Coherence is a term used to describe the relationship between the physical quantities of a single wave or multiple waves. For two waves to be considered coherent, they must have a constant relative phase or a zero or constant phase difference, along with the same frequency.
Coherence also refers to the property that allows waves to produce stationary interference. The level of coherence is often determined by measuring interference visibility. For example, when a laser beam illuminates two parallel slits, they can be considered as two coherent point sources. In this article, we will delve deeper into this concept, discussing its types, characteristics, and examples of coherent sources.
Exploring the Types of Coherence
Coherence can be categorized into two types: temporal coherence and spatial coherence. Let's take a closer look at what these terms mean.
Delving into Temporal Coherence
Temporal coherence refers to the correlation between the value of a wave at two different points in time, with a delay of τ.
Temporal coherence is used to measure how monochromatic a source is. It provides insight into a wave's ability to interfere with itself at different times.
The coherence time is defined as the delay after which the phase or amplitude varies by a significant amount, leading to a noticeable decrease in correlation.
Understanding Spatial Coherence
Spatial coherence is observed in systems such as optics or water waves, where the dimension of waves extends across one or two spaces.
Spatial coherence can be defined as the ability of two points in the wave space (x1 and x2) to interfere with each other.
Simply put, spatial coherence refers to the cross-correlation between two points in a wave at any given time.
A wave that maintains a single amplitude value over an infinite length is said to possess perfect spatial coherence. The significant interference between the range of separation and the two points can be used to define the diameter of the coherence area, denoted as Ac.
What are Coherent Sources?
Coherent sources of light are those that emit light waves with the same frequency, wavelength, and phase, or those that maintain a constant phase difference. When the superposition of waves occurs, a coherent source forms sustained interference patterns, with fixed positions of maxima and minima.
It's essential to note that two independent sources cannot be considered coherent, as they cannot simultaneously maintain all the above-mentioned factors.
Examples of Coherent Sources
Here are some examples of coherent sources:
The sound waves produced by speakers are driven by electrical signals. These signals maintain the same frequency and a definite phase, making them coherent.
Lasers are a well-known example of coherent sources, as they employ a phenomenon known as stimulated emission to produce highly coherent light.
Small light sources can be partially coherent. This property allows us to see interference patterns on soap bubbles and appreciate the iridescence of butterfly wings.
While sunlight is generally incoherent, small portions of it falling on small areas can be partially coherent.
Characteristics of Coherent Sources
Coherent sources exhibit the following characteristics:
The generated waves maintain a constant phase difference (they are in phase with each other).
Creating a coherent source of light can sometimes be challenging. However, there are several methods that can be used to produce such sources:
1. By Dividing the Wavefront
The wavefront is divided into several parts using lenses, mirrors, or prisms. Techniques such as Young’s double-slit experiment, Lloyd’s mirror arrangement, Fresnel’s biprism method, etc., can be used for this purpose.
2. By Dividing the Amplitude
A coherent source can also be created by dividing the amplitude of the incoming beam into different parts through partial reflection or refraction. These parts, which travel along new paths, meet with each other to create an interference.
Examples of this method include the phenomenon of Newton’s rings or the use of Michelson’s interferometer arrangement.
Incoherent Sources
Incoherent sources are the exact opposite of coherent sources. They emit light with frequency, but the phase between the photons changes randomly.
Conventional light sources, such as incandescent bulbs, are examples of incoherent sources. The transitions between energy levels in an atom are a completely random process, so we cannot control when an atom will lose energy in the form of radiation.
The image below illustrates an incoherent wave.
Interference
Interference is a phenomenon where two waves superimpose to form a resultant wave of greater, lower, or the same amplitude. Interference can be constructive or destructive, resulting from the combination of waves that are coherent with each other, either because they come from the same source or because they have the same or nearly the same frequency.
Why Are Coherent Sources Essential for Observable Interference?
Coherent sources of light are crucial for observing interference effects. Since coherent sources maintain the same phase, the phase difference between the two sources remains constant. This constant phase difference is a necessary condition for observable and distinct interference. Coherent sources help us identify interference patterns that result from phase changes at a given point (either at the source or on the screen). These patterns also give us the minima and maxima, i.e., points of constructive and destructive interference, which can be seen simultaneously at different points on the screen.
Applications of Coherence
The concept of coherence has wide-ranging applications, particularly in the field of radiography. The coherence of a next-generation facility beam makes it possible to overcome the usual barrier to absorption and to visualize phase features. The X-ray beam has:
High spatial coherence, which means that the size and the divergence of the beam are very small.
Good temporal coherence after monochromatization.
These characteristics of the beam, which are due to its super brilliance, allow new techniques to be developed in the X-ray field: