In physics, two wave sources are perfectly coherent if they have a constant phase difference and the same frequency, and the same waveform. Coherence is an ideal property of waves that enables stationary (i.e. temporally and spatially constant) interference. It contains several distinct concepts, which are limiting cases that never quite occur in reality but allow an understanding of the physics of waves, and has become a very important concept in quantum physics. More generally, coherence describes all properties of the correlation between physical quantities of a single wave, or between several waves or wave packets.
Consider a wave propagating through space. Coherence is a measure of the correlation that exists between the phases of the wave measured at different points. The coherence of a wave depends on the characteristics of its source.
Let us look at a simple example. Imagine two corks bobbing up and down on a wavy water surface. Suppose the source of the water waves is a single stick moved harmonically in and out of the water, breaking the otherwise smooth water surface. There exists a perfect correlation between the motions of the two corks. They may not bop up and down exactly in phase, one may go up while the other one goes down, but the phase difference between the positions of the two corks is constant in time. We say that the source is perfectly coherent. A harmonically oscillating point source produces a perfectly coherent wave.
When we describe the coherence of light waves, we distinguish two types of coherence.
Temporal coherence is a measure of the correlation between the phases of a light wave at different points along the direction of propagation. Temporal coherence tells us how monochromatic a source is.
Spatial coherence is a measure of the correlation between the phases of a light wave at different points transverse to the direction of propagation. Spatial coherence tells us how uniform the phase of the wave front is.