Coherent and Incoherent Addition of Waves
Coherence was originally conceived in connection with Thomas Young's double-slit experiment in optics but is now used in any field that involves waves, such as acoustics,electrical engineering, neuroscience, and quantum mechanics.
The property of coherence is the basis for commercial applications such as holography, the Sagnac gyroscope, radio antenna arrays, optical coherence tomography and telescope interferometers .
Coherent and Incoherent Waves
Two waves produce the interference pattern only if they originate from coherent sources. The process of light emission from ordinary sources such as the sun, a candle, an electric bulb, is such that one to use special techniques to get the coherent sources.
In order to obtain the fine interference pattern the path difference between the two waves originating from the sources should be very small.
In practice the path difference should not be exceed a few centimeters to observe a good interference pattern.
1. Coherent light is light in which the photons are all in 'step' – other words the change of phase within the beam occurs for all the photons at the same time.
There are no abrupt phase changes within the beam. Light produced by lasers is both coherent and monochromatic .
(Coherent Waves)
(Incoherent Waves)
2. Incoherent sources emit light with frequent and random changes of phase between the photons.
Conventional light sources are incoherent sources. The transitions between energy levels in an atom is a completely random process and so we have no control over when an atom is going to lose energy in the form of radiation.
The light that comes from a laser, however, is coherent, parallel, monochromatic and in unbroken wave chains .We can make a normal light source more coherent by making it smaller, so reducing the number of atoms that may emit quanta, but if we do this the intensity is reduced.
Addition of two waves
The addition of two waves emitting from two sources having intensities I1 and I2 . These two waves interfere each other so that the intensity of the resulting wave will be I as shown in following relation.
I = I1 + I2 + 2(I1I2 cos q)1/2
Where q is the phase difference between two waves.
For the constructive interference the value of q = 0°, so that the Cos q = 1 and
for the destructive interference the value of q = 90°, so that the Cos q = 0.
In case of the incoherent waves the intensity I = I1 + I2
Types of coherence
Spatial coherence
In the case of systems such as optics or water waves, the amplitude of the wave extends to one or two places.
Spatial coherence is known as the potential of two points denoted by x1 and x2 in the field of a wave that can interfere.
When a wave has a single amplitude value at infinite length, we can say that it has perfect spatial coherence.
Temporary coherence
Temporal coherence is a measure of the relationship between the value of a wave and itself producing a delay of t at any given time-wide combination.
Measurement of how monochromatic a particular source is using temporal coherence. This involves determining how well a wave can interfere at a different time.
The delay by a phase or amplitude which must be a sufficient amount is known as coherence time.
Characteristics of coherent sources
The generated waves have a constant phase difference.
Waves are of one frequency.
The amplitude of the waves should be the same.