A novel optical method of measuring 2-D surface strain is proposed. Two linear strains along orthogonal axes and the shear strain between those axes is determined by a variation of Yamaguchi's laser-speckle strain gage technique. It offers the advantages of shorter data acquisition times, less stringent alignment requirements, and reduced decorrelation effects when compared to a previously implemented optical strain rosette technique. The method automatically cancels the translational and rotational components of rigid body motion while simplifying the optical system and improving the speed of response

Barranger, John P.

English

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NASA Technical Memorandum 103162
Two-Dimensional Surface Strain Measurement
Based on a Variation of Yamaguchi's
Laser-Speckle Strain Gauge
John P. Barranger
Lewis Research Center
Cleveland, Ohio
Prepared for the
Conference on Optical Testing and Metrology III
sponsored by the Society of Photo-Optical Instrumentation Engineers
San Diego, California, July 8-13, 1990
https://ntrs.nasa.gov/search.jsp?R=19900013468 2020-03-19T23:10:08+00:00Z

Two-Dimensional Surface Strain Measurement Based on a Variation of
Yamaguchi's Laser-Speckle Strain Gauge
John P. Barranger
NASA Lewis Research Center
Cleveland, Ohio 44135
ABSTRACT
A novel optical method of measuring two---dimensional surface strain is proposed.
Two linear strains along orthogonal axes and the shear strain between those axes is
determined by a variation of Yamaguchi's laser---speckle strain gage technique. It offers the
advantages of shorter data acquisition times, less stringent alignment requirements, and
reduced decorrelation effects when compared to a previously implemented optical strain
rosette technique. The method automatically cancels the translational and rotational
components of rigid body motion while simplifying the optical system and improving the
speed of response.
i. INTRODUCTION
Elevated temperature tension tests are required to assess the performance of
materials intended for use in hostile environments. Conventional wire strain gauges face
severe limitations of accuracy, life, and reliability. Non-contact optical techniques can
overcome many of the disadvantages of conventional gauges for high temperature strain
measurements.
An automatic method of measuring linear surface strain has been described by
Yamaguchi [1,2]. Two sequentially applied thin laser beams are incident on an optically
rough measurement point. The resulting speckle patterns are recorded by a linear detector
array that is aligned parallel to the plane of incidence. After straining, another pair of
speckle patterns is recorded. These patterns have been displaced relative to the original
"reference" patterns. A cross---correlation of the reference and the shifted patterns gives the
displacement of each pattern. The difference between speckle displacements is proportional
to the linear surfacestrain parallel to the planeof incidence.The optical geometryand use
of symmetrically incident beamsallow automatic cancellationof any pattern displacements
along the plane of incidence due to rigid body motion. The magnitude of cancellation is
limited by decorrelationeffects [2].
The technique wasextendedto measuretwo---dimensionalsurfacestrains at a point.
Linear strains were determined at three angular orientations by rotating both the planeof
incidence and the linear array. Strain rosette equations were applied to calculate the
magnitude and direction of the principal strains. The implementation suffered from long
data acquisition times, stringent alignment requirements, and decorrelation causedby
pattern displacementsperpendicular to the direction of the linear array.
An alternative method of determining two---dimensionalsurfacestrain is to measure
two linear strains along orthogonal axesand the shear strain between thoseaxes. In this
paper, a variation of Yamaguchi's technique is describedthat yields shear surfacestrain
while maintaining the advantagesof the original form. An area detector array is used to
measurespeckle pattern displacementsperpendicular as well as parallel to the plane of
incidence. The summation of the difference between the perpendicular speckle
displacementsfor eachaxis results in an expressionthat is proportional to the shearstrain
and independentof the translational and rotational componentsof rigid body motion.
2. OPTICAL STRAIN ROSETTE SYSTEM WITH LINEAR DETECTOR ARRAY
Two---dimensional surface strains at a point were measured by extending
Yamaguchi's technique [3]. The use of symmetrical beams to cancel rigid body motion, the
optical strain rosette implementation, and other system features are described in this
section.
2.1 Speckle Displacement Relations
The optical geometry of the system is shown in figure 1. The points S mark the
center of curvature L of the incident laser wavefronts. Object deformation a(z, y) of the
S
diffuse surface causes speckle displacement A(Ax, A y) at the observation plane a distance
Lo away from the object plane. A laser positioning lens (not shown) provides a nearly flat
wavefront at the object plane causing L s to be much larger than L o. A far-field diffraction
pattern is formed at the observation plane on the assumption that L o is much larger than
the spot size of the incident beam.
The speckledisplacementsaregiven by (equations(1), [1])
Az= %- Lo[%A_+ %lsy- f(lsz + 1)+ _zls_] (1)
Ay= %- go[%_Isy+ %Zs_+ a_(Isz+ 1)- fzlsj (2)
where a_az, ay, az) and fl(fz' f_y' fz ) are the translation vector and rotation vector,
respectively. The components of a T and fl are the rotational and translational components
of rigid body motion, respectively. The unit vector representing the direction of the center
S is denoted by ls(Isz, Isy, Isz ). The linear z and y components of the strain tensor are
designated Exz and Eyy, respectively, and _xy is the in-plane shear component.
For the angle of incidence 0s in the z-z plane (Fig. 1), /s = (sin 0s, 0, cos 0s), and
the X and Y components of A, denoted by Ax, zz and A Y, zz respectively, are given by
Ax, zz = ax - Lo[czsin 0s - fly(COS 0s + 1)] (3)
Ay, zz = aN - Lo[Exy sin 0s + flz(cos 0s + 1) - fzSin 0s]. (4)
The speckle displacement Ax, zz is measured by one--dimensional cross-correlation of the
reference and the shifted speckle patterns• Because the linear array is is aligned parallel to
the X axis, the perpendicular displacement A Y, zz cannot be measured by this method.
To eliminate the dependency on the components of rigid body motion, the difference
between the speckle displacements for the angles 0s and -0 s is calculated. Thus,
AAx, zz = Ax, zz ( Os) - Ax, zz(-Os) = - 2Loezzsin 0s (5)
and
E
ZX
AAx_ zz
2L o sin 0s
(6)
The measurement of linear strain through equation (6) is independent of the rigid body
motion components in equation (3).
3
2.2 Optical Strain Rosette
To completely characterize two---dimensional surface strain the magnitude and
direction of the principal strains must be determined. The required quantities can be
obtained from a three-element strain gauge rosette bonded to the surface. The optical
analog is the measurement of linear strain at three angular orientations (Fig. 2). This was
implemented by rotating both the plane of incidence and the linear array [3]. The principal
strains were found from
1[ j_1=_ % + cc+ (_ - %)2 + (2% - _a - %)2 (7)
1[ je2=2 Ca + cc- (Ea - cc)2 + (2eb - ca - cc)2 (8)
g - g
tan 2¢ =- a c (9)
2c b - c a - c c
where the two solutions of equation (9) differ by 90" [4].
2.3 Optical System Configuration
The schematic of the optical system is given in figure 3. The beam of an argon ion
laser is switched by an acousto--optic modulator (AOM). Positioning lenses focus the beam
to provide a nearly fiat wavefront at the specimen surface. Polarization sensitive optics are
used to provide the symmetrically incident beams. A polarization beam-splitting cube
reflects the beam to the 0s side or transmits it to the -Os side, depending on the orientation
of the polarization vector. The linear array in the line camera consists of 2048 photodiodes
on 15 pzn centers with a photodiode height H (Fig. 1) of 0.3 ram. The linear array is one
meter away from the specimen surface.
Angular orientation of the plane of incidence and the linear array is achieved by
mounting the beam steering optics and the line scan camera on a goniometer cradle. The
orientation in figure 2 is dictated by the goniometer which is free to rotate :_45" about its
center point.
4
Two quarter-wave (A/4) retardation plates are used to provide rotational
invariance for the polarization sensitive beam steering optics. The first waveplate is
stationary and converts the beam from linear to circular polarization; the second
waveplate, on the rotating assembly, converts the beam back to linear polarization.
2.4 Experimental Results
Static two-dimensional strain measurements were demonstrated using the optical
rosette system. