Michelson line

How well known is it, I wonder, that only two years after Bahner s publication, and twenty six years before Bohr s interpretation of it, MICHELSON and MORLEY, in 1887. showed that Balmer-a consisted of two lines [26]. In this research the prime objective was to investigate the possibility of making the wavelength of sodium light the... 

Experimental recordings of Balmer-a showed three components Michelson s doublet - (5,4,1) of fig. 1 appeared as one strong line, 2 as a somewhat weaker line, and 3, weak and barely resolved even in the best work, as the third. Attention focussed on the position of 3. In 1938 the most distinguished schools of spectroscopists were divided as to whether it was, or was not, in the position predicted by Dirac s theory. R.C. WILLIAMS [42] asserted that it was not so, and PASTERNACK [43] pointed out that William s observations could be explained on the assumption of an upward shift of the 2S,/2 level by 0.03 cm- . And that is how it is. 

Figure 1. Schematic of a Michelson interferometer. The dashed lines show the paths of light which return to the source and the solid lines show the rays which propagate to the detector. The signal at the detector is the result of two light waves which have each been reflected and transmitted once by the beamsplitter. BF and BM are the respective distances of the fixed mirror and the moving mirror from the beamsplitter. Note that 8 = 2(BM - BF).

There was one additional shortcoming with Bohr s model. In 1891, Albert Ahraham Michelson discovered that the first Balmer line, called H , with a wavelength of 6,562 A, was not one bright line, but two lines with almost equal wavelengths, very close together. Their discovery was made possible by the highly refined optical method Michelson applied to his observation of the Balmer spectral lines. This doublet structure of the Balmer line could not be accounted for by Bohr s model. 

Michelson interferometers can be combined with Rayleigh line filters (or subtractive double monochromators) in order to prevent the consequences of the multiplex disadvantage (Secs. 3.1.6, 3.3.6 Fig. 3.4-1). 

The spatial resolution of FT-IR microspectroscopy, without sacrificing spectral quality and resolution, makes imaging possible. Shortly after the introduction of the first research-quality IR microscope by Messerschmidt and Sting in 1986, Wetzel, Messerschmidt and Fulcher reported spectra obtained from wheat kernel transverse sections in situ, and compared them with flour milling fractions [7]. This was achieved with an accessory IR-PLAN microscope optically interfaced to a Nicolet interferometer bench. Subsequently, at the Agriculture Canada laboratory the same model IR-PLAN was interfaced to a Bomen Michelson IR 100 spectrometer such that, over the period of a year, transverse sections of wheat kernels, vanilla beans, peppercorns and soybeans were manually line-mapped to reveal any differences in microchemical structural characteristics between their different botanical parts [8]. 

Fig. 2. Upper part Michelson interferometer (L = source, BS = beamsplitter, FM = fixed mirror, MM = movable mirror, S = sample focus, and D = detector). Lower part Spectra I (v) and interferograms I (s) for one, two and three narrow laser lines...

The problem is how to convert the interferogram I (s) obtained with a Michelson interferometer into the spectrum I (i>). Problems of this kind are met with in many areas of physics and technology for example, the problem of determining the spectrum of harmonics for a musical instrument (flute or violin). At audiofrequencies the problem is easily solved with an appropriate set of electronic circuits that performs a so-called Fourier analysis. In Fourier transform spectroscopy the solution is obtained by mathematical treatment of the interferogram 7(s). In order to illustrate the principle of this treatment in a simple way, let us go back to the case of a single narrow laser line, i.e. monochromatic radiation. 

If I (5) is other than a few discrete narrow lines, the tool to evaluate / (5) from I[s) is the Fourier transform, where I ) is the interferogram measured with a two-beam (Michelson) interferometer. This is the fundamental idea of Fourier transform spectroscopy. We have left aside the question of whether the Fourier integral Eq. (2.12) exists and whether it is meaningful or not. For the mathematical requirements on I (s), the reader is referred to the literature 34). it is sufficient to say here that, for all physically and experimentally reasonable interferograms I s), these requirements are usually met. 

We can conclude from this that the resolution of a Michelson interferometer is proportional to the maximum path difference up to which the interferogram has been measured. When we now consider the case of three narrow lines, we must remember that we have to calculate I (v) from I (s) by means of a Fourier transform [see Eqs. (2.10) and (2.12)]. However, the Fourier integral cannot be executed over s from — oo to - -oo, since the interferogram I s) can be determined experimentally only over a finite range ( —Smax s -j-Smax)- Therefore, the integration too can be performed only over a finite range. 

Turning back to the Michelson interferometer and Fourier transform spectroscopy, let us first consider the interferogram of a continuous spectrum. Each spectral element of infinitesimal width rf and intensity I (v) gives rise to the same interferogram pattern as a narrow line [see Eq. (2.6)], and the actual interferogram is the superposition of all these... 

The perturbational effects have been variously described as interruption broadening, resonance broadening, and statistical broadening. The perturbational line shape derived by Michelson was not correct even for pure interruption broadening because he neglected to average over all times between collisions. To do so results in the simplified Lorentz model. ... 

Two-beam interference microscopes operating according to the principle of the Michelson interferometer and accessory devices converting an ordinary microscope into a two-beam interferometer are commercially available. In such microscopes, collimated monochromatic light is half reflected onto the sample surface and half transmitted to an adjustable flat reference mirror by a beam splitter. The two reflected beams recombine in the microscope and the resulting variation in the optical path difference of the beams produces parallel interference lines of equal thickness which are also displaced at the position of the film step. The lines obtained are, however, relatively broad limiting the resolution and the accuracy of such measurements by the uncertainty in selecting the line centre. 

Figure 9 Diagram of a Michelson interferometer I, unmodulated incident beam A, moving mirror B, stationary mirror D, detector MD, mirror drive broken line, beam splitter. 

Fig. 3.1. The Michelson-Morley experimental framewoit We have two identical V-shaped right-angle objects, each associated with a Cartesian coordinate system (with origins O and O ). The first is at rest (solid line), while the second (dashed) moves with velocity v with respect to the first (along coordinate x). We are going to measure the velocity of light in two laboratories rigidly bound to the two coordinate systems. The mirrors are at the ends of the objects C, E in O and C , E in O, while at the origins, two semitransparent mirrors Z and Z are installed. Time 2f3 = is the time it takes for light to go down and up the vertical arm.

In 1875, the Conventimi du Metre defined the unit in terms of engraved lines on a platinum-iridium artifact stored at the Bureau International des Poids et Mesures (BIPM) at Sevres on the outskirts of Paris practical realizaticms required comparison of artifacts with the meter. In 1892-1893 Michelson and Benoit made the first measurement of the meter by comparisOTi to... 

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