a) temporal coherence: consider a light wave traveling along +X axis. Consider two different points A and B along the same wave train that is along +X axis.

If Φ(A) is phase of point A at any time and Φ(B) is phase of point B at any time, then

phase difference between these point is given by

Φ = Φ(A) – Φ(B)

If Φ is independent of time then points A and B are said to exhibit temporal coherence or longitudinal coherence

In other words, a beam of laser is said to exhibit temporal coherence if the phase difference of the waves crossing the two points lying on a plane parallel to the direction of the propagation of beam is independent of time.

Note: try the make the diagram yourself.

a) spatial coherence: consider a light wave traveling along +X axis. Draw a line perpendicular to the direction of the beam. Consider two different points C and D on this line.

If Φ(C) is phase of point C at any time and Φ(D) is phase of point D at any time, then

phase difference between these point is given by

Φ = Φ(C) – Φ(D)

If Φ is independent of time then points C and D are said to exhibit spatial coherence or transverse coherence or lateral coherence.

In other words, a beam of laser is said to exhibit spatial coherence if the phase difference of the waves crossing the two points lying on a plane perpendicular to the direction of the propagation of beam is independent of time.

Note: try the make the diagram yourself.

Reference: This article is referred from my authored book “optics and lasers” having ISBN 81-272-2948-2. In case of any doubt, post in the comment section.

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