Beam Interferometry Research Articles

Wavefront sensing by diffracted beam interferometry

We consider the reconstruction of an optical wavefront by means of the interference of a light beam with a diffracted copy of itself. We present the basis of the method and a numerical algorithm for phase retrieval from the experimental data.

Confinement-Induced Film Thickness Transitions in Liquid Crystals between Two Alkanethiol Monolayers on Gold

We describe the use of two semitransparent gold layers of equal thickness as substrates in the interferometric surface forces apparatus. The continuous gold layers were evaporated onto an adhesion layer of chromium on muscovite mica that had been exposed to water vapor plasma to introduce reactive groups on its surface. Multiple beam interferometry was used to measure the thickness of mixed alkanethiol monolayers covalently bound to the gold and the film thickness of homeotropically oriented liquid crystals confined between these monolayers. In 4‘-n-pentyl-4-cyanobiphenyl, quasi-periodic structural forces with transitions comparable to the length of a liquid crystal dimer were observed at film thicknesses below 13 nm, indicating that confinement-induced smecticlike ordering can occur also between two surfaces with a root-mean-square roughness of ≤1 nm. Similar transitions could also be observed in 4‘-n-octyl-4-cyanobiphenyl.

Hot topics in structural acoustics: Optical imaging of surface vibrations—Some new developments and applications

Laser Doppler vibrometry is routinely used for a vast range of applications to measure surface vibrations in the nanometer range. Some new developments include the use of laser vibrometers with continuous tracking on moving targets, the detection of the vector displacement of a surface (either with multiple beam interferometry or with a photo-emf probe), and the direct measurement of torsional vibrations on rotating shafts. Electronic speckle pattern interferometry (ESPI) is a full-field optical technique that is also commonly used to image surface vibrations. An interesting development of ESPI is electronic shearography. Some applications of these optical techniques will be discussed. These include calibrations of transducers and MEMS devices, imaging of rotating parts, mapping of structural intensity, characterization of the dynamic response of viscoelastic materials, as well as some more exotic applications such as damage assessment of frescoes and painting, three-dimensional vibration imaging of the ossicular chain in cats, and dynamic characterization of human teeth.

In situ imaging of shearing contacts in the surface forces apparatus

Multiple beam interferometry (MBI) can be used in the surface forces apparatus for in situ topographical imaging in real-time of the contact between two shearing surfaces at ultrahigh resolution in the normal direction at the same time as friction forces are measured. Simultaneous measurements were made of the friction forces between two shearing mica surfaces separated by WS 2 (inorganic) fullerene, and non-fullerene WS 2 nanoparticle additives in tetradecane. The results were correlated with the very different transfer layers formed in each case, as visualized by in situ MBI and ex situ atomic force microscopy.

Polarizabilities of atoms and molecules, new insights into an old subject

The importance of electric polarizabilities is discussed in detail. Emphasis is given not only to the dipole–dipole polarizability α ̂ , but also to the dipole–quadrupole, dipole–octopole and quadrupole–quadrupole polarizabilities Â, Ê, and Ĉ, respectively, as examples for the higher-order polarizabilities. In the case of the nonlinear polarizabilities we concentrate on the second hyperpolarizability γ ̂ and the quadrupole–dipole–dipole polarizability B̂. New experimental techniques such as the asymmetric white-light interferometry, atomic–beam interferometry, electric field deflection techniques, and collision-induced spectroscopy are discussed. Recent experimental and theoretical results are presented for the frequency, density, and temperature dependence of the polarizabilities. Special emphasis is given to new results concerning the frequency dependences of the mean dipole-polarizability of molecular iodine and of the polarizability anisotropy of carbon dioxide in the gas phase. An outlook is given for future work devoted to polarizabilities.

Generic Substrate for the Surface Forces Apparatus: Deposition and Characterization of Silicon Nitride Surfaces

We introduce a novel substrate for direct normal and lateral force measurements in the surface forces apparatus (SFA). While most SFA experiments are typically carried out using molecularly smooth mica surfaces, the new layered structure allows the use of just about any material which can be deposited as a thin film using evaporation or chemical vapor deposition. In this work, we demonstrate the use of this method for preparing plasma enhanced chemical vapor deposited silicon nitride substrates. Chemical, structural, optical and mechanical characterization of the substrates was carried out using secondary ion mass spectrometry, atomic force microscopy, transmission electron microscopy, ellipsometry, multiple beam interferometry and SFA force measurements. The latter showed an extremely low adhesion energy (γ < 1 μJ/m2) between silicon nitride surfaces prepared using this method, which is attributed to the surface roughness (ca. 2.2 nm rms).

Measurement of axisymmetric temperature fields using reference beam and shearing interferometry for application to flames

A unified methodology for the application of reference beam and shearing interferometry to measure axisymmetric temperature fields within flames is proposed. Sensitivity and accuracy of the techniques are analyzed basing on interferograms of reference temperature profiles and CARS measurements obtained in test laminar flames. The rapid decay of temperature measurements accuracy with increasing both intensity of errors sources and uncertainty on independent parameters is assessed. The spatial variation of mixture composition in diffusive combusting flows requires the application of complementary methods to obtain a satisfactory accuracy, while flow fields with lean premixed combustion can be treated as optically-homogeneous media. The temperature maps resulting from the investigation of the test laminar flames are presented and discussed. The capability to disclose the thermal structure and to provide reliable quantitative data is demonstrated.

Dynamics of layering transitions in confined liquids.

Multiple beam interferometry and video microscopy were used to investigate the layering transition of thin liquid films of 1-undecanol confined between atomically smooth mica surfaces. The expulsion of a molecularly thin lubricant layer was followed directly in two dimensions. Overall, the dynamics of the transition follows theoretical predictions based on two-dimensional hydrodynamics. Frequently, pockets of liquid remain trapped inside the contact area at the end of the transition. The trapped pockets undergo shape transformations to minimize elastic and interfacial energy.

Shear-Induced Dilation of Confined Liquid Films

We demonstrate that sheared molecularly-thin fluid films dilate at the point of stick-to-slip (which is the transition from static to kinetic friction), indicating that density decreases when sliding occurs. This contrasts with incompressibility characteristic of bulk fluids when they are deformed. The magnitude of dilation was less than the size of the molecule and was larger in a polymer system (large molecules) than for small-molecule fluids. The experiments employed a surface forces apparatus modified to measure, using piezoelectric methods, sub-angstrom variations of film thickness during dynamic shear excitations that were performed at rates too rapid to allow fluid to enter and exit the zone of shear contact during the period of shear excitation. To demonstrate generality of the dilation effect, the specific systems studied included nonpolar fluids whose complexity was varied (a globular-shaped molecule, OMCTS; a branched alkane, squalane; a tethered diblock copolymer, polyvinylpyridine–polybutadiene) and also an aqueous electrolyte, MgCl2 dissolved in water. Extensive analysis is also presented of the piezoelectric methods that were employed to detect volume changes too small to observe by the methods of multiple beam interferometry that are traditional for thickness measurement in a surface forces apparatus.

Simultaneous optical detection techniques, interferometry, and optical beam deflection for dynamic mode control of scanning force microscopy

In dynamic mode control of scanning force microscopy (SFM), optical beam deflection and interferometry are the techniques most used for detection of force gradients by means of a tip and a microcantilever that usually vibrates at the first resonant mode. In order to increase the sensitivity of these kinds of microscopes, one possible means is to investigate the potential of the highest resonance modes which allow an increase in the operating frequencies. For these two detection techniques, according to the local displacement slope, care must be taken in the choice of an appropriate microcantilever point where the laser beam is focused. In this article, an original technique based on simultaneous detection, interferometry, and the beam deflection method is introduced. These techniques are able to characterize within two degrees of freedom, normal displacement and angular deflection, thus resonating the SFM cantilever.

Topographic Information from Multiple Beam Interferometry in the Surface Forces Apparatus

This paper shows how multiple-beam interferometry can be used to unambiguously determine the topography of both surfaces in the surface forces apparatus at nanometer resolution. The conventional fringe pattern which is widely used to determine surface separations exhibits a fine background modulation. Under favorable conditions, i.e., low mirror reflectivity and unlike layer thickness (asymmetry), these background variations, which consist of a number of superimposed but distinguishable fringe patterns, provide valuable additional information about surface topography. This allows one to determine the surface topography in contact and noncontact. We present the results of extensive numerical calculations for the three-layer interferometer system using a generalized numerical algorithm. The comparison of measured and simulated interference patterns illustrates the influence of various parameters such as refractive index, layer thickness, mirror reflectivity, asymmetry, and topographic features on specific fringe properties such as their visibility, position, and shape. We also demonstrate the new method by analyzing experimental data of a mica−polymer contact.

The f.c.c. to h.c.p. martensitic phase transformation in CoNi studied by TEM and AFM methods

The thermally induced martensitic phase transformation from the high temperature (f.c.c.) to the low temperature (h.c.p.) phase was studied in a Co32% Ni single crystal by transmission electron microscopy (TEM), atomic force microscopy (AFM) and light microscopy with multiple beam interferometry (MBI). Quantitative analysis of the TEM results shows that the transformation takes place by consecutive glide of partial dislocations of the same Shockley partial Burgers vector on every other close packed plane. The tapering h.c.p. lamellae contain high shear strains and cause long range internal stresses that facilitate transformation induced plasticity. The AFM and MBI results show that the transformation shear strains are compensated on a mesoscopic scale. This indicates that the transformation induced stresses trigger the formation of new self-accommodating h.c.p. lamellae by an autocatalytic process. It should be pointed out that the reverse transformation (h.c.p. → f.c.c.) previously investigated in the same material showed the occurrence of a different transformation mechanism based on an atomistic compensation.

Characterization of the Interface between a Rough Metal and Smooth Mica in Contact

We introduce a technique to characterize,in situ,the solid–solid interface formed when a rough metal surface is placed in contact with a smooth mica surface. The technique is based on the use of extended spectral analysis of multiple beam interferometry in conjunction with the surface forces apparatus (SFA). The intensity versus wavelength spectra of light transmitted through the rough metal/mica interface is measured and compared to that transmitted through a smooth metal/mica interface. Interference theory is used to characterize the rough interface based on differences in the measured spectra. Roughness on the order of nanometers can be resolved. The key to our technique is the creation of a perfectly smooth metal/mica interface that is in all respects, except for roughness, identical to the metal/mica interface created in the SFA. We accomplish this by thermal evaporation of a metal film directly onto mica. We demonstrate the effectiveness of the technique by characterizing the structure of silver/mica and gold/mica interfaces. We also show how the technique can be used to investigate the exchange of fluids within the contact region.

On the equivalence principle in quantum theory

The role of the equivalence principle in the context of non-relativistic quantum mechanics and matter wave interferometry, especially atom beam interferometry, will be discussed. A generalised form of the weak equivalence principle which is capable of covering quantum phenomena too, will be proposed. It is shown that this generalised equivalence principle is valid for matter wave interferometry and for the dynamics of expectation values. In addition, the use of this equivalence principle makes it possible to determine the structure of the interaction of quantum systems with gravitational and inertial fields. It is also shown that the path of the mean value of the position operator in the case of gravitational interaction does fulfill this generalised equivalence principle.

Structure, Composition, Dielectric, and AC Conduction Studies on Tin Selenide Films

Al-Snse-Al thin film capacitors were fabricated onto well cleaned glass substrates by thermal evaporation under a pressure of 2 mPa. Multiple beam interferometry (MBI) was used to measure the thicknesses of the SnSe films. The composition and structure of Sn x Se 1-x films were analysed using Rutherford backscattering spectrometry and X-ray diffractogram, respectively. The capacitor samples were stabilised by aging and annealing. The variations of the dielectric constant and loss as a function of frequency at different temperatures were observed and the results are discussed. AC conduction studies reveal that the conduction mechanism is due to hopping of holes. The activation energies were also calculated.

