectrum; see also spectral linewidth.

Spectrometry is the spectroscopic technique used to assess the concentration or amount of a given species. In those cases, the instrument that performs such measurements is a spectrometer or spectrograph.

Spectroscopy/spectrometry is often used in physical and analytical chemistry for the identification of substances through the spectrum emitted from or absorbed by them.

Spectroscopy/spectrometry is also heavily used in astronomy and remote sensing. Most large telescopes have spectrometers, which are used either to measure the chemical composition and physical properties of astronomical objects or to measure their velocities from the Doppler shift of their spectral lines.

Contents   1 Classification of methods 1.1 Nature of excitation measured 1.2 Measurement process 2 Common types 2.1 Absorption 2.2 Fluorescence 2.3 X-ray 2.4 Flame 2.5 Visible 2.6 Ultraviolet 2.7 Infrared 2.8 Near Infrared (NIR) 2.9 Raman 2.10 Coherent anti-Stokes Raman spectroscopy (CARS) 2.11 Nuclear magnetic resonance 2.12 Photoemission 2.13 Mössbauer 3 Other types 4 Background subtraction 5 Applications 6 See also 7 References 8 External links

 Classification of methods

 Nature of excitation measured

The type of spectroscopy depends on the physical quantity measured. Normally, the quantity that is measured is an intensity, either of energy absorbed or produced.

• Electromagnetic spectroscopy involves interactions of matter with electromagnetic radiation, such as light.
• Electron spectroscopy involves interactions with electron beams. Auger spectroscopy involves inducing the Auger effect with an electron beam. In this case the measurement typically involves the kinetic energy of the electron as variable.
• Acoustic spectroscopy involves the frequency of sound.
• Dielectric spectroscopy involves the frequency of an external electrical field
• Mechanical spectroscopy involves the frequency of an external mechanical stress, e.g. a torsion applied to a piece of material.

 Measurement process

Most spectroscopic methods are differentiated as either atomic or molecular based on whether or not they apply to atoms or molecules. Along with that distinction, they can be classified on the nature of their interaction:

• Absorption spectroscopy uses the range of the electromagnetic spectra in which a substance absorbs. This includes atomic absorption spectroscopy and various molecular techniques, such as infrared spectroscopy in that region and nuclear magnetic resonance (NMR) spectroscopy in the radio region.
• Emission spectroscopy uses the range of electromagnetic spectra in which a substance radiates (emits). The substance first must absorb energy. This energy can be from a variety of sources, which determines the name of the subsequent emission, like luminescence. Molecular luminescence techniques include spectrofluorimetry.
• Scattering spectroscopy measures the amount of light that a substance scatters at certain wavelengths, incident angles, and polarization angles. The scattering process is much faster than the absorption/emission process. One of the most useful applications of light scattering spectroscopy is Raman spectroscopy.

 Common types

 Absorption

Main article: Absorption spectroscopy

Absorption spectroscopy is a technique in which the power of a beam of light measured before and after interaction with a sample is compared. When performed with tunable diode laser, it is often referred to as Tunable diode laser absorption spectroscopy (TDLAS). It is also often combined with a modulation technique, most often wavelength modulation spectrometry (WMS) and occasionally frequency modulation spectrometry (FMS) in order to reduce the noise in the system.

 Fluorescence

Main article: Fluorescence spectroscopy

Fluorescence spectroscopy uses higher energy photons to excite a sample, which will then emit lower energy photons. This technique has become popular for its biochemical and medical applications, and can be used for confocal microscopy, fluorescence resonance energy transfer, and fluorescence lifetime imaging.

Spectrum of light from a fluorescent lamp showing prominent mercury peaks

 X-ray

Main articles: X-ray spectroscopy and X-ray crystallography

When X-rays of sufficient frequency (energy) interact with a substance, inner shell electrons in the atom are excited to outer empty orbitals, or they may be removed completely, ionizing the atom. The inner shell "hole" will then be filled by electrons from outer orbitals. The energy available in this de-excitation process is emitted as radiation (fluorescence) or will remove other less-bound electrons from the atom (Auger effect). The absorption or emission frequencies (energies) are characteristic of the specific atom. In addition, for a specific atom small frequency (energy) variations occur which are characteristic of the chemical bonding. With a suitable apparatus, these characteristic X-ray frequencies or Auger electron energies can be measured. X-ray absorption and emission spectroscopy is used in chemistry and material sciences to determine elemental composition and chemical bonding.

X-ray crystallography is a scattering process; crystalline materials scatter X-rays at well-defined angles. If the wavelength of the incident X-rays is known, this allows calculation of the distances between planes of atoms within the crystal. The intensities of the scattered X-rays give information about the atomic positions and allow the arrangement of the atoms within the crystal structure to be calculated.

 Flame

Liquid solution samples are aspirated into a burner or nebulizer/burner combination, desolvated, atomized, and sometimes excited to a higher energy electronic state. The use of a flame during analysis requires fuel and oxidant, typically in the form of gases. Common fuel gases used are acetylene (ethyne) or hydrogen. Common oxidant gases used are oxygen, air, or nitrous oxide. These methods are often capable of analyzing metallic element analytes in the part per million, billion, or possibly lower concentration ranges. Light detectors are needed to detect light with the analysis information coming from the flame.

