Spectrum

Spectrum

Overview

A spectrum is a condition that is not limited to a specific set of values but can vary infinitely within a continuum
Continuum (theory)
Continuum theories or models explain variation as involving a gradual quantitative transition without abrupt changes or discontinuities. It can be contrasted with 'categorical' models which propose qualitatively different states.-In physics:...

. The word saw its first scientific use within the field of optics
Optics
Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...

 to describe the rainbow
Rainbow
A rainbow is an optical and meteorological phenomenon that causes a spectrum of light to appear in the sky when the Sun shines on to droplets of moisture in the Earth's atmosphere. It takes the form of a multicoloured arc...

 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
Political spectrum
A political spectrum is a way of modeling different political positions by placing them upon one or more geometric axes symbolizing independent political dimensions....

, or the spectrum of activity of a drug, or the autism spectrum
Autism spectrum
The term "autism spectrum" is often used to describe disorders that are currently classified as pervasive developmental disorders. Pervasive developmental disorders include autism, Asperger syndrome, Childhood disintegrative disorder, Rett syndrome and Pervasive Developmental Disorder Not Otherwise...

.
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Encyclopedia

A spectrum is a condition that is not limited to a specific set of values but can vary infinitely within a continuum
Continuum (theory)
Continuum theories or models explain variation as involving a gradual quantitative transition without abrupt changes or discontinuities. It can be contrasted with 'categorical' models which propose qualitatively different states.-In physics:...

. The word saw its first scientific use within the field of optics
Optics
Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...

 to describe the rainbow
Rainbow
A rainbow is an optical and meteorological phenomenon that causes a spectrum of light to appear in the sky when the Sun shines on to droplets of moisture in the Earth's atmosphere. It takes the form of a multicoloured arc...

 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
Political spectrum
A political spectrum is a way of modeling different political positions by placing them upon one or more geometric axes symbolizing independent political dimensions....

, or the spectrum of activity of a drug, or the autism spectrum
Autism spectrum
The term "autism spectrum" is often used to describe disorders that are currently classified as pervasive developmental disorders. Pervasive developmental disorders include autism, Asperger syndrome, Childhood disintegrative disorder, Rett syndrome and Pervasive Developmental Disorder Not Otherwise...

. 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.

Origins


In Latin
Latin
Latin is an Italic language originally spoken in Latium and Ancient Rome. It, along with most European languages, is a descendant of the ancient Proto-Indo-European language. Although it is considered a dead language, a number of scholars and members of the Christian clergy speak it fluently, and...

 spectrum means "image" or "apparition
Apparition
Generally, an apparition is an instance of something's appearing, i.e. being seen. The term may refer to:- Supernatural :*Apparitional experience, an anomalous, quasi-perceptual experience...

", including the meaning "spectre". Spectral evidence
Spectral evidence
Spectral evidence is a form of evidence based upon dreams and visions. It was admitted in court during the Salem witch trials by the appointed chief justice, William Stoughton. The booklet A Tryal of Witches taken from a contemporary report of the proceedings of the Bury St...

 is testimony about what was done by spectres of persons not present physically, or hearsay
Hearsay
Hearsay is information gathered by one person from another person concerning some event, condition, or thing of which the first person had no direct experience. When submitted as evidence, such statements are called hearsay evidence. As a legal term, "hearsay" can also have the narrower meaning of...

 evidence about what ghost
Ghost
In traditional belief and fiction, a ghost is the soul or spirit of a deceased person or animal that can appear, in visible form or other manifestation, to the living. Descriptions of the apparition of ghosts vary widely from an invisible presence to translucent or barely visible wispy shapes, to...

s or apparitions of Satan
Satan
Satan , "the opposer", is the title of various entities, both human and divine, who challenge the faith of humans in the Hebrew Bible...

 said. It was used to convict a number of persons of witchcraft
Witchcraft
Witchcraft, in historical, anthropological, religious, and mythological contexts, is the alleged use of supernatural or magical powers. A witch is a practitioner of witchcraft...

 at Salem, Massachusetts
Salem, Massachusetts
Salem is a city in Essex County, Massachusetts, United States. The population was 40,407 at the 2000 census. It and Lawrence are the county seats of Essex County...

 in the late 17th century. The word "spectrum" [Spektrum] was strictly used to designate a ghostly optical afterimage
Afterimage
An afterimage or ghost image or image burn-in is an optical illusion that refers to an image continuing to appear in one's vision after the exposure to the original image has ceased...

 by Goethe
Johann Wolfgang von Goethe
Johann Wolfgang von Goethe was a German writer, pictorial artist, biologist, theoretical physicist, and polymath. He is considered the supreme genius of modern German literature. His works span the fields of poetry, drama, prose, philosophy, and science. His Faust has been called the greatest long...

 in his Theory of Colors and Schopenhauer
Arthur Schopenhauer
Arthur Schopenhauer was a German philosopher known for his pessimism and philosophical clarity. At age 25, he published his doctoral dissertation, On the Fourfold Root of the Principle of Sufficient Reason, which examined the four separate manifestations of reason in the phenomenal...

 in On Vision and Colors
On Vision and Colors
On Vision and Colors is a treatise by Arthur Schopenhauer that was published in May 1816 when the author was 28 years old. Schopenhauer had extensively discussed with Johann Wolfgang von Goethe about the poet's Theory of Colours of 1810, in the months around the turn of the years 1813 and 1814,...

.

Modern meaning in the physical sciences


In the 17th century the word spectrum was introduced into optics
Optics
Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...

, referring to the range of color
Color
Color or colour is the visual perceptual property corresponding in humans to the categories called red, green, blue and others. Color derives from the spectrum of light interacting in the eye with the spectral sensitivities of the light receptors...

s observed when white light was disperse
Dispersion (optics)
In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency, or alternatively when the group velocity depends on the frequency.Media having such a property are termed dispersive media...

d through a prism
Prism (optics)
In optics, a prism is a transparent optical element with flat, polished surfaces that refract light. The exact angles between the surfaces depend on the application. The traditional geometrical shape is that of a triangular prism with a triangular base and rectangular sides, and in colloquial use...

. Soon the term referred to a plot of light intensity
Intensity (physics)
In physics, intensity is a measure of the energy flux, averaged over the period of the wave. The word "intensity" here is not synonymous with "strength", "amplitude", or "level", as it sometimes is in colloquial speech...

 or power
Power (physics)
In physics, power is the rate at which energy is transferred, used, or transformed. For example, the rate at which a light bulb transforms electrical energy into heat and light is measured in watts—the more wattage, the more power, or equivalently the more electrical energy is used per unit...

 as a function of frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...

 or wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.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...

, also known as a spectral density
Spectral density
In statistical signal processing and physics, the spectral density, power spectral density , or energy spectral density , is a positive real function of a frequency variable associated with a stationary stochastic process, or a deterministic function of time, which has dimensions of power per hertz...

.
The term spectrum was soon applied to other waves
WAVES
The WAVES were a World War II-era division of the U.S. Navy that consisted entirely of women. The name of this group is an acronym for "Women Accepted for Volunteer Emergency Service" ; the word "emergency" implied that the acceptance of women was due to the unusual circumstances of the war and...

, such as sound waves, and now applies to any signal that can be decomposed into frequency components. A spectrum is a usually 2-dimensional
Dimension
In physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it...

 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
Visible spectrum
The visible spectrum is the portion of the electromagnetic spectrum that is visible to the human eye. Electromagnetic radiation in this range of wavelengths is called visible light or simply light. A typical human eye will respond to wavelengths from about 390 to 750 nm. In terms of...

", a reference to those electromagnetic
Electromagnetism
Electromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...

 wave
Wave
In physics, a wave is a disturbance that travels through space and time, accompanied by the transfer of energy.Waves travel and the wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium—that is, with little or no associated mass...

s which are visible
Visual perception
Visual perception is the ability to interpret information and surroundings from the effects of visible light reaching the eye. The resulting perception is also known as eyesight, sight, or vision...

 to the human eye
Human eye
The human eye is an organ which reacts to light for several purposes. As a conscious sense organ, the eye allows vision. Rod and cone cells in the retina allow conscious light perception and vision including color differentiation and the perception of depth...

