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BACKGROUND OF THE INVENTION
This invention relates to the measurement of strain and more particularly
relates to the measurement of strain using optical techniques.
It is known to measure the strain and deformation of objects using
extensometers or electrical resistance strain gauges. Unfortunately,
dynamic systems such as rotating shafts, extreme environments, such as
high temperature or corrosive gas environments, and inaccessible
locations, such as large structures or small openings have proven
difficult applications for these devices.
Strain measurements may also be made using optical techniques which do not
require constant contact with the object to be measured nor exposure of
testing apparatus components to a severe environment. The known methods
utilize optical phenomena such as photoelasticity, moire interferometry,
holography, speckle interferometry, heterodyning and target tracking.
In some methods for optical strain measurement, interference effects are
exploited which generally make use of the properties of coherent
monochromatic light to produce interference patterns correlated to the
strain. An advantage of some interference methods is the ability to
measure complete two dimensional strain fields For example, holography can
be used for out-of-plane displacements, and moire and speckle methods for
in-plane displacements.
A diffraction grating may also be placed on a substrate to be measured and
illuminated with coherent, monochromatic radiation. The resulting
diffraction pattern is then analyzed to determine strain.
Extensive use of optical techniques for strain measurement has been
limited, however, by several disadvantages, including sensitivity to
vibration, difficulty in removing the effect of rigid body motions,
interference due to the natural irradiance of specimens, and the cost of
optics and supporting electronics.
SUMMARY OF THE INVENTION
It is an object of the present invention to circumvent the problems of
traditional strain measurement techniques and current optical methods by
exploiting the diffractive properties of polychromatic radiation. In the
invention, a diffraction grating on a test specimen is illuminated by a
coherent, polychromatic, at least dichromatic, light source to give rise
to a diffraction pattern. This pattern is a composite pattern of the
maxima and minima arising from the various wavelengths incident upon the
grating. An imposed strain perpendicular to the grating lines in the plane
of the grating affects the grating spacing. The features of the
diffraction pattern, for example, the minima and maxima, corresponding to
different wavelengths of radiation change relative to each other in angle
of diffraction and intensity in response to the change in grating spacing.
This relative change can be correlated with strain.
The relative change between diffraction pattern features from different
wavelengths is also independent of the angle of incidence of radiation
upon the grating. Thus, measurement of strain independent of some rigid
body motions is possible.
It is also the object of this invention to provide an optical extensometer
for measuring displacements using a diffraction grating illuminated with
polychromatic radiation that enables high resolution and provides a
digital or analog feedback signal for strain control testing.
In one aspect, the invention provides a method for measuring strain of an
object by providing the object with a diffraction grating, and
illuminating the grating with radiation including at least two frequencies
to produce an interference pattern corresponding to the frequencies. At
least a portion of the interference pattern corresponding to one of the
frequencies is detected, and analyzed to determine strain.
A feature of the invention is that detecting may comprise detecting the
frequency of the radiation of the interference pattern.
Another feature is that analyzing may include comparing the detected
frequency with known frequencies indicative of the strain.
Yet another feature is that the detector may be a human eye.
Another feature is that detecting may include detecting at least a portion
of the interference pattern corresponding to at least two frequencies and
comparing the two frequencies to known frequencies indicative of the
strain.
Another feature is that the detecting may include detecting the intensity
of the frequency.
In yet another feature, the interference pattern detected may correspond to
at least two frequencies, and the detecting may include detecting the
intensity distribution of the interference pattern for the frequencies.
The analyzing may include analyzing the distribution.
Another feature is that the detecting may comprise detecting the angular
position of the portion of the interference pattern.
Yet another feature is that the detecting may comprise detecting the
angular position for portions of the interference pattern corresponding to
at least two different frequencies, and the analyzing includes comparing
the positions to determine strain. Yet another feature is that the
comparing may include finding the difference between the angles and
comparing the differences to known differences to determine strain.
Yet another feature includes modulating the radiation before illuminating
the diffraction grating. Another feature is that the analyzing includes
demodulating the signal. Another feature is that the modulating includes
chopping the radiation.
Yet another feature includes the radiation to have frequencies different
from emission frequencies of the object and the detecting includes
detecting the different frequencies.
Another feature is that the portion of the diffraction pattern detected may
be a maximum. Another feature is that the maximum may be a first order
maximum.
Another feature is that the detector detects the intensity of the portion
of the diffraction pattern.
In another aspect, the invention provides an apparatus for measuring strain
of an object. The apparatus includes a diffraction grating fixed to the
object, and a source of radiation including two frequencies for
illuminating the grating and producing an interference pattern. A detector
means detects at least a portion of the interference pattern corresponding
to at least one of the frequencies, and an analysis means analyzes the
portion of the pattern for determining the strain.
A feature of the apparatus is that the detector may detect the angular
position of a portion of the interference pattern corresponding to at
least two frequencies and the analyzing means compares the positions to
determine strain.
Another feature is that the detector may be a frequency detector which
detects the frequency of the portion of the interference pattern and the
analyzing means compares the frequency to known frequencies to determine
strain.
Yet another feature is that the detector may detect the intensity
distribution of a portion of the interference pattern corresponding to at
least two frequencies and the analyzing includes analyzing a distribution
pattern.
Another feature is that the detector may be the human eye.
Yet another feature is that the apparatus may further comprise a modulator
for modulating the radiation before illuminating the grating.
Yet another feature is that the modulator is a chopper.
Another feature is that the surface may be heated and in another feature
the temperature of the surface is over about 1000.degree. C. The
diffraction grating may be formed of a refractory metal or ceramic.
Another feature is that grating may be electrodeposited, vapor deposited or
formed integrally with the object.
Another feature is that the grating is a reflective grating or in another
feature the surface is transparent to the radiation and the grating is a
transmission grating.
Another feature is that the grating may be fixed on a rotating surface.
BRIEF DESCRIPTION OF THE DRAWING
FIG. 1 illustrates a strain measurement device according to the invention.
FIG. 2 illustrates interference phenomena arising from a diffraction
grating on an unstrained surface when illuminated with dichromatic
radiation according to the invention.
FIG. 2a illustrates diffraction phenomena as in FIG. 2 but from a
relatively strained grating.
FIG. 2b illustrates the effect of a rigid body rotation on diffraction
phenomena in a strained grating as in FIG. 2a.
FIG. 3 illustrates the change in angular separation as a function of strain
for strain measurement using the method of the invention.
FIG. 4 illustrates another embodiment of the invention in which radiation
is modulated prior to impinging upon a grating.
FIG. 5 illustrates another embodiment employing a transmission grating.
FIG. 6 illustrates strain measurement on a rotating object according to the
invention.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
In the invention an optical extensometer measures the effect of a strained
diffraction grating upon an incident, coherent, polychromatic light
source. Referring to FIG. 1, a diffraction grating 1 is oriented on a
surface of substrate S which is subject to strain so that the grating
lines 7 are perpendicular to the direction of deformation; a component of
strain perpendicular to the grating lines will change the grating spacing
Radiation 5 from a dichromatic source 2 includes, for example, at least
two wavelengths (or frequencies), .lambda., .lambda..sub.2 which
illuminate the grating giving rise to an interference pattern. The pattern
is a composite sum of the patterns arising from the various wavelengths in
the incident radiation. The composite pattern thus includes features, for
example, feature 12 from .lambda. and feature 14 from .lambda..sub.2 which
may be detected by detector 13 in the viewing field. The features 12, 14
may be a diffraction minimum or maximum or another portion of the pattern.
As the grating spacing changes in response to strain, the diffracted angle
or angular position of the features of the pattern corresponding to each
wavelength also change. The relative change in angular position of
features from different wavelengths may then be measured to determine the
amount of strain.
A particular advantage of the invention is that the diffracted angles for
features from the various wavelengths are affected identically by rigid
body rotations where the axis of rotation is parallel to the grating
lines, but differently by strain-induced change in the grating spacing.
Strain measurement may then be made free of error arising from these rigid
body rotations by comparison of the angular position for features arising
from at least two wavelengths.
Another advantage of the invention is that the detector may detect the
relative angular position of the features or may even be a human eye
detecting the color or frequency as well as the angular position of the
diffracted radiation which may be correlated with a degree of strain. In
the latter case, the measurement may not include a relative measurement of
features from different wavelengths but, rather, detection of frequency or
change in a frequency distribution at a particular angular position may
provide a simple, rapid, accurate measurement of strain.
Referring to FIGS. 2-2b, diffraction using a polychromatic source according
to the invention is illustrated, schematically. A diffraction grating 1
with line spacing, d.sub.1, is fixed to a surface 6 of a substrate S by a
securing means 8, for example, an adhesive, a weld or the like. In other
embodiments the grating may be integral with or deposited onto the
surface.
