Multiple-beam Interferometry Research Articles

Optical properties of multilayer overcoated aluminum films in the uv (2000–2500 Å)

Optical properties of high reflectance, low absorptance coatings consisting of aluminum films overcoated with multilayers of Al(2)O(3) and MgF(2) are reported in the far ultraviolet. Coating design considerations and preparation techniques are described and the potential of such reflectors for multiple-beam interferometry is considered. Transmission characteristics of experimental Fabry-Perot type interference filters constructed from these Al-multilayer coatings are discussed.

Dielectric Permittivity and Breakdown Strength of Molybdenum Trioxide Films

Dielectric behaviour of molybdenum trioxide films as a function of frequency (up to 10 MHz), thickness (from nearly 350 to 5000Å) and temperature (room temperature to nearly 200°C) is reported. The films were prepared by vacuum evaporation technique and their thickness was measured by multiple beam interferometry. Electron diffraction patterns were obtained for material identification. It is observed that the dielectric constant for MoO 3 films is sensitive to frequency and temperature. A dispersion in frequency response is also observed at frequencies between 10 kHz at room temperature. The relaxation appears to be dipolar in nature. The relaxation time decreases as the thickness of the film increases and finally it tends to stabilize as the structure of the film stabilizes. The stabilization of film structure is also confirmed by the stabilization of low frequency dielectric constant and density of the prepared films. The stabilized value of the static dielectric constant and density of the films reaches the bulk value at about 4000Å thickness. The films show a breakdown strength of 3×10 6 volts/cm.

Application of interferometry to the study of density gradients in emulsion creaming II some theoretical aspects

Multiple beam interferometry was applied as an analysis system to the creaming of a pentane-water system in a previous paper 1 (Part I). The Bragg relationship 2nd = Nλ was used to calculate volume percentage of pentane and water. This work presents a formal derivation of how the relationship applies to the system. Theory is advanced further by application of Twersky's treatment of tenuous scattering to get both phase shift (used in Pt I) and attenuation. Adopting attainable experimental conditions, limitations of concentration, drop-size, wave-length, and path-lengths are obtained from coherence calculations with the consequent maximum refractive index differences between phases. A practical limit on density differences is suggested. Finally, the limitations are applied to some practical systems and the generality of results shown.

A Study of Crack Tip Plastic Zone Topography in Beryllium

Abstract Multiple-beam interferometry has been used to study the size and shape of plastic zones both at the tip of subcritical cracks and at the edges of running cracks in rolled ingot and in hot pressed, fully dense and porous beryllium. It is shown that from the zone shape an effective yield stress for the material can be derived and that this stress corresponds to somewhere between the 0.2% proof stress and the microyield stress of the material as measured under uniaxial tension. The relevance of this effective yield stress to practical fracture toughness testing is discussed and it is shown that from the points of view of both overall crack tip plastic zone shape and of the effects of plasticity on elastic stress redistribution, the 0.2% proof stress is probably the best choice.

Recent developments in multiple beam interferometry in the ultraviolet region 1700–2500 Å

New results are given for Fabry-Pérot interferometry in the ultraviolet below 2500 Å down to 1700 Å. Better performances are obtained with improved Al−MgF 2 double layers. Reflective finesse values in the range of 20–30 are obtained for various wavelengths. Interferograms are shown for 1702, 2062 and 2537 Å.

A technique for measuring film thickness on curved substrates

A technique for measuring the thickness of thin films deposited on curved substrates is described. Conventional multiple beam interferometry with a flat Fizeau plate normally cannot be used with great precision on curved surfaces since the Fizeau fringe spacing is not constant. The technique described in this note takes into consideration the modified Newton's rings which result from such a measurement and gives a precise method of calculating the film thickness.

Thickness Measurement of Built-Up Monolayers by Multiple Beam Interferometry

Thickness Measurement of Built-Up Monolayers by Multiple Beam Interferometry

Comment on: Thickness Measurement of Built-Up Monolayers by Multiple Beam Interferometry

Comment on: Thickness Measurement of Built-Up Monolayers by Multiple Beam Interferometry

Investigation of Film Thickness Uniformity on Substrates Located Close to the Source Axis

The thickness uniformity that can be obtained near the source axis in evaporation systems having long source-to-substrate distances (~50 cm) and small area sources has been investigated using multiplebeam interferometry. Silver films were evaporated from resistance-heated dimple boats in standard vacuum and ultrahigh vacuum onto stationary and rotating substrates 3.86 cm in diameter symmetrically placed about the source axis. Thickness variations in the films were measured across substrate diameters, and the average film thicknesses were compared. Similar data were also obtained for aluminum, aluminum oxide, and germanium films. Random thickness variations have been found on all the films, which are much larger than the uniform thickness gradations predicted by the geometric theory. These variations can be minimized but not eliminated by planetary rotation of the substrates.

Application of interferometry to the study of density gradients in emulsion creaming. I. The effect of inclined baffles

The technique of multiple beam interferometry was applied to the creaming of an emulsion of pentane in water. It was shown that in a cell which can be rotated to various orientations and which contains a baffle fixed at 45°, the known convective flow patterns are delineated and accurate concentrations can be calculated when the transmitted light reaches a certain level. Only relative concentrations were found from the refractive index changes, but an improvement of the optical system should yield absolute values for the concentration gradients in suitable emulsions.