. 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
Charge-coupled device
A charge-coupled device is a device for the movement of electrical charge, usually from within the device to an area where the charge can be manipulated, for example conversion into a digital value. This is achieved by "shifting" the signals between stages within the device one at a time...

. 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.

Physical science

  • Electromagnetic spectrum
    Electromagnetic spectrum
    The electromagnetic spectrum is the range of all possible frequencies of electromagnetic radiation. The "electromagnetic spectrum" of an object is the characteristic distribution of electromagnetic radiation emitted or absorbed by that particular object....

    • Visible spectrum
      Visible spectrum
      The visible spectrum is the portion of the electromagnetic spectrum that is visible to the human eye. Electromagnetic radiation in this range of wavelengths is called visible light or simply light. A typical human eye will respond to wavelengths from about 390 to 750 nm. In terms of...

       or optical spectrum, a subset of the electromagnetic spectrum
    • Emission spectrum
      Emission spectrum
      The emission spectrum of a chemical element or chemical compound is the spectrum of frequencies of electromagnetic radiation emitted by the element's atoms or the compound's molecules when they are returned to a lower energy state....

       observed in light
    • Absorption spectrum observed in light
  • Energy spectrum of a collection of particles (particle physics)
  • Frequency spectrum
    Frequency spectrum
    The frequency spectrum of a time-domain signal is a representation of that signal in the frequency domain. The frequency spectrum can be generated via a Fourier transform of the signal, and the resulting values are usually presented as amplitude and phase, both plotted versus frequency.Any signal...

     of a signal
  • Mass spectrum
    Mass spectrum
    A mass spectrum is an intensity vs. m/z plot representing a chemical analysis. Hence, the mass spectrum of a sample is a pattern representing the distribution of ions by mass in a sample. It is a histogram usually acquired using an instrument called a mass spectrometer...

     chemical analysis of atoms and molecules
  • Power spectrum of a signal
  • Spectrogram
    Spectrogram
    A spectrogram is a time-varying spectral representation that shows how the spectral density of a signal varies with time. Also known as spectral waterfalls, sonograms, voiceprints, or voicegrams, spectrograms are used to identify phonetic sounds, to analyse the cries of animals; they were also...

  • Spectrometer
    Spectrometer
    A spectrometer is an instrument used to measure properties of light over a specific portion of the electromagnetic spectrum, typically used in spectroscopic analysis to identify materials. The variable measured is most often the light's intensity but could also, for instance, be the polarization...


Social and medical sciences

  • Economic spectrum
  • Political spectrum
    Political spectrum
    A political spectrum is a way of modeling different political positions by placing them upon one or more geometric axes symbolizing independent political dimensions....

     of opinion
  • Spectrum disorder
    Spectrum disorder
    A spectrum in psychiatry is a range of linked conditions, such that there is "not a unitary disorder but rather a syndrome composed of subgroups". The subgroups may be linked together by clinical appearance or by shared underlying causation...

    , in psychiatry

Mathematics

  • Spectrum (homotopy theory)
    Spectrum (homotopy theory)
    In algebraic topology, a branch of mathematics, a spectrum is an object representing a generalized cohomology theory. There are several different constructions of categories of spectra, any of which gives a context for the same stable homotopy theory....

  • Spectrum of a matrix
    Spectrum of a matrix
    In mathematics, the spectrum of a matrix is the set of its eigenvalues. This notion can be extended to the spectrum of an operator in the infinite-dimensional case.The determinant equals the product of the eigenvalues...

    , in linear algebra
  • Spectrum of an operator, in functional analysis (a generalisation of the spectrum of a matrix)
  • Spectrum of a ring
    Spectrum of a ring
    In abstract algebra and algebraic geometry, the spectrum of a commutative ring R, denoted by Spec, is the set of all proper prime ideals of R...

    , in commutative algebra
  • Spectrum of a C*-algebra
  • Spectrum of a theory
    Spectrum of a theory
    In model theory, a branch of mathematical logic, the spectrum of a theoryis given by the number of isomorphism classes of models in various cardinalities. More precisely,...

    , in mathematical logic
  • Stone space of Boolean algebra