The shearing interferometer is an extremely simple means to observe interference and to use this phenomenon to test the collimation of light beams, especially from laser sources which have a coherence length which is usually significantly longer than the thickness of the shear plate (see graphics) so that the basic condition for interference is fulfilled.
The testing device consists of a high-quality optical glass, like N-BK7, with extremely flat optical surfaces that are usually at a slight angle to each other. When a plane wave is incident at an angle of 45°, which gives maximum sensitivity, it is reflected two times. The two reflections are laterally separated due to the finite thickness of the plate and by the wedge. This separation is referred to as the shear and has given the instrument its name. The shear can also be produced by gratings.
Parallel-sided shear plates are sometimes used, but the interpretation of the interference fringes of wedged plates is relatively easy and straightforward. Wedged shear plates produce a graded path difference between the front and back surface reflections; as a consequence, a parallel beam of light produces a linear fringe pattern within the overlap.
With a plane wavefront incident, the overlap of the two reflected beams shows interference fringes with a spacing of , where is the spacing perpendicular to shear, is the wavelength of the beam, n the refractive index, and the wedge angle. This equation makes the simplification that the distance from the wedged shear plate to the observation plane is small relative to the wavefront radius of curvature at the observation plane. The fringes are equally spaced and will be exactly perpendicular to the wedge orientation and parallel to a usually present wire cursor aligned along the beam axis in the shearing interferometer. The orientation of the fringes varies when the beam is not perfectly collimated. In the case of a noncollimated beam incident on a wedged shear plate, the path difference between the two reflected wavefronts is increased or decreased from the case of perfect collimation depending on the sign of the curvature. The pattern is then rotated and the beam's wavefront radius of curvature can be calculated: , with the shear distance, the fringe distance, the wavelength and the angular deviation of the fringe alignment from that of perfect collimation. If the spacing normal to the fringes is used instead, this equation becomes , where is the fringe spacing normal to the fringes. [1]
Diffraction is the deviation of waves from straight-line propagation due to an obstacle or through an aperture. The diffracting object or aperture effectively becomes a secondary source of the propagating wave. Diffraction is the same physical effect as interference, but interference is typically applied to superposition of a few waves and the term diffraction is used when many waves are superposed.
In physics, interference is a phenomenon in which two coherent waves are combined by adding their intensities or displacements with due consideration for their phase difference. The resultant wave may have greater intensity or lower amplitude if the two waves are in phase or out of phase, respectively. Interference effects can be observed with all types of waves, for example, light, radio, acoustic, surface water waves, gravity waves, or matter waves as well as in loudspeakers as electrical waves.
In physics, coherence length is the propagation distance over which a coherent wave maintains a specified degree of coherence. Wave interference is strong when the paths taken by all of the interfering waves differ by less than the coherence length. A wave with a longer coherence length is closer to a perfect sinusoidal wave. Coherence length is important in holography and telecommunications engineering.
The Michelson–Morley experiment was an attempt to measure the motion of the Earth relative to the luminiferous aether, a supposed medium permeating space that was thought to be the carrier of light waves. The experiment was performed between April and July 1887 by American physicists Albert A. Michelson and Edward W. Morley at what is now Case Western Reserve University in Cleveland, Ohio, and published in November of the same year.
Interferometry is a technique which uses the interference of superimposed waves to extract information. Interferometry typically uses electromagnetic waves and is an important investigative technique in the fields of astronomy, fiber optics, engineering metrology, optical metrology, oceanography, seismology, spectroscopy, quantum mechanics, nuclear and particle physics, plasma physics, biomolecular interactions, surface profiling, microfluidics, mechanical stress/strain measurement, velocimetry, optometry, and making holograms.
Ray transfer matrix analysis is a mathematical form for performing ray tracing calculations in sufficiently simple problems which can be solved considering only paraxial rays. Each optical element is described by a 2 × 2ray transfer matrix which operates on a vector describing an incoming light ray to calculate the outgoing ray. Multiplication of the successive matrices thus yields a concise ray transfer matrix describing the entire optical system. The same mathematics is also used in accelerator physics to track particles through the magnet installations of a particle accelerator, see electron optics.
In optics, a Fabry–Pérot interferometer (FPI) or etalon is an optical cavity made from two parallel reflecting surfaces. Optical waves can pass through the optical cavity only when they are in resonance with it. It is named after Charles Fabry and Alfred Perot, who developed the instrument in 1899. Etalon is from the French étalon, meaning "measuring gauge" or "standard".
Coherence expresses the potential for two waves to interfere. Two monochromatic beams from a single source always interfere. Wave sources are not strictly monochromatic: they may be partly coherent. Beams from different sources are mutually incoherent.
The Michelson interferometer is a common configuration for optical interferometry and was invented by the 19/20th-century American physicist Albert Abraham Michelson. Using a beam splitter, a light source is split into two arms. Each of those light beams is reflected back toward the beamsplitter which then combines their amplitudes using the superposition principle. The resulting interference pattern that is not directed back toward the source is typically directed to some type of photoelectric detector or camera. For different applications of the interferometer, the two light paths can be with different lengths or incorporate optical elements or even materials under test.
In optics, the Fraunhofer diffraction equation is used to model the diffraction of waves when plane waves are incident on a diffracting object, and the diffraction pattern is viewed at a sufficiently long distance from the object, and also when it is viewed at the focal plane of an imaging lens. In contrast, the diffraction pattern created near the diffracting object and is given by the Fresnel diffraction equation.
The Sagnac effect, also called Sagnac interference, named after French physicist Georges Sagnac, is a phenomenon encountered in interferometry that is elicited by rotation. The Sagnac effect manifests itself in a setup called a ring interferometer or Sagnac interferometer. A beam of light is split and the two beams are made to follow the same path but in opposite directions. On return to the point of entry the two light beams are allowed to exit the ring and undergo interference. The relative phases of the two exiting beams, and thus the position of the interference fringes, are shifted according to the angular velocity of the apparatus. In other words, when the interferometer is at rest with respect to a nonrotating frame, the light takes the same amount of time to traverse the ring in either direction. However, when the interferometer system is spun, one beam of light has a longer path to travel than the other in order to complete one circuit of the mechanical frame, and so takes longer, resulting in a phase difference between the two beams. Georges Sagnac set up this experiment in 1913 in an attempt to prove the existence of the aether that Einstein's theory of special relativity makes superfluous.
An optical flat is an optical-grade piece of glass lapped and polished to be extremely flat on one or both sides, usually within a few tens of nanometres. They are used with a monochromatic light to determine the flatness of other surfaces, by means of wave interference.
Interference lithography is a technique that uses coherent light for patterning regular arrays of fine features without the use of complex optical systems or photomasks.
The air-wedge shearing interferometer is probably the simplest type of interferometer designed to visualize the disturbance of the wavefront after propagation through a test object. This interferometer is based on utilizing a thin wedged air-gap between two optical glass surfaces and can be used with virtually any light source even with non-coherent white light.
Wafer bond characterization refers to the process of evaluating the quality and strength of a bond between two semiconductor wafers. The wafer bond characterization is based on different methods and tests. Considered a high importance of the wafer are the successful bonded wafers without flaws. Those flaws can be caused by void formation in the interface due to unevenness or impurities. The bond connection is characterized for wafer bond development or quality assessment of fabricated wafers and sensors.
Self-mixing or back-injection laser interferometry is an interferometric technique in which a part of the light reflected by a vibrating target is reflected into the laser cavity, causing a modulation both in amplitude and in frequency of the emitted optical beam. In this way, the laser becomes sensitive to the distance traveled by the reflected beam thus becoming a distance, speed or vibration sensor. The advantage compared to a traditional measurement system is a lower cost thanks to the absence of collimation optics and external photodiodes.
A common-path interferometer is a class of interferometers in which the reference beam and sample beams travel along the same path. Examples include the Sagnac interferometer, Zernike phase-contrast interferometer, and the point diffraction interferometer. A common-path interferometer is generally more robust to environmental vibrations than a "double-path interferometer" such as the Michelson interferometer or the Mach–Zehnder interferometer. Although travelling along the same path, the reference and sample beams may travel along opposite directions, or they may travel along the same direction but with the same or different polarization.
As described here, white light interferometry is a non-contact optical method for surface height measurement on 3D structures with surface profiles varying between tens of nanometers and a few centimeters. It is often used as an alternative name for coherence scanning interferometry in the context of areal surface topography instrumentation that relies on spectrally-broadband, visible-wavelength light.
In theoretical physics, the dual graviton is a hypothetical elementary particle that is a dual of the graviton under electric-magnetic duality, as an S-duality, predicted by some formulations of eleven-dimensional supergravity.
Optical holography is a technique which enables an optical wavefront to be recorded and later re-constructed. Holography is best known as a method of generating three-dimensional images but it also has a wide range of other applications.
