Misplaced Pages

#752247

66-477: A spectrometer is used in spectroscopy for producing spectral lines and measuring their wavelengths and intensities. Spectrometers may operate over a wide range of non-optical wavelengths, from gamma rays and X-rays into the far infrared . If the instrument is designed to measure the spectrum on an absolute scale rather than a relative one, then it is typically called a spectrophotometer . The majority of spectrophotometers are used in spectral regions near

132-450: A diffraction grating , a movable slit , and some kind of photodetector , all automated and controlled by a computer . Recent advances have seen increasing reliance of computational algorithms in a range of miniaturised spectrometers without diffraction gratings, for example, through the use of quantum dot-based filter arrays on to a CCD chip or a series of photodetectors realised on a single nanostructure. Joseph von Fraunhofer developed

198-459: A time-of-flight mass spectrometer . When a fast charged particle (charge q , mass m ) enters a constant magnetic field B at right angles, it is deflected into a circular path of radius r , due to the Lorentz force . The momentum p of the particle is then given by where m and v are mass and velocity of the particle. The focusing principle of the oldest and simplest magnetic spectrometer,

264-531: A camera in place of the viewing tube. In recent years, the electronic circuits built around the photomultiplier tube have replaced the camera, allowing real-time spectrographic analysis with far greater accuracy. Arrays of photosensors are also used in place of film in spectrographic systems. Such spectral analysis, or spectroscopy, has become an important scientific tool for analyzing the composition of unknown material and for studying astronomical phenomena and testing astronomical theories. In modern spectrographs in

330-405: A chemical explanation of stellar spectra , including Fraunhofer lines . When a material is heated to incandescence it emits light that is characteristic of the atomic makeup of the material. Particular light frequencies give rise to sharply defined bands on the scale which can be thought of as fingerprints. For example, the element sodium has a very characteristic double yellow band known as

396-413: A communications signal, for instance, and its information only travels at the group velocity rate, even though it consists of wavefronts advancing at a faster rate (the phase velocity). It is possible to calculate the group velocity from the refractive-index curve n ( ω ) or more directly from the wavenumber k = ωn / c , where ω is the radian frequency ω  = 2 πf . Whereas one expression for

462-404: A function of frequency, leading to attenuation distortion ; this is not dispersion, although sometimes reflections at closely spaced impedance boundaries (e.g. crimped segments in a cable) can produce signal distortion which further aggravates inconsistent transit time as observed across signal bandwidth. The most familiar example of dispersion is probably a rainbow , in which dispersion causes

528-451: A given gemstone is a function of the gemstone's facet angles, the polish quality, the lighting environment, the material's refractive index, the saturation of color, and the orientation of the viewer relative to the gemstone. In photographic and microscopic lenses, dispersion causes chromatic aberration , which causes the different colors in the image not to overlap properly. Various techniques have been developed to counteract this, such as

594-468: A higher refractive index, will be bent more strongly than red light, resulting in the well-known rainbow pattern. Beyond simply describing a change in the phase velocity over wavelength, a more serious consequence of dispersion in many applications is termed group-velocity dispersion (GVD). While phase velocity v is defined as v = c / n , this describes only one frequency component. When different frequency components are combined, as when considering

660-415: A negatively chirped signal in the acoustic domain is that of an approaching train hitting deformities on a welded track. The sound caused by the train itself is impulsive and travels much faster in the metal tracks than in air, so that the train can be heard well before it arrives. However, from afar it is not heard as causing impulses, but leads to a distinctive descending chirp, amidst reverberation caused by

726-418: A net negative dispersion. Waveguides are highly dispersive due to their geometry (rather than just to their material composition). Optical fibers are a sort of waveguide for optical frequencies (light) widely used in modern telecommunications systems. The rate at which data can be transported on a single fiber is limited by pulse broadening due to chromatic dispersion among other phenomena. In general, for

SECTION 10

#1732859183753

792-458: A result of polarization mode dispersion (since there are still two polarization modes). These are not examples of chromatic dispersion, as they are not dependent on the wavelength or bandwidth of the pulses propagated. When a broad range of frequencies (a broad bandwidth) is present in a single wavepacket, such as in an ultrashort pulse or a chirped pulse or other forms of spread spectrum transmission, it may not be accurate to approximate

858-405: A signal or a pulse, one is often more interested in the group velocity , which describes the speed at which a pulse or information superimposed on a wave (modulation) propagates. In the accompanying animation, it can be seen that the wave itself (orange-brown) travels at a phase velocity much faster than the speed of the envelope (black), which corresponds to the group velocity. This pulse might be

924-452: A slit is used and a CCD-chip records the spectrum. Both gratings have a wide spacing, and one is blazed so that only the first order is visible and the other is blazed with many higher orders visible, so a very fine spectrum is presented to the CCD. In conventional spectrographs, a slit is inserted into the beam to limit the image extent in the dispersion direction. A slitless spectrograph omits

990-473: A spectrum. A mass spectrometer measures the spectrum of the masses of the atoms or molecules present in a gas. The first spectrometers were used to split light into an array of separate colors. Spectrometers were developed in early studies of physics , astronomy , and chemistry . The capability of spectroscopy to determine chemical composition drove its advancement and continues to be one of its primary uses. Spectrometers are used in astronomy to analyze

1056-402: A waveguide mode with an angular frequency ω ( β ) at a propagation constant β (so that the electromagnetic fields in the propagation direction z oscillate proportional to e ), the group-velocity dispersion parameter D is defined as where λ  = 2 π c / ω is the vacuum wavelength, and v g  =  dω / dβ is the group velocity. This formula generalizes the one in

1122-411: Is a closely related electronic device. Spectrometers are used in many fields. For example, they are used in astronomy to analyze the radiation from objects and deduce their chemical composition. The spectrometer uses a prism or a grating to spread the light into a spectrum. This allows astronomers to detect many of the chemical elements by their characteristic spectral lines. These lines are named for

1188-464: Is a property of telecommunication signals along transmission lines (such as microwaves in coaxial cable ) or the pulses of light in optical fiber . In optics, one important and familiar consequence of dispersion is the change in the angle of refraction of different colors of light, as seen in the spectrum produced by a dispersive prism and in chromatic aberration of lenses. Design of compound achromatic lenses , in which chromatic aberration

1254-429: Is applied through a high voltage on the surface which vaporizes particles into a plasma. The particles and ions then emit radiation that is measured by detectors (photomultiplier tubes) at different characteristic wavelengths. Some forms of spectroscopy involve analysis of electron energy rather than photon energy. X-ray photoelectron spectroscopy is an example. A mass spectrometer is an analytical instrument that

1320-485: Is important. Spectrometer A spectrometer ( / s p ɛ k ˈ t r ɒ m ɪ t ər / ) is a scientific instrument used to separate and measure spectral components of a physical phenomenon. Spectrometer is a broad term often used to describe instruments that measure a continuous variable of a phenomenon where the spectral components are somehow mixed. In visible light a spectrometer can separate white light and measure individual narrow bands of color, called

1386-572: Is largely cancelled, uses a quantification of a glass's dispersion given by its Abbe number V , where lower Abbe numbers correspond to greater dispersion over the visible spectrum . In some applications such as telecommunications, the absolute phase of a wave is often not important but only the propagation of wave packets or "pulses"; in that case one is interested only in variations of group velocity with frequency, so-called group-velocity dispersion . All common transmission media also vary in attenuation (normalized to transmission length) as

SECTION 20

#1732859183753

1452-441: Is much larger than atomic dimensions, because the dielectric kernel dies out at macroscopic distances. Nevertheless, it can result in non-negligible macroscopic effects, particularly in conducting media such as metals , electrolytes and plasmas . Spatial dispersion also plays role in optical activity and Doppler broadening , as well as in the theory of metamaterials . In the technical terminology of gemology , dispersion

1518-474: Is the column density of free electrons ( total electron content ) – i.e. the number density of electrons n e integrated along the path traveled by the photon from the pulsar to the Earth ;– and is given by with units of parsecs per cubic centimetre (1 pc/cm = 30.857 × 10  m ). Typically for astronomical observations, this delay cannot be measured directly, since

1584-451: Is the difference in the refractive index of a material at the B and G (686.7  nm and 430.8 nm) or C and F (656.3 nm and 486.1 nm) Fraunhofer wavelengths , and is meant to express the degree to which a prism cut from the gemstone demonstrates "fire". Fire is a colloquial term used by gemologists to describe a gemstone's dispersive nature or lack thereof. Dispersion is a material property. The amount of fire demonstrated by

1650-596: Is the separation of white light into a color spectrum by a prism . From Snell's law it can be seen that the angle of refraction of light in a prism depends on the refractive index of the prism material. Since that refractive index varies with wavelength, it follows that the angle that the light is refracted by will also vary with wavelength, causing an angular separation of the colors known as angular dispersion . For visible light, refraction indices n of most transparent materials (e.g., air, glasses) decrease with increasing wavelength λ : or generally, In this case,

1716-446: Is to use soliton pulses in the regime of negative dispersion, a form of optical pulse which uses a nonlinear optical effect to self-maintain its shape. Solitons have the practical problem, however, that they require a certain power level to be maintained in the pulse for the nonlinear effect to be of the correct strength. Instead, the solution that is currently used in practice is to perform dispersion compensation, typically by matching

1782-689: Is too high, a group of pulses representing a bit-stream will spread in time and merge, rendering the bit-stream unintelligible. This limits the length of fiber that a signal can be sent down without regeneration. One possible answer to this problem is to send signals down the optical fibre at a wavelength where the GVD is zero (e.g., around 1.3–1.5 μm in silica fibres ), so pulses at this wavelength suffer minimal spreading from dispersion. In practice, however, this approach causes more problems than it solves because zero GVD unacceptably amplifies other nonlinear effects (such as four-wave mixing ). Another possible option

1848-412: Is used to construct spectrometers and spectroradiometers . However, in lenses, dispersion causes chromatic aberration , an undesired effect that may degrade images in microscopes, telescopes, and photographic objectives. The phase velocity v of a wave in a given uniform medium is given by where c is the speed of light in vacuum, and n is the refractive index of the medium. In general,

1914-414: Is used to identify the amount and type of chemicals present in a sample by measuring the mass-to-charge ratio and abundance of gas-phase ions . The energy spectrum of particles of known mass can also be measured by determining the time of flight between two detectors (and hence, the velocity) in a time-of-flight spectrometer . Alternatively, if the particle-energy is known, masses can be determined in

1980-468: Is used to refer to optics specifically, as opposed to wave propagation in general. A medium having this common property may be termed a dispersive medium . Although the term is used in the field of optics to describe light and other electromagnetic waves , dispersion in the same sense can apply to any sort of wave motion such as acoustic dispersion in the case of sound and seismic waves, and in gravity waves (ocean waves). Within optics, dispersion

2046-435: The kernel f i k {\displaystyle f_{ik}} is dielectric response (susceptibility); its indices make it in general a tensor to account for the anisotropy of the medium. Spatial dispersion is negligible in most macroscopic cases, where the scale of variation of E k ( t − τ , r ′ ) {\displaystyle E_{k}(t-\tau ,r')}

Optical spectrometer - Misplaced Pages Continue

2112-407: The resolution of an instrument tells us how well two close-lying energies (or wavelengths, or frequencies, or masses) can be resolved. Generally, for an instrument with mechanical slits, higher resolution will mean lower intensity. Dispersion (optics) Dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency. Sometimes the term chromatic dispersion

2178-484: The Sodium D-lines at 588.9950 and 589.5924 nanometers, the color of which will be familiar to anyone who has seen a low pressure sodium vapor lamp . In the original spectroscope design in the early 19th century, light entered a slit and a collimating lens transformed the light into a thin beam of parallel rays. The light then passed through a prism (in hand-held spectroscopes, usually an Amici prism ) that refracted

