Coherence

Coherence

Waves are said to be coherent if they have a constant phase difference and the same frequency. It is an ideal property of waves that enables (temporally and spatially constant) interference (Wikipedia:coherence). A full treatment of coherence is outside the scope of this training module, please see references below for more information.

Interference is nothing more than the addition, in the mathematical sense, of wave functions. A single wave can interfere with itself, but this is still an addition of two waves. Constructive or destructive interferences are limit cases, and two waves always interfere, even if the result of the addition is complicated or not remarkable (Wikipedia:coherence).

When interfering, two waves can add together to create a wave of greater amplitude than either one (constructive interference) or subtract from each other to create a wave of lesser amplitude than either one (destructive interference), depending on their relative phase. Two waves are said to be coherent if they have a constant relative phase (Wikipedia:coherence).

Spatial coherence describes the correlation (or predictable relationship) between waves at different points in space, either lateral or longitudinal. Temporal coherence describes the correlation between waves observed at different moments in time (Wikipedia:coherence).

Temporal Coherence

Temporal coherence is the measure of the average correlation between the value of a wave and itself delayed by τ, at any pair of times. Temporal coherence tells us how monochromatic a source is. In other words, it characterizes how well a wave can interfere with itself at a different time. The delay over which the phase or amplitude wanders by a significant amount (and hence the correlation decreases by significant amount) is defined as the coherence timeτ_c (Wikipedia:coherence).

The relationship between coherence time and bandwidth

It can be shown that the larger the range of frequencies Δf a wave contains, the faster the wave decorrelates (and hence the smaller τ_cis) (Wikipedia:coherence).

τ_cΔf >/= 1

Examples of Temporal Coherence

• A wave containing only a single frequency (monochromatic) is perfectly correlated with itself at all time delays, in accordance with the above relation. (example: laser)
• Conversely, a wave whose phase drifts quickly will have a short coherence time.
• Finally, white light, which has a very broad range of frequencies, is a wave which varies quickly in both amplitude and phase. Since it consequently has a very short coherence time (just 10 periods or so), it is often called incoherent.

(Wikipedia:coherence).

This page takes a lot of information directly from the Wikipedia page on coherence. This is only a small portion; for more information, it is recommended to visit the page.