## Introduction

In physics, two waves are said to be coherent if their frequencies and waveforms are identical, and the phase difference between them is constant.

Coherence is the property of a wave that causes stationary interference. Several distinct concepts explain coherence. These phenomena don't usually occur in reality but allow a brief understanding of waves. It has become an important concept in quantum physics.

Coherence describes the properties of the correlation between physical quantities of a single wave, several waves, or that of wave packets.

For instance, if two parallel slits are lighted by a single laser beam, then those slits can be classified as two coherent sources.

(Image will be Uploaded Soon)

Coherence light is a type of light in which the photons are all in step. The change of phase for the light beam occurs at the same time. Also, no abrupt phase change occurs within the beam. The light produced by lasers is coherent and monochromatic (made up of single wavelength) in nature.

Incoherent sources emit light with random and frequent change in phase within the photons. For example, ordinary fluorescent tubes and tungsten filament lamps emit incoherent light.

(Image will be Uploaded Soon)

Further, conventional lights are incoherent sources. The drift from one atomic energy level to the next is a random method & one cannot have control over it when an atom loses its energy radiating all over.

### Types of Coherence

Here you can find what are the two types of coherence. Well, there are two different types of coherent sources, temporal coherence, and spatial coherence. These two types of coherence are explained below.

1. Temporal Coherence: Temporal coherence is a measure of the average relationship between the value of a wave and the coherence itself, making a delay of τ, at any considerable pair of time. It measures how monochromatic a source of light is.

Its characteristic is that the wave can well interfere with it at different points of time. If the phase or amplitude is significant above the delay, the correlation also decreases significantly.

It is defined as the coherence time τc. Keeping a delay of τ = 0, the degree of coherence becomes ideal. If the delay is τ = τc, the degree of coherence drops significantly. The coherence length Lc is defined as the distance traveled by the wave in time τc.

(Image will be Uploaded Soon)

The figure represents the amplitude of a single frequency wave over a function of time (in red) and the amplitude of the same wave delayed by τ (blue). Since it is perfectly correlated with itself for all delays in time τ, therefore coherence time of the wave is infinite.

2. Spatial Coherence: In light waves and water waves, it is found that the dimension of the wave extends from one or two spaces. Spatial coherence is the ability of two points in the space of a wave that interferes. In simple words, spatial coherence is the cross-relation between two points of a wave.

A wave is said to be perfectly spatial coherence if it has a single amplitude value over an infinite length. The significant interference between the range of separation and two points can be used to define the diameter of the coherence area, Ac.

(Image will be Uploaded Soon)

(A plane wave with an infinite coherence length)

(Image will be Uploaded Soon)

(A wave with a wavefront and infinite coherence length)

(Image will be Uploaded Soon)

(A wave with a wavefront and finite coherence length)

(Image will be Uploaded Soon)

A wave with a finite coherence area is incident on a pinhole, and the wave will be diffracted out of the pinhole. The emerging spherical wavefronts are approximately flat, far from the pinhole. The coherence area becomes infinite, but the coherence length remains unchanged.

(Image will be Uploaded Soon)

A wave with an infinite coherence area is combined with a spatially shifted copy of the same wave. Se sections of the wave interfere constructively and some destructively.

By averaging these sections with the help of a detector of length D, we can measure the reduced interference visibility.

An example of this is a misaligned Mach–Zehnder interferometer.

### How to Produce Coherent Sources?

Methods of producing coherent source

Here are some of the methods to produce a coherent source of light.

a. By Dividing the Wavefront: A wavefront can be divided into several parts. It can be used by using different lenses, mirrors, and prisms. Young's double-slit experiment, Lloyd's mirror arrangement and Fresnel's biprism method are some of the techniques to do it.

b. By Dividing the Amplitude: If the amplitude of an incoming beam of light is divided, then a coherent source can be created. This can be done by the process of partial reflection or refraction. These divided parts further meet with each other to create interference.

