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M J BOX COMPLEX METHOD MACH LINES MACH NUMBER MACH NUMBER, IN NOZZLES MACH WAVES MACH, ERNST 1838-1916 MACH-ZEHNDER INTERFEROMETRY MACHINE LANGUAGE MACLAURIN SERIES MACRO-POROUS AND MACRO-RETICULAR RESINS MAGNESIUM MAGNETIC FIELDS MAGNETIC FUSION REACTORS Magnetic Prandtl number MAGNETIC REYNOLDS NUMBER Magnetic Reynolds number Magnetic Reynolds number MAGNETIC SEALS MAGNETICALLY DRIVEN ARC MAGNETO ACOUSTIC WAVES MAGNETOHYDRODYNAMIC ELECTRICAL POWER GENERATORS MAGNETOHYDRODYNAMIC FLOWS OF A SECOND GRADE FLUID MAGNETOHYDRODYNAMIC METHODS Magnetohydrodynamics MAGNETOHYDRODYNAMICS AND RADIATIVE EFFECTS ON FREE CONVECTION FLOW OF FLUID MAGNETOHYDRODYNAMICS IN LIQUID METALS MAGNOX MAGNOX POWER STATION Magnus Force MAGNUSSEN AND HJERTAGER MODEL MAINFRAME COMPUTERS MALDISTRIBUTION OF FLOW MALVERN, SCATTERING, METHOD FOR PARTICLE SIZING MANOMETERS MANOMETRY MARANGONI CONVECTION Marangoni effect MARGULES EQUATION MARINE FUEL OILS MARINE GAS TURBINES MARIOTTE LAW MASS ACTION LAW MASS FLOW METERS MASS MEDIAN DIAMETER, MMD MASS SPECTROSCOPY MASS TRANSFER MASS TRANSFER COEFFICIENTS MASS TRANSFER UNDER REDUCED GRAVITY MASS TRANSFER, ELECTROCHEMICAL, PROBE MASSACHUSETTS INSTITUTE OF TECHNOLOGY, MIT Mathematical formulation MATHEMATICAL METHODS MATHEMATICAL MODELING Matrix operator method MATTE MAXI-COMPUTERS MAXIMUM HEAT FLUX MAXIMUM HYGROSCOPIC MOISTURE CONTENT MAXIMUM LIQUID TEMPERATURE MAXWELL EQUATION MAXWELL EQUATION FOR ELECTRICAL CONDUCTIVITY MAXWELL FLUIDS MAXWELL MODEL FOR ACCOMMODATION COEFFICIENT MAXWELL RELATIONS MAXWELL'S EQUATIONS MAXWELL-BOLTZMANN DISTRIBUTION MAXWELL-STEFAN EQUATIONS McCABE - THIELE METHOD McCABE-THlELE METHOD McREYNOLDS CONSTANT Mean absorption coefficients (Planck, Rosseland) Mean Free Path MEAN PHASE CONTENT MEAN TEMPERATURE DIFFERENCE MEAN TEMPERATURE DRIVING FORCE MEASUREMENT TECHNIQUES MEASURING ELECTRIC FIELDS WITH LASER-INDUCED FLUORESCENCE-DIP STARK SPECTROSCOPY MECHANICAL DESIGN OF HEAT EXCHANGERS MECHANICAL HEART VALVE MEISSNER EFFECT MELT FILMS MELTING MELTING HEAT MELTING OF ICE MEMBRANE POLARIZATION MEMBRANE PROCESSES MEMBRANE TYPE FILTERS MEMBRANES, ION EXCHANGE MENDELEEV-CLAPEYRON EQUATION MERCURY MERKEL'S EQUATION MESOSCOPIC ENERGY SYSTEMS MESOSPHERE METAL POWDERS METAL SURFACES Metal-coated polymer fibers in infrared and microwave METALLURGICAL PLASMA REACTORS METALS METHANE METHANOL METHOD OF CHARACTERISTICS METHODS OF SUPERPOSED GRIDS AND OF VIRTUAL Z-MESHES METHYLAMINE METHYLCHLORIDE METRE METZNER-OTTO CONSTANTS FOR IMPELLERS MICELLAR CATALYSIS MICELLES MICHAELIS-MENTEN RELATIONSHIP MICHELSON INTERFEROMETRY MICROBUBBLE MICROCHANNEL FLOW MICROCHANNELS MICROCIRCULATORY CELL OF THE PLANT LEAF MICROCOMPUTERS MICRODAMAGE MICROELECTRONIC EQUIPMENT MICROFILTRATION MICROFIN TUBES MICROGRAVITY CONDITIONS MICROLEVEL FLOWS