2244-445: The UV, visible, and near-IR spectral ranges, the spectrum is generally given in the form of photon number per unit wavelength (nm or μm), wavenumber (μm, cm), frequency (THz), or energy (eV), with the units indicated by the abscissa . In the mid- to far-IR, spectra are typically expressed in units of Watts per unit wavelength (μm) or wavenumber (cm). In many cases, the spectrum is displayed with

2310-401: The beam into a spectrum because different wavelengths were refracted different amounts due to dispersion . This image was then viewed through a tube with a scale that was transposed upon the spectral image, enabling its direct measurement. With the development of photographic film , the more accurate spectrograph was created. It was based on the same principle as the spectroscope, but it had

2376-410: The change in refractive index with optical frequency. However, in a waveguide there is also the phenomenon of waveguide dispersion , in which case a wave's phase velocity in a structure depends on its frequency simply due to the structure's geometry. More generally, "waveguide" dispersion can occur for waves propagating through any inhomogeneous structure (e.g., a photonic crystal ), whether or not

2442-419: The chemical composition of stars and planets , and spectrometers gather data on the origin of the universe . Examples of spectrometers are devices that separate particles , atoms , and molecules by their mass , momentum , or energy . These types of spectrometers are used in chemical analysis and particle physics . Optical spectrometers (often simply called "spectrometers"), in particular, show

2508-421: The complexity of the vibrational modes of the track. Group-velocity dispersion can be heard in that the volume of the sounds stays audible for a surprisingly long time, up to several seconds. The result of GVD, whether negative or positive, is ultimately temporal spreading of the pulse. This makes dispersion management extremely important in optical communications systems based on optical fiber, since if dispersion

2574-413: The components of each pulse emitted at higher radio frequencies arrive before those emitted at lower frequencies. This dispersion occurs because of the ionized component of the interstellar medium , mainly the free electrons, which make the group velocity frequency-dependent. The extra delay added at a frequency ν is where the dispersion constant k DM is given by and the dispersion measure (DM)

2640-443: The different-frequency components within the pulse travel at different velocities. Group-velocity dispersion is quantified as the derivative of the reciprocal of the group velocity with respect to angular frequency , which results in group-velocity dispersion  =  d k / dω . If a light pulse is propagated through a material with positive group-velocity dispersion, then the shorter-wavelength components travel slower than

2706-415: The dispersion by a constant over the entire bandwidth, and more complex calculations are required to compute effects such as pulse spreading. In particular, the dispersion parameter D defined above is obtained from only one derivative of the group velocity. Higher derivatives are known as higher-order dispersion . These terms are simply a Taylor series expansion of the dispersion relation β ( ω ) of

Optical spectrometer - Misplaced Pages Continue

2772-605: The duration of the pulses emitted by the laser. A pair of prisms can be arranged to produce net negative dispersion, which can be used to balance the usually positive dispersion of the laser medium. Diffraction gratings can also be used to produce dispersive effects; these are often used in high-power laser amplifier systems. Recently, an alternative to prisms and gratings has been developed: chirped mirrors . These dielectric mirrors are coated so that different wavelengths have different penetration lengths, and therefore different group delays. The coating layers can be tailored to achieve

2838-570: The elements which cause them, such as the hydrogen alpha , beta, and gamma lines. A glowing object will show bright spectral lines. Dark lines are made by absorption, for example by light passing through a gas cloud, and these absorption lines can also identify chemical compounds. Much of our knowledge of the chemical makeup of the universe comes from spectra. Spectroscopes are often used in astronomy and some branches of chemistry . Early spectroscopes were simply prisms with graduations marking wavelengths of light. Modern spectroscopes generally use

2904-409: The energy spectrum of alpha particles in an alpha particle spectrometer, of beta particles in a beta particle spectrometer, of particles (e.g., fast ions ) in a particle spectrometer, or to measure the relative content of the various masses in a mass spectrometer . Since Danysz' time, many types of magnetic spectrometers more complicated than the semicircular type have been devised. Generally,