### Application of Coherence

Radiography is a technique that uses coherence of next-generation facility beams and makes it possible to break the usual barrier easily.

The X-ray beam has:

A high spatial coherence - In this the size and divergence of the beam are small

A good temporal coherence - It occurs after monochromatization.

These characteristics of the beam are because of its super brilliance. It allows new techniques to be developed in the X-ray field:

Phase-contrast, tomography, and imaging

Photon correlation spectroscopy

In-line holography.

Coherence also forms the basis of some other applications. Some of the applications are mentioned below:

i. Holography: It uses coherent superposition of optical waves, and its use is commonly found in credit cards.

ii. Non-optical Wavefield: The superposition of non-optical wave fields also occurs, which is opposite to holography. For example, a probability field related to a wave function is considered in quantum mechanics. Coherent waves also have applications in future technologies like quantum computing.

iii. Modal Analysis: Coherence is also used in the model analysis to maintain the quality of the transfer function.

## FAQs on Coherence and Coherent Sources

**1. Is Sun a Coherent Source?**

Sun is an incoherent source of light. However, sunlight can impart a coherence speckle to the image of a microscope. Most of the light sources bother spatial coherence (related to angular size) and temporal coherence (related to wavelength).

**2. Can Two Independent Sources be Coherent?**

No, two independent sources of light can never be coherent. When individual atoms return to the ground state, light is emitted. Even the smallest light source cannot emit light waves of the same phase.

**3. Can Two Independent Monochromatic Sources of Light be Coherent?**

No, two independent monochromatic sources of light cannot be coherent. Since two sources of light have a different frequency, wavelength, and phase; so they cannot produce any interference.

**4. Why is a Coherent Source Needed for Interference?**

Coherent sources of light have the same frequency, wavelength, and are in the same phase. This is required to produce a sustained interference pattern. This is the new intensity of light.

**5. What is coherence?**

The interrelation properties between physical quantities of a single wave or between several waves are described by coherence. If the waves have a constant relative phase or zero or constant phase difference and the same frequency then the two waves are said to be coherent.

To have stationary interference, coherence enables the wave's property besides, the amount of coherence measured by interference visibility. For instance, if two parallel slits lighted by a laser beam are classified by two coherent point sources.

**6. What is spatial coherence?**

In the case of optics or water waves, we should find the dimension of the wave that extends from one or two spaces.

The ability of two points in a wave space such as x1 and x2 is said to interfere is said to be a Spatial coherence.

Spatial coherence is said to be the cross-relation of two points in a wave.

For perfect spatial coherence, the wave should have a single amplitude value over an infinite length. To define the diameter of the coherence area Ac, the significant interference between the range of separation and the two points can be used.

**7. What is temporal coherence?**

The measure of the average relationship of the wave value and itself makes a delay of τ, at any definite number of times is called temporal coherence.

It gives the measure of a monochromatic source and characterizes the interference of a wave with itself at a different time.

The significant amount above which the phase or amplitude gets delayed (thus, the correlation decreases by a significant amount) is defined as the coherence time.

**8. What are coherent sources?**

To have stationary interference, coherence enables the wave's property besides, the amount of coherence measured by interference visibility. The source which emits light waves has the same frequency, wavelength and is in the same phase or they have a constant phase difference is called a coherent source of light. When superimposition of waves occurs and the positions of maxima and minima are fixed, it forms sustained interference patterns.

Two independent sources cannot be coherent as all the factors cannot be present in the source at the same time.

**9. What are the applications of Coherence?**

Radiography is a classic, old technique. Which is replaced by a next-generation facility beam that makes it easy and possible to break the usual barrier to absorb and visualize phase features.

A high spatial coherence. which has a very small size and divergence of the beam.

Holography uses coherent superpositions of optical wave fields and is commonly found in credit cards.

The superposition of non-optical wavefields opposite to holography is also considered. For example, there is a consideration for the probability field in quantum mechanics which is related to the wave function. The applications of coherent waves are seen in quantum computing, etc.