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Optical Interferometry, Screenshot (28), Related Formula, Application and…
Optical Interferometry
Introduction
:star: An instrument designed to exploit the interference of light and the fringe pattern that result from optical path differences.
:star: To achieve interference between two coherent beams of light, an interferometer divides an initial beam into two or more parts that travel diverse then reunite to produce an interference pattern.
Michelson Interferometer
:pencil2: Produces interference fringes by splitting a beam of monochromatic light such that one beam hits a fixed mirror and the other hits a moveable mirror. When reflected beams are combined, an interference pattern is formed.
:pencil2: simple in operation, possess the largest field of view for a specified wavelength and possess a relatively low temperature sensitivity.
Working principle
1) The light from source strikes a partially silvered beam splitter, causing part of the beam to be transmitted toward M1, fixed to moveable carriage.
2) The remainder of the beam is reflected from the beam splitter toward a fixed M2. A glass compensation plate along the path M1 ensures that the two paths are effectively identical.
3) The two beams reflected from M1 and M2, re-converge at the beam splitter.
4) The beams fall on the interferometer's viewing screen as the resultant light exhibits interference effects dependent on the length differences between two paths .
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6) When 2d = integer multiple of the light's wavelength, constructive interference is observed at the viewing screen as the crests of the beams overlap and a bright spot or ring is seen as the viewing screen.
Fabry Perot
:pencil2:The Fabry-Perot Interferometer makes use of multiple reflections which follow the interference condition for thin films.
:pencil2:The Fabry-Perot interferometer makes use of the plane parallel to produce an interference pattern by the multiple beams of the transmitted light.
:pencil2:This instrument has been used in precision wavelength measurements, analysis of hyperfine spectral line structure, determination of refractive indices of gases, and the calibration of the standard meter in terms of wavelength.
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How it happened?
:check: Two thick glass or plates are used to enclose a plane parallel "plate" of air between them, which forms the medium within which the beams are multiply.
:check: The important surfaces of the glass plates are therefore the inner ones.
:check: The surfaces are generally polished to a flatness and coated with a highly reflective layer of silver or aluminum.
:check: Silver films are useful in visible region of spectrum while aluminum films are useful in applications below 400 nm.
:check: The interferometer makes use of multiple reflections between two closely spaced partially silvered surfaces. The films must be thin enough to be partially transmitting.
:check: The outer surfaces of the glass plate are purposely formed at a small angle relative to inner faces to eliminate spurious fringe patterns that can arise from the glass itself acting as a parallel plate.
:check: Part of the light is transmitted each time the light reaches the second surface, resulting in multiple offset beams which can be interfere with each other.
:check: The large number of interfering rays produces an interferometer, with extremely high resolution, somewhat like the multiple slits of a diffraction grating increase its resolution.
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Formula related
Fabry-Perot Resolution - Part 1
A high-resolution interferometer, the Fabry-Perot Interferometer has a resolvance of (refer to Diagram provided):
Fabry-Perot Resolution - Part 2
which means that the least separation of two spectral lines is (given by diagram)
Fabry-Perot Resolution - Part 3
This separation means that the two wavelengths satisfy the Rayleigh criterion. The interferometer can also be characterized by its free spectral range, the change in wavelength necessary to shift the fringe system by one fringe: (refer to Diagram)
Mach Zehnder
:pen: Mach–Zehnder interferometer is a device used to determine the relative phase shift variations between two collimated beams derived by splitting light from a single source.
:pen: The interferometer has been used, among other things, to measure phase shifts between the two beams caused by a sample or a change in length of one of the paths.
:pen: The apparatus is named after the physicists Ludwig Mach (the son of Ernst Mach) and Ludwig Zehnder
How Mach Zehnder work?
:fountain_pen: Mach Zehnder interferometer is a particularly simple device for demonstrating interference by division of amplitude.
:fountain_pen: A light beam is first split into two parts by beamsplitter and then recombined by a second bemsplitter.
:fountain_pen: Depending on the relative phase acquired by the beam along the two paths the second beamsplitter will reflect the beam with efficiency between 0 and 100%.
:fountain_pen: The operation of a Mach-Zehnder interferometer is often used as an example in quantum mechanics because it shows a clear path-choice problem.
:fountain_pen: However, it is not at all obvious at first glance that it works as claimed, until reflection phase shifts are considered in detail.
THE MACH-ZEHNDER INTERFEROMETER EXPLAINED:check: A wave can experience a phase shift upon full or partial reflection. This is a feature that is applied in the Mach-Zehnder interferometer to induce phase differences in split light waves en thus invoke interference effects when they are combined again. :check: In the Mach-Zehnder interferometer beam splitters are used to achieve several things like split a light beam in two equal and synchronous beams, a reflected beam and a strait-through passing beam, induce a phase shift in the reflected beam. NB: The strait-through passing beam does not experience a phase shift and recombine the two light beams in order to let them interfere. 
:check: When light travels from at less dense medium (air) and then reflects upon a denser medium (glass) it will experience a phase shift of 180o. The other way around, traveling from a more dense to a lesser dense medium, there is no phase shift. So the light traveling in the above figure from the right will, when reflected upwards, experience a 180o phase shift. Should it however travel from the left, go through the glass and then be reflected downwards, there will be no phase shift.
:check: The mirror M1 is fixed to a moveable carriage and can be moved along the well machined ways or tracks. This slow and accurately controlled motion is accomplished by means of the screw.
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:check: The light must originate from an extended source and light must in general be monochromatic or nearly so
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:warning: In analyzing the upper atmosphere by revealing temperatures and winds, by measuring the Doppler widths and shifts in the spectra of airglow and aurora.
:warning: As a component in the heliosemismic and magnetic images to study solar variability and to illustrate the sun's interior along with many aspects of magnetic activity.
:warning: For the detection of gravitational waves
:warning: As a tunable narrow band filter
:warning: As the core of Fourier transform spectroscopy
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