CA1333752C - Universal interferometric strain gauge - Google Patents

Abstract

A novel interferometer and method of determining incremental movement are provided herein. The interferometer includes a source of a laser beam of radiant energy; a beam splitter disposed across the path of the beam of radiant energy for splitting the beam into reflected beams and transmitted beams;
a reflector for receiving or reflecting a beam of radiant energy which has been reflected by the beam splitter; an optical recording device disposed in the path of a beam reflected by the beam splitter; a rigid cantilevered arm having a coating thereon whose incremental movement is to be measured; and a mirror, mounted on the cantilevered arm, for reflecting a beam of radiant energy reflected by the beam splitter. The incremental movement is measured by a determination of the movement of an interference pattern produced by interference of the two beams of the radiant energy. The interferometer is capable of measuring a deflection of at least 1/20th of a wave-length of light (?300.ANG. or 30 nm) in an arm, e.g. of stainless steel, with the sensitivity being dependent on the size of the steel arm. A long steel arm increases the sensitivity, while a thicker steel arm decreases it.

Description

1333~2 This invention relates to an interferometric strain gauge.
In general terms, the invention relates to measurement employing interference between two or more wave trains coming from the same large luminous area for observing the displacement of a movable part in order, e.g., to provide a measurement of the force which initiates the movement. Such measurements have shown that absolute determinations by interference methods generally cause a distinctive pattern of interference fringes which may be compared for measuring extremely small displacement patterns about a reference position. The results can be interpreted to obtain indirect measurements of the driving force responsible for the displacement of the interference fringe pattern.
Torsion balance systems in the past which have been known to rely upon interferometry optics have been capable of measuring static forces with only a moderate degree of accuracy. The effects of undesired friction between the relatively moveable elements of prior art systems is chiefly the most serious defect in such measuring devices. Efforts to balance the fixed mirror portion of the interferometer system so as to ensure an unfluctuating mirror alignment have frequently been resolved with compromise measures having a degrading effect upon the results achieved. It has also been found in instruments of this kind that oscillations of the load-responsive member introduce a frequently expensive concern for the exact means to be employed in balancing out oscillations caused by overly compliant suspension systems.
Interferometer techniques are now utilized for detecting relative movement between any two selected objects by having two mirrors of an interferometer connected to the two points of interest so that information concerning movement of the objects can be obtained by observing the changes in the resulting interference pattern, In these and other systems wherein interference patterns of electromagnetic energy, e.g. visible light, are used, it is important to be able to count the actual member of fringe shifts which occur as well as to be able to detect and determine the extent of a partial fringe shift.
One of the methods by which spectral information has been obtained in the past involves the use of a Michelson interferometer. In this method, electromagnetic radiation is passed through the interferometer, and successive readings are taken of the intensity of the beam (by the use of a suitable detector) leaving the interferometer as the scanning mirror is moved, both with and without a sample in the beam.
The beam entering the interferometer is split into two components by a semi-transparent and reflecting coated glass flat or prism beam splitter and the reflected and transmitted components are reflected back onto the beam splitter by two mirrors in such a way that the components are recombined into one beam which then leaves the interferometer.

One of the mirrors, the so-called scanning mirror, is movable in a direction parallel to the direction of the component of the beam that is incident on it. As the scanning mirror is moved, the path difference between the two components changes (the change in path difference between the components for any displacement of the scanning mirror being twice that displacement) and a plot of the intensity of the beam leaving the interferometer against the path difference between the components is termed an interferogram. A measure of the spectrum of the beam leaving the interferometer (that is, a plot of energy of the lo radiation against frequency) may be obtained by Fourier transformation of the interferogram.
There are many instances where it is desired to measure very small forces. Strain gauges have sometimes been used for this purpose, but they are difficult to use and frequently give inaccurate readings. For example, if the internal strain developed in a paint as it dries is to be measured by visually noting the curl in a piece of shim stock by eye or by microscope or by capacitance change, a relatively large movement is required, necessitating a thin substrate.
As another example, such devices may be used to measure the thermal expansion of polymeric materials, rather than the heretofore most common means of measuring thermal expansion in polymeric materials by either measuring fluid or gas displacement in a closed system as the material expands, or by measuring the ; _ 4 _ 1333752 linear displacement of a mechanical rod that is placed against the material.
By another example, information about the absorption characteristics of a sample may be obtained by plotting an interferogram with the sample in the beam either before splitting or after recombination, and by plotting a further so-called "background" interferogram without a sample so as to give the characteristics of the background radiation. From the Fourier transformations of the twolinterferograms, the absorption lo coefficient for the sample as a function of frequency can be obtained over a selected bandwidth.
By yet another example, information about the refractive index of a sample may be obtained by positioning the sample so that a part, but not the whole, of one of the components of the beam split by the semi-transparent and reflecting mirror in a Michelson interferometer passes through it. An interferogram plotted with the sample in this position has two main peaks, and from a knowledge of the separation between these peaks and the thickness of the sample, the average refractive index over a selected bandwidth of radiation may be calculated.
In yet another example, the thickness of a film after deposition on a substrate may be determined by using interference techniques, e.g. as shown in U.S. Pat. No. 3,059,611, continuously to monitor the growth of a film on a substrate by measuring successive minima in light transmitted through the substrate.

_ 5 _ 1 333752 As a further example, such devices may be used for determining early fatigue damage and surface stress in metals.
With the increased use of exotic metals and the increased use of common metals to their maximum capability in aircraft, space flight paraphernalia and undersea exploration, the need for the early determination of fatigue damage and surface stress becomes more urgent than in the past. Early fatigue damage appears first at the surface of the metal and can best be detected ultrasonically by using the highest practical surface wave lo frequency which travels in very close proximity to the metal surface. In order to detect early damage, where the signs are not readily apparent, the velocity and attenuation rate must be measured with extreme accuracy if they are to reveal these very small changes associated with the early stages of fatigue damage.
In yet another example, the Ep-layer may be monitored in thickness where a substrate of structure in which an epitaxial growth layer (Ep-layer) is formed on a substrate of sapphire or silicon by a vapour growth is used as a substrate for forming semiconductor element therein from the viewpoint of improving their properties. The Ep-layer is required to have a uniform thickness, for example, 1.5 um in the Ep-layer for a bipolar memory. In a heteroepitaxial treatment, e.g. an Ep-layer of silicon on sapphire, the thickness of the Ep-layer has conventionally been monitored at the time of its growth. In order to apply such a method to practice in a homoepitaxial treatment, e.g. an Ep-layer of silicon on silicon (Si/Si), it is necessary to employ a dummy substrate made of sapphire, polycrystalline silicon or the like which differs in property from a silicon substrate, considering that the substrate has the same optical property (refractive index, absorption coefficient) as the Ep-layer. The Ep-layer on the silicon substrate, however, has a speed growth different from that of the Ep-layer on the dummy substrate (sapphire or polycrystalline silicon). Further, particularly in the case of a sapphire substrate, impurities contained in sapphire are apt to out-diffuse in an ambient atmosphere whereby contamination of the epitaxial layer occurs.

In spite of its importance, a relatively small number of investigations have been carried out in the field of internal stress in plastic materials and inorganic coatings.
It is well known that during film formation and the drying process coatings tend to shrink. This shrinkage may be accommodated by a weaker substrate or may lead to cracking, partial adherence or detachment. There are many factors which may affect that shrinkage, e.g. type of vehicle, type of pigment, presence of filler, type of solvent, and percent of solids in one component, non-polymerizing paints. In polymerizing paints, the conditions are further complicated by the presence (usually) of catalysts and shrinkage on polymerization.
Among the methods of measurement of the internal stress in coatings, photoelasticity, stress gauge, and cantilever (beam and plate) may be mentioned.

- 7 - 13337~2 The cantilever method has been used for some years to measure stresses developed in inorganic coatings and organic coatings stress studies. The cantilever method was suggested for organic coatings and has become the most frequently used method.
Devices and methods for detecting the spacial relationship between points each on a member have been provided in Bell, U.S.
Patent No. 2,929,242. As shown in the Bell patent, strain in a member is determined by providing a member with a finely ruled diffraction grating and determining strain from changes in the lo separation of the lines by determining, by means of an intensity measurement, changes in an angle of a diffracted order of light.
A uniform light field is focussed on the grating and the angle of a diffracted order is determined by measuring the intensity of light passing through a "V" slit.
U.S. Patent No. 3,354,311 provided a fringe movement detector and measuring system that was said to be useful for measuring the fringe shift of a radiation interference pattern, e.g. that produced by an interferometer used for measuring relative movement between two points. Interferometric measuring techniques have been applied to detecting relative movement between two points on the surface of the earth in order to measure long earth strains resulting from earth tides and other geophysical phenomena.
U.S. Patent 3,354,311 patented November 21, 1967 by V. Vale et al provided a system for detecting and counting the movement ~ ; - 8 - 1333752 of a radiant energy interference pattern. Radiant energy detecting means was mounted on a movable support and in a predetermined portion of the pattern. As the pattern attempted to move relative to the detector means a high gain servo loop moved the support in a direction to reduce such relative movement. The support drive signal thus was proportional to the fringe movement. Limit switches were actuated when the movement corresponded to a complete fringe shift so that the mount was returned to its initial position and a counter was actuated.
lo U.S. Patent 3,612,692 patented October 12, 1971 by R.W.
Kruppa et al provided an automatic thickness monitoring and control system and method for monitoring the growth of a dielectric film on a reflective substrate, e.g. a silicon wafer during an RF sputtering deposition process and for stopping the deposition process when the film reached a predetermined thickness. The successive minima (or maxima) in the interference pattern of light reflected from the wafer were counted to determine the film thickness and the sputtering was stopped at a predetermined count.
U.S. Patent 3,639,063 patented February 1, 1972 by R.S.
Krogstad et al provided a fringe movement detector in which a radiation interference pattern was deflected by a galvanometer mirror to illuminate two photoelectric cells with selected portions of the interference pattern. As the interference pattern shifted, the change in output of the photoelectric detectors was differentially amplified and applied to the galvanometer coil to deflect the interference pattern back to the original or reference position on the photoelectric detectors.
The magnitude of the electrical signal required to return the galvanometer mirror to the reference position was proportional to the amount of shift of the intèrference pattern. After a shift of a predetermined amount, reset means were used to return the galvanometer mirror to approximately its original position to illuminate the photoelectric detectors with selected portions of lo the next following fringe.
U.S. Patent 3,664,739 patented May 23, 1972 by J.R. Pryor provided a technique whereby the separation of two points, each located on a member and being separated by an aperture, was measured by directing waves, e.g. light waves, on the points to form a diffraction pattern of the single aperture type. A change in dimension of the member, or in the spacing between two adjacent members, caused the separation of the edges to change which, in turn, caused a change in the configuration of the pattern. By comparing the intensity of a given portion of the pattern with a portion of a pattern produced under known conditions, a change in the separation of the points could be determined from which measurement of dimension, strain, etc.
could therefore be determined.
U.S. Patent 3,854,325 patented December 17, 1974 by F.M.
Coate provided a technique whereby a test specimen was mounted on a movable table, ultrasonic surface waves were caused to travel across the specimen by a transducer fed from a CW signal source, a laser beam was passed through a beam splitter, one portion being reflected onto a photo-detector measuring signal amplitude, an output signal was compared with the output of the CW signal and the CW signal was shifted in phase by 90~. These outputs measured ultrasonic phase difference, at points along the specimen. The second portion of laser beam was reflected from a mirror attached to the specimen table and back to a screen where lo an interference pattern was formed as the table is moved. Photo detectors sensed the changes in interference pattern and determined specimen displacement.
U.S. Patent 3,905,215 patented September 16, 1975 by J.R.
Wright provided a force measuring instrument which employed light interference fringes for measuring extremely small magnitudes of force, e.g. those encountered in the weighing of small ob~ects or in determining the forces of attraction or repulsion between two relatively small bodies. A fixed mirror of the displacement mechanism was provided with needle point pivot shafts in which balance oscillations -could be dampened by applying a viscous damping material in the conical recesses receiving the pivot points. Torsion fiber beams permitted a small angular displacement of the fixed mirror.
U.S. Patent 3,938,889 patented February 17, 1976 by J.A.
McKinnes provided a method and apparatus for measuring the linear thermal expansion of a polymeric material wherein a sample with a wedge surface was mounted on a graphite block within a temperature controlled chamber. The incident and reflected beam of a laser were in a plane perpendicular to the plane of the base of the sample and made equal angles with a line perpendicular to the plane of the base of the sample. A holographic plate was exposed by the object beam from a sample and a reference beam.
The temperature is gradually increased between a first exposure and a second exposure. A thermocouple and indicator were used to indicate the temperature of the sample at the time of each exposure of the holographic plate. The holographic plate was then developed and replaced in the plate holder for reconstruction of the images and the fringe pattern, which indicated the expansion of the sample.
U.S. Patent 4,203,799 patented May 20, 1980 by K. Sugawara et al provided a technique whereby, in growing on a substrate film of substance of a similar kind to the substrate, ions were implanted into the substrate to form, within the substrate, a layer of substance having an optical property different from that of the substrate. An epitaxial film was then grown, The thickness of the film could be monitored with an interference waveform appearing with its growth.
Canadian Patent 939,528 issued January 8, 1974 to Leslie W.
Thorpe et al provided spectroscopic apparatus comprising means for producing two parallel beams of radiation adapted selectively ~ 12 - 1333752 to pass through a sample. Means were provided upon which each of the beams is incident for dividing said beams into partially reflected and partially transmitted components. Means were also provided for superimposing the reflected and transmitted components of each beam upon each other to recombine the respective beams. Such superimposing means included at least one reflecting means for reflecting one of the components of each beam which was movable in a direction parallel to the direction of incidence of the beam components. Means were provided for lo modulating the intensity of each beam at a different frequency.
Detector means were adapted to receive radiation from each of the modulated beams, and means were provided for measuring the amplitudes of the components of the detector output produced by each of the respective beams.
Canadian Patent 1,082,486 issued July 29, 1980 to Horst Schwielker et al provided an improvement in a device of the type used for detecting the reflection and transmission behaviour of layer thicknesses between fractions and some multiples of the wavelength of the essentially monochromatic measurement light used, and by interrupting the coating process when a predetermined layer thickness has been obtainéd. The arrangement included a measurement light source for emitting a focussed measurement light beam, a chopper device, a beam divider arranged at an angle of 45 degrees on the axis of the measurement light beam, that part of the measurement light beam passing behind the J.,~ "~, - 13 ~ 1 333752 beam divider being directed on the measurement ob~ect, a measurement light receiver with a monochromator connected thereto, as well as a differentiation device for the measurement signal and an interruption device for the coating process.
R.N. O'Brien, and W. Michalik, in "Journal of Coatings Technology", 57, No. 722,84(1985), described a cheap, simple, easily mounted and dismounted apparatus for detecting internal stress. The substrate was a clamped, stainless steel shim stock, but the means of detection was by laser interferometry. The shim 10 stock had the coating applied to one side and a small first surface mirror was glued to the other side. The interferometer detected the movement of fringes to one tenth of a fringe (which is l/20th of the wave-length of the laser light, He/Ne at 632.8 mm). The detection limit of deflection was 30 namometers or 0.03 ~m or ~10-6 inches.
R.N. O'Brien and W. Michalik also reported, in an article in "The Journal of Coatings Technology", Vol. 58, No. 735, April 1986 on a method of measuring the internal strain developed in drying paint. The paint was applied to a metallic strip of known dimensions and modulus. The drying paint caused bending of the plate as stress developed in the paint. A small mirror attached to the end of the plate was one part of a modified Michelson laser interferometer. The number and spacing of the fringes in the mirror change as the mirror moves to reduce the light path and change the angle of reflection. It was suggested that great _ - 14 - 1333752 accuracy can be obtained by projecting the fringes for viewing at a distance, by using a light detecting array at a distance, by using lengthy plates, by using plates with a lower modulus, or by using thicker pain.t films.
Accordingly, the present invention has many objects in mind.
An object of one aspect is to provide such a device which does not suffer the disadvantage of being cumbersome or of introducing stress or deformation into the specimen, by weight or contact pressure from measuring equipment, and, in failing to lo provide the extreme accuracy needed to detect signs of metal fatigue.
An object of another aspect is to provide an improved fringe movement detector measurement system having increased resolution, greater sensitivity, higher frequency response, and greater isolation from thermal and mechanical ambient variations, An object of yet another aspect of the present invention is to provide a novel system for detecting movement of an interference pattern produced by interfering beams of laser energy.
An object of still another aspect of this invention is to provide an apparatus for measuring the fringe shift of an interference pattern that is relatively insensitive to temperature variations and technical noise.
Interferometer techniques making use of a laser have recently been used in an entirely new manner for detecting _ - 15 ~ 1 3337 S2 relative movement between two points on the surface of the earth so that the earth tides and oscillations can be studied.
However, the present invention now provides an interferometer also making use of a laser, which is capable of measuring a deflection equal to at least 1/2Oth of a wave-length of light (z300A or 30nm) in a rigid cantilevered arm with the sensitivity being dependent on the size of the rigid cantilevered arm.
By one broad aspect of this invention, an interferometer is provided for determining incremental movement in a substrate comprising: (a) a source of a laser beam of radiant energy;
(b) a beam splitter disposed across the path of the beam of such laser beam radiant energy to provide reflected beams and transmitted beams; (c) a reflector for reflecting a beam of radiant energy which has been reflected by the beam splitter; (d) an optical recording device disposed in the path of a beam reflected by the beam splitter; (e) a rigid cantilevered arm having a coating thereon whose incremental movement is to be measured; and (f) a mirror mounted on the cantilevered arm, for receiving or reflecting a beam of radiant energy deflected by the beam splitter. The incremental movement is measured by a determination of the movement of an interference pattern produced by interference of the two beams of the radiant energy.
In one variant thereof, the laser beams of radiant energy are preferably created by a He/Ne laser of nominal lmW power.
The optical recorder may be a camera, or a photomultiplier, or a photosensitive array inputting to a microcomputer, or a camera with screen labelling. The beam splitter may be either a 50%
reflecting glass flat mirror or a prism.

. ., .;,. _ - 16 s 1 333 752 By still another variant thereof, the rigid cantilevered arm preferably is a steel arm whose length/thickness ratio is at least 150. By a variant thereof, the mirror on the cantilevered arm may be spring mounted to the cantilevered arm to be adjustable and removable.
By still another variant thereof, the interferometer includes a heat shield around the interferometer, the heat shield being adapted to admit thermal radiation to the coating but not to the optical components.
The substrate may be a paint coating, or an electroplated or vacuum evaporated metal coating, or an electroplated coating.
In such variant, the interferometer thereby includes an electro-chemical cell with a vertical cathode to which a mirror is attached to monitor the strain-producing current density for plating.
By one embodiment, the interferometer is used for determining internal stress in the substrate by solving the equation:

S dEI' d~(t+C) (I) - 3CLl(t + C) (I-v) L2(1_~rc) where d is the deflection of the rigid cantilever arm, E is the elastic modulus of the material of the cantilever arm, L is the length of the cantilever arm between the point at which it is clamped and the point at which deflection is measured, Ec is the elastic modulus of the substrate, v is the Poisson's ratio of the rigid cantilever arm, VC is the Poisson's ratio of the substrate, . . .,:

- 17 _ 1 3337~2 C is the thickness of the substrate, and t is the thickness of the cantilever arm.
By another aspect of this invention a method is provided for determining the incremental movement of a substrate, by creating an interference pattern by reflection of a laser beam from a mirror secured to the substrate which is physically associated with a cantilevered beam; and measuring the movement of the interference pattern with time.
The stress within the substrate is determined by means of the equation S = 3CLl(l + C) (I-v) + L2(1-V~) where d is the deflection of the rigid cantilever arm, E is the elastic modulus of the material of the cantilever arm, L is the length of a cantilever arm between the point at which it is clamped and the point at which deflection is measured, Ec is the elastic modulus of the substrate, v is the Poisson's ratio of the rigid cantilever arm, VC is the Poisson's ratio of the substrate, C is the thickness of the substrate, and t is the thickness of the cantilever arm.
By another variant thereof, the method may also include the steps of: shielding only the optical components from thermal radiation; and monitoring the temperature of the atmosphere in the region of the substrate.

~ - 18 - 1333752 As described above, the basis of the present invention is that the internal stress in a substrate can be calculated from the equation:

S = 3CLl(t+C) (I V) + L1(I-Y ) (I) where d is the deflection of the rigid cantilever arm, E is the elastic modulus of the material of the cantilever arm, L is the length of the cantilever arm between the point at which it is clamped and the point at which deflection is measured, Ec is the elastic modulus of the substrate, v is the Poisson's ratio of the cantilever arm, VC is the Poisson's ratio of the substrate, C is the thickness of the substrate, and t is the thickness of the cantilever arm.
The elastic modulus of a steel substrate is two orders of magnitude greater than that of most organic coatings; thus the last term in the expression can be eliminated without introducing an error greater than 1%. The error in the internal stress measurement is caused mainly by the uncertainties of d lg- 1333752 (deflection), t (plate thickness), and C (coating thickness), and the clamping effect. S becomes practically independent of L for L greater than 8 cm. For L less than 8 cm the error introduced can be more than 9%.
In the accompanying drawings, Figure 1 is a schematic drawing of the optical components of an interferometric strain gauge, and Figure 2 is a plan view of a apparatus used in one embodiment of this invention.
As seen in Figure 1, all optical parts are supported on a flat metal stand indicated generally as 10. A laser 11, e.g. a He/Ne laser of nominal 1 mW power is mounted so that its beam 12 is directed towards a beam splitter 13 which is a 50% reflecting glass flat. The beam 12 is split so that one reflected beam 14 passes to a recording device 15, e.g. a camera, while a second transmitted beam 16 passes to a first flat surface mirror 17 and is reflected thereby as beam 18, back to the beam splitter 13 and is then reflected to the recording device 15 as beam 19.
Another reflected split beam 20 is directed towards an end mirror 21 which is glued on to clamped cantilevered arm 22, e.g.
formed of steel, to which a coating 23 is applied. The beam 20 is reflected by end coverslip mirror 21 as beam 24 to the recording device 15.
The interference patterns are obtained by ad~usting the beam splitter mirror 13 so that the light reflected from the coverslip - 20 _ 1 333752 mirror 21 cemented to the cantelevered arm 22 strikes the beam splitter mirror 13 at an angle of incidence very close to 90-.
As the coating solidifies, the path iength changes by deflection of the cantelever arm 22 causing a change in angle in the optical air wedge between the end coverslip mirror 21 and the beam splitter mirror 13 and hence a change in N (the order of interference) and so also the distance between fringes. It is also possible to replace the coverslip mirror by a l/8" thick first surface mirror spring mounted to the steel arm, the mirror lo being removable and adjustable.
One embodiment of the interferometric strain gauge of the invention is shown in Figure 2. This strain gauge 50 includes a source 51 of collimated, monochromatic light, e.g. a laser. The strain gauge 50 includes a supporting plate 52, fitted with a cover having suitable beam entrance and exit holes (not shown).
The entrance hole is aligned with the laser from the source 51, while the exit hole is aligned with an optical recorder 53, e.g.
a camera or VCR. Supported by the supporting plate 52 is a beam splitter 54, e.g. a half-silvered mirror or split prism, and an adjustable first surface mirror 55. Also supported by the supporting plate 52 is a clamp 56 to hold the coated cantelevered plate 57 which is provided with a removable mirror 58 on its free end.

` - ' - 21 - 13337~2 Specifically, the apparatus consisted of a He-Ne laser, (known by the Trade-mark SPECTRA-PHYSICS, Model 132), a camera (known by the trade-mark NIKON), a shim-stock stainless steel arm, an aluminized microscope coverslip, a beam splitter (1/2 silvered glass flat), and a first surface mirror. In this embodiment of the strain gauge, the cantelevered arm was a stainless steel bar 75 mm long, 8 mm wide and 0.485 mm thick. The actual free length (not clamped and unencumbered by the mirror) was 50 mm. Since the error is a maximum at effectively zero length and can be expected to decrease in a curve asymptotic to increasing length of cantelever beam and essentially zero at 80 mm, it is believed that the error in the 75 mm cantelevered arm (50 cm without mirror, 62 mm with mirror) will be at least less than 1/2 of 9% and probably at the order of 1%.
The use of a thinner cantilevered arm is recommended to increase the accuracy and precision of measurement, i.e., a cantelelevered arm of one half the thickness should give almost, 8 times, an order of magnitude more deflection and hence more fringes to count. At some level of thickness, it would be necessary to build a special acoustic shield to eliminate acoustic interference and also eventually to shield the apparatus from air currents.
Such a shield has been adapted to the strain gauge as described above. The shield also admits thermal radiation to the coating but not to the optics. The temperature of the atmosphere at the coating is monitored by a thermocouple or by a thermometer.

