Spatial Coherence

A fixed strong phase relationship between the differentiation regions of the beam profile is termed spatial coherence. The best-demonstrated example of the concept is a laser beam focused over a cross-section area. In this scenario, the beams of electricity act in different ways at different locations. The concept of spatial coherence is the basic principle and requirement in the production of laser beams. To achieve high spatial coherence of light, resonator modes are employed. 

The major difference between spatial coherence and another related term (temporal coherence) is that spatial coherence defines the change concerning different points in space whereas temporal coherence defines the change concerning time.

Overview of Spatial Coherence

Particularly, when talking about waves, the waves are called coherent when their waveforms and frequencies are similar. Coherence is a property that allows the molecules to exhibit constant interference. It also describes all the relationships between the physical qualities exhibited by a single wave or packets of different waves.

Meaning of Spatial Coherence

The concept of spatial coherence mainly focuses on and infers on the relationship established between different waves in space at different points. Any two waves are said to be coherent if they exhibit a relative phase that is stable and constant. For given waves, the spatial coherence amount can be identified by interference visibility. The relationship between two waves in terms of spatial coherence can be either lateral or longitudinal.

For instance, consider a bulb filament made up of tungsten. At different points, the filament emits different lights and shows no relationship with each other. At this point, the emitted light starts diffraction, and with a change in time, it also changes considerably. For white light, spatial coherence is termed incoherent (since only a single kind of light is emitted). For a radio antenna array, the spatial coherence is very large because antennas at the opposite ends emit a fixed phase relationship.

Temporal Coherence

Temporal coherence also describes the relationship between two waves, but it describes this relationship between those waves that are at different time points. It can be defined as the measure of the correlation between the wave and its times. 

The time here is represented as ‘τ’. Both Young’s interference experiment and Michelson Morley’s experiment provide evidence in support of temporal coherence. These experiments were demonstrated to support evidence for coherence.

Michelson Morley Experiment

The experiment carried out the obtaining fringes on the Michelson interferometer. In the initial step, the experiment involved the removal of one mirror. So now, the required time for the beam to travel increases gradually. Due to this, the fringes start to appear dull, and at a point, they finally diminish this property. This is known as spatial coherence.

Young’s Experiment

Also known as the double-slit experiment, the basic principle here is increasing the distance between the two slits. Once again, the coherence starts appearing as the distance is increased and the fringes disappear. 

From both experiments, it was observed that by increasing the distance, the fringes start disappearing. Therefore, the concept of spatial coherence was defined and concluded.

Applications of Spatial Coherence

Some of the major applications of spatial coherence are given below:

• Holography: Holographics are widely used in art. These are based on the concept of coherent superpositions of optical wave fields.
• Non-optical wave fields: Just like superpositions of optical wave fields, coherent superpositions of non-optical wavefields are also in great use in quantum mechanics.
• Modal analysis: In recent advances, the coherent signal is used to detect the signal transfer qualities. A poor signal to noise ratio is indicated by low coherence, which means the frequency resolution is inadequate.

These are some of the general applications of spatial coherence. Apart from these, there are many applications of the concept in recent technologies.

Correlation and Coherence

Coherence, as we know, defines how two waves are related. The correlation or cross-correlation defines the capability to infer the phase of the given second wave based on the given first wave. 

For instance, consider two waves that are perfectly correlated to each other every time (this can be achieved by using a monochromatic light). At any point for the given waves, the phase difference will be constant. When they are combined, a perfect constructive wave interference is produced. The measuring of the correlation in this situation is sometimes also described as self coherence or autocorrelation function.

Conclusion

The concept of spatial coherence helps in determining the relationship established between two waves in space. Young’s double-slit experiment was able to prove this concept by an experiment on the detection of fringes, on which a beam of the laser was focused. In the end, it was analysed that after some time, the fringes eventually get diminished. In today’s world, spatial coherence has established its various applications in holography, modal analysis, and laser systems.