• Atomic Emission Spectroscopy - This method uses flame excitation; atoms are excited from the heat of the flame to emit light. This method commonly uses a total consumption burner with a round burning outlet. A higher temperature flame than atomic absorption spectroscopy (AA) is typically used to produce excitation of analyte atoms. Since analyte atoms are excited by the heat of the flame, no special elemental lamps to shine into the flame are needed. A high resolution polychromator can be used to produce an emission intensity vs. wavelength spectrum over a range of wavelengths showing multiple element excitation lines, meaning multiple elements can be detected in one run. Alternatively, a monochromator can be set at one wavelength to concentrate on analysis of a single element at a certain emission line. Plasma emission spectroscopy is a more modern version of this method. See Flame emission spectroscopy for more details.
• Atomic absorption spectroscopy (often called AA) - This method commonly uses a pre-burner nebulizer (or nebulizing chamber) to create a sample mist and a slot-shaped burner which gives a longer pathlength flame. The temperature of the flame is low enough that the flame itself does not excite sample atoms from their ground state. The nebulizer and flame are used to desolvate and atomize the sample, but the excitation of the analyte atoms is done by the use of lamps shining through the flame at various wavelengths for each type of analyte. In AA, the amount of light absorbed after going through the flame determines the amount of analyte in the sample. A graphite furnace for heating the sample to desolvate and atomize is commonly used for greater sensitivity. The graphite furnace method can also analyze some solid or slurry samples. Because of its good sensitivity and selectivity, it is still a commonly used method of analysis for certain trace elements in aqueous (and other liquid) samples.
• Atomic Fluorescence Spectroscopy - This method commonly uses a burner with a round burning outlet. The flame is used to solvate and atomize the sample, but a lamp shines light at a specific wavelength into the flame to excite the analyte atoms in the flame. The atoms of certain elements can then fluoresce emitting light in a different direction. The intensity of this fluorescing light is used for quantifying the amount of analyte element in the sample. A graphite furnace can also be used for atomic fluorescence spectroscopy. This method is not as commonly used as atomic absorption or plasma emission spectroscopy.

Plasma Emission Spectroscopy In some ways similar to flame atomic emission spectroscopy, it has largely replaced it.

• Direct-current plasma (DCP)

A direct-current plasma (DCP) is created by an electrical discharge between two electrodes. A plasma support gas is necessary, and Ar is common. Samples can be deposited on one of the electrodes, or if conducting can make up one electrode.

• Glow discharge-optical emission spectrometry (GD-OES)

• Inductively coupled plasma-atomic emission spectrometry (ICP-AES)

• Laser Induced Breakdown Spectroscopy (LIBS) (LIBS), also called Laser-induced plasma spectrometry (LIPS)

• Microwave-induced plasma (MIP)

Spark or arc (emission) spectroscopy - is used for the analysis of metallic elements in solid samples. For non-conductive materials, a sample is ground with graphite powder to make it conductive. In traditional arc spectroscopy methods, a sample of the solid was commonly ground up and destroyed during analysis. An electric arc or spark is passed through the sample, heating the sample to a high temperature to excite the atoms in it. The excited analyte atoms glow emitting light at various wavelengths which could be detected by common spectroscopic methods. Since the conditions producing the arc emission typically are not controlled quantitatively, the analysis for the elements is qualitative. Nowadays, the spark sources with controlled discharges under an argon atmosphere allow that this method can be considered eminently quantitative, and its use is widely expanded worldwide through production control laboratories of foundries and steel mills.

 Visible

Many atoms emit or absorb visible light. In order to obtain a fine line spectrum, the atoms must be in a gas phase. This means that the substance has to be vaporised. The spectrum is studied in absorption or emission. Visible absorption spectroscopy is often combined with UV absorption spectroscopy in UV/Vis spectroscopy. Although this form may be uncommon as the human eye is a similar indicator, it still proves useful when distinguishing colours.

 Ultraviolet

All atoms absorb in the Ultraviolet (UV) region because these photons are energetic enough to excite outer electrons. If the frequency is high enough, photoionization takes place. UV spectroscopy is also used in quantifying protein and DNA concentration as well as the ratio of protein to DNA concentration in a solution. Several amino acids usually found in protein, such as tryptophan, absorb light in the 280 nm range and DNA absorbs light in the 260 nm range. For this reason, the ratio of 260/280 nm absorbance is a good general indicator of the relative purity of a solution in terms of these two macromolecules. Reasonable estimates of protein or DNA concentration can also be made this way using Beer's law.

 Infrared

Main article: Infrared spectroscopy

Infrared spectroscopy offers the possibility to measure different types of inter atomic bond vibrations at different frequencies. Especially in organic chemistry the analysis of IR absorption spectra shows what type of bonds are present in the sample. It is also an important method for analysing polymers and constituents like fillers, pigments and plasticizers.

 Near Infrared (NIR)

Main article: Near infrared spectroscopy

The near infrared NIR range, immediately beyond the visible wavelength range, is especially important for practical applications because of the much greater penetration depth of NIR radiation into the sample than in the case of mid IR spectroscopy range. This allows also large samples to be measured in each scan by NIR spectroscopy, and is currently employed for many practical applications such as: rapid grain analysis, medical diagnosis pharmaceuticals/medicines^[1], biotechnology, genomics analysis, proteomic analysis, interactomics research, inline textile monitoring, food analysis and chemical imaging/hyperspectral imaging of intact organisms^[2][3][4], plastics, textiles, insect detection, forensic lab application, crime detection, various military applications, and so on.

 Raman

Main article: Raman spectroscopy

Raman spectroscopy uses the inelastic scattering of light to analyse vibrational and rotational modes of molecules. The resulting 'fingerprints' are an aid to analysis.

 Coherent anti-Stokes Raman spectroscopy (CARS)

Main article: Coherent anti-Stokes Raman spectroscopy

CARS is a recent technique that has high sensitivity and powerful applications for in vivo spectroscopy and imaging^[5].

 Nuclear magnetic resonance

Main article: NMR spectroscopy

Main article: 2D-FT NMRI and Spectroscopy

Nuclear magnetic resonance spectroscopy analyzes the magnetic properties of certain atomic nuclei to determine different electronic local environments of hydrogen, carbon, or other atoms in an organic compound or other compound. This is used to help determine the structure of the compound.

 Photoemission

Main article: Photoemission

 Mössbauer

Transmission or conversion-electron (CEMS) modes of Mössbauer spectroscopy probe the properties of specific isotope nuclei in different atomic environments by analyzing the resonant absorption of characteristic energy gamma-rays known as the Mössbauer effect.

 Other types

Main article: List of materials analysis methods

There are many different types of materials analysis techniques under the broad heading of "spectroscopy", utilizing a wide variety of different approaches to probing material properties, such as absorbance, reflection, emission, scattering, thermal conductivity, and refractive index.

• Acoustic spectroscopy
• Auger Spectroscopy

A method used to study surfaces of materials on a micro-scale. It is often used in connection with electron microscopy.

• Cavity ring down spectroscopy
• Circular Dichroism spectroscopy
• Dielectric spectroscopy
• Dual polarisation interferometry

Measures the real and imaginary components of the complex refractive index

• Force spectroscopy
• Fourier transform spectroscopy

An efficient method for processing spectra data obtained using interferometers. Nearly all infrared spectroscopy (Such as FTIR) and Nuclear Magnetic Resonance (NMR) spectroscopy are based on Fourier transforms.

• Fourier transform infrared spectroscopy (FTIR)
• Hadron spectroscopy

Studies the energy/mass spectrum of hadrons according to spin, parity, and other particle properties. Baryon spectroscopy and meson spectroscopy are both types of hadron spectroscopy.

• Inelastic electron tunnelling spectroscopy (IETS)

Uses the changes in current due to inelastic electron-vibration interaction at specific energies which can also measure optically forbidden transitions.

• Inelastic neutron scattering

Like Raman spectroscopy, but with neutrons instead of photons.

• Laser Spectroscopy

Uses lasers^[6] and other types of coherent emission sources, such as optical parametric oscillators,^[7] for selective excitation of atomic or molecular species.

• • Ultra fast laser spectroscopy
• Mechanical spectroscopy

Involves interactions with macroscopic vibrations, such as phonons. An example is acoustic spectroscopy, involving sound waves.

• Neutron spin echo spectroscopy

Measures internal dynamics in proteins and other soft matter systems

• Nuclear magnetic resonance (NMR)
• Photoacoustic spectroscopy

Measures the sound waves produced upon the absorption of radiation.

• Photothermal spectroscopy

Measures heat evolved upon absorption of radiation.

• Raman optical activity spectroscopy

Exploits Raman scattering and optical activity effects to reveal detailed information on chiral centers in molecules.

• Terahertz spectroscopy

Uses wavelengths above infrared spectroscopy and below microwave or millimeter wave measurements.

• Time-resolved spectroscopy

Spectroscopy of matter in situations where the properties are changing with time.

• Thermal infrared spectroscopy

Measures thermal radiation emitted from materials and surfaces and is used to determine the type of bonds present in a sample as well as their lattice environment. The techniques are widely used by organic chemists, mineralogists, and planetary scientists.

 Background subtraction

Background subtraction is a term typically used in spectroscopy when one explains the process of acquiring a background radiation level (or ambient radiation level) and then makes an algorithmic adjustment to the data to obtain qualitative information about any deviations from the background, even when they are an order of magnitude less decipherable than the background itself.

Background subtraction can effect a number of statistical calculations (Continuum, Compton, Bremsstrahlung) leading to improved overall system performance.

 Applications

• Estimate weathered wood exposure times using Near infrared spectroscopy.^[8]

 See also

• Absorption cross section
• Astronomical spectroscopy
• Atomic spectroscopy
• Nuclear magnetic resonance
• 2D-FT NMRI and Spectroscopy
• Near infrared spectroscopy
• Coherent spectroscopy
• Cold vapour atomic fluorescence spectroscopy
• Deep-level transient spectroscopy
• EPR spectroscopy
• Gamma spectroscopy
• Kelvin probe force microscope
• Metamerism (color)
• Rigid rotor
• Rotational spectroscopy
• Saturated spectroscopy
• Scanning tunneling spectroscopy
• Scattering theory
• Spectral power distributions
• Spectral reflectance
• Spectrophotometry
• Spectroscopic notation
• Spectrum analysis
• The Unscrambler (CAMO Software)
• Vibrational spectroscopy
• Vibrational circular dichroism spectroscopy
• Joseph von Fraunhofer
• Robert Bunsen
• Gustav Kirchhoff

