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 was first used scientifically within the field of optics to describe the rainbow of colors in visible light when separated using a prism. As scientific understanding of light advanced, it came to apply to the entire electromagnetic spectrum.

Spectrum has since been applied by analogy to topics outside of 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.

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. The word "spectrum" [Spektrum] was strictly used to designate a ghostly optical afterimage by Goethe in his Theory of Colors and Schopenhauer in On Vision and Colors.

Modern meaning in the physical sciences

A white light spectrum rendered into the sRGB color space.

In the 17th century the word spectrum was introduced into optics by Isaac Newton, 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.

Mass spectrum of a peptide showing the isotopic distribution

The term spectrum was expanded to apply to other waves, such as sound waves that could also be measured as a function of frequency. The term now applies to any signal that can be measured or decomposed along a continuous variable such as energy in electron spectroscopy or mass to charge ratio in mass spectrometry. Spectrum is also used to refer to a graphical representation of the signal as a function of the dependent variable.

See also

Wikimedia Commons has media related to Spectrum.

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
• Radio spectrum
• Spectral class of a star
• Spectrogram
• Spectrometer

Social and medical sciences

• Antibiotic classification
• 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