Diffusion and adsorption of proteins in a model pore in the surface forces apparatus

When the energetic interactions between proteins and pore surfaces are favorable, both hindered diffusion and adsorption govern the overall transport rates in fine pores. To study these effects, we have used the narrow gap between mica surfaces in a surface forces apparatus (SFA) as a model slit-like pore that has a well-characterized geometry and surface chemistry. The optical technique of multiple beam interferometry used in the SFA for measuring surface separations also provides a means for determining protein concentrations inside the pore. The results obtained show the effect of ionic strength on the net transport rates for lysozyme diffusing in a mica-bounded pore, a consequence of the influence of electrolyte screening on the extent of adsorption. It is also seen how adsorption on opposing surfaces leads to pore blockage once the pore size decreases to 2–3 times the molecular diameter. Although quantitative determination of hindrance effects is potentially also possible using the method, an improved method for acquisition of the interferometry data must first be implemented.

Gas flow visualization by means of sheared beam interferometry: sensitivity, maximum measurable gradient of the density fluctuation, and integrated density estimation

A technique for visualizing the density distribution of a gas flow using sheared beam interferometry was analyzed. The interference pattern which arises in the shearing interferometer encodes information about the gradient of the line integral of the density fluctuation along the propagation path of the light. While this method of flow visualization has been previously used, the sensitivity and dynamic range of this technique have not been analyzed. It is also shown that it is possible to obtain quantitative information about the integral of the density fluctuations along the path of light propagation using shearing interferometry. This paper presents the theoretical aspects of this technique, and provides an analysis of the sensitivity and maximum measurable gradient of the line integral of the density fluctuation. Representative results from a laboratory experiment conducted on a shear-layer gas flow are shown.

Refractive Index Measurements to Study the Structural Behavior of Anisotropic Macromolecules Confined between Two Mica Surfaces

A study was performed with a surface force apparatus (SFA) in which the automation of a mica surface displacement at very low speed and the use of multiple beam interferometry yield force profiles and variations of the refractive index of the macromolecular layers adsorbed between the two mica plates of the device. The performances of such an SFA are illustrated by the identification of the two molecular types of the plant lectin concanavalin A (Con A) when the anisotropic dimer Con A is converted into an isotropic tetramer form. Thus, the SFA can be a good model device for studying macromolecular interactions submitted to a variable compression stress in a confined space.

Diffracted beam interferometry for EM and materials research

Diffracted beam interferometry, DBI, is a practical method of interferometry which removes the strict requirement for a bright, coherent source and extends the availability of holography to a wider community of electron microscopists. The only alteration to the microscope is the installation of an electron biprism into a post-objective lens position. DBI is very flexible as the interferogram can be produced from the conditions of the infocus diffraction (Fraunhofer plane), through the Fresnel (de)focus region to the infocus specimen plane by varying the strength of the post-objective lenses, Fig. 1. As well the convergence of the interfering beams can vary from highly convergent (Fig. 1) to pseudoparallel (Fig. 2). Although the phase in the interferogram due to beam tilt and the contrast transfer function of the prefield objective lens cancel out when the interfering beams are exactly overlaid, the phase due to the spatial frequency of the biprism, KB, the contrast transfer function, uL,R, of the postfield objective lens for each beam, L,R, and the inherent material phase, FL,R, remain.

Reflection diffracted beam interferometry (RDBI) applied to the study of surfaces

Diffracted beam interferometry, DBI, (previously referred to as Convergent Beam Electron Diffraction + Electron Biprism Interferometry, CBED+EBI) which uses an electron biprism to deflect diffracted beams (convergent or parallel) can produce an interferogram between any two beams within the information envelope of the microscope such that the beam's amplitude and phase can be measured and studied. As well, the electron source need not be highly coherent. So far, DBI has been applied only to transmission electron diffraction, although there is no reason why it shouldn't be applicable to all electron diffraction methods including reflection high (low) energy electron diffraction, RH(L)EED and, possibly, back-scattered electron diffraction, BSED, in the SEM for the study of surfaces. DBI has already shown that substantial phase information, such as strain at interfaces and dislocations, compositional gradients and small defect clusters which are on the size scale of the unit cell, are retrievable from its holograms.