What does it mean for a light to have low-coherence? I've been searching about OCT imaging and understood that it is based on low-coherence light source. The problem is, I don't understand what is a low-coherence light source. Based on what points that we call a light source have low-coherence? My reading source so far hasn't come up with anything about this.
 A: The coherence of a wave is the extent to which its phase (how far along it is in its "cycle") at some point in space (or time) is predictable from its phase at some other point in space in (or time). If the wave is perfectly coherent, the difference in phase between two points is constant. Otherwise, the phase difference may change randomly. The "coherence length" of the wave is the maximum separation distance for which the phase distance can be expected to be constant (most of the time.)
A simple physical example: a finger wiggling at a constant frequency without interruption will produce a coherent wave on the surface of a pond. But several wiggling fingers, each starting and stopping at independent, random times, will generate an incoherent wave, even if they all wiggle at the same, constant frequency.
A: There are two aspects of coherence: temporal snd spatial.  If light is temporally coherent, it has a very narrow frequency bandwidth.  If light is spatially coherent, the source is physically very small.
In an interferometer using light of high temporal coherence and high spatial coherence,  interference fringes can form even if the two beams in the interferometer travel paths of substantially different lengths.  But if the temporal coherence is low, fringes may form only if the two path lengths are very nearly the same- e.g., within a micron or so.  In OCT, that effect of low temporal allows distances to be determined precisely down to that micron or so.
A: Adding to the contributions from the others, a laser beam is highly coherent.  It emerges from a small aperture, has a sharply defined frequency, maintains a tight beam, and the wave packets associated with the photons are all in phase over a significant length of the beam. Light from an incandescent filament has none of these properties.
A: Coherence is related to correlation, I.e what is the correlation between optical waveforms. Intereference occurs when there is correlation, and no interference when the correlation is zero. So for a single waveform, it's coherence is the correlation of  the waveform at a point with the same waveform but shifted in space or time or both. The auto-correlation function, which is the same as coherence function, is the Fourier Transform of the Power Spectral Density of the source. For short coherence, a wide band source, I.e white light source is needed. The greater the bandwidth the shorter coherence length, but coherence function is maximum at zero time shift.
For a long coherence length, a monochromatic, I.e very narrow linewidth source such as single mode laser is required.
Similar treatment can be used to determine the correlation between waveforms at different points in space.