Interaction Forces between Mica Sheets at Small Separations

WHEN thin sheets of mica are brought very near to each other they deform; we decided that this deformation could be used to investigate the strength of the intermolecular attraction. The system we used in this study consisted of two narrow strips ∼5 µm thick, in contact over part of their length and held apart by external forces at one end, thus forming a double cantilever. Near the line of bifurcation, the attractive forces deflect the sheets towards each other and a non-uniform loading applied to the cantilevers has been used to simulate the attraction. We measured the deflection by multiple-beam interferometry. At the same time the surface energy γ, required to overcome the forces of attraction, was determined as described previously1,2. The result is shown as curve a in Fig. 1; curve b is the calculated shape of a similar cantilever which carries no distributed load. Suitable mathematical functions containing a number of adjustable parameters may be used to represent the loading and the beam equation solved for particular values of the parameters.

Method of Stationary Phase for Analysis of Fringe Functions in Hologram Interferometry

In this paper, a mathematical technique called the method of stationary phase is presented for the purpose of obtaining approximate solutions for characteristic fringe functions in hologram interferometry. The cases of greatest concern are where holograms are formed of objects that vibrate simultaneously in different geometrical patterns according to sinusoidal time functions whose frequencies are related by rational numbers. The method assumes that the object motion is sufficiently large that contributions to the fringe function come only from the holographic recordings of the object at positions where its velocity is zero. At such position, the phase of the light scattered from an object point is stationary with respect to time, and the method permits the approximate calculation of the relative intensity of the partial recording at these positions. The fringe functions become expressions similar to those found in multiple-beam interferometry,and fringe patterns can be understood more easily. The case of two sinusoidal vibrations at a frequency ratio of 2: 1 is considered experimentally and theoretically according to the method presented.

Optical and interferometric studies on ferroelectric guanidinium aluminum sulphate hexahydrate cleavages and their etch patterns

GASH single crystals have been cleaved along (0001) planes and the cleavage faces have been studied by multiple-beam interferometry. The cleavage faces have also been chemically etched and the etch patterns studied optically. By etching a cleavage successively for three different periods it was found that the bottoms of the point-bottomed pits follow a linear etch path. Correspondence both in the etch patterns on matched pairs and in the etch patterns on the opposite sides of thin plates has been established. From the displacement in the etch patterns on the two sides of thin plates, the angle of inclination of dislocation lines has been determined to be about 10°. Intersecting rows of pits forming nodes at which three or four rows meet have been observed. The implications are discussed.

A comparison of methods for accurate film thickness measurement

Three methods, two optical and one electromechanical, have been employed for determining film thickness by measuring the step height at the edge of the film. The optical techniques were multiple-beam Fizeau interferometry and photoelectric shearing interferometry while the RPI Talystep, a stylus measuring instrument, provided the third method. The three techniques have the common feature of possessing extremely high sensitivity and their merits and disadvantages are discussed. A comparison of measurements on magnesium fluoride, aluminium and gold films with thicknesses ranging between 100 and 2000 AA is presented and shows that results from the three methods were generally in excellent agreement, the overall spread of values rarely exceeding 10 AA.

Domain structures in KNbO3 single crystals associated with step ladders on pseudocubic (001) planes

Domain structures are considerably influenced by the effect of conductivity, imperfections, etc. in a real crystal. The domain walls are found in positions which are not normally expected in a perfect insulating crystal. This leads to head-to-head or tail-to-tail couplings, while the normal way of the coupling of dipoles is head-to-tail, for no charge condition on the wall. The step ladders on pseudocubic (001) planes have been studied from this point of view using the technique of multiple beam interferometry. It has been found that an association of 180° domains with 60° domains can also be indicated in a simple way.

Thickness of Monolayers of the Fatty Acids by Multiple Beam Interferometry

Thickness of Monolayers of the Fatty Acids by Multiple Beam Interferometry

Allowance for the diffraction divergence of a laser beam in multiple-beam interferometry

Allowance for the diffraction divergence of a laser beam in multiple-beam interferometry

Applications of the two beam and the multiple beam interferometry techniques to polymer crystals

AbstractTwo beam interference fringes over hedrites, sheaves, and spherulites of cellulose triacetate are obtained on crystals grown on carbon coated slides. The multiple beam interference fringes over the same crystals are obtained after silvering. The ratio of the fringes observed by the two beam to the multiple beam interferometry over the same crystal gave the refractive index of the crystal along the direction of the beam. Application of these techniques showed that the change of thickness of hedrites and sheaves due to increase in polymer concentration is the same. The hedrites of cellulose triacetate are diagonally thin and have a square depression at the centre. The surfaces of spherulites grown from solution are uneven.

Interferometre fabry-perot enregistreur dans l'ultraviolet a vide (λ > 1800 Å)

Photometric recordings of interferograms at λ 1850 Hg I, λ 1820 S I and λ 1807 S I show the feasibility of multiple beam interferometry down 1800 Å with double layer coatings of aluminum and magnesium flouride. The Fabry-Pérot spectrometer is constituted with a silica etalon and a vacuum monochromator. The method of pressure scanning is used with argon.

Multiple beam interferometry in elementary teaching

An educational review of practice and theory in multiple beam interferometry discussed techniques and applications as applicable to schools and students generally.