MICROORGANISM MICROPOLAR FLUID MICROSCALE PHENOMENA Microscale/nanoscale radiative heat transfer MICROSTRUCTURAL EVOLUTION MICROSTRUCTURE OF HETEROGENEOUS MIXTURE MICROSYSTEMS MICROWAVE DRYING MICROWAVE HEATING MICROWAVE PLASMA TREATMENT MICROWAVES MIE SCATTERING MIE SERIES Mie solution for spherical particles MIE THEORY MIKIC, ROHSENOW AND GRIFFITH EQUATION, FOR BUBBLE GROWTH MINIATURE HEAT PIPES MINIATURE OSCILLATING HEAT PIPES MINICOMPUTERS MINIMUM FILM BOILING TEMPERATURE MINIMUM FLUIDIZATION VELOCITY MIROPOLSKII FORMULA, FOR POST DRYOUT HEAT TRANSFER MIST COOLING MIST ELIMINATORS MISTS MIT MIXED (COMBINED) CONVECTION MIXED SPECTRAL-FINITE DIFFERENCE TECHNIQUE MIXER SETTLERS MIXER-HEAT EXCHANGERS MIXERS MIXERS, STATIC MIXING MIXING GAS-LIQUID MIXING IN ROD BUNDLES MIXING LENGTH MIXING LENGTH HYPOTHESIS MIXING LENGTH MODELS MIXING OF PARTICLES IN FLUIDIZED BEDS MIXING REYNOLDS NUMBER MIXTURE CONSERVATION EQUATIONS MIXTURES MODEL BANDWIDTH MODELING SUBSURFACE FLOW MODELING TECHNIQUES MODERATING RATIO MODERATORS Modified discrete ordinates and finite volume methods Modified Mach number (velocity coefficient) MODULUS OF THE SOLID MOIRÉ FRINGES MOISTURE ISOTHERM MOISTURE MEASUREMENT MOISTURE METER MOLALITY OF A SOLUTION MOLAR MASS MOLD CONSTANT MOLE MOLECULAR DIFFUSION MOLECULAR DYNAMICS MOLECULAR FLOW OF GAS MOLECULAR INTERACTIONS MOLECULAR MASS MOLECULAR PARTITION FUNCTION MOLECULAR PHYSICS MOLECULAR SCALE VISUALIZATION OF MICRO-FLOWS MOLECULAR SCATTERING MOLECULAR SIEVES Molecular spectra in the infrared MOLECULAR SPECTROSCOPY MOLECULAR SPEEDS MOLECULAR WEIGHT MOLECULE MOLLIER DIAGRAM MOLTEN DROPLET MOLYBDENUM Momentum thickness MONOCHROMATIC LIGHT MONOD MODEL OF CELL GROWTH MONODISPERSE AEROSOLS Monte Carlo method Monte Carlo method Monte Carlo method Monte Carlo method for exchange among diffuse-gray surfaces MONTE CARLO MODELING, OF TURBULENCE Monte Carlo simulation of radiative transfer MONTREAL PROTOCOL MOODY CHART MOODY, OR WEISBACH, FRICTION FACTOR MOSSBAUER SPECTROSCOPY MOTOR GASOLINE MOULD MOUNTAIN DRAG MOVEMENT OF TWO CONSECUTIVE TAYLOR BUBBLES MOVING BOUNDARY PROBLEMS MOVING FRONT OF AN INSTANTANEOUS IRREVERSIBLE REACTION MTBE MUFFLE FURNACE MULTI FLUID MODELS MULTICOMPONENT MIXTURES, BOILING IN MULTICOMPONENT MIXTURES, DIFFUSION IN MULTICOMPONENT SYSTEMS THERMODYNAMICS MULTICOMPONENT VAPOR CONDENSATION MULTIGRID SOLUTION OF MODIFIED REYNOLDS EQUATION MULTILINGUAL PROGRAMMING MULTIMODE FIBRE MULTIPHASE DENSITY Multiphase Flow Multiphase medium MULTIPLE BEAMLETS MULTISCALE ANALYSIS MULTISCALE DIFFUSION MULTISCALE ELECTROMAGNETIC SIMULATION MULTISCALE MODELING MULTISCALE SIMULATION MULTISCALE TRANSPORT MULTISTAGE TURBINES MULTISTART HELICALLY COILED TUBE BOILER MURPHREE EFFICIENCY MUTUAL DIFFUSION COEFFICIENT
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MACH-ZEHNDER INTERFEROMETRY

