WO2010068482A1

WO2010068482A1 - Laser interferometer

Info

Publication number: WO2010068482A1
Application number: PCT/US2009/065874
Authority: WO
Inventors: Feredoon Behroozi
Original assignee: University Of Northern Iowa Research Foundation
Priority date: 2008-11-25
Filing date: 2009-11-25
Publication date: 2010-06-17

Abstract

An apparatus and method for non-contact measurement, with nanometer precision, of surface properties such as the local slope and/or vibration amplitude of a solid material, or the surface tension of a small liquid sample. The apparatus provides a laser light source and optic transmission line adapted to be positioned above and near the sample surface, together with a mechanism adapted to move and/or vibrate or oscillate either the surface or probe, or both, with respect to each other. In turn, an interference pattern by the interaction of reflected light from the surface and light reflected by the terminus, that can be correlated to either: i) the amplitude of vibrations imparted to the surface, or ii) the local slope of the surface as determined in the course of controlled oscillation of the terminus.

Description

LASER INTERFEROMETER

TECHNICAL FIELD The present invention relates to an apparatus and method for non-contact measurement of physical properties of solid surfaces (e.g., local slope and vibration amplitude) and liquid surfaces (e.g., wave amplitude and surface tension) with nanometer resolution.

BACKGROUND OF THE INVENTION

The ability to determine surface properties at the micron and submicron levels has many applications in research and industry. Various instruments have evolved for such purposes over the years. According to online literature, Canon developed an interferometer based on the Michelson interferometer method that achieves a resolution of 0.08 nm. Canon's optical design provides a lightweight and compact interferometer weighing about 50 grams and measuring 38 mm x 47 mm x 19 mm. This size reduction is said to enable the interferometer to be used in piezoelectric measurement equipment, wafer-stage position control for EB drawing systems, and surface measurement of silicon wafers.

Applicant has previously patented an interferometer having unique properties for use with fluid samples, e.g., as described in US Patent No. 6,563,588 (Apparatus and Method for Measurement of Fluid Viscosity), granted on May 13, 2003.

What is clearly needed is an improved interferometer for use in detecting surface properties at the micron and submicron levels, on the surface of solid, semisolid, and liquid materials.

BRIEF DESCRIPTION OF THE DRAWING

Figure 1 is a schematic of one embodiment of a laser interferometer of the present invention.

Figure 2 is a schematic of an optical fiber that can be used above a vibrating sample surface.

Figure 3 provides graphs depicting a representative surface vibration and corresponding interference pattern. Figure 4 shows the vibration amplitude of a piezoelectric transducer as a function of applied voltage.

Figure 5 shows the vibration amplitude as a function of position over a sample surface. Figure 6 shows a contour plot depicting the amplitude vs. position over a sample surface.

Figure 7 shows the schematic of a fiber probe over a sloping surface.

Figure 8 shows a schematic of the cylindrical well for containing a small liquid sample, placed on the vibrating piezoelectric transducer. Figure 9 shows a graph of ω2/k vs. k2 for pure water at 24 C using the apparatus of

Figure 8. The slope of this graph gives the surface tension of pure water as σ = 72.2 dyne/cm.

Figure 10 shows a graph of ω²/k vs. k² for water +10% acetone at 24.75 C. The slope of this graph gives the surface tension of this solution as σ = 45 dyne/cm. Figure 11 shows a graph of ω²/k vs. k² for water covered by a soap film at 24.75 C.

The slope of this graph gives the surface tension of the soap film as σ = 24.7 dyne/cm. Figure 12 shows a graph of ω²/k vs. k² for water+20% glycerol at 24 C. The si this graph gives the surface tension of this solution as σ = 69.6 dyne/cm.

SUMMARY OF THE INVENTION

The present invention provides an apparatus and corresponding method for non- contact measurement of properties such as the local slope (and in turn, optionally topography) and the vibration amplitude of material surfaces with nanometer precision.