- 22 - 13337~2 Example 1 The apparatus described above was used to determine the internal stress within a drying paint film. The substrate, i.e.
the paint film was coated onto the cantelevered arm by brush.
The substrate tested was an enamel of 38% solids (soya alkyd) and a cycloalkyl commercial solvent of a white (for tinting) marine enamel. The thickness of the substate coating was measured after two days by micrometer.
While the apparatus described above was designed to hold up to three metal strips at once, it is believed as many as 10 strips could be accommodated at once.
The preferred recording device should be a video cassette recorder and camera with screen labelling.
The results of several tests is shown below in Table 1.

Table I - Internal Stress Movement Laser Interferometry Method Number of Fringe Deflection Number of N Deflection t Fringes- Shift d(mm x 102) Fringes- nl-nO d(mm x 102)(Mins) Mirror 1 Mirror 2 7 18 1 0.063 14 0 0 14 18 1 0.063 15 1 0.063 19 2 0.126 16 2 0.126 19 2 0.126 17 3 0.190 22 5 0.316 19 5 0.316 128 27 10 0.63 25 11 0.696 200 31 14 0.885 27 13 0.822 300 33 16 0.01 29 15 0.948 400 34 17 1.08 29 15 0.948 520 34 17 1.08 29 15 0.948 600 34 17 1.08 29 15 0.948 Maximum Sl 287 MPa Maximum S2 241 MPa Paint: Swittsette Marine Enamel Cantelever: Stainless Steel Strip length = 75 mm; width = 8 mm; thickness = 0.485 mm The change in spacing is proportional to a change in path length between the mirror cemented to the plate and the detector (camera) compared to that from the mirror to the camera in what is essentially a Michelson interferometer with division of amplitude, the path length varying regularly along the cemented mirror.
The bright fringes in the interferogram are formed by conditions:
(N + 1/2)~ = 2 nt cos ~ (2) lo where N is the order of interference, n is the refractive index (of air), t is the thickness of the air wedge between the mirrors, ~ is the wave length of light, and ~ is the angle of incidence of the light to the surface of the mirrors.
The refractive index of air is close to 1 and care should be taken that it does not change.
The basic formula for dark fringes is:
N~ = 2 nt cos~ (3) The calculation of d, the deflection, is simpler. The number of fringes in the mirror cemented to the plate, which is 17 at the beginning of the run, denotes the opposite side of a very thin triangle whose angle (opposite the opposite side) is much less than 1 of arc and therefore the side opposite to the angle ~ the angle. The side can be calculated to be 17 x the wave length of the laser light, i.e., 17 x 6.328 x 10-4 mm =
1.075 x 102 mm or 4.24 x 10-4 in., or .0004 in. After 600 - 25 -~ 1333752 minutes, the fringe shift was steady at 34 or 17 extra fringes had appeared or the small angle had doubled to just under 1- of arc or the mirror had moved to open the angle under the strain imposed by the drying coating on the obverse side of the steel plate. The maximum movement is again calculated to be 1.075 x 102 mm.
The angle of the fringes remains constant during the contraction of the paint film, showing that the angle of twist to the plate has remained constant, or that the paint film is both uniform in thickness and stress.
The path difference or cantilever plate deflection "d" is calculated from the equation by simple trigonometry.
The wedge angle between the two mirrors is calculated by assuming a simple uniform air wedge, with the opposite side being the number of fringes in the mirror divided by the mirror length multiplied by the plate length. For each increment in time and increment in number of fringes, d can be calculated.
The development of internal stress in coatings is expressed as the change of order of interference (or more simply the fringe separation, the fringe shifts) with time. After the drying process the thickness of these two coatings was measured at 60.9 microns and 53.7 microns, respectively. The ratios of the thickness of the coatings 60.9/53.7 = 1.134, and that of the change in fringe count 17/15 = 1.133 at + 0.05% are satisfactorily close together.

- 26 - ~ 1333752 Thus, it has been shown that the method of an aspect of the present invention can be used to measure the stress in drying paint film.
The following conclusions can be drawn: the thicker film takes longer to reach the maximum change in the order of interference ~ ~, i.e., greater deflection; the use of special protection against vibration will increase the precision of "d"
measurement as vibration can blur the fringes; and this interferometric set-up can be miniaturized to give a very useful 10 tool for the examination of internal stress in coating. Other optical arrangements can be used, e.g., a photomultiplier to count the fringes as they appear, or to allow the fringes to be projected to a distant wall and to count the fringes as they pass a fiduciary mark, or an array of photosensitive cells to digitalize the fringe movement.
It is now proposed that minor alterations will allow the interferometric strain meter to be used for almost any adhesive or adhering coating. For example, at present electrodeposited coatings are subject to strain, but the amount is unknown. It is 20 believed that such strain is at least partly responsible for failure in flaking and could contribute to corrosive undercutting at the plating or coating edge. An electrochemical cell with a vertical cathode to which a mirror was attached could monitor the strain producing current density for plating.

