Michelson-Interferometer
The Michelson interferometer [ maɪkəlsn - ] is an interferometer, which was named after the physicist Albert Abraham Michelson. Became famous for this measuring instrument primarily by the Michelson - Morley experiment, by which the so-called light ether should be investigated as a medium for the propagation of light. With the Michelson interferometer, the phenomenon of interference is used, which can be observed only in coherent light. Normally, therefore, special light sources normally used lasers for interference experiments. In the experiment, it can then be split by a beam splitter and finally brought with itself to interference. The special feature of the Michelson interferometer is that the beam splitter and the partially transparent mirror in which the beams are recombined, is the same.
Here, the path difference of the superimposed waves must be less than the coherence length. For media with dispersion and light sources with broad-spectrum therefore a correction plate is installed in the interferometer. The corrector plate is made of the same material as the beam splitter and has the same thickness, but is fully translucent. It rests on the part side of the beam splitter, and is mounted so that the path difference of the two beams is balanced.
Operation
The general operation of an interferometer, is that a light wave is divided into two parts. These two waves will pass through different length paths or media in which the speed of light is different. This results in a phase shift between the two waves. These are then brought together again, interference occurs.
The Michelson interferometer is done, the layout of the light wave by means of a semitransparent mirror. The light emanating from the light source is at the semi- transparent mirror ( beam splitter ) and partly by left ( marked in red), but partly reflected by 90 degrees ( blue). The transmitted and the reflected light now meet each have a ( fully reflective ) mirror and be thrown back on the semi-transparent mirror. Another part is reflected and part is transmitted. Behind the semitransparent mirror then superimpose the two waves ( marked in yellow), interference occurs.
By changing the optical path length of one of the two waves, for example, by moving one of the two mirrors, or by changing the refractive index of the medium in one of the two interferometer arms, then shift the phases of the two waves opposite to each other. Are they now in phase, then its amplitude is added ( this is called constructive interference ), but when they are out of phase, they cancel each other out (destructive interference). Smallest changes of the path difference between the two waves can already be measured by the intensity measurement of the resulting wave.
Occurrence of the interference fringes
From the light source is a parallel pencil beams ( plane wave ). This is " expanded " by a lens array and then passes divergent ( divergent ) with a new imaginary origin G ( spherical wave ), which is in the range of the lens assembly.
This divergent beam is split by the beam splitter into two divergent beam. The two beams are reflected by a respective mirror ( depending on the design ), recombined and directed onto a screen. Therefore, the interference pattern come about because of the direct routes " beam splitter mirror 1 beam splitter screen " (L1) and " beam splitter mirror 2, beam splitter screen " (L2) have different lengths. From the imaginary origin G to the beam splitter is the constant distance (G). When two beams of the two beams at the same time ( distance d from the center of the interference rings ) are incident at the same location, then they have traveled different paths w long. The exact path can be calculated by the equation
Calculate.
At the same distance d from the center of the interference fringes the paths W1 and W2 are different in length. If d is increased linearly, then rise w1 and w2 at different rates. If a plane wave is considered, appears on the screen when constructive interference a bright spot, with destructive this remains dark. The interference fringes are a consequence of the Gaussian beams which are spherical waves from a given length.
Relative position measurement
The interferometer is thus adapted to measure slow changes in the path length difference between the two sub-beams, so as the change in position of one of the mirror opaque, the achievable resolution is of the order of half the wavelength of the light used. Visible laser light in the wavelength of a few hundred nanometers.
To measure one shifts one of the two opaque mirrors and counts the number of interference minima (or maxima ), which are run through during the movement. Each minimum then corresponds to a path length to a wavelength, that is, a change of position of the mirror to one-half wavelength. The absolute path lengths, or their absolute difference can not be measured, nor the direction of the movement. The speed of the measurable change is limited by the achievable count rate of the minima.
Improve the position measurement
Changes the direction of movement of the mirror, there is a problem in that at the extreme points of the sine wave ( the lightest and darkest points of the interference pattern ) is not known whether the movement of the mirror continued in the same direction or vice versa, since both generate the same waveform would. Therefore, in this case, a second sensor at another point must be placed so that both signals are never simultaneously at extreme points.
The displacement measurement by Michelson interferometer is characterized by a ( depending on the wavelength of the laser) high resolution and linearity, but offers some high demands on the evaluating electronics, since very high frequencies occur at high velocities of the mirror.
The current gravitational wave detectors represent the most elaborate variant of the Michelson interferometer for path length with movably mounted mirrors dar.
Heterodyne Michelson interferometer
Many of today's Michelson interferometer as a heterodyne interferometer are arranged. In this case, in the two arms of the interferometer, a slightly different wavelength will be used. The recombined beams so produce a beat in the detector. In parallel, a part of the light of both wavelengths is stored in a reference detector that is not reflected at the mirrors. The actual measurement is then a comparison of the phase position between the beat on the detector and the reference detector. Since phase measurements with significantly better accuracy than the interpolation of the interference signal of a homodyne interferometer are possible resolutions of 10 pm have been achieved with heterodyne Michelson interferometers already. The above problem with the direction reversal at extreme points is dispensed with, since the phase of the beat with a suitable design always increases and thus the phase difference between the signal arm and reference detector can be unambiguously determined.
For generating the two wavelengths based laser, or an acousto-optic modulator are used usually in the Zeeman effect.
Use as a spectrometer
If one uses an IR source and lets you go the beam before the detector through a sample cell with a substance to be measured, one can obtain the spectrum. This must be the position of a mirror x, for example using a piezo element to change over time, to pass through the measured frequency band in order to produce different path differences, and as to generate resonance, and Extinktionsfall at different wavelengths. The Fourier transform of the interferogram from the location I (x ) or the time domain I (t) in the frequency domain gives the spectrum of the substance.
Determining the refractive index of a gas
To determine the refractive index of a gas, bringing one filled with the appropriate gas cuvette in the sub beam, the path length has previously been varied ( the mirror now remain fixed). A pump connected to this cell can be the gas pressure, and thus the number of gas molecules through which the light passes therethrough varies. If one describes the linear relationship between pressure and refractive index than
And exploits the fact that the increase in the refractive index by
Can be expressed, leads to ( n = 1, p = 0):
Here N is the number of intensity maxima in the interference pattern, p is the gas pressure, the wavelength of the laser light used and the optical path length s of the cuvette.
Measuring the wavelengths
The two beams are not always consistent if its optical path difference is smaller than the coherence length of the light source. If the distances between the semi-permeable plate and the mirrors are each equal to the arriving at the detector beams have a phase difference of 0 Moves you enter one of the two mirrors by the distance, the result between the two beams of a path difference, and the light intensity changes.
If one now specify the number of interference maxima at a distance of travel, then the wavelength can be calculated easily, as always: