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         Michelson Interferometer Whitepaper

Table of contents

1 History
2 Simple Theory
3 Comparison to other common spectrometers
4 Uses
5 Spectroscopy
6 Construction
7 Theory details

History

Michelson-Morley experiment to measure the “ether”. The first Michelson interferometer was constructed in 1881 to try and measure the motion of Earth relative to the "ether" that was supposed to enable the transmission of light through space. There was no measurable effect. See for example the following link for a detailed explanation of the experiment: Michelson-Morley

Simple Theory

A Michelson interferometer divides a beam of light into two, then recombines the beams using the same beam splitter. Usually, flat mirrors reflect each beam back through the beam splitter, and usually, the paths are not identical. Where the light beams overlap after recombining, there will be an interference pattern (light and dark bands) that results from the variation of the optical path over the aperture of the Michelson.

Building a michelson Interferometer

To build a Michelson interferometer, you will need a beam splitter, two mirrors, some ajustable mounts for the mirrors and a light source. A laser pointer, or a helium neon laser make good light sources because you will see fringes even if the two paths are not perfectly matched. A moderate focal length lens (a few hunderd millimetres) is helpful to enlarge the laser beam as well. A paper screen will show a pattern of light and dark rings when everything is lined up--do not look into the laser beam!

A bench top set up like this one is useful for demonstrating how a Michelson works, but it is not likely to be a useful measurement instrument. Depending on the desired measurement, and the environment for the instrument, Michelsons can be very complex pieces of glass.

The key questions for specifying a Michelson are: what wavelength is to be studied? how much light is available? how will the Michelson be scanned? how stable does the Michelson have to be, or can a person easily adjust the alignment if necessary?

Effect of Path Difference

Often, a Michelson is constructed with arms that have a different length. The path difference will result in a wavelength dependent phase at the output. This effect makes a Michelson interferometer a very sensitive detector of small wavelength or frequency differences. For example if the light source has two narrow spectral features that are separated by 1 cm-1 (30 GHz or 0.04 nm at 600 nm), then a Michelson with a 1 cm path difference will have overlapped bright and dark fringes, and the doublet will not be detected. However, if the source has spectral features separated by a smaller amount, 0.1 cm-1 for example, varying the path difference of the same Michelson will reveal the structure.

In general, a Michelson can not easily distinguish wavelengths that are separated by multiples of its free spectral range (FSR), so pre-filtering will be required for sensitive spectroscopy. Increasing the path difference will increase the resolution, at the expense of a narrower operating wavelength range. The aliasing problem can be overcome by scanning the Michelson over many orders. This is the principle of the Fourier transform spectrometer which is widely used in the infrared range (2-20 µm wavelength).

Coherence length (frequency bandwidth), beating -interference effects will only be seen if the path difference is short relative to the coherence length of the input light -coherence length is inversely proportional to the bandwidth of the light -two narrow lines (a doublet for example) will "beat" in and out of phase as the path difference changes. As the path difference is increased, the fringes will disappear (because the bright fringes of the two wavelengths are out of phase), but a further increase in path length will cause the fringes to reappear. Fringes from a light source with a continuous spectral bandwidth equal to the spacing of the doublet will disappear at the same path difference, but further increase in the path difference will not cause the fringes to reappear.

Image brightness, contrast, energy conservation

Etendue

 

Comparison to other common spectrometers

Prism spectrometer

Grating spectrometer
A Michelson interferometer has very high brightness for the same spectral resolution as a grating spectrometer, but a very narrow spectral range. Because of the very high brightness, Michelson interferometers are ideal for imaging applications. For example, measuring the brightness of a CO2 emission feature over a wide field of view.

Fabry-Perot interferometer Compared to a Fabry-Perot with the same path difference, a Michelson has lower resolution, but greatly reduced sensitivity to the angle of incidence, especially at larger field angles. For imaging applications, Michelsons are the ultimate spectral filters.

Uses

Distance measurement (eg. HP, Zygo, etc.)

