The coherence length, usually applied to light waves, gives the distance over which a wave can
interfere with itself. For example, imagine a source of light being split into two beams.
The beams are then taken on different paths and later recombined. If the difference between the path
lengths is less than the coherence length then the beams will interfere with each other and an interference
pattern can be observed. If the difference is greater than the coherence length then no interference will
From this it can be seen that the concept of coherence length is extremely important in
holography as it is the process of splitting and recombining a beam to produce and interference pattern that
makes a hologram. This is why laser light is usually used in holography, as lasers have extremely long coherence
lengths, in the order of a few metres is possible. Compare this with the few centimetres possible with a sodium lamp.
The coherence length depends on the purity of the light source. A laser emitting at a single wavelength,
λ, will have a very narrow spread in wavelengths, Δλ. Traditional light sources, such as sodium
lamps, whilst only emitting "one" frequency will have a larger spread in wavelength, Δλ, than the laser.
Formally, coherence length is defined as
L = λ² / nΔλ
where λ and Δλ are defined as above and n is the refractive index of the
medium in which the wave is travelling.1
To fully understand the origins of coherence length you have to appreciate that for most light sources the light
is not emitted in a continuous wave, but in discrete bundles, or wave packets. A wave packet is released from an atom
as one of its electrons drops from an excited level to a lower energy level, releasing the difference in energy as a
photon, or wave packet:
2ZU; N E: 2m.
m;J2 N VJ HJV
.J N ,m H JZ N K
NH, N .H ,m .H ,E H
JU:K H N JV N JZ Z2 77
, N. M JV H ZJ H U7 JV JZJU
,,,. .;77. 2V2K. .E m; YL K: U: N K. N N ZY 2YY7 ,,,:
777J2222;.:LYYV; :H m; 2Y U; m, E H. N N .H E;7V7 ,LYY2777J222J
7K.N .K N JZ H ZJ N U7 m7 2;
7Y: N N 7U N LL ,E :K N
E, H ,m H JV LY MYY
7VLY .H ,E H U7 ;2
.KK: N 7U N K:
ZK H ZJ N N
Each of these wave packets has absolutely
no relationship to any of the others, so there is no fixed phase relationship between them. If you take two wave packets
arriving at the same point, they may interfere constructively or they may interfere
destructively. Take two other packets at the same point and they may do the complete
opposite. So, on average after many hundreds of millions of these wavepackets you get no fixed interference pattern.
This is the reason we only see laser speckle with laser illumination, not normal, white light.
In lasers, because the radiation emitted is stimulated by the other photons present, each wave
packet is emitted in phase with the rest. This has the effect of making one big long wave packet, leading to a large