-- 27 ~ 1333752 A similar, but modified set-up could be used to test adhesives and the bond between substrate, adhesive and a thin layer of a desired material, e.g. vinyl on steel.
Similarly, grouting and sealing compounds and even concrete and mortar made of fine sand could be tested. Finally, in the modern computer chip, a metallic coating is sometimes applied either electrochemically or by vacuum evaporation. It seems likely that strain in the substrate could also be measured by this instrument.

Claims (18)

1. Interferometer for determining incremental movement in a substrate comprising:
(a) a source of a laser beam of radiant energy;
(b) a beam splitter disposed across the path of said beam of radiant energy to provide reflected beams and transmitted beams;
(c) a reflector for reflecting a beam of radiant energy which has been reflected by said beam splitter;
(d) an optical recording device disposed in the path of a beam reflected by said beam splitter;
(e) a rigid cantilevered arm having a coating thereon whose incremental movement is to be measured; and (f) a mirror mounted on said rigid cantilevered arm for reflecting a beam of radiant energy deflected by said beam splitter;
whereby said incremental movement is measured by a determination of the movement of an interference pattern produced by interference of the two beams of said radiant energy.

2. The interferometer of claim 1 wherein said laser is a He/Ne laser of nominal 1 mW power.

3. The interferometer of claim 1 wherein said optical recorder comprises a camera.

4. The interferometer of claim 1 wherein said optical recorder is a photomultiplier.

5. The interferometer of claim 1 wherein said optical recorder is a photosensitive array inputting to a computer for digital read-out.

6. The interferometer of claim 1 wherein said optical recorder comprises a camera recorder is a video cassette recorder and camera with screen labelling.

7. The interferometer of claim 1 wherein said beam splitter is a 50% reflecting glass flat mirror.

8. The interferometer of claim 1 wherein said beam splitter is a prism.

9. The interferometer of claim 1 wherein said rigid cantilevered arm is a steel arm whose length/thickness ratio is at least 150.

10. The interferometer of claim 1 wherein said mirror is spring mounted to said cantilevered arm to be adjustable and removable.

11. The interferometer of claim 1 including a heat shield around said interferometer, said heat shield being adapted to admit thermal radiation to said coating but not to the optical components.

12. The interferometer of claim 1 wherein said substrate comprises a paint coating.

13. The interferometer of claim 1 wherein said substrate comprises an electroplated or vacuum evaporated metal coating.

14. The interferometer of claim 1 wherein said substrate comprises an electroplated or vacuum evaporated metal coating and including a electrochemical cell with a vertical cathode to which a mirror is attached to monitor the strain-producing current density for plating.

15. The interferometer of claim 1 for determining internal stress in said substrate by means of the equation:

where d is the deflection of the rigid cantilever arm, E is the elastic modulus of the material of the cantilever arm, L is the length of a cantilever arm between the point at which it is clamped and the point at which deflection is measured, Ec is the elastic modulus of the substrate, v is the Poisson's ratio of the rigid cantilever arm, vc is the Poisson's ratio of the substrate, C is the thickness of the substrate, and t is the thickness of the cantilever arm.

16. A method for determining the incremental movement of a substrate which comprises: creating an interference pattern by reflection of a laser beam from a mirror secured to said substrate which is physically associated with a cantilevered beam; and measuring movement of said interference pattern with time.

17. The method of claim 16 wherein the internal stress within said substrate is determined by means of the equation where d is the deflection of the rigid cantilever arm, E is the elastic modulus of the material of the cantilever arm, L is the length of a cantilever arm between the point at which it is clamped and the point at which deflection is measured, Ec is the elastic modulus of the substrate, v is the Poisson's ratio of the rigid cantilever arm, vc is the Poisson's ratio of the substrate, C is the thickness of the substrate, and t is the thickness of the cantilever arm.

18. The method of claim 16 including the steps of:
shielding only the optical components from thermal radiation; and monitoring the temperature of the atmosphere in the region of the substrate.