Editing Coherence (physics) (section)

== Spectral coherence of short pulses  ==
[[File:Coherent superposition.svg|thumb|right|350px|Figure 10: Waves of different frequencies interfere to form a localized pulse if they are coherent.]]
[[File:spectral coherence continuous.png|thumb|right|350px|Figure 11: Spectrally incoherent light interferes to form continuous light with a randomly varying phase and amplitude.]]

Waves of different frequencies (in light these are different colours) can interfere to form a pulse if they have a fixed relative phase-relationship (see [[Fourier transform]]). Conversely, if waves of different frequencies are not coherent, then, when combined, they create a wave that is continuous in time (e.g. white light or [[white noise]]). The temporal duration of the pulse <math>\Delta t</math> is limited by the spectral bandwidth of the light <math>\Delta f</math> according to:

:<math>\Delta f\Delta t \ge 1</math>,

which follows from the properties of the Fourier transform and results in [[Küpfmüller's uncertainty principle]] (for quantum particles it also results in the [[Heisenberg uncertainty principle]]).

If the phase depends linearly on the frequency (i.e. <math>\theta (f) \propto f</math>) then the pulse will have the minimum time duration for its bandwidth (a ''transform-limited'' pulse), otherwise it is chirped (see [[Dispersion (optics)|dispersion]]).

=== Measurement of spectral coherence ===
Measurement of the spectral coherence of light requires a [[nonlinear optics|nonlinear]] optical interferometer, such as an intensity [[optical autocorrelation|optical correlator]], [[frequency-resolved optical gating]] (FROG), or [[spectral phase interferometry for direct electric-field reconstruction]] (SPIDER).
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