Note: Descriptions are shown in the official language in which they were submitted.
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
1333752
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.
- 3 - 1333752
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
1333752
- 6
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
- 9 - 1333752
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
- 10- 1333752
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
11 1333752
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.
- 23 - 1333752
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
0 17 0 0 14 0 0
4 17 0 0 14 0 0
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
- 24 - 1333752
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
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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.
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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.
