Thin-film interference
Thin-film interference is the phenomenon that occurs when incident light waves reflected by the upper and lower boundaries of a thin film
Thin film
A thin film is a layer of material ranging from fractions of a nanometer to several micrometers in thickness. Electronic semiconductor devices and optical coatings are the main applications benefiting from thin film construction....

 interfere with one another to form a new wave. Studying this new wave can reveal information about the surfaces from which its components reflected, including the thickness of the film or the effective refractive index
Refractive index
In optics the refractive index or index of refraction of a substance or medium is a measure of the speed of light in that medium. It is expressed as a ratio of the speed of light in vacuum relative to that in the considered medium....

 of the film medium. Thin films have many commercial applications including anti-reflection coatings, mirror
A mirror is an object that reflects light or sound in a way that preserves much of its original quality prior to its contact with the mirror. Some mirrors also filter out some wavelengths, while preserving other wavelengths in the reflection...

s, and optical filters.


A thin film
Thin film
A thin film is a layer of material ranging from fractions of a nanometer to several micrometers in thickness. Electronic semiconductor devices and optical coatings are the main applications benefiting from thin film construction....

 is a layer of material with thickness in the sub-nanometer to micron range. As light strikes the surface of a film it is either transmitted or reflected at the upper surface. Light that is transmitted reaches the bottom surface and may once again be transmitted or reflected. The Fresnel equations
Fresnel equations
The Fresnel equations , deduced by Augustin-Jean Fresnel , describe the behaviour of light when moving between media of differing refractive indices...

 provide a quantitative description of how much of the light will be transmitted or reflected at an interface. The light reflected from the upper and lower surfaces will interfere. The degree of constructive or destructive interference between the two light waves is dependent upon the difference in their phase. This difference is dependent upon the thickness of the film layer, the refractive index of the film, and the angle of incidence of the original wave on the film. Additionally, a phase shift of 180° or radians may be introduced upon reflection at a boundary depending on the refractive indices of the materials on either side of the boundary. This phase shift occurs if the refractive index of the medium the light is travelling through is less than the refractive of the material it is striking. In other words, if and the light is travelling from material 1 to material 2, then a phase shift will occur upon reflection. The pattern of light that results from this interference can appear either as light and dark bands or as colorful bands depending upon the source of the incident light.

Consider light incident on a thin film and reflected by both the upper and lower boundaries. The optical path difference (OPD) of the reflected light must be calculated in order to determine the condition for interference. Referring to Figure 1, the OPD between the two waves is the following:
Using Snell's Law,
Interference will be constructive if the optical path difference is equal to an integer multiple of the wavelength of light, .
This condition may change after considering possible phase shifts that occur upon reflection.

Monochromatic source

In the case where incident light is monochromatic
Monochrome describes paintings, drawings, design, or photographs in one color or shades of one color. A monochromatic object or image has colors in shades of limited colors or hues. Images using only shades of grey are called grayscale or black-and-white...

 in nature, interference patterns will appear as light and dark bands. Light bands correspond to regions at which constructive interference is occurring between the reflected waves and dark bands correspond to destructive interference regions. As the thickness of the film varies from one location to another, the interference may change from constructive to destructive. A good example of this phenomenon, termed "Newton's rings
Newton's rings
The phenomenon of Newton's rings, named after Isaac Newton who first studied them in 1717, is an interference pattern caused by the reflection of light between two surfaces - a spherical surface and an adjacent flat surface...

," demonstrates the interference pattern that results when light is reflected from a spherical surface adjacent to a flat surface. Concentric rings are viewed when the surface is illuminated with monochromatic light.

Broadband source

If the incident light is broadband, or white, such as light from the sun, interference patters will appear as colorful bands. Different wavelengths of light will create constructive interference for different film thicknesses. Different regions of the film will appear to be different colors depending on the local film thickness.


The type of interference that occurs when light is reflected from a thin film is dependent upon the wavelength and angle of the incident light, the thickness of the film, the refractive indices of the material on either side of the film, and the index of the film medium. Various possible film configurations and the related equations are explained in more detail in the examples below.

Soap bubble

In the case of a soap bubble
Soap bubble
A soap bubble is a thin film of soapy water enclosing air, that forms a hollow sphere with an iridescent surface. Soap bubbles usually last for only a few seconds before bursting, either on their own or on contact with another object. They are often used for children's enjoyment, but they are also...

, light travels through air and strikes a soap film. The air has a refractive index of 1 () and the film has an index that is larger than 1 (). The reflection that occurs at the upper boundary of the film (the air-film boundary) will introduce a 180° phase shift in the reflected wave because the refractive index of the air is less than the index of the film (). Light that is transmitted at the upper air-film interface will continue to the lower film-air interface where it can be reflected or transmitted. The reflection that occurs at this boundary will not change the phase of the reflected wave because . The condition for interference for a soap bubble is the following: for constructive interference of reflected light for destructive interference of reflected light
Where is the film thickness, is the refractive index of the film, is the angle of incidence of the wave on the lower boundary, is an integer, and is the wavelength of light.

Oil film

In the case of a thin oil film, a layer of oil sits atop a layer of water. The oil may have an index of refraction near 1.5 and the water has an index of 1.33. As in the case of the soap bubble, the materials on either side of the oil film (air and water) both have refractive indices that are less than the index of the film. . There will be a phase shift upon reflection from the upper boundary because but no shift upon reflection from the lower boundary because . The equations for interference will be the same. for constructive interference of reflected light for destructive interference of reflected light

Anti-reflection coatings

An anti-reflection coating eliminates reflected light and maximizes transmitted light in an optical system. A film is designed such that reflected light produces destructive interference and transmitted light produces constructive interference for a given wavelength of light. In the simplest implementation of such a coating, the film is created so that its optical thickness is a quarter-wavelength of the incident light and its refractive index is greater than the index of air and less than the index of glass.
A 180° phase shift will be induced upon reflection at both the top and bottom interfaces of the film because and . The equations for interference of the reflected light are: for constructive interference for destructive interference
If the optical thickness is equal to a quarter-wavelength of the incident light and if the light strikes the film at normal incidence , the reflected waves will be completely out of phase and will destructively interfere. Further reduction in reflection is possible by adding more layers, each designed to match a specific wavelength of light.

It should also be noted that interference of transmitted light will be completely constructive for these films.


Thin films are used commercially in anti-reflection coatings, mirrors, and optical filters. They can be engineered to control the amount of light reflected or transmitted at a surface for a given wavelength. A Fabry–Pérot etalon takes advantage of thin film interference to selectively choose which wavelengths of light are allowed to transmit through the device. These films are created through deposition processes in which material is added to a substrate in a controlled manner. Methods include chemical vapor deposition
Chemical vapor deposition
Chemical vapor deposition is a chemical process used to produce high-purity, high-performance solid materials. The process is often used in the semiconductor industry to produce thin films. In a typical CVD process, the wafer is exposed to one or more volatile precursors, which react and/or...

 and various physical vapor deposition
Physical vapor deposition
Physical vapor deposition is a variety of vacuum deposition and is a general term used to describe any of a variety of methods to deposit thin films by the condensation of a vaporized form of the desired film material onto various workpiece surfaces...


Thin films are also found in nature. Many animals have a layer of tissue behind the retina, the Tapetum lucidum
Tapetum lucidum
The tapetum lucidum is a layer of tissue in the eye of many vertebrate animals....

, that aids in light collecting. The effects of thin-film interference can also be seen in oil slicks and soap bubbles.

Ellipsometry is an optical technique for the investigation of the dielectric properties of thin films....

 is a technique that is often used to measure properties of thin films. In a typical ellipsometry experiment polarized light is reflected off a film surface and is measured by a detector. The complex reflectance ratio, , of the system is measured. A model analysis in then conducted in which this information is used to determine film layer thicknesses and refractive indices.

Dual polarisation interferometry
Dual Polarisation Interferometry
Dual polarization interferometry is an analytical technique that can probe molecular scale layers adsorbed to the surface of a waveguide by using the evanescent wave of a laser beam confined to the waveguide...

 is an emerging technique for measuring refractive index and thickness of molecular scale thin films and how these change when stimulated.


Iridescence is generally known as the property of certain surfaces which appear to change color as the angle of view or the angle of illumination changes...

 caused by thin-film interference is a commonly observed phenomenon in nature, being found in a variety of plants and animals. One of the first known studies of this phenomenon was conducted by Robert Hooke
Robert Hooke
Robert Hooke FRS was an English natural philosopher, architect and polymath.His adult life comprised three distinct periods: as a scientific inquirer lacking money; achieving great wealth and standing through his reputation for hard work and scrupulous honesty following the great fire of 1666, but...

 in 1665. In Micrographia
Micrographia is a historic book by Robert Hooke, detailing the then thirty year-old Hooke's observations through various lenses. Published in September 1665, the first major publication of the Royal Society, it was the first scientific best-seller, inspiring a wide public interest in the new...

, Hooke postulated that the iridescence in peacock feathers was caused by thin, alternating layers of plate and air. In 1704, Isaac Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...

 stated in his book, Opticks
Opticks is a book written by English physicist Isaac Newton that was released to the public in 1704. It is about optics and the refraction of light, and is considered one of the great works of science in history...

, that the iridescence in a peacock feather was due to the fact that the transparent layers in the feather were so thin. In 1801, Thomas Young
Thomas Young (scientist)
Thomas Young was an English polymath. He is famous for having partly deciphered Egyptian hieroglyphics before Jean-François Champollion eventually expanded on his work...

 provided the first explanation of constructive and destructive interference. Young's contribution went largely unnoticed until the work of Augustin Fresnel, in 1816, helped to establish the wave theory of light. However, very little explanation could be made of the iridescence until the late 1800s, when James Maxwell
James Clerk Maxwell
James Clerk Maxwell of Glenlair was a Scottish physicist and mathematician. His most prominent achievement was formulating classical electromagnetic theory. This united all previously unrelated observations, experiments and equations of electricity, magnetism and optics into a consistent theory...

 and Heinrich Hertz helped to explain the electromagnetic nature of light. After the invention of the Fabry–Perot interferometer, in 1899, the mechanisms of thin-film interference could be demonstrated on a larger scale.

In much of the early work, scientists tried to explain iridescence, in animals like peacocks and scarab beetle
The family Scarabaeidae as currently defined consists of over 30,000 species of beetles worldwide. The species in this large family are often called scarabs or scarab beetles. The classification of this family is fairly unstable, with numerous competing theories, and new proposals appearing quite...

s, as some form of surface color, such as a dye or pigment that might alter the light when reflected from different angles. In 1919, Lord Rayleigh proposed that the bright, changing colors were not caused by dyes or pigments, but by microscopic structures, which he termed "structural colors." In 1923, C. W. Mason noted that the barbules in the peacock feather were made from very thin layers. Some of these layers were colored while others were transparent. He noticed that pressing the barbule would shift the color toward the blue, while swelling it with a chemical would shift it toward the red. He also found that bleaching the pigments from the feathers did not remove the iridescence. This helped to dispel the surface color theory and reinforce the structural color theory.

In 1925, Ernest Merritt
Ernest Merritt
Ernest George Merritt was Dean of the Graduate School, Cornell University; Chair of the Physics Department.-Early life and career :...

, in his paper A Spectrophotometric Study of Certain Cases of Structural Color, first described the process of thin-film interference as an explanation for the iridescence. The first examination of iridescent feathers by an electron microscope
Electron microscope
An electron microscope is a type of microscope that uses a beam of electrons to illuminate the specimen and produce a magnified image. Electron microscopes have a greater resolving power than a light-powered optical microscope, because electrons have wavelengths about 100,000 times shorter than...

 occurred in 1939, revealing complex thin-film structures, while an examination of the morpho
Morpho (butterfly)
A Morpho butterfly may be one of over 80 species of butterflies in the genus Morpho. They are Neotropical butterflies found mostly in South America as well as Mexico and Central America. Morphos range in wingspan from the 7.5 cm M. rhodopteron to the imposing 20 cm Sunset Morpho, M....

A butterfly is a mainly day-flying insect of the order Lepidoptera, which includes the butterflies and moths. Like other holometabolous insects, the butterfly's life cycle consists of four parts: egg, larva, pupa and adult. Most species are diurnal. Butterflies have large, often brightly coloured...

, in 1942, revealed an extremely tiny array of thin-film structures on the nanometer scale.

The first production of thin-film coatings occurred quite by accident. In 1817, Joseph Fraunhofer discovered that, by tarnishing glass
Glass is an amorphous solid material. Glasses are typically brittle and optically transparent.The most familiar type of glass, used for centuries in windows and drinking vessels, is soda-lime glass, composed of about 75% silica plus Na2O, CaO, and several minor additives...

 with nitric acid
Nitric acid
Nitric acid , also known as aqua fortis and spirit of nitre, is a highly corrosive and toxic strong acid.Colorless when pure, older samples tend to acquire a yellow cast due to the accumulation of oxides of nitrogen. If the solution contains more than 86% nitric acid, it is referred to as fuming...

, he could reduce the reflections on the surface. In 1819, after watching a layer of alcohol evaporate from a sheet of glass, Fraunhofer noted that colors appeared just before the liquid evaporated completely, deducing that any thin film of transparent material will produce colors.

Little advancement was made in thin-film coating technology until 1936, when John Strong began evaporating fluorite
Fluorite is a halide mineral composed of calcium fluoride, CaF2. It is an isometric mineral with a cubic habit, though octahedral and more complex isometric forms are not uncommon...

 in order to make anti-reflection coatings on glass. During the 1930s, improvements in vacuum pump
Vacuum pump
A vacuum pump is a device that removes gas molecules from a sealed volume in order to leave behind a partial vacuum. The first vacuum pump was invented in 1650 by Otto von Guericke.- Types :Pumps can be broadly categorized according to three techniques:...

s made vacuum deposition
Vacuum deposition
Vacuum deposition is a family of processes used to deposit layers atom-by-atom or molecule-by-molecule at sub-atmospheric pressure on a solid surface. The layers may be as thin as one atom to millimeters thick . There may be multiple layers of different materials...

 methods, like sputtering
Sputtering is a process whereby atoms are ejected from a solid target material due to bombardment of the target by energetic particles. It is commonly used for thin-film deposition, etching and analytical techniques .-Physics of sputtering:...

, possible. In 1939, W. Geffcken created the first interference filter
Interference filter
An interference filter or dichroic filter is an optical filter that reflects one or more spectral bands or lines and transmits others, while maintaining a nearly zero coefficient of absorption for all wavelengths of interest...

s using dielectric
A dielectric is an electrical insulator that can be polarized by an applied electric field. When a dielectric is placed in an electric field, electric charges do not flow through the material, as in a conductor, but only slightly shift from their average equilibrium positions causing dielectric...


See also

  • Thin-film optics
    Thin-film optics
    Thin-film optics is the branch of optics that deals with very thin structured layers of different materials. In order to exhibit thin-film optics, the thickness of the layers of material must be on the order of the wavelengths of visible light...

  • Transfer-matrix method (optics)
    Transfer-matrix method (optics)
    The transfer-matrix method is a method used in optics and acoustics to analyze the propagation of electromagnetic or acoustic waves through a stratified medium. This is for example relevant for the design of anti-reflective coatings and dielectric mirrors.The reflection of light from a single...

  • Reflectometric interference spectroscopy
    Reflectometric interference spectroscopy
    Reflectometric interference spectroscopy is a physical method based on the interference of white light at thin films, which is used to investigate molecular interaction.-Principle:...

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