 References

1. ^ J. Dubois, G. Sando, E. N. Lewis, Near-Infrared Chemical Imaging, A Valuable Tool for the Pharmaceutical Industry, G.I.T. Laboratory Journal Europe, No. 1-2, 2007
2. ^ https://www.malvern.com/LabEng/products/sdi/bibliography/sdi_bibliography.htm E. N. Lewis, E. Lee and L. H. Kidder, Combining Imaging and Spectroscopy: Solving Problems with Near-Infrared Chemical Imaging. Microscopy Today, Volume 12, No. 6, 11/2004.
3. ^ Near Infrared Microspectroscopy, Fluorescence Microspectroscopy,Infrared Chemical Imaging and High Resolution Nuclear Magnetic Resonance Analysis of Soybean Seeds, Somatic Embryos and Single Cells., Baianu, I.C. et al. 2004., In Oil Extraction and Analysis., D. Luthria, Editor pp.241-273, AOCS Press., Champaign, IL.
4. ^ Single Cancer Cell Detection by Near Infrared Microspectroscopy, Infrared Chemical Imaging and Fluorescence Microspectroscopy.2004.I. C. Baianu, D. Costescu, N. E. Hofmann and S. S. Korban, q-bio/0407006 (July 2004)
5. ^ C.L. Evans and X.S. Xie.2008. Coherent Anti-Stokes Raman Scattering Microscopy: Chemical Imaging for Biology and Medicine., doi:10.1146/annurev.anchem.1.031207.112754 Annual Review of Analytical Chemistry, 1: 883-909.
6. ^ W. Demtroder, Laser Spectroscopy, 3rd Ed. (Springer, 2003).
7. ^ F. J. Duarte (Ed.),Tunable Laser Applications, 2nd Ed. (CRC, 2009) Chapter 2.
8. ^ "Using NIR Spectroscopy to Predict Weathered Wood Exposure Times". https://www.fpl.fs.fed.us/documnts/pdf2006/fpl_2006_wang002.pdf. 

 

 External links

• Spectroscopy links at the Open Directory Project
• Amateur spectroscopy links at the Open Directory Project
• History of Spectroscopy
• Chemometric Analysis for Spectroscopy
• The Science of Spectroscopy - supported by NASA, includes OpenSpectrum, a Wiki-based learning tool for spectroscopy that anyone can edit
• A Short Study of the Characteristics of two Lab Spectroscopes
• NIST government spectroscopy data
• Potentiodynamic Electrochemical Impedance Spectroscopy

 

Wavelength Wavelength of a sine wave, λ, can be measured between any two points with the same phase, such as between crests, or troughs, or corresponding zero crossings as shown. In physics, the wavelength of a sinusoidal wave is the spatial period of the wave – the distance over which the wave's shape repeats.[1] It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a characteristic of both traveling waves and standing waves.[2] Wavelength is commonly designated by the Greek letter lambda (λ). The concept can also be applied to periodic waves of non-sinusoidal shape.[1][3] The term wavelength is also sometimes applied to modulated waves, and to the sinusoidal envelopes of modulated waves or waves formed by interference of several sinusoids.[4]
Assuming a sinusoidal wave moving at a fixed wave speed, wavelength is inversely proportional to frequency: waves with higher frequencies have shorter wavelengths, and lower frequencies have longer wavelengths.[5]
Examples of wave-like phenomena are sound waves, light, and water waves. A sound wave is a periodic variation in air pressure, while in light and other electromagnetic radiation the strength of the electric and the magnetic field vary. Water waves are periodic variations in the height of a body of water. In a crystal lattice vibration, atomic positions vary periodically in both lattice position and time.
Wavelength is a measure of the distance between repetitions of a shape feature such as peaks, valleys, or zero-crossings, not a measure of how far any given particle moves. For example, in waves over deep water a particle in the water moves in a circle of the same diameter as the wave height, unrelated to wavelength.[6]
Contents  1 Sinusoidal waves 1.1 Standing waves 1.2 Mathematical representation 1.3 General media 1.3.1 Nonuniform media 1.3.2 Crystals 2 More general waveforms 2.1 Envelope waves 2.2 Wave packets 3 Interference and diffraction 3.1 Double-slit interference 3.2 Single-slit diffraction 3.3 Diffraction-limited resolution 4 Subwavelength 5 See also 6 References 7 External links //
 Sinusoidal waves In linear media, any wave pattern can be described in terms of the independent propagation of sinusoidal components.
The wavelength λ of a sinusoidal waveform traveling at constant speed v is given by:[7]
Refraction: when a plane wave encounters a medium in which it has a slower speed, the wavelength decreases, and the direction adjusts accordingly. where v is called the phase speed (magnitude of the phase velocity) of the wave and f is the wave's frequency.
In the case of electromagnetic radiation such as light in free space, the speed is the speed of light, about 3×108 m/s. For sound waves in air, the speed of sound is 343 m/s (1238 km/h) (at room temperature and atmospheric pressure). As an example, the wavelength of a 100 MHz electromagnetic (radio) wave is about: 3×108 m/s divided by 100×106 Hz = 3 metres.
Visible light ranges from deep red, roughly 700 nm, to violet, roughly 400 nm (430–750 THz) (for other examples, see electromagnetic spectrum). The wavelengths of sound frequencies audible to the human ear (20 Hz–20 kHz) are between approximately 17 m and 17 mm, respectively, assuming a typical speed of sound of about 343 m/s; the wavelengths in audible sound are much longer than those in visible light.
Frequency and wavelength can change independently, but only when the speed of the wave changes. For example, when light enters another medium, its speed and wavelength change while its frequency does not; this change of wavelength causes refraction, or a change in propagation direction of waves that encounter the interface between media at an angle.
Sinusoidal standing waves in a box that constrains the end points to be nodes will have an integer number of half wavelengths fitting in the box.
 Standing waves A standing wave (black) depicted as the sum of two propagating waves traveling in opposite directions (red and blue). A standing wave is an undulatory motion that stays in one place. A sinusoidal standing wave includes stationary points of no motion, called nodes, and the wavelength is twice the distance between nodes. The wavelength, period, and wave velocity are related as before, if the stationary wave is viewed as the sum of two traveling sinusoidal waves of oppositely directed velocities.[8]

 Mathematical representation Traveling sinusoidal waves are often represented mathematically in terms of their velocity v (in the x direction), frequency f and wavelength λ as:
where y is the value of the wave at any position x and time t, and A is the amplitude of the wave. They are also commonly expressed in terms of (radian) wavenumber k (2π times the reciprocal of wavelength) and angular frequency ω (2π times the frequency) as:
in which wavelength and wavenumber are related to velocity and frequency as:
or
Dispersion causes separation of colors when light is refracted by a prism. The relationship between ω and λ (or k) is called a dispersion relation. This is not generally a simple inverse relation because the wave velocity itself typically varies with frequency.[9]
Wavelength is decreased in a medium with higher refractive index. In the second form given above, the phase (kx − ωt) is often generalized to (k•r − ωt), by replacing the wavenumber k with a wave vector that specifies the direction and wavenumber of a plane wave in 3-space, parameterized by position vector r. In that case, the wavenumber k, the magnitude of k, is still in the same relationship with wavelength as shown above, with v being interpreted as scalar speed in the direction of the wave vector. The first form, using reciprocal wavelength in the phase, does not generalize as easily to a wave in an arbitrary direction.
Generalizations to sinusoids of other phases, and to complex exponentials, are also common; see plane wave. The typical convention of using the cosine phase instead of the sine phase when describing a wave is based on the fact that the cosine is the real part of the complex exponential in the wave

 General media The speed of a wave depends upon the medium in which it propagates. In particular, the speed of light in most media is lower than in vacuum, which means that the same frequency will correspond to a shorter wavelength in the medium than in vacuum. The wavelength in the medium is
Various local wavelengths on a crest-to-crest basis in an ocean wave approaching shore.[10] where λ0 is the wavelength in vacuum, and n is the refractive index of the medium. When wavelengths of electromagnetic radiation are quoted, the vacuum wavelength is usually intended unless the wavelength is specifically identified as the wavelength in some other medium. In acoustics, where a medium is essential for the waves to exist, the wavelength value is given for a specified medium.
In general, the refractive index is a function of wavelength. This variation of n with λ, called dispersion, causes different colors of light to be separated when light is refracted by a prism.

 Nonuniform media A sinusoidal wave in a nonuniform medium, with loss. As the wave slows down, the wavelength gets shorter and the amplitude increases; after a place of maximum response, the short wavelength is associated with a high loss and the wave dies out. Wavelength can be a useful concept even if the wave is not periodic in space. For example, in an ocean wave approaching shore, shown in the figure, the incoming wave undulates with a varying local wavelength that depends in part on the depth of the sea floor compared to the wave height. The analysis of the wave can be based upon comparison of the local wavelength with the local water depth.[10]
Waves that are sinusoidal in time but propagate through a medium whose properties vary with position (an inhomogeneous medium) may propagate at a velocity that varies with position, and as a result may not be sinusoidal in space. The analysis of differential equations of such systems is often done approximately, using the WKB method (also known as the Liouville–Green method). The method integrates phase through space using a local wavenumber, which can be interpreted as indicating a "local wavelength" of the solution as a function of time and space.[11][12] This method treats the system locally as if it were uniform with the local properties; in particular, the local wave velocity associated with a frequency is the only thing needed to estimate the corresponding local wavenumber or wavelength. In addition, the method computes a slowly changing amplitude to satisfy other constraints of the equations or of the physical system, such as for conservation of energy in the wave.

 Crystals A wave on a line of atoms can be interpreted according to a variety of wavelengths. Waves in crystalline solids are not continuous, because they are composed of vibrations of discrete particles arranged in a regular lattice. This produces aliasing because the same vibration can be considered to have a variety of different wavelengths, as shown in the figure.[13] Descriptions using more than one of these wavelengths are redundant; it is conventional to choose the longest wavelength that fits the phenomenon. The range of wavelengths sufficient to provide a description of all possible waves in a crystalline medium corresponds to the wave vectors confined to the Brillouin zone.[14]
This indeterminacy in wavelength in solids is important in the analysis of wave phenomena such as energy bands and lattice vibrations. It is mathematically equivalent to the aliasing of a signal that is sampled at discrete intervals.

 More general waveforms Wavelength of an irregular periodic waveform at a particular moment in time. The same λ separates any two similarly situated points in the waveform.[15] A wave moving in space is called a traveling wave. If the shape repeats itself, it is also a periodic wave.[15] At a fixed moment in time, a snapshot of the wave shows a repeating form in space, with characteristics such as peaks and troughs repeating at equal intervals. To an observer at a fixed location the amplitude appears to vary in time, and repeats itself with a certain period, for example T. If the spatial period of this wave is referred to as its wavelength, then during every period, one wavelength of the wave passes the observer. If the wave propagates with unchanging shape and the velocity in the medium is uniform, this period implies the wavelength is:
Near-periodic waves over shallow water have sharper crests and flatter troughs than those of a sinusoid. This duality of space and time is expressed mathematically by the fact that the wave's behavior does not depend independently on position x and time t, but rather on the combination of position and time x − vt. A wave's amplitude u is then expressed as u(x − vt) and in the case of a periodic function u with period λ, that is, u(x + λ − vt) = u(x − vt), the periodicity of u in space means that a snapshot of the wave at a given time t finds the wave varying periodically in space with period λ. In a similar fashion, this periodicity of u implies a periodicity in time as well: u(x − v(t + T)) = u(x − vt) using the relation vT = λ described above, so an observation of the wave at a fixed location x finds the wave undulating periodically in time with period T = λ/v.[15]
Traveling waves with non-sinusoidal wave shapes can occur in linear dispersionless media such as free space, but also may arise in nonlinear media under certain circumstances. For example, large-amplitude ocean waves with certain shapes can propagate unchanged, because of properties of the nonlinear surface-wave medium.[16] An example is the cnoidal wave, a periodic traveling wave named because it is described by the Jacobian elliptic function of m-th order, usually denoted as cn (x; m).[17]