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The Mach-Zehnder interferometer is a classical mirror-interferometer. For a long time it was the most common dual-beam-interferometer used to measure continuously refractive index distributions of transparent objects. Developed by Mach and Zehnder in 1892, it has been frequently used in heat and mass transfer and in gas dynamics, for example combustion, until it was superceded by the holographic interferometer.

Figure 1 shows a Mach-Zehnder interferometer with a specific phase object ("phase object" is used to denote the transparent object being studied which influences the phase of light passing through it) in its measuring beam. It consists of two reflecting and two beam-splitting mirrors in a parallelogram (can also be a rectangle) arrangement. First the interferometer has to be adjusted in such a way that the two beams have equal optical path lengths. When the physical process of interest, for example heat transfer, is introduced into the measuring beam an optical path difference between reference and measuring beam is produced. A superposition of the two beams then generates an interference pattern in which the interference fringes correspond to lines of uniform difference of the refractive index.

Parallelogram arrangement of a Mach-Zehnder lnterferometer, M1, beamsplitting mirrors, M2, reflecting mirrors, L1 and L2 lenses, MS test section with a constant temperature gradient (and so a constant refractive index gradient), tm — tm adjustment plane, ti — ti image plane.

Figure 1. Parallelogram arrangement of a Mach-Zehnder lnterferometer, M1, Parallelogram arrangement of a Mach-Zehnder lnterferometer, M1, beamsplitting mirrors, M2, reflecting mirrors, L1 and L2 lenses, MS test section with a constant temperature gradient (and so a constant refractive index gradient), tm — tm adjustment plane, ti — ti image plane. beamsplitting mirrors, M2, Parallelogram arrangement of a Mach-Zehnder lnterferometer, M1, beamsplitting mirrors, M2, reflecting mirrors, L1 and L2 lenses, MS test section with a constant temperature gradient (and so a constant refractive index gradient), tm — tm adjustment plane, ti — ti image plane. reflecting mirrors, L1 and L2 lenses, MS test section with a constant temperature gradient (and so a constant refractive index gradient), tm — tm adjustment plane, ti — ti image plane.

Test section windows in the measuring beam, and corresponding plates compensating their effect in the reference beam, have to be manufactured with special precision and accuracy. The same goes for mirrors and lenses of all optical components because imperfections influence the beams differently. This makes the Mach-Zehnder interferometer very expensive.

Example

Figure 2 shows the interference pattern of a horizontal annulus filled with air when the inner cylinder is heated isothermally. The outer tube is cooled by water at constant temperature. When evaluating the interferogram the origin, i.e., the position of the inner wall, has to be determined. But the interference line close to the wall cannot be distinguished because of defraction effects. This problem is solved by extrapolating the temperature distribution—known from the interference pattern—from the wall temperature (measured by thermocouples) so the wall position and, as a result, the temperature gradient and the heat transfer coefficient can be determined.

Interferogram of a horizontal annulus with infinite fringe field. di = 40 mm; da = 98 mm; s = 29 mm; = 0, 73;. Angle position 30°: Nus = 4, 82; Grs = 7, 28×104; = 29, 7 K [Photo according to Hauf (1966)].

Figure 2. Interferogram of a horizontal annulus with infinite fringe field. di = 40 mm; da = 98 mm; s = 29 mm; Interferogram of a horizontal annulus with infinite fringe field. di = 40 mm; da = 98 mm; s = 29 mm; = 0, 73;. Angle position 30°: Nus = 4, 82; Grs = 7, 28×104; = 29, 7 K [Photo according to Hauf (1966)]. = 0, 73;. Angle position 30°: Nus = 4, 82; Grs = 7, 28×104; Interferogram of a horizontal annulus with infinite fringe field. di = 40 mm; da = 98 mm; s = 29 mm; = 0, 73;. Angle position 30°: Nus = 4, 82; Grs = 7, 28×104; = 29, 7 K [Photo according to Hauf (1966)]. = 29, 7 K [Photo according to Hauf (1966)].

REFERENCES

Mach, L. (1892) Über einen Interferenzrefraktor. Z. Instrumentenk. 12:89-93.

Zehnder, L. (1891) Ein neuer Interferenzrefraktor. Z. Instrumentenk. 11:275-285.

Grigull, U. and Hauf, W. (1966) Natural convection in horizontal cylindrical annuli. Proc. Inter. Heat Transfer Conf. 3rd. 11:182-195. Chicago.

Bennett, F. D. and Kahl, G. D. (1953) A generalized vector theory for the Mach-Zehnder-Interferometer. J. Opt. Soc. Am. 43:71-78.

Price, E. W. (1952) Initial adjustment of the Mach-Zehnder-Interferometer. Rev. Sci. Instr. 23:162.

References

  1. Mach, L. (1892) Über einen Interferenzrefraktor. Z. Instrumentenk. 12:89-93.
  2. Zehnder, L. (1891) Ein neuer Interferenzrefraktor. Z. Instrumentenk. 11:275-285.
  3. Grigull, U. and Hauf, W. (1966) Natural convection in horizontal cylindrical annuli. Proc. Inter. Heat Transfer Conf. 3rd. 11:182-195. Chicago.
  4. Bennett, F. D. and Kahl, G. D. (1953) A generalized vector theory for the Mach-Zehnder-Interferometer. J. Opt. Soc. Am. 43:71-78.
  5. Price, E. W. (1952) Initial adjustment of the Mach-Zehnder-Interferometer. Rev. Sci. Instr. 23:162. DOI: 10.1063/1.1746214

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