2970-418: The fiber with another fiber of opposite-sign dispersion so that the dispersion effects cancel; such compensation is ultimately limited by nonlinear effects such as self-phase modulation , which interact with dispersion to make it very difficult to undo. Dispersion control is also important in lasers that produce short pulses . The overall dispersion of the optical resonator is a major factor in determining

3036-466: The first modern spectroscope by combining a prism, diffraction slit and telescope in a manner that increased the spectral resolution and was reproducible in other laboratories. Fraunhofer also went on to invent the first diffraction spectroscope. Gustav Robert Kirchhoff and Robert Bunsen discovered the application of spectroscopes to chemical analysis and used this approach to discover caesium and rubidium . Kirchhoff and Bunsen's analysis also enabled

3102-432: The gem. A spectrograph is an instrument that separates light into its wavelengths and records the data. A spectrograph typically has a multi-channel detector system or camera that detects and records the spectrum of light. The term was first used in 1876 by Dr. Henry Draper when he invented the earliest version of this device, and which he used to take several photographs of the spectrum of Vega . This earliest version of

3168-516: The intensity of light as a function of wavelength or of frequency. The different wavelengths of light are separated by refraction in a prism or by diffraction by a diffraction grating . Ultraviolet–visible spectroscopy is an example. These spectrometers utilize the phenomenon of optical dispersion . The light from a source can consist of a continuous spectrum , an emission spectrum (bright lines), or an absorption spectrum (dark lines). Because each element leaves its spectral signature in

3234-424: The longer-wavelength components. The pulse therefore becomes positively chirped , or up-chirped , increasing in frequency with time. On the other hand, if a pulse travels through a material with negative group-velocity dispersion, shorter-wavelength components travel faster than the longer ones, and the pulse becomes negatively chirped , or down-chirped , decreasing in frequency with time. An everyday example of

3300-450: The medium is said to have normal dispersion . Whereas if the index increases with increasing wavelength (which is typically the case in the ultraviolet ), the medium is said to have anomalous dispersion . At the interface of such a material with air or vacuum (index of ~1), Snell's law predicts that light incident at an angle θ to the normal will be refracted at an angle arcsin( ⁠ sin θ / n ⁠ ). Thus, blue light, with

3366-465: The medium or waveguide around some particular frequency. Their effects can be computed via numerical evaluation of Fourier transforms of the waveform, via integration of higher-order slowly varying envelope approximations , by a split-step method (which can use the exact dispersion relation rather than a Taylor series), or by direct simulation of the full Maxwell's equations rather than an approximate envelope equation. In electromagnetics and optics,

SECTION 50

#1732859183753

3432-417: The pattern of lines observed, a spectral analysis can reveal the composition of the object being analyzed. A spectrometer that is calibrated for measurement of the incident optical power is called a spectroradiometer . Optical emission spectrometers (often called "OES or spark discharge spectrometers"), is used to evaluate metals to determine the chemical composition with very high accuracy. A spark

3498-426: The phase velocity is v p  =  ω / k , the group velocity can be expressed using the derivative : v g  =  dω / dk . Or in terms of the phase velocity v p , When dispersion is present, not only the group velocity is not equal to the phase velocity, but generally it itself varies with wavelength. This is known as group-velocity dispersion and causes a short pulse of light to be broadened, as

3564-504: The previous section for homogeneous media and includes both waveguide dispersion and material dispersion. The reason for defining the dispersion in this way is that | D | is the (asymptotic) temporal pulse spreading Δ t per unit bandwidth Δ λ per unit distance travelled, commonly reported in ps /( nm ⋅ km ) for optical fibers. In the case of multi-mode optical fibers , so-called modal dispersion will also lead to pulse broadening. Even in single-mode fibers , pulse broadening can occur as

3630-527: The refractive index is some function of the frequency f of the light, thus n  =  n ( f ), or alternatively, with respect to the wave's wavelength n  =  n ( λ ). The wavelength dependence of a material's refractive index is usually quantified by its Abbe number or its coefficients in an empirical formula such as the Cauchy or Sellmeier equations . Because of the Kramers–Kronig relations ,

3696-419: The semicircular spectrometer, invented by J. K. Danisz, is shown on the left. A constant magnetic field is perpendicular to the page. Charged particles of momentum p that pass the slit are deflected into circular paths of radius r = p/qB . It turns out that they all hit the horizontal line at nearly the same place, the focus; here a particle counter should be placed. Varying B , this makes possible to measure

3762-452: The slit; this results in images that convolve the image information with spectral information along the direction of dispersion. If the field is not sufficiently sparse, then spectra from different sources in the image field will overlap. The trade is that slitless spectrographs can produce spectral images much more quickly than scanning a conventional spectrograph. That is useful in applications such as solar physics where time evolution

3828-486: The spatial separation of a white light into components of different wavelengths (different colors ). However, dispersion also has an effect in many other circumstances: for example, group-velocity dispersion causes pulses to spread in optical fibers , degrading signals over long distances; also, a cancellation between group-velocity dispersion and nonlinear effects leads to soliton waves. Most often, chromatic dispersion refers to bulk material dispersion, that is,

3894-513: The spectrograph was cumbersome to use and difficult to manage. There are several kinds of machines referred to as spectrographs , depending on the precise nature of the waves. The first spectrographs used photographic paper as the detector. The plant pigment phytochrome was discovered using a spectrograph that used living plants as the detector. More recent spectrographs use electronic detectors, such as CCDs which can be used for both visible and UV light. The exact choice of detector depends on

3960-400: The term dispersion generally refers to aforementioned temporal or frequency dispersion. Spatial dispersion refers to the non-local response of the medium to the space; this can be reworded as the wavevector dependence of the permittivity. For an exemplary anisotropic medium, the spatial relation between electric and electric displacement field can be expressed as a convolution : where

4026-399: The units left implied (such as "digital counts" per spectral channel). Gemologists frequently use spectroscopes to determine the absorption spectra of gemstones, thereby allowing them to make inferences about what kind of gem they are examining. A gemologist may compare the absorption spectrum they observe with a catalogue of spectra for various gems to help narrow down the exact identity of

SECTION 60

#1732859183753

4092-432: The use of achromats , multielement lenses with glasses of different dispersion. They are constructed in such a way that the chromatic aberrations of the different parts cancel out. Pulsars are spinning neutron stars that emit pulses at very regular intervals ranging from milliseconds to seconds. Astronomers believe that the pulses are emitted simultaneously over a wide range of frequencies. However, as observed on Earth,

4158-418: The visible spectrum. A spectrometer that is calibrated for measurement of the incident optical power is called a spectroradiometer . In general, any particular instrument will operate over a small portion of this total range because of the different techniques used to measure different portions of the spectrum. Below optical frequencies (that is, at microwave and radio frequencies), the spectrum analyzer

4224-543: The wavelength dependence of the real part of the refractive index is related to the material absorption , described by the imaginary part of the refractive index (also called the extinction coefficient ). In particular, for non-magnetic materials ( μ  =  μ 0 ), the susceptibility χ that appears in the Kramers–Kronig relations is the electric susceptibility χ e  =  n  − 1. The most commonly seen consequence of dispersion in optics

4290-664: The wavelengths of light to be recorded. A spectrograph is sometimes called polychromator , as an analogy to monochromator . The star spectral classification and discovery of the main sequence , Hubble's law and the Hubble sequence were all made with spectrographs that used photographic paper. James Webb Space Telescope contains both a near-infrared spectrograph ( NIRSpec ) and a mid-infrared spectrograph ( MIRI ). An echelle -based spectrograph uses two diffraction gratings , rotated 90 degrees with respect to each other and placed close to one another. Therefore, an entrance point and not

4356-475: The waves are confined to some region. In a waveguide, both types of dispersion will generally be present, although they are not strictly additive. For example, in fiber optics the material and waveguide dispersion can effectively cancel each other out to produce a zero-dispersion wavelength , important for fast fiber-optic communication . Material dispersion can be a desirable or undesirable effect in optical applications. The dispersion of light by glass prisms

#752247