 Envelope waves The term wavelength is also sometimes applied to the envelopes of waves, such as the traveling sinusoidal envelope patterns that result from the interference of two sinusoidal waves close in frequency; such envelope characterizations are used in illustrating the derivation of group velocity, the speed at which slow envelope variations propagate.[18][19]

 Wave packets A propagating wave packet; in general, the envelope of the wave packet moves at a different speed than the constituent waves.[20] Main article: Wave packet Localized wave packets, "bursts" of wave action where each wave packet travels as a unit, find application in many fields of physics; the notion of a wavelength also may be applied to these wave packets.[21] The wave packet has an envelope that describes the overall amplitude of the wave; within the envelope, the distance between adjacent peaks or troughs is sometimes called a local wavelength.[22][23] Using Fourier analysis, wave packets can be analyzed into infinite sums (or integrals) of sinusoidal waves of different wavenumbers or wavelengths.[24]
Louis de Broglie postulated that all particles with a specific value of momentum have a wavelength
where h is Planck's constant, and p is the momentum of the particle. This hypothesis was at the basis of quantum mechanics. Nowadays, this wavelength is called the de Broglie wavelength. For example, the electrons in a CRT display have a De Broglie wavelength of about 10−13 m. To prevent the wave function for such a particle being spread over all space, De Broglie proposed using wave packets to represent particles that are localized in space.[25] The spread of wavenumbers of sinusoids that add up to such a wave packet corresponds to an uncertainty in the particle's momentum, one aspect of the Heisenberg uncertainty principle.[24]

 Interference and diffraction
 Double-slit interference Main article: Interference Pattern of light intensity on a screen for light passing through two slits. The pattern is idealized: an observed intensity pattern is modified by diffraction. When sinusoidal waveforms add, they may reinforce each other (constructive interference) or cancel each other (destructive interference) depending upon their relative phase. This phenomena is used in the interferometer. A simple example is an experiment due to Young where light is passed through two slits.[26] As shown in the figure, light is passed through two slits and shines on a screen. The path of the light to a position on the screen is different for the two slits, and depends upon the angle θ the path makes with the screen. If we suppose the screen is far enough from the slits (that is, s is large compared to the slit separation d) then the paths are nearly parallel, and the path difference is simply d sin θ. Accordingly the condition for constructive interference is:[27]
where m is an integer, and for destructive interference is:
Thus, if the wavelength of the light is known, the slit separation can be determined from the interference pattern or fringes, and vice versa.
It should be noted that the effect of interference is to redistribute the light, so the energy contained in the light is not altered, just where it shows up.[28]

 Single-slit diffraction Main articles: Diffraction and Diffraction formalism The notion of path difference and constructive or destructive interference used above for the double-slit experiment applies as well to the display of a single slit of light intercepted on a screen. The main result of this interference is to spread out the light from the narrow slit into a broader image on the screen. This distribution of wave energy is called diffraction.
Two types of diffraction are distinguished, depending upon the separation between the source and the screen: Fraunhofer diffraction or far-field diffraction at large separations and Fresnel diffraction or near-field diffraction at close separations.
In the analysis of the single slit, the non-zero width of the slit is taken into account, and each point in the aperture is taken as the source of one contribution to the beam of light (Huygen's wavelets). On the screen, the light arriving from each position within the slit has a different path length, albeit possibly a very small difference. Consequently, interference occurs.
In the Fraunhofer diffraction pattern sufficiently far from a single slit, within a small-angle approximation, the intensity spread S is related to position x via a squared sinc function:[29]
 with  where L is the slit width, R is the distance of the pattern (on the screen) from the slit, and λ is the wavelength of light used. The function S has zeros where u is a non-zero integer, where are at x values at a separation proportion to wavelength.

 Diffraction-limited resolution Main articles: Angular resolution and Diffraction-limited system Diffraction is the fundamental limitation on the resolving power of optical instruments, such as telescopes (including radiotelescopes) and microscopes.[30] For a circular aperture, the diffraction-limited image spot is known as an Airy disk; the distance x in the single-slit diffraction formula is replaced by radial distance r and the sine is replaced by 2J1, where J1 is a first order Bessel function.[31]
The resolvable spatial size of objects viewed through a microscope is limited according to the Rayleigh criterion, the radius to the first null of the Airy disk, to a size proportional to the wavelength of the light used, and depending on the numerical aperture:[32]
where the numerical aperture is defined as for θ being the half-angle of the cone of rays accepted by the microscope objective.
The angular size of the central bright portion (radius to first null of the Airy disk) of the image diffracted by a circular aperture, a measure most commonly used for telescopes and cameras, is:[33]
where λ is the wavelength of the waves that are focused for imaging, D the entrance pupil diameter of the imaging system, in the same units, and the angular resolution δ is in radians.
As with other diffraction patterns, the pattern scales in proportion to wavelength, so shorter wavelengths can lead to higher resolution.

 Subwavelength The term subwavelength is used to describe an object having one or more dimensions smaller than the length of the wave with which the object interacts. For example, the term subwavelength-diameter optical fibre means an optical fibre whose diameter is less than the wavelength of light propagating through it.
A subwavelength particle is a particle smaller than the wavelength of light with which it interacts (see Rayleigh scattering). Subwavelength apertures are holes smaller than the wavelength of light propagating through them.
Subwavelength may also refer to a phenomenon involving subwavelength objects; for example, subwavelength imaging.

