Wavelength Interferometry

Radio astronomy was discovered at 20 MHz, but the quest for higher angular resolution with the single-dish telescopes then available, led quickly to most observations being conducted at higher frequencies. Interferometers were constructed to operate at frequencies below 100 MHz, but they had short baselines ( 5 km). Short baselines were motivated by the belief that ionospherically induced phase fluctuations would destroy coherence on longer baselines. 

The development of self-calibration algorithms in the 1980s led to the realization that they could be employed to remove ionospheric phase fluctuations. Subsequently, interferometer baselines have been extended to tens of kilometers, and the success of these relatively long baseline interferometers (particularly the 74 MHz system on the Very Large Array, cf. Table I) have spurred plans for a Low Frequency Array (LOFAR, Fig. 4B). This instrument will have baselines of order 100 km and a collecting area of order 10 m at 15 MHz, leading to a sensitivity that will be competitive with centimeter-wavelength interferometers. 

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In partly ionized plasmas, where both the charged and neutral particles are in concentrations large enough to make measurable contributions to the refractive index, single wavelength interferometry cannot separate that part of refractivity resulting from the neutral components. 

Until 1992, the accuracy of spectroscopic measurements was limited to 1.6 parts in 1010 by the reproducibility of the 12-stabilized HeNe laser at 633 nm which served as an optical frequency standard, and by the unavoidable geometric wave-front errors in wavelength interferometry. To overcome this limitations it was necessary to measure the optical frequency rather than the wavelength. 

Nonnal spontaneous Raman scahering suffers from lack of frequency precision and thus good spectral subtractions are not possible. Another limitation to this technique is that high resolution experiments are often difficult to perfomi [39]. These shortcomings have been circumvented by the development of Fourier transfomi (FT) Raman spectroscopy [40]. FT Raman spectroscopy employs a long wavelength laser to achieve viable interferometry. 

Interferometry is difficult in the uv because of much greater demands on optical alignment and mechanical stabiUty imposed by the shorter wavelength of the radiation (148). In principle any fts interferometer can be operated in the uv when the proper choice of source, beam spHtter, and detector is made, but in practice good performance at wavelengths much shorter than the visible has proved difficult to obtain. Some manufacturers have claimed operating limits of 185 nm, and Fourier transform laboratory instmments have reached 140 nm (145). 

Fig. 8. (ii) Geometry and interferometry in the SFA. The distance between the surfaces is determined from the wavelengths of FECO. (a) The PECO fringes when the surfaces are in contact. The separation profile, D versus r, can be measured from the fringe profile, and compared to that predicted by the JKR theory of contact mechanics, (b) The FECO when the surfaces are separated. By measuring the wavelengths of the fringes when the surfaces are in contact and when they are separated, we can determine the distance between the two surfaces. 

An Introduction to Multiple Telescope Array Interferometry at Optical Wavelengths... 

The diameter of a telescope entrance pupil or the distance between two telescopes determine the baseline, which determines the resolution of the interferometer in combination with the detected wavelength. The table compares the resolution of single telescopes and interferometers at optical and radio wavelengths. Note that the resolution of optical interferometers is comparable to that of radio very long baseline interferometry (VLBI). 

The two limitations of optical interferometry, the one-quarter wavelength of light limit and the low resolution, have been addressed by using a combination of a fixedthickness spacer layer and spectral analysis of the reflected beam. The first of these overcomes the minimum film thickness that can normally be measured and the second addresses the limited resolution of conventional chromatic interferometry. 

Spherical rollers were machined from AISI 52100 steel, hardened to a Rockwell hardness of Rc 60 and manually polished with diamond paste to RMS surface roughness of 5 nm. Two glass disks with a different thickness of the silica spacer layer are used. For thin film colorimetric interferometry, a spacer layer about 190 nm thick is employed whereas FECO interferometry requires a thicker spacer layer, approximately 500 nm. In both cases, the layer was deposited by the reactive electron beam evaporation process and it covers the entire underside of the glass disk with the exception of a narrow radial strip. The refractive index of the spacer layer was determined by reflection spectroscopy and its value for a wavelength of 550 nm is 1.47. 

The interferometric measurements with RIfS can be parallelized as demonstrated in Figure 18. In this case, instead of white light interferometry, only a few wavelengths are used to allow parallel detection of all measurement dots. A filter wheel selects one wavelength at a time from the white light source, while the CCD camera monitors the intensity distribution at the transducer for all spots, in this case in a microtiter plate35. 

As indicated, the specific refractive index increment is best measured by differential refractometry or interferometry. Experimental procedures as well as tabulated values of dn/ dc for many systems have been presented elsewhere40,63K The relevant wavelength and temperature are those used for LS. The value of X0 is invariably 436 or 546 nm, but with the advent of laser LS, values of dn/dc at other wavelengths are required. These can be estimated with good reliability using a Cauchy type of dispersion (dn/dc a 1/Xq). For example the values of dn dc for aqueous solutions of the bacterium T-ferrioxidans at 18 °C are 0.159, 0.141 and 0.125 ml/gm at X0 = 488, 633 and 1060 nm respectively64 ... 

The application of holography to plasma interferometry has several advantages 276) accurate alignment and precision optical elements are not required. A complete three-dimensional record of the interference phenomena is obtained and the technique is well suited to record stationary and transient plasmas. Two-wavelength holographic interferometry of partially ionized plasmas has been performed by Jeffries 277). 

An interferometer can be used to very accurately measure the thermal expansion of solids. Although not utilized commercially to the level of dilatometry, NIST standard materials, which are in turn used to calibrate dilatometers, have had their expansion characteristics determined using interferometry. In fact, the formal definition of the meter is based on interferometric measurements. The operation of the device is based on the principle of interference of monochromatic light. The fundamental relations between wavelength and distance will first... 

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