A report on Wave interference

The interference of two waves. When in phase, the two lower waves create constructive interference (left), resulting in a wave of greater amplitude. When 180° out of phase, they create destructive interference (right).
Interference of right traveling (green) and left traveling (blue) waves in Two-dimensional space, resulting in final (red) wave
Interference of waves from two point sources.
A magnified image of a coloured interference pattern in a soap film. The "black holes" are areas of almost total destructive interference (antiphase).
Geometrical arrangement for two plane wave interference
Interference fringes in overlapping plane waves
Optical interference between two point sources that have different wavelengths and separations of sources.
Creation of interference fringes by an optical flat on a reflective surface. Light rays from a monochromatic source pass through the glass and reflect off both the bottom surface of the flat and the supporting surface. The tiny gap between the surfaces means the two reflected rays have different path lengths. In addition the ray reflected from the bottom plate undergoes a 180° phase reversal. As a result, at locations (a) where the path difference is an odd multiple of λ/2, the waves reinforce. At locations (b) where the path difference is an even multiple of λ/2 the waves cancel. Since the gap between the surfaces varies slightly in width at different points, a series of alternating bright and dark bands, interference fringes, are seen.
White light interference in a soap bubble. The iridescence is due to thin-film interference.
The Very Large Array, an interferometric array formed from many smaller telescopes, like many larger radio telescopes.

Phenomenon in which two waves combine by adding their displacement together at every single point in space and time, to form a resultant wave of greater, lower, or the same amplitude.

- Wave interference
The interference of two waves. When in phase, the two lower waves create constructive interference (left), resulting in a wave of greater amplitude. When 180° out of phase, they create destructive interference (right).

27 related topics with Alpha

Overall
Same double-slit assembly (0.7 mm between slits); in top image, one slit is closed. In the single-slit image, a diffraction pattern (the faint spots on either side of the main band) forms due to the nonzero width of the slit. This diffraction pattern is also seen in the double-slit image, but with many smaller interference fringes.

Double-slit experiment

6 links

Demonstration that light and matter can display characteristics of both classically defined waves and particles; moreover, it displays the fundamentally probabilistic nature of quantum mechanical phenomena.

Demonstration that light and matter can display characteristics of both classically defined waves and particles; moreover, it displays the fundamentally probabilistic nature of quantum mechanical phenomena.

Same double-slit assembly (0.7 mm between slits); in top image, one slit is closed. In the single-slit image, a diffraction pattern (the faint spots on either side of the main band) forms due to the nonzero width of the slit. This diffraction pattern is also seen in the double-slit image, but with many smaller interference fringes.
Buildup of interference pattern from individual particle detections
Photons in a Mach–Zehnder interferometer exhibit wave-like interference and particle-like detection at single-photon detectors.
A diagram of Wheeler's delayed choice experiment, showing the principle of determining the path of the photon after it passes through the slit
A laboratory double-slit assembly; distance between top posts approximately 2.5 cm (one inch).
Near-field intensity distribution patterns for plasmonic slits with equal widths (A) and non-equal widths (B).
Two-slit diffraction pattern by a plane wave
Photo of the double-slit interference of sunlight.
Two slits are illuminated by a plane wave.
One of an infinite number of equally likely paths used in the Feynman path integral (see also: Wiener process)
An example of the uncertainty principle related to the relational interpretation. The more that is known about the position of a particle, the less is known about the velocity, and vice versa

Changes in the path-lengths of both waves result in a phase shift, creating an interference pattern.

Figure 1: The amplitude of a single frequency wave as a function of time t (red) and a copy of the same wave delayed by τ (blue). The coherence time of the wave is infinite since it is perfectly correlated with itself for all delays τ.

Coherence (physics)

5 links

In physics, two wave sources are coherent if their frequency and waveform are identical.

In physics, two wave sources are coherent if their frequency and waveform are identical.

Figure 1: The amplitude of a single frequency wave as a function of time t (red) and a copy of the same wave delayed by τ (blue). The coherence time of the wave is infinite since it is perfectly correlated with itself for all delays τ.
Figure 2: The amplitude of a wave whose phase drifts significantly in time τc as a function of time t (red) and a copy of the same wave delayed by 2τc(green). At any particular time t the wave can interfere perfectly with its delayed copy. But, since half the time the red and green waves are in phase and half the time out of phase, when averaged over t any interference disappears at this delay.
Figure 3: The amplitude of a wavepacket whose amplitude changes significantly in time τc (red) and a copy of the same wave delayed by 2τc(green) plotted as a function of time t. At any particular time the red and green waves are uncorrelated; one oscillates while the other is constant and so there will be no interference at this delay. Another way of looking at this is the wavepackets are not overlapped in time and so at any particular time there is only one nonzero field so no interference can occur.
Figure 4: The time-averaged intensity (blue) detected at the output of an interferometer plotted as a function of delay τ for the example waves in Figures 2 and 3. As the delay is changed by half a period, the interference switches between constructive and destructive. The black lines indicate the interference envelope, which gives the degree of coherence. Although the waves in Figures 2 and 3 have different time durations, they have the same coherence time.
Figure 10: Waves of different frequencies interfere to form a localized pulse if they are coherent.
Figure 11: Spectrally incoherent light interferes to form continuous light with a randomly varying phase and amplitude
Figure 5: A plane wave with an infinite coherence length.
Figure 6: A wave with a varying profile (wavefront) and infinite coherence length.
Figure 7: A wave with a varying profile (wavefront) and finite coherence length.
Figure 8: A wave with finite coherence area is incident on a pinhole (small aperture). The wave will diffract out of the pinhole. Far from the pinhole the emerging spherical wavefronts are approximately flat. The coherence area is now infinite while the coherence length is unchanged.
Figure 9: A wave with infinite coherence area is combined with a spatially shifted copy of itself. Some sections in the wave interfere constructively and some will interfere destructively. Averaging over these sections, a detector with length D will measure reduced interference visibility. For example, a misaligned Mach–Zehnder interferometer will do this.

Coherence is an ideal property of waves that enables stationary (i.e. temporally or spatially constant) interference.

Figure 1. The light path through a Michelson interferometer. The two light rays with a common source combine at the half-silvered mirror to reach the detector. They may either interfere constructively (strengthening in intensity) if their light waves arrive in phase, or interfere destructively (weakening in intensity) if they arrive out of phase, depending on the exact distances between the three mirrors.

Interferometry

5 links

Figure 1. The light path through a Michelson interferometer. The two light rays with a common source combine at the half-silvered mirror to reach the detector. They may either interfere constructively (strengthening in intensity) if their light waves arrive in phase, or interfere destructively (weakening in intensity) if they arrive out of phase, depending on the exact distances between the three mirrors.
Figure 2. Formation of fringes in a Michelson interferometer
Figure 3. Colored and monochromatic fringes in a Michelson interferometer: (a) White light fringes where the two beams differ in the number of phase inversions; (b) White light fringes where the two beams have experienced the same number of phase inversions; (c) Fringe pattern using monochromatic light (sodium D lines)
Figure 4. Four examples of common-path interferometers
Figure 5. Two wavefront splitting interferometers
Figure 6. Three amplitude-splitting interferometers: Fizeau, Mach–Zehnder, and Fabry Pérot.
Interferometry is used in radio astronomy, with timing offsets of D sin θ
Figure 11. The VLA interferometer
ALMA is an astronomical interferometer located in Chajnantor Plateau
Figure 13. Optical flat interference fringes. (left) flat surface, (right) curved surface.
How interference fringes are formed by an optical flat resting on a reflective surface. The gap between the surfaces and the wavelength of the light waves are greatly exaggerated.
Figure 14. Twyman–Green Interferometer
Figure 15. Optical testing with a Fizeau interferometer and a computer generated hologram
Figure 16. Frequency comb of a mode-locked laser. The dashed lines represent an extrapolation of the mode frequencies towards the frequency of the carrier–envelope offset (CEO). The vertical grey line represents an unknown optical frequency. The horizontal black lines indicate the two lowest beat frequency measurements.
Figure 17. Phase shifting and Coherence scanning interferometers
Figure 18. Lunate cells of Nepenthes khasiana visualized by Scanning White Light Interferometry (SWLI)
Figure 19. Twyman–Green interferometer set up as a white light scanner
Figure 20. InSAR Image of Kilauea, Hawaii showing fringes caused by deformation of the terrain over a six-month period.
Figure 21. ESPI fringes showing a vibration mode of a clamped square plate
Figure 24. Spyrogira cell (detached from algal filament) under phase contrast
Figure 25. Toxoplasma gondii unsporulated oocyst, differential interference contrast
Figure 26. High resolution phase-contrast x-ray image of a spider

Interferometry is a technique which uses the interference of superimposed waves to extract information.

Wave functions of the electron in a hydrogen atom at different energy levels. Quantum mechanics cannot predict the exact location of a particle in space, only the probability of finding it at different locations. The brighter areas represent a higher probability of finding the electron.

Quantum mechanics

4 links

Fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles.

Fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles.

Wave functions of the electron in a hydrogen atom at different energy levels. Quantum mechanics cannot predict the exact location of a particle in space, only the probability of finding it at different locations. The brighter areas represent a higher probability of finding the electron.
Fig. 1
Position space probability density of a Gaussian wave packet moving in one dimension in free space.
1-dimensional potential energy box (or infinite potential well)
Some trajectories of a harmonic oscillator (i.e. a ball attached to a spring) in classical mechanics (A-B) and quantum mechanics (C-H). In quantum mechanics, the position of the ball is represented by a wave (called the wave function), with the real part shown in blue and the imaginary part shown in red. Some of the trajectories (such as C, D, E, and F) are standing waves (or "stationary states"). Each standing-wave frequency is proportional to a possible energy level of the oscillator. This "energy quantization" does not occur in classical physics, where the oscillator can have any energy.
Schematic of a Mach–Zehnder interferometer.
Max Planck is considered the father of the quantum theory.
The 1927 Solvay Conference in Brussels was the fifth world physics conference.

Another consequence of the mathematical rules of quantum mechanics is the phenomenon of quantum interference, which is often illustrated with the double-slit experiment.

Surface waves in water showing water ripples

Wave

4 links

Propagating dynamic disturbance of one or more quantities.

Propagating dynamic disturbance of one or more quantities.

Surface waves in water showing water ripples
Example of biological waves expanding over the brain cortex, an example of spreading depolarizations.
Wavelength λ, can be measured between any two corresponding points on a waveform
Animation of two waves, the green wave moves to the right while blue wave moves to the left, the net red wave amplitude at each point is the sum of the amplitudes of the individual waves. Note that f(x,t) + g(x,t) = u(x,t)
Sine, square, triangle and sawtooth waveforms.
Amplitude modulation can be achieved through f(x,t) = 1.00×sin(2π/0.10×(x−1.00×t)) and g(x,t) = 1.00×sin(2π/0.11×(x−1.00×t))only the resultant is visible to improve clarity of waveform.
Illustration of the envelope (the slowly varying red curve) of an amplitude-modulated wave. The fast varying blue curve is the carrier wave, which is being modulated.
The red square moves with the phase velocity, while the green circles propagate with the group velocity
A wave with the group and phase velocities going in different directions
Standing wave. The red dots represent the wave nodes
Light beam exhibiting reflection, refraction, transmission and dispersion when encountering a prism
Sinusoidal traveling plane wave entering a region of lower wave velocity at an angle, illustrating the decrease in wavelength and change of direction (refraction) that results.
Identical waves from two sources undergoing interference. Observed at the bottom one sees 5 positions where the waves add in phase, but in between which they are out of phase and cancel.
Schematic of light being dispersed by a prism. Click to see animation.
400px
Formation of a shock wave by a plane.
300 px
A propagating wave packet; in general, the envelope of the wave packet moves at a different speed than the constituent waves.
Animation showing the effect of a cross-polarized gravitational wave on a ring of test particles
One-dimensional standing waves; the fundamental mode and the first 5 overtones.
A two-dimensional standing wave on a disk; this is the fundamental mode.
A standing wave on a disk with two nodal lines crossing at the center; this is an overtone.

This phenomenon arises as a result of interference between two waves traveling in opposite directions.

Thomas Young's sketch of two-slit diffraction of waves, 1803

Wave–particle duality

4 links

Concept in quantum mechanics that every particle or quantum entity may be described as either a particle or a wave.

Concept in quantum mechanics that every particle or quantum entity may be described as either a particle or a wave.

Thomas Young's sketch of two-slit diffraction of waves, 1803
The photoelectric effect. Incoming photons on the left strike a metal plate (bottom), and eject electrons, depicted as flying off to the right.
Propagation of de Broglie waves in 1d—real part of the complex amplitude is blue, imaginary part is green. The probability (shown as the colour opacity) of finding the particle at a given point x is spread out like a waveform; there is no definite position of the particle. As the amplitude increases above zero the curvature decreases, so the amplitude decreases again, and vice versa—the result is an alternating amplitude: a wave. Top: Plane wave. Bottom: Wave packet.
Couder experiments, "materializing" the pilot wave model
Particle impacts make visible the interference pattern of waves.
A quantum particle is represented by a wave packet.
Interference of a quantum particle with itself.

The resulting Huygens–Fresnel principle was extremely successful at reproducing light's behaviour and was subsequently supported by Thomas Young's discovery of wave interference of light by his double-slit experiment in 1801.

Figure 1. A basic Michelson interferometer, not including the optical source and detector.

Michelson interferometer

4 links

Common configuration for optical interferometry and was invented by the 19/20th-century American physicist Albert Abraham Michelson.

Common configuration for optical interferometry and was invented by the 19/20th-century American physicist Albert Abraham Michelson.

Figure 1. A basic Michelson interferometer, not including the optical source and detector.
This image demonstrates a simple but typical Michelson interferometer. The bright yellow line indicates the path of light.
Figure 2. Path of light in Michelson interferometer.
Figure 3. Formation of fringes in a Michelson interferometer
This photo shows the fringe pattern formed by the Michelson interferometer, using monochromatic light (sodium D lines).
Figure 4. Michelson interferometers using a white light source
Figure 5. Fourier transform spectroscopy.
Figure 6. Twyman–Green interferometer.
Figure 7. Helioseismic Magnetic Imager (HMI) dopplergram showing the velocity of gas flows on the solar surface. Red indicates motion away from the observer, and blue indicates motion towards the observer.
Figure 8. Typical optical setup of single point OCT
Figure 9. Magnetogram (magnetic image) of the Sun showing magnetically intense areas (active regions) in black and white, as imaged by the Helioseismic and Magnetic Imager (HMI) on the Solar Dynamics Observatory

The resulting interference pattern that is not directed back toward the source is typically directed to some type of photoelectric detector or camera.

The wavelength of a sine wave, λ, can be measured between any two points with the same phase, such as between crests (on top), or troughs (on bottom), or corresponding zero crossings as shown.

Wavelength

3 links

Spatial period of a periodic wave—the distance over which the wave's shape repeats.

Spatial period of a periodic wave—the distance over which the wave's shape repeats.

The wavelength of a sine wave, λ, can be measured between any two points with the same phase, such as between crests (on top), or troughs (on bottom), or corresponding zero crossings as shown.
Sinusoidal standing waves in a box that constrains the end points to be nodes will have an integer number of half wavelengths fitting in the box.
A standing wave (black) depicted as the sum of two propagating waves traveling in opposite directions (red and blue)
Wavelength is decreased in a medium with slower propagation.
Refraction: upon entering a medium where its speed is lower, the wave changes direction.
Separation of colors by a prism (click for animation)
Various local wavelengths on a crest-to-crest basis in an ocean wave approaching shore
A sinusoidal wave travelling in a nonuniform medium, with loss
A wave on a line of atoms can be interpreted according to a variety of wavelengths.
Near-periodic waves over shallow water
Wavelength of a periodic but non-sinusoidal waveform.
A propagating wave packet
Pattern of light intensity on a screen for light passing through two slits. The labels on the right refer to the difference of the path lengths from the two slits, which are idealized here as point sources.
Diffraction pattern of a double slit has a single-slit envelope.
Relationship between wavelength, angular wavelength, and other wave properties.

The term wavelength is also sometimes applied to modulated waves, and to the sinusoidal envelopes of modulated waves or waves formed by interference of several sinusoids.

Figure 1. The Mach–Zehnder interferometer is frequently used in the fields of aerodynamics, plasma physics and heat transfer to measure pressure, density, and temperature changes in gases. In this figure, we imagine analyzing a candle flame. Either output image may be monitored.

Mach–Zehnder interferometer

3 links

Device used to determine the relative phase shift variations between two collimated beams derived by splitting light from a single source.

Device used to determine the relative phase shift variations between two collimated beams derived by splitting light from a single source.

Figure 1. The Mach–Zehnder interferometer is frequently used in the fields of aerodynamics, plasma physics and heat transfer to measure pressure, density, and temperature changes in gases. In this figure, we imagine analyzing a candle flame. Either output image may be monitored.
Figure 2. Localized fringes result when an extended source is used in a Mach–Zehnder interferometer. By appropriately adjusting the mirrors and beam splitters, the fringes can be localized in any desired plane.
Figure 3. Effect of a sample on the phase of the output beams in a Mach–Zehnder interferometer

White light in particular requires the optical paths to be simultaneously equalized over all wavelengths, or no fringes will be visible (unless a monochromatic filter is used to isolate a single wavelength).

A triangular prism dispersing a beam of white light. The longer wavelengths (red) and the shorter wavelengths (blue) are separated.

Light

3 links

Electromagnetic radiation within the portion of the electromagnetic spectrum that is perceived by the human eye.

Electromagnetic radiation within the portion of the electromagnetic spectrum that is perceived by the human eye.

A triangular prism dispersing a beam of white light. The longer wavelengths (red) and the shorter wavelengths (blue) are separated.
The electromagnetic spectrum, with the visible portion highlighted
800px
Beam of sun light inside the cavity of Rocca ill'Abissu at Fondachelli-Fantina, Sicily
Due to refraction, the straw dipped in water appears bent and the ruler scale compressed when viewed from a shallow angle.
Hong Kong illuminated by colourful artificial lighting.
Pierre Gassendi.
Christiaan Huygens.
Thomas Young's sketch of a double-slit experiment showing diffraction. Young's experiments supported the theory that light consists of waves.
400x400px

Soon after, Heinrich Hertz confirmed Maxwell's theory experimentally by generating and detecting radio waves in the laboratory and demonstrating that these waves behaved exactly like visible light, exhibiting properties such as reflection, refraction, diffraction and interference.