Accurate distance measurements (100 nm accuracy) over 10s of metres (108 dynamic range)

Used in high accuracy machinery, surveying, measurement equipment. Used in gravity wave detectors (LIGO for example).

The other major use for Michelson interferometers is for spectroscopy. Some important applications include, measuring surface motion of the sun (through Doppler shifts), measuring atmospheric winds (again through Doppler shifts), measuring vegetation from satellites, measuring trace gas emissions (CO2 for example).

Spectroscopy

FTIR spectrometers (ABB Bomem, etc)

High resolution infra-red spectroscopy. As the Michelson is scanned, intensity output is Fourier transform of the input spectrum. Typically, a helium neon laser is used to track the changing path difference while a camera or single element detector records the intensity at the output of the Michelson. Compared to a grating based spectrometer with similar resolution, the FTIR has much higher brightness which results in much shorter observation time.

Imaging spectrometers (field widening)

One of the most powerful features of a Michelson spectrometer is the ability to maintain a constant optical path difference over a large range of field angles. This is possible because the two arms can be made with different materials having different refractive indices. If the ratio of the arm length to its refractive index is the same for both arms, then to second order the path difference is independent of field angle. With this in mind, a very narrow filter (the field widened Michelson) can be placed in non-colimated space for wide field imaging systems.

Path difference—sets resolution and nominal bandwidth. A larger path difference (the optical path difference between the two arms delta = 2 * (n1 * D1 - n2 * D2)), the smaller the separation will be between transmission peaks. In other words, the resolution will be higher, but adjacent peaks will be harder to separate.

Typically scanned by moving one mirror (piezo electric transducers for example)

Output data is 3D (spectrum vs area, collected by scanning in time)

Spatial heterodyne spectrometer

In this version of the Michelson interferometer, the return mirrors are replaced with a matched pair of gratings mounted at the Littrow angle. The two recombined beams are at an angle that varies with wavelength. For each wavelength there will be a fringe pattern with spatial frequency varying linearly with the shift from the Littrow angle. By recording the fringe pattern with a CCD, and taking the Fourier transform, the spectrum of the input light source can be measured without any moving parts. In the direction perpendicular to the grating dispersion, imaging is possible.

In a slightly more complex version of the spatial hetrodyne spectrometer, field widening prisms can be added to each arm to increase the field of view.

Output data is 3D(amplitude vs wavelength and linear distance); no moving parts are required to collect spectral data

Ref:

Field-widened spatial heterodyne spectroscopy: correcting for optical defects and new vacuum ultraviolet performance tests
Harlander, John M.; Tran, Huan T.; Roesler, Fred L.; Jaehnig, Kurt A.; Seo, Scott M.; Sanders, Wilton T.; Reynolds, Ronald J.
Proc. SPIE Vol. 2280, p. 310-319, EUV, X-Ray, and Gamma-Ray Instrumentation for Astronomy V, Oswald H. Siegmund; John V. Vallerga; Eds. 09/1994

 

 

Polarizing, non-polarizing, benefits of reduced angle designs

Polarization effects on nominally unpolarized Michelsons

Use of hexagonal beam splitter to reduce angle of incidence

Polarization Michelson, relation to birefringent filters

Construction

Factors that affect the quality of a Michelson Interferometer The beam splitter must be flat, the glass must be homogenous, the mirrors must be flat, the beam splitter must be uniform, and all of the angles must be accurate. Apart from these factors, Michelsons are easy to build.

Depending on the actual application, not all of these factors may be equally important. Anything that varies the phase over the aperture may degrade the performance of the interferometer. Small angular errors in particular tend to cause problems when the Michelson has significant wavelength bandwidth (due to dispersion).

Mirrors, beam splitter, stability

Theory details

Polarization effects

Beam splitter phase effects

Metallic vs. dielectric beam splitters

Retrieved from "/opticswiki/index.php/Michelson_Interferometer_Whitepaper"

1. G. Hernandez (1986) 'Fabry-Perot Interferomters, Cambridge Studies in Modern optics', Cambridge University Press

 

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