In one preferred embodiment, the present invention provides an interferometer apparatus comprising: a) an optic transmission line having a proximal end and a terminus adapted to be positioned above and near the surface of a material in a manner sufficient to permit laser light to be directed substantially perpendicularly onto the material surface, the terminus adapted to internally reflect some laser light into the optic transmission line while also receiving laser light reflected from the surface; b) a laser light source adapted to be coupled to the optic transmission line in order to pass laser light thereinto; c) a mechanism adapted to provide relative movement in a controlled manner as between the material surface and the terminus, the mechanism selected from the group consisting of: i) a surface support adapted to impart controlled vibration to the surface of the material; ii) one or more transducers adapted to impart controlled oscillation to the terminus; and/or iii) one or more micropositioners adapted to provide multidirectional movement of the material surface or terminus, or both, with respect to the other. d) a detector operably connected to the optic transmission line and adapted to detect an interference pattern created by the interaction of reflected light from the surface and light reflected by the terminus, the interference pattern being correlated to either: i) the amplitude of vibrations imparted to the surface; or ii) the local slope of the surface as determined in the course of controlled oscillation of the terminus.

In a particularly preferred embodiment, the method and apparatus of the present invention can be used to determine both slope and vibration amplitude. In slope measurement using such an embodiment, the surface will typically be kept stationary, while the probe itself oscillates (e.g., vibrates) back and forth along the surface (See Fig. 7). On the other hand, for measurement of vibration amplitude, the surface will typically be vibrating while the probe is kept stationary with respect thereto. The probe position over the surface can be controlled in any such embodiment, for instance, by the use of one or more, and preferably two or more independent micropositioners. For instance, the fiber probe can be attached to a piezoelectric transducer which can be energized to vibrate the probe.

Consequently, one instrument can be used that is capable of performing both measurements as required.

In one preferred embodiment, the terminus is laterally moveable, while remaining at a set distance from the material surface, and the apparatus further comprises a measurement element to measure lateral movement of the terminus, whereby both the surface slope and the amplitude profile of the vibrations may be mapped, e.g., to provide the topography of the surface.

In one such preferred embodiment, the invention provides a method of determining the slope and/or amplitude of vibrations in a sample surface, comprising: a) providing an apparatus as described herein; b) positioning the terminus of the optic transmission line above and near the sample surface; - A -

c) passing laser light through the fiber and onto the surface while imparting relative movement as between the sample surface and terminus; d) detecting the interference pattern generated; and e) correlating the interference pattern to determine either slope or amplitude of vibrations of the surface.

In turn, the invention can further provide a method for determining the topography of a surface comprising: a) providing an apparatus as described herein; b) determining the local slope at each point along a path (e.g., line) in a stepwise sequence; c) integrating the slope data to obtain the topography along that line; and d) constructing the surface topography for a given area by obtaining the topography of a network of paths covering the area of interest.

The invention further provides a method for determining the surface tension of a small sample of fluid (e.g., on the order of 5 ml or less, and preferably on the order of 2 ml or less), without contacting the surface, in one preferred embodiment the method comprising: a) providing an apparatus as described herein; b) positioning the fluid in a vessel (e.g., cylindrical cavity) placed upon a surface adapted to impart vibrations to the vessel (e.g., by means of a piezoelectric transducer); d) positioning the terminus of the optic transmission line above and near the fluid surface, e) passing laser light through the fiber and onto the surface while exciting surface waves on the fluid (e.g., by energizing the transducer at various frequencies); f) detecting the resonance frequencies by monitoring the number of fringes in the interference pattern; and g) obtaining the surface tension of the fluid from the resonance frequencies.

An interferometer of the present invention provides new options and opportunities not currently possible with commercial devices, including for use with solid, semi-solid, and liquids having suitable small surface areas, and in particular, the ability to measure both the local slope and the amplitude of surface vibrations.