 See also Emission spectrum Fraunhofer lines – dark lines in the solar spectrum, traditionally used as standard optical wavelength references Spectral line Spectrum Spectrum analysis
 References ^ a b Hecht, Eugene (1987). Optics (2nd ed.). Addison Wesley. pp. 15–16. ISBN 0-201-11609-X.  ^ Raymond A. Serway, John W. Jewett. Principles of physics (4th ed.). Cengage Learning. p. 404, 440. ISBN 053449143X. https://books.google.com/books?id=1DZz341Pp50C&pg=PA404.  ^ Brian Hilton Flowers (2000). "§21.2 Periodic functions". An introduction to numerical methods in C++ (2nd ed.). Cambridge University Press. p. 473. ISBN 0198506937. https://books.google.com/books?id=weYj75E_t6MC&pg=RA1-PA473.  ^ Keqian Zhang and Dejie Li (2007). Electromagnetic Theory for Microwaves and Optoelectronics. Springer,. p. 533. ISBN 9783540742951. https://books.google.com/books?id=3Da7MvRZTlAC&pg=PA533&dq=wavelength+modulated-wave+envelope&as_brr=3&ei=8GFZSsXdNJTklASShfGrBw.  ^ Theo Koupelis and Karl F. Kuhn (2007). In Quest of the Universe. Jones & Bartlett Publishers. ISBN 0763743879. https://books.google.com/books?id=WwKjznJ9Kq0C&pg=PA102&dq=wavelength+lambda+light+sound+frequency+wave+speed&lr=&as_brr=3&ei=nfIpSazAMIzukgSP04nODg.  ^ Paul R Pinet (2008). Invitation to Oceanography (5th ed.). Jones & Bartlett Publishers. p. 237. ISBN 0763759937. https://books.google.com/books?id=6TCm8Xy-sLUC&pg=PA237.  ^ David C. Cassidy, Gerald James Holton, Floyd James Rutherford (2002). Understanding physics. Birkhäuser. pp. 339 ff. ISBN 0387987568. https://books.google.com/books?id=rpQo7f9F1xUC&pg=PA340.  ^ John Avison (1999). The World of Physics. Nelson Thornes. p. 460. ISBN 9780174387336. https://books.google.com/books?id=DojwZzKAvN8C&pg=PA460&dq="standing+wave"+wavelength&lr=&as_brr=3&ei=CDFMStC9JZDOlQTtzqgW.  ^ John A. Adam (2003). Mathematics in nature. Princeton University Press. p. 148. ISBN 0691114293. https://books.google.com/books?id=2gO2sBp4ipQC&pg=PA148. "The relation between the frequency of a wave and its wavelength λ … is referred to as a dispersion relation."  ^ a b Paul R Pinet. op. cit.. p. 242. ISBN 0763759937. https://books.google.com/books?id=6TCm8Xy-sLUC&pg=PA242.  ^ Bishwanath Chakraborty. Principles of Plasma Mechanics. New Age International. p. 454. ISBN 9788122414462. https://books.google.com/books?id=_MIdEiKqdawC&pg=PA454&dq=wkb+local-wavelength&lr=&as_brr=0&ei=ZHZASqOwLY7skwTuodyLDw.  ^ Jeffrey A. Hogan and Joseph D. Lakey (2005). Time-frequency and time-scale methods: adaptive decompositions, uncertainty principles, and sampling. Birkhäuser. p. 348. ISBN 9780817642761. https://books.google.com/books?id=YOf0SRzxz3gC&pg=PA348&dq=wkb+local-wavelength&lr=&as_brr=3&ei=oHhASubOH4SkkASI4ciEDw.  ^ See Figure 4.20 in A. Putnis (1992). Introduction to mineral sciences. Cambridge University Press. p. 97. ISBN 0521429471. https://books.google.com/books?id=yMGzmOqYescC&pg=PA97.  and Figure 2.3 in Martin T. Dove (1993). Introduction to lattice dynamics (4th ed.). Cambridge University Press. p. 22. ISBN 0521392934. https://books.google.com/books?id=vM50l2Vf7HgC&pg=PA22.  ^ Manijeh Razeghi (2006). Fundamentals of solid state engineering (2nd ed.). Birkhäuser. pp. 165 ff. ISBN 0387281525. https://books.google.com/books?id=6x07E9PSzr8C&pg=PA165.  ^ a b c Alexander McPherson (2009). "Waves and their properties". Introduction to Macromolecular Crystallography (2 ed.). Wiley. p. 77. ISBN 0470185902. https://books.google.com/books?id=o7sXm2GSr9IC&pg=PA77.  ^ Ken'ichi Okamoto (2001). Global environment remote sensing. IOS Press. p. 263. ISBN 9781586031015. https://books.google.com/books?id=tXQy5JdQyZoC&pg=PA263&dq=wave-length++non-sinusoidal&lr=&as_brr=3&ei=g1kwSsTyDYzqzATx06ydDg.  ^ Roger Grimshaw (2007). "Solitary waves propagating over variable topography". in Anjan Kundu. Tsunami and Nonlinear Waves. Springer. pp. 52 ff. ISBN 3540712550. https://books.google.com/books?id=2Dtgq-1CGWIC&pg=PA52.  ^ Mark W. Denny (1995). Air and Water: The Biology and Physics of Life's Media. Princeton University Press. p. 289. ISBN 9780691025186. https://books.google.com/books?id=XjNS6v7q130C&pg=PA289&dq=envelope+wavelength+group-velocity&lr=&as_drrb_is=q&as_minm_is=0&as_miny_is=&as_maxm_is=0&as_maxy_is=&as_brr=3&ei=h_FOSpTVBYrglASAr-TLAg.  ^ W. P. Graebel (2007). Advanced Fluid Mechanics. Academic Press. p. 124. ISBN 9780123708854. https://books.google.com/books?id=SH9ELP0Re4oC&pg=PA124&dq=envelope+wavelength+group-velocity&lr=&as_drrb_is=q&as_minm_is=0&as_miny_is=&as_maxm_is=0&as_maxy_is=&as_brr=3&ei=h_FOSpTVBYrglASAr-TLAg.  ^ A. T. Fromhold (1991). "Wave packet solutions". Quantum Mechanics for Applied Physics and Engineering (Reprint of Academic Press 1981 ed.). Courier Dover Publications. pp. 59 ff. ISBN 0486667413. https://books.google.com/books?id=3SOwc6npkIwC&pg=PA59. "(p. 61) …the individual waves move more slowly than the packet and therefore pass back through the packet as it advances"  ^ Paul A. LaViolette (2003). Subquantum Kinetics: A Systems Approach to Physics and Cosmology. Starlane Publications. p. 80. ISBN 9780964202559. https://books.google.com/books?id=8HQJAvA1EqkC&pg=PA80&dq=wave-packet-wavelength+de-Broglie-wavelength&as_brr=3&ei=rn5ZStKTKpOilQSPhLmtDQ.  ^ Peter R. Holland (1995). The Quantum Theory of Motion: An Account of the de Broglie–Bohm Causal Interpretation of Quantum Mechanics. Cambridge University Press. p. 160. ISBN 9780521485432. https://books.google.com/books?id=BsEfVBzToRMC&pg=PA160&dq=wave-packet+local-wavelength&ei=4OhOSsbmNo32kASKyc31Ag.  ^ Jeffery Cooper (1998). Introduction to partial differential equations with MATLAB. Springer. p. 272. ISBN 0817639675. https://books.google.com/books?id=l0g2BcxOJVIC&pg=PA272. "The local wavelength λ of a dispersing wave is twice the distance between two successive zeros.…the local wave length and the local wave number k are related by k = 2π / λ."  ^ a b See, for example, Figs. 2.8 – 2.10 in Joy Manners (2000). "Heisenberg's uncertainty principle". Quantum Physics: An Introduction. CRC Press. pp. 53–56. ISBN 9780750307208. https://books.google.com/books?id=LkDQV7PNJOMC&pg=PA54&dq=wave-packet+wavelengths&lr=&as_drrb_is=q&as_minm_is=0&as_miny_is=&as_maxm_is=0&as_maxy_is=&as_brr=0&ei=UtpKSsvVH4WWkgTQ0om_Cw.  ^ Ming Chiang Li (1980). "Electron Interference". in L. Marton & Claire Marton. Advances in Electronics and Electron Physics. 53. Academic Press. p. 271. ISBN 0120146533. https://books.google.com/books?id=g5q6tZRwUu4C&pg=PA271.  ^ Greenfield Sluder and David E. Wolf (2007). "IV. Young's Experiment: Two-Slit Interference". Digital microscopy (3rd ed.). Academic Press. p. 15. ISBN 0123740258. https://books.google.com/books?id=H--zxc_N-jMC&pg=PA15.  ^ Halliday, Resnick, Walker (2008). "§35-4 Young's interference experiment". Fundamentals of Physics (Extended 8th ed.). Wiley-India. p. 965. ISBN 8126514426. https://books.google.com/books?id=RVCE4EUjDCgC&pg=PT965.  ^ Douglas B. Murphy (2002). Fundamentals of light microscopy and electronic imaging. Wiley/IEEE. p. 64. ISBN 047123429X. https://books.google.com/books?id=UFgdjxTULJMC&pg=PA64.  ^ John C. Stover (1995). Optical scattering: measurement and analysis (2nd ed.). SPIE Press. p. 64. ISBN 9780819419347. https://books.google.com/books?id=ot0tjJL72uUC&pg=PA65&dq=single-slit+diffraction+sinc-function&lr=&as_brr=3&ei=jgxkSu5jkMqQBOqKgLEO.  ^ Graham Saxby (2002). "Diffraction limitation". The science of imaging. CRC Press. p. 57. ISBN 075030734X. https://books.google.com/books?id=e5mC5TXlBw8C&pg=PA57.  ^ Grant R. Fowles (1989). Introduction to Modern Optics. Courier Dover Publications. p. 117–120. ISBN 9780486659572. https://books.google.com/books?id=SL1n9TuJ5YMC&pg=PA119&dq=Airy-disk+Bessel+slit+diffraction+sin&as_brr=3&ei=JLdeSpyzIYLckATAvMC-Bg.  ^ James B. Pawley (1995). Handbook of biological confocal microscopy (2nd ed.). Springer. p. 112. ISBN 9780306448263. https://books.google.com/books?id=16Ft5k8RC-AC&pg=PA112.  ^ Ray N. Wilson (2004). Reflecting Telescope Optics I: Basic Design Theory and Its Historical Development. Springer. p. 302. ISBN 9783540401063. https://books.google.com/books?id=PuN7l2A2uzQC&pg=PA302&dq=telescope+diffraction-limited+resolution+sinc&as_brr=3&ei=sY1dSuL1KJ7kkQTvwrHwAg. 
 External links Conversion: Wavelength to Frequency and vice versa - Sound waves and radio waves Teaching resource for 14-16yrs on sound including wavelength The visible electromagnetic spectrum displayed in web colors with according wavelengths