The strain of the substrate S is to be measured. Radiation 5 from a source
2 illuminates the diffraction grating forming a diffraction pattern
comprising intensity minima and maxima. In the present example, the
diffraction grating is reflective and the diffracted angle of interference
maxima or minima are illustrated as 12, 14, 16, 18 which may be detected
at a detection plane, 20.
The radiation 5 is incident upon the grating at an incident angle
.phi..sub.1 and according to the invention includes at least two
wavelengths forming a diffraction pattern with features whose reflected
angle is dependent thereon. As is known in the art, the diffraction
patterns are alternating regions of intensity minima and maxima. The
minima and maxima are by convention numbered as orders. The zeroth order
corresponds to that order due to direct transmission in the case of a
transmission grating, or perfect reflection in the case of a reflection
grating. The first maximum and minimum in a reflection grating is
determined as the first diffracted maximum and minimum encountered as the
angle measured from the normal to the grating increases beyond that angle
associated with the zeroth order. The second maximum is the next maximum
encountered as the angle from the normal increases from the first maximum,
and so on. The maxima and minima detected at angles less than that from
the grating normal to the zeroth order are denoted -1 maximum, minimum,
and so on.
In the example in FIG. 2-2b, the first order feature 12 for .lambda..sub.1,
is produced at angle .phi..sub.1, .sub.1 and detected at a position
P.sub.A at plane 20. Similarly, the first order feature 14 for
.lambda..sub.2, is produced at angle .phi..sub.1 .sub.2 and detected at
position P.sub.B and other order features, for example second order
features 16 and 18 for .lambda..sub.1 and .lambda..sub.2, respectively may
also be detected.
The basic diffraction grating equation is:
##EQU1##
Where .phi..sub.1 is the incident angle, .phi..sub.1, .sub.1 is the
reflected angle (angular position) of the first diffraction order, 12 in
the diffraction pattern of .lambda..sub.1, d is the grating line spacing
(d.sub.1 in FIG. 2, d.sub.2 in FIG. 2a-b), and m is the order number.
For two wavelengths striking the grating at the same incident angle, the
diffraction equation becomes:
##EQU2##
Where .phi..sub.1, .sub.2 is the reflected angle (angular position) of the
first order feature 14 of the second wavelength, .lambda..sub.2. As
evident from equation 2, the relative angular position of the interference
features for the two wavelengths is independent of the incident angle
.phi..sub.1.
Referring now to FIG. 2a, as substrate S is strained perpendicular to the
grating lines, the spacing of the grating lines is changed from d.sub.1 to
d.sub.2. In the present example, strain in the direction of arrows 22, 24
causes an increase in the line spacing. The angular position .phi..sub.1,
.sub.1 and .phi..sub.1, .sub.2 of each interference features 12 and 14
therefore, changes with grating spacing according to equation 2. The new
grating spacing, or change in grating spacing can be calculated from eq
(2) and related to strain. Even if the spacings are not calculated,
however, the relative change in the angular position before and after
strain can be compared and related to strain.
In the illustration of FIG. 2-2a, the relative change is such that the
relative angular position (.phi..sub.1.sup.a,.sub.1 -.phi..sub.1.sup.a,
.sub.2) in the strained condition (FIG. 2a) is greater than
(.phi..sub.1,.sub.1 -.phi..sub.1,.sub.2) in the unstrained condition (FIG.
2). Calculation of strain from a detected surface motion is discussed in,
for example, J. F. Bell, "Diffraction Grating Strain Gauge", Proceedings,
Society for Experimental Stress Analysis, Vol. 17, number 2, p. 5. A
general discussion of diffraction optics may be found in Diffraction
Gratings by M. C. Hutley, Academic Press, 1982.
Referring now to FIG. 2b, a rigid body rotation of the substrate S, also
having the same magnitude and direction (relative to the substrate) of
strain as in FIG. 2a is illustrated. The substrate S has been rotated in a
plane perpendicular to the grating lines (axis of rotation parallel to
grating lines) as indicated by the arrow 23. In this instance the
radiation 5 is incident upon the grating at a new angle, .phi..sub.n as a
result of the rigid body rotation. The absolute angular position of both
interference features 12 and 14 is affected according to equation (1).
Feature 12, now has angular position .phi..sub.1.sup.b, .sub.1 and feature
14, position .phi..sub.1.sup.b, .sub.2 respectively. However, the relative
angular position of the features arising from the two wavelengths,
(.phi..sub.1.sup.b, .sub.1 -.phi..sub.1.sup.b, .sub.2), is independent of
incident angle and therefore, unaffected. The relative angular position in
FIG. 2b, (.phi..sub.1.sup.b, .sub.1 -.phi..sub.1.sup.b, .sub.2) is the
same as in FIG. 2a, (.phi..sub.1.sup.a, .sub.1 -.phi..sub.1.sup.a, .sub.2)
since the substrate is in the same strain condition. If the material in
FIG. 2b was unstrained as in FIG. 2, the detected relative angular
position would be equal to .phi..sub.1, .sub.1 -.phi..sub.1, .sub.2.
Thus, in the preferred embodiment, the method provides for measurement of
the state of strain, by detecting the change in interference features
arising from illumination of a grating, on the surface with radiation
having at least two wavelengths. The technique is inherently free of error
caused by rigid body rotation in a plane perpendicular to the grating
lines. It will be understood that the relative position, intensity, or
relative distribution of frequencies of the diffraction features are all
affected by a strained diffraction grating and may also be detected and
analyzed for determining strain.
Referring now to FIG. 3, the change in angular separation is plotted
against strain for the diffracted first order feature of an incident beam
from an argon laser having two wavelengths, 488 and 515 nm. The incident
angle was 45.degree. from grating normal and the diffraction grating had
500 lines per millimeter. As the diffraction spacing varies by a factor of
2, the variation in the diffracted angle changes by over 0.60 degrees.
Such a relative variation can easily be detected by position sensitive
devices which outputs a voltage proportional to the position of the
incident light. A photodiode array or charge coupled device (CCD) detector
might also be used.
In another embodiment for strain measurement, also free of rigid body
rotations about an axis parallel with the grating lines, a polychromatic,
for example, white light beam may be used to illuminate the grating and
the intensity distribution of resulting interference features found at a
given angular position. In this case, the character of the distribution,
i.e., presence and intensity of certain frequencies, may be related to
strain. Changes in the distribution may also be observed to differentiate
strain effects from rigid body rotation effects. In the example of a white
light beam, a distribution of frequencies can be detected at any given
angle of diffraction. The relative frequency content of that distribution
will be different given either a rigid body motion or an imposed surface
strain. The character of narrowing or broadening of the distribution,
(broading is reduction in intensity at the maximum frequency and
enhancement at the frequencies higher and lower than the maximum) will
thus differentiate strain from rigid body motions.
Another embodiment of the present invention does not require comparison of
the angular position of interference features but rather strain
measurement may be simply and quickly made by detection, of the frequency
or distribution of frequencies in an interference feature at a single
point when a plurality of wavelengths are incident upon a grating. In this
instance, the absolute position of the interference feature of a given
frequency may be correlated with a given degree of strain.
For example, in FIG. 2b, an observer at position P'.sub.A detecting a
frequency corresponding to .lambda..sub.1 would be indicative of the
strain condition of material S, as illustrated. If another frequency is
detected at position P'.sub.A, a different strain condition would be
indicated. Similarly, it may be a distribution of frequencies (the
apparent color in the case of a human eye detector) that is detected.
Alternatively, the source may include a number of wavelengths, the
frequency may be detected at a plurality of known position and the pattern
of detected frequencies used to indicate strain. For visible light strain
may be detected by the human eye. Such a scheme provides an easy and
convenient method for measurement on large structures. A bridge or
building, for example, could include a grating or gratings which could be
strain inspected with a portable light source. It should be noted,
however, that freedom from errors arising from rigid body rotations is
realized by comparison of the relative position of features from different
wavelengths. This type of measurement, it will also be realized, may be
made using a frequency detector such as the human eye.
Preferably the grating is attached to the test material in a way which will
ensure its relative motion in coordination with the material itself. The
grating may be, for example, electrodeposited, or vapor deposited. The
grating may also be integrally formed of the material to be measured and,
for example, ruled or etched. In some embodiments, it is preferable that
the grating possess high specular reflection. In others, the grating may
be a transmitting grating as will be described further below. The grating
may even be embedded within a material which is transparent to the
illuminating radiation.
The source of radiation should supply at least two primary wavelengths and
preferably coherent radiation such as that from a laser. Coherent light as
is known improves the resolution of diffraction features. In other
embodiments, noncoherent light might be used. In some embodiments the
source may include a nonlinear crystal placed in the beam path of a
monochromatic source and before the grating. Such crystals are known to
transmit more than one wavelength as discussed in, for example in
Introduction to Nonlinear Optics, by G. Baldwin, 1969, Ch. 4, p. 71-107,
Plenum Press. The wavelengths of radiation may be selected so as not to
coincide with natural sample irradiance or absorbance or that of the
environment about the grating. The radiation may also be chopped or
otherwise modulated to differentiate sample or other ambient irradiance.
The wavelength of radiation and the grating spacing are also selectable to
effect the resolution of the measurement and the distance of the detector
from the grating affects the relative absolute angular position and
magnitude of change of the diffraction features as is known. It will be
recognized that both the plurality of wavelengths may illuminate the
grating and the resultant features detected, either simultaneously or
sequentially.
The surface to be measured may be any strained surface. Applications
include strain measurement in metals, ceramics, polymers, crystalline
substances, superconductors, and composite materials. Specific
applications include: aircraft structures, turbines, engine components,
buildings, bridges, test specimens, or railroad structures.
An important application of the invention is for the measurement of strain
in high temperature environments, for example, for measurement of heat
resistant ceramic materials. In this case, a pulse laser of sufficiently
short period may be used so that the natural radiance of the specimen will
not interfere with the diffracted light. The frequencies of the impinging
radiation may also be selected as mentioned such that they are
sufficiently separated from known sample radiance, thereby avoiding
interference. In some high temperature strain measurements, the grating
may be a refractory metal, capable of withstanding temperatures of
1000.degree. C. or more. Examples of refractory metals include niobium and
tantalum which may be, for example, deposited on the surface of the
material to be measured.
Referring now to FIG. 4 an embodiment of the invention is shown wherein the
radiation 10 is modulated by modulation unit 30 prior to illuminating the
diffraction grating. The diffraction features 32 carry, superimposed, the
characteristics of the modulation and are detected at detector 36 which
produces a signal delivered along line 38 to analyzing circuitry 40. The
circuitry may include, for example, demodulating processors 42 for
decoding the modulation features imposed at modulator 30 and analysis
circuitry 44 where the detected signal may be analyzed for determining
relative motion and strain. A readout or display 46 may also be provided
for real time and histographic display of results. Similarly storage means
48 may be provided for storing motion data for later manipulation.
In the present embodiment the modulator 30 may be, for example, a chopper
whereby radiation produced by the grating or material itself may be
discriminated against at detector 36. In another embodiment the source 29
may be a broadband source and the modulator 30 a transforming modulator,
for example an interferometer for Fourier transforming. In this last
embodiment the interference features for many wavelengths may be
simultaneously detected by detector 36. The resulting signal is then
transformed, for example Fourier transformed, by circuitry 42 prior to
analysis. Fourier analysis can be used to produce a frequency distribution
for example, and as discussed hereinbefore, analysis of the frequency
distribution can be used for strain measurement, free of certain rigid
body rotations.
Referring now to FIG. 5 in other embodiments a transmission grating may be
employed. The grating 60 is formed of a substrate which is opaque to
incident radiation 64 arising from source 66. Grating 60 includes
apertures 68 formed in the opaque substrate 62 by way of which diffraction
features 70, 72 are formed and detected, for example, at detection plane
74. Similar to the reflected diffraction embodiments, strain in the
direction perpendicular to the lines 68 of the grating produces a
variation in their spacing d and consequently a change in the angular
position and intensity of the interference features 70, 72. Also similar
to the reflective embodiment, rigid body rotation perpendicular to the
lines 68 does not affect the relative position of the interference
features.
Referring now to FIG. 6 a diffraction grating 80 according to the invention
may be positioned on a surface 82 rotating, for example, in the direction
of arrow 84. Optical strain detection according to the invention offers a
particular advantage for measurement of strain of the material 82 while
rotating. Since the speed of light is necessarily faster than the rotation
of the material 82 the interference features may be intermittently
detected upon passage of the grating beneath an incident polychromatic
beam held stationary.
Many modifications and variations of the present invention are possible
when considered in light of the above teachings. For example, it will be
recognized by those skilled in the art that the relative intensity of the
interference features from various incident wavelengths may be detected at
various angular positions and compared to determine strain. It is
therefore understood that the scope of the present invention is not to be
limited to the details disclosed herein, may be practiced and otherwise
than as specifically described.
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