The two reflected beams are used to form an interference signal, and in turn, an interference pattern that can be used in a variety of ways and for a corresponding variety of purposes. For instance, the surface displacement due to vibration at a particular frequency can be determined by the number of fringes in the interference pattern, which in turn, corresponds to the amplitude of vibration. In particular, the number of fringes in the interference signal is proportional to the amplitude of the vibrating surface. The amplitude will typically vary over the surface, depending for instance, on the distance from the center of the surface. Such differences can themselves be determined and used, e.g., to provide a contour map that can be used to reveal hidden surface flaws such as cracks, surface strains, hidden defects, surface roughness, or thickness variations.

The apparatus can also be used to determine local slope, e.g., by allowing the fiber to oscillate harmonically over the surface within a controlled range and frequency. As the optical fiber moves over a sloping surface, the gap between the fiber tip and the underlying surface changes accordingly, producing an interference signal, the pattern of which can be correlated with the gap variation. The number of fringes in the interference signal gives the height change over the travel distance, while the slope is the ratio of the rise over run.

The apparatus can also be used to determine the surface tension of fluids by detecting the resonance frequencies of surface waves. In one such application a suitable vessel, such as a small cylindrical cell, containing the fluid is placed on a piezoelectric transducer (Figure 8). The vessel is preferably provided with an internal configuration sufficient to provide a surface area of about 50 mm² or more, and preferably about 100 mm² or more, when containing a fluid sample of 2 ml. The amplitude of the surface waves are monitored by the fiber-optic probe as the transducer frequency is ramped. The number of fringes in the interference signal increases dramatically at resonance frequencies. The data on resonance frequencies yield the surface tension as described herein.

The method and apparatus can include various optional and preferred embodiments, including the use of vibration isolation, e.g., in the form of a suspended platform or an isolation table. Other preferred options include the use of micropositioners (interfaced with a computer) to track the probe position over the sample surface.

In one such preferred embodiment, a plurality (e.g., two) of micropositioners are used to move the probe to any desired location over the sample surface. A third micropositioner is used to adjust the height of the probe above the surface. These micropositioners are interfaced with a computer to keep track of the probe position relative to the surface. Furthermore, harmonic (e.g., sinusoidal) and/or aharmonic (e.g., square, triangular, or sawtooth) oscillations can be imparted to the surface or the probe in unison or independently by piezoelectric transducers. The word "above" when used with respect to the position of probe and surface, refers to the proximity of the two, as compared to the orientation of both in space. In other words, the apparatus can be provided, and the probe tip in turn used, so as to determine surface properties of any suitable surface, and in any suitable orientation (e.g., vertical or horizontal with respect to the ground).

In one preferred embodiment the specimen is coupled to a piezoelectric transducer which may or may not be energized to impart surface oscillation. The fiber probe is also attached to a mini-transducer which may or may not be energized to set the fiber into harmonic or aharmonic oscillation. In this option, the probe is positioned over the surface at a desired position. To measure the local slope the fiber transducer is energized briefly and slope data recorded.

The local topography of a spot can be explored or determined by measuring the slope in multiple directions. Furthermore, stepwise integration of local slopes along a line can be used to obtain the global topography of the surface. At any point of the surface, the vibration amplitude may be measured by turning off the fiber transducer and energizing the specimen transducer. It is therefore practical to perform both measurements on the same apparatus.

DETAILED DESCRIPTION The determination of surface properties in the manner presently described provides a non-contact method for measuring various surface and material properties. The instant invention can provide a non-contact method and apparatus for precision measurement of the local slope of a surface as well as the amplitude of vibrations imparted to a surface. Data regarding the location and amplitude of vibration can be used, for instance, to determine the contour map of the surface vibrations, and in turn, potential structural defects within the material itself.

In a particularly preferred embodiment, the method and apparatus of this invention can be used to obtain a contour map of a sample surface. For instance, the apparatus can employ a fiber-optic detection system that functions as a miniature laser interferometer. In one preferred embodiment, the apparatus includes a single mode optical fiber, one end of which is positioned a short distance above the material surface. Laser light traveling through the optical fiber is partially reflected from the cleaved tip of the fiber and again from the surface. The two reflected beams travel back through the same fiber forming an interference pattern. As the surface position changes due to vibrational motion, the interference signal portrays an accurate record, in real time, of the variation of the gap between the end of the fiber optic cable and the solid surface.

Those skilled in the art, given the present description, will be able to obtain or provide suitable optical fibers for use in the present invention. Fibers having tips that have been cleaved in order to provide a mirrored end (perpendicular to the fiber axis) are available commercially, e.g., from Gould Fiber Optics (gouldfo.com), or can be created using conventional techniques, such as a diamond-tipped mechanical cleaver.

The invention can be used to obtain a vibrational profile with a resolution of between about 1 and about 100 nanometers, and preferably between about 5 and about 20 nanometers. By comparison, a resolution of 10 nanometers, for instance, is on the order of fifty times better than the resolution of a typical optical microscope. The surface can be vibrated using any suitable means, e.g., by means of a piezoelectric or acoustic transducer, which can be used to vibrate the surface. In one preferred embodiment, the fiber optic probe is attached to three micropositioners. Two micropositioners in the X-Y directions are equipped with digital micrometers to track the position of the probe in the horizontal plane. The third micropositioner in the Z-direction is used to adjust the height of the probe above the sample. To obtain the vibration profile of the surface, suitable vibrational forces are imparted to the surface by placing the sample on a piezoelectric transducer or by other means. The probe is then placed above the vibrating surface at a known position. The interference data is recorded in digital form and analyzed to obtain the vibration amplitude. This procedure is repeated for other points to obtain a vibration profile of the surface.

In turn, the present invention can provide a non-contact method and apparatus to precisely measure the vibration profile of a surface at various frequencies to reveal surface and structural defects. The invention further provides a miniature laser interferometer apparatus which may be used without mechanical contact with a material surface, to determine the local slope of the surface of the material. Such an apparatus and method can be used to measure surface properties without risk of contamination of the material under examination.

The apparatus and method of the present invention will be further described with reference to the Figures. In use, a laser can be operated to generate a polarized light beam which may be within or without the visible spectrum. The laser light beam is transmitted through air or a fiber optic transmission element such as fiber optic cable to a first beam splitter wherein a portion of the laser light is siphoned to a reference amplifier/detector.

In the schematic of Figure 1, the polarized laser beam is divided into two beams by a beam splitter. One beam is directed to the detector to serve as reference, the other passes through a Faraday rotator and a birefringent cube to generate two beams. Each beam enters an optical cable via a graded index (GRIN) lens which serves as the input into a multiplexer. The multiplexer directs half of the input beam to the measurement surface and the other half to the detector. The beam which is directed to the surface produces two reflections, one at the cleaved terminus of the fiber and the other at the surface. These two reflected beams re- enter the said fiber to reach the multiplexer as a combined modulating beam which is sent to the detector. The detector is designed to cancel the DC part of the signal against the reference beam and amplify the AC signal produced by the interference of the two reflected beams.

The Faraday rotator serves an important function by isolating the laser from any reflected light that may find its way back to the laser cavity. This is because any reflected light returning to the laser cavity will provide a positive feedback to the laser turning it into an echo chamber and thus rendering any measurement useless. To prevent this, the polarization angle of the main beam passing through the Faraday rotator changes by 45°. Any returning light passing through the Faraday rotator suffers a further 45° shift in polarization. Consequently when this reflected light reaches the laser, it is 90° out of phase with the laser light and is rendered harmless.

Those skilled in the art, given the present description, will appreciate the manner in which various embodiments and corresponding iterations can be used to provide an apparatus of this invention. For instance, as an alternative to the arrangement of beam splitters and a Faraday isolator, an acousto-optic modulator can be used to isolate the laser from laser light reflected from downstream components. In this arrangement the acousto-optic modulator splits the beam into two off-axis beams plus a center beam. The center beam serves as the reference beam, while the two off-axis beams provide the inputs to the multiplexers. An acousto-optic modulator causes a slight shift in frequency of the two off-axis beams, raising one and lowering the other, and thus, provides the necessary isolation of the laser cavity from reflected light.

In the schematic of Fig. 1, after the main beam passes through the Faraday rotator, it is further split by the birefringent cube into two beams. Each of these beams is in turn coupled to a multiplexer via a GRIN lens. This arrangement provides two independent measuring stations from the same laser. The detector is also designed to accept two inputs as shown in the schematic.

The reference beam serves as the input to a separate reference amplifier/detector to detect fluctuations in the laser beam due to small variations in line voltage or due to temperature drifts. Reference amplifier/detector provides a reference signal to each of first and second detection units such that variations in the output of laser will be normalized to cancel effects of line voltage and temperature variation. The same reference signal is also used to cancel the DC part of the interference signal.

The schematic of Fig. 2 shows the optical fiber above the vibrating surface. The laser beam is partially reflected back into the fiber as it exits the fiber tip. Most of the beam exits the fiber and is reflected at the surface. Part of this reflection also reenters the fiber. The two reflected beams reach the multiplexer and are directed to the detector, where they combine to form the interference pattern.

In a particularly preferred embodiment, the interferometer consists of a single mode optical fiber placed a short distance above the surface of the solid or liquid. Laser light (He- Ne λ=632.8nm) is directed through the fiber onto the vibrating surface. Two reflections are produced, one from the cleaved tip of the fiber, the other from the vibrating surface. These two reflected beams reenter the fiber, and produce an interference signal at the detector. Fig. 3 provides graphs depicting a representative surface vibration and corresponding interference pattern.

Interference signals produced using an apparatus of the present invention can be used in a variety of ways and for a corresponding variety of purposes. For instance, the surface displacement due to vibration at frequency/ may be described by

Y(t) = a sin (ω t) (1) where, a is the amplitude of vibration, ω = 27τf is the angular frequency, and t stands for time. The path difference Δ between the beam reflected from the vibrating surface and the beam reflected from the fiber tip is given by:

A = 2 [do - a sin (ω t)] (2) where, do is the equilibrium (i.e., static) distance between the fiber tip and the surface. The interference signal at the detector is given by

Y(t) = A cos [(2 π AZA₁) + π] (3)

Substitution of Eq. 2 in Eq. 3 results in,

Y(t) = A cos [b sin (cot) - φ], (4) where, b = 4πa/λι , and φ = π + (4πdo)/λι.

In Eq. 4, A is the amplitude of the interference signal which is typically normalized to unity. The parameter b when divided byπ( i. e. b/π) gives the number of fringes in the interference pattern and contains the information on the amplitude of vibration. The parameter φ is a constant phase determined by the equilibrium distance between the fiber and the surface. Furthermore, the number of fringes in the interference signal is proportional to the amplitude of the vibrating surface. Indeed the wave amplitude is simply the number of interference fringes (b/π) times λι /4 : a = b λt /4π (5)

Thus a higher number of fringes in the interference pattern corresponds to a larger amplitude.

A fitting program is used to fit Eq. 4 to the digitized data to obtain the two parameters b and φ. Once b is determined, Eq. 5 gives the amplitude of vibration.

EXAMPLES EXAMPLE 1

MEASUREMENT OF THE VIBRATION AMPLITUDE

A circular piezoelectric disk was excited by a sinusoidal voltage from a signal generator at the desired frequency. The laser interferometer was used to detect and measure the vibration amplitude of points across the disk. Fig. 4 shows the vibration amplitude of the center of the disk as a function of the exciting voltage at a frequency of 197 Hz.

For exciting voltages up to 5 V the vibration amplitude increases linearly with the applied voltage (see Fig. 4). Indeed for this piezoelectric transducer the vibration amplitude increases at the rate of 250 nm per volt of applied voltage. Therefore, one can obtain a given vibration amplitude by selecting the proper voltage. This ability is only possible because the laser interferometer serves as an accurate and absolute calibrator.

At excitation voltage above 5 V, the disk response deviates slightly from linearity. All measurements are confined to the linear region. In Fig. 5, the vibration amplitude is shown as a function of position. To make these measurements, the transducer was excited at a frequency of 523 Hz at a voltage of 4Vpp. The fiber optic probe was moved across the disk surface along a diagonal to measure the vibration amplitude at many points. As expected, the vibration amplitude is a maximum near the center of the disk and diminishes as one approaches the edges of the disk. The resolution of these measurements is about ± 5 nm.

The area near the center of the disk was chosen for a closer examination. The fiber probe was used to obtain data on the vibration amplitude of a dense grid of points within a small surface area of 1.2 mm by 0.8 mm near the center of the disk. The result is shown in Fig. 6 as a color map. The vibration amplitude of each region is color coded as shown on top of the figure.

Fig. 6 shows a contour map of the vibration amplitude,the data taken at a frequency of 523 Hz and an excitation voltage of 4V peak to peak. Each region differs in vibration amplitude by 10 nm from its neighbor. The position of the peak is about (-0.4 mm, 0.45 mm) away from the geometric center of the disk. The maximum variation in the vibration amplitude represented in this plot is only 20nm in the Z-direction. A contour map of this kind may be used to reveal hidden surface flaws such as cracks, surface strains, or thickness variations.

This example demonstrates that the apparatus can measure the vibration amplitude of a solid surface with a resolution of +/- 5 nm. This resolution is about 100 times better than the typical resolution of an optical microscope filling the gap between optical systems and atomic scale microscopy. Furthermore, this example points to how the vibrational profile of a surface can reveal structural defects. For example, the data of Fig. 5 shows that the vibrating disk is non-symmetric, while Figure 6 shows the detail vibration asymmetry of the surface at the center of the disk.

EXAMPLE 2 MEASUREMENT OF LOCAL SLOPE

In this application, the optical fiber is attached to a piezoelectric transducer as shown in Fig. 7. This arrangement allows the fiber to oscillate harmonically over the surface with a range and frequency controlled by the voltage applied to the piezoelectric transducer. As the optical fiber moves over the sloping surface, the gap between the fiber tip and the underlying surface changes, producing an interference signal which encodes the gap variation in its pattern. The number of fringes in the interference signal gives the height change over the travel distance. The slope is the ratio of the rise over run. Preferably, for instance, the apparatus can be used to measure local slope of up to about 7° for a linear distance of about one micron. Fig. 7 shows the schematic of the fiber probe over a sloping surface. The fiber can oscillate back and forth horizontally at a set frequency and over a distance of about one micron or more depending on the exciting voltage of the transducer. The number of fringes in the resulting interference signal gives the change in the distance between the fiber tip and the surface below as the fiber moves through its range. This information yields the local slope. This example demonstrates that the apparatus can measure the local slope of the surface over a microscopic interval of about 5 microns. This capability may be exploited to map the microscopic profile of a surface along a given direction by stepwise progression of the probe over the surface. This procedure may be automated to produce the profile under computer control of the probe.

EXAMPLE 3

MEASUREMENT OF SURFACE TENSION

A circular cavity of diameter 1.25 cm and depth 1.5 cm was machined on one face of a Teflon cube of side 2 cm. The cube was placed on a piezoelectric transducer and the cavity was filled with liquid. When the disk was excited with an ac voltage of less than one volt, it oscillated at the exciting frequency and with amplitude of about 200 nm. The low amplitude oscillation was transmitted to the Teflon cube through a thin layer of silicon grease which bonded the cube to the oscillating surface. Normally, the resulting waves on the fluid surface are quickly damped due to phase mismatch at the well boundaries. However, at certain frequencies, known as resonance frequencies, radial standing waves with relatively large amplitude were generated and sustained on the surface. The diameter of the cavity and the surface tension of the fluid determine the resonance frequencies. The laser interferometer was used to detect the resonance frequencies. Data on resonance frequencies was used to determine the surface tension of the fluid. The vibration amplitude of the piezoelectric transducer was a linear function of the applied voltage. Fig. 5 shows the response of a piezoelectric transducer (Radio Shack #273- 073A) to the exciting voltage, by measuring the amplitude of vibration using the laser interferometer described herein. The following procedure was used to measure surface tension. A Teflon well of small diameter (1.27 cm) was placed on a piezoelectric disk. The well was filled with pure water and set in vibration to excite radial waves.

The oscillation frequency was ramped gradually. When the exciting frequency matched the resonant conditions of the apparatus, the wave amplitude increased dramatically as monitored by the interferometer.

Once several resonance frequencies are measured, surface tension was determined by the following analysis.

In the course of data analysis, the dispersion equation governing capillary-gravity waves is given by, ω² = kg + k³σ/p (6) where k is the wave number, σis surface tension, p is fluid density and ω is the angular frequency.

Equation 6 may be recast into a more convenient form, co²/k = g + k²σ/p (7)

The diameter of the cavity determines the particular wave numbers that produce standing radial waves. For a cylindrical cavity of diameter D, these special wave numbers are given by, k_n = n π/D n=l, 3, 5, 7 (8) According to Eq. 6, the corresponding resonance frequencies are therefore,

2πf_n = fg k_n + k_n ³ σ/pj ^'A (9)

For example, the first resonance occurs at a frequency of, fj = [ _g/4πD + π σ/4p D³ J ^'A (10)

Since the cavity diameter D, and the fluid density p are known, Eq. 10 gives the surface tension σonce the first resonance frequency is measured. In practice greater accuracy is assured when several resonance frequencies are measured.

In particular, when/} ,/3 ,fs , and /7 are measured, the corresponding wave numbers ki , £3 , £j , and k? are known from Eq. 8. From this data ω²/k is plotted as a function ofk². The slope of this graph is the surface tension. Fig. 9 gives the graph for pure water. The cavity used had a diameter D =1.27 cm, and the temperature was 24 C. The slope of this graph gives the surface tension of pure water as σ= 72.2 dyne/cm. The apparatus can and has been used to measure the surface tension of several fluids. The following graphs give the results for water-acetone (Fig. 10), water covered by a soap film (Fig. 11), and water-glycerol mixture (Fig. 12). In each case, the slope of the ω²/k vs. k² gives the surface tension. The radial waves established on the surface are Bessel functions of the first kind. The resonance wave numbers k_n are determined by the boundary conditions. This more involved analysis gives results comparable to the simple theory.

When a Teflon well is used the fluid surface may assume a curved shape depending on the value of the contact angle between the fluid and Teflon. For example pure water has a contact angle θ = 1200 with Teflon. In such cases, the effective diameter of the well is given by

D_eff = D (θ - π/2)/sin (θ - π/2)

This correction has been applied to the data in Figures 9-12. A more convenient remedy is the use of gold plated brass wells. In this case the contact angle reverts to (π/2) and no curvature correction is needed. Fig. 8 shows a schematic of the well placed on the vibrating piezoelectric transducer. The resonance vibration mode shown is for n=3. In this mode the wavelength is 2/3 of the well diameter. Fig. 4 shows the vibration amplitude of the piezoelectric transducer as a function of the applied voltage. The frequency of vibration was chosen to be 197 Hz. Fig. 9 shows a graph of ω²/k vs. k² for pure water at 24 C. The cavity used had a diameter of 1.27 cm. The slope of this graph gives the surface tension σ = 71.3 dyne/cm. Fig. 10 shows a graph of ω²/k vs. k² for water+10% acetone at 24.75 C. The cavity used had a diameter of 1.03 cm. The slope of this graph gives the surface tension σ = 45.0 dyne/cm. Fig. 11 shows a graph of ω²/k vs. k² for water+10% acetone at 24.75 C. The cavity used had a diameter of 1.03 cm. The slope of this graph gives the surface tension σ = 24.7 dyne/cm. Fig. 12 shows a graph of ω2/k vs. k2 for water+20% glycerol at 24 C. The cavity used had a diameter of 1.03 cm. The slope of this graph gives the surface tension σ= 69.6 dyne/cm.

Claims

CLAIMSWhat is claimed is:

1. An interferometer apparatus comprising: a) an optic transmission line having a proximal end and a terminus adapted to be positioned above and near the surface of a material in a manner sufficient to permit laser light to be directed substantially perpendicularly onto the material surface, the terminus adapted to internally reflect some laser light into the optic transmission line while also receiving laser light reflected from the surface; b) a laser light source adapted to be coupled to the optic transmission line in order to pass laser light thereinto; c) a mechanism adapted to provide relative movement in a controlled manner as between the material surface and the terminus, the mechanism selected from the group consisting of: i) a surface support adapted to impart controlled vibration to the surface of the material; ii) one or more transducers adapted to impart controlled oscillation to the terminus; and/or iii) one or more micropositioners adapted to provide multidirectional movement of the material surface or terminus, or both, with respect to the other. d) a detector operably connected to the optic transmission line and adapted to detect an interference pattern created by the interaction of reflected light from the surface and light reflected by the terminus, the interference pattern being correlated to either: i) the amplitude of vibrations imparted to the surface; or ii) the local slope of the surface as determined in the course of controlled oscillation of the terminus.

2. An apparatus according to Claim 1 wherein the optic transmission line comprises a fiber optic having a terminus comprising a cleaved tip.

3. An apparatus according to Claim 2 wherein the terminus is laterally moveable, while remaining at a set distance from the material surface, and the apparatus further comprises a measurement element to measure lateral movement of the terminus.

4. An apparatus according to Claim 2 wherein a plurality of micropositioners are used to move the probe to any desired location over the sample surface, and at least one micropositioner is used to adjust the height of the probe above the surface.

5. An apparatus according to Claim 4 wherein the micropositioners are interfaced with a computer to keep track of the probe position relative to the surface.

6. An apparatus according to Claim 5 wherein harmonic and/or aharmonic oscillations can be imparted to the surface or the probe in unison or independently by piezoelectric transducers.

7. An apparatus according to Claim 5 wherein the apparatus can be used to provide a vibrational profile with resolution of between about 1 and about 100 nanometers.

8. An apparatus according to Claim 7 wherein the resolution is between about 5 and about 20 nanometers.

9. An apparatus according to Claim 1 wherein the optic transmission line comprises a fiber optic having a terminus comprising a cleaved tip; the terminus is laterally moveable, while remaining at a set distance from the material surface, and the apparatus further comprises a measurement element to measure lateral movement of the terminus.

10. An apparatus according to Claim 9 wherein a plurality of micropositioners are used to move the probe to any desired location over the sample surface, and at least one micropositioner is used to adjust the height of the probe above the surface, and the apparatus can be used to provide a vibrational profile with resolution of between about 1 and about 100 nanometers.

11. A method of determining the slope and/or amplitude of vibrations in a sample surface, comprising: a) providing an apparatus according to Claim 1; b) positioning the terminus of the optic transmission line above and near the sample surface; c) passing laser light through the fiber and onto the surface while imparting relative movement as between the sample surface and terminus; d) detecting the interference pattern generated; and e) correlating the interference pattern to determine either slope or amplitude of vibrations of the surface.

12. A method for determining the topography of a surface comprising: a) providing an apparatus according to Claim 1 ; b) determining the local slope at each point along a path in a stepwise sequence; c) integrating the slope data to obtain the topography along that line; and d) constructing the surface topography for a given area by obtaining the topography of a network of paths covering the area of interest.

13. A method for determining the surface tension of a small sample of fluid, without contacting the surface, the method comprising: a) providing an apparatus according to Claim 1 ; b) positioning the fluid in a vessel placed upon a surface adapted to impart vibrations to the vessel; d) positioning the terminus of the optic transmission line above and near the fluid surface, e) passing laser light through the fiber and onto the surface while exciting surface waves on the fluid; f) detecting the resonance frequencies by monitoring the number of fringes in the interference pattern; and g) obtaining the surface tension of the fluid from the resonance frequencies.

14. A method according to Claim 13 wherein the vessel comprises a substantially cylindrical cavity and the surface is vibrated by a piezoelectric transducer.

15. A method according to Claim 13 wherein the fluid sample is on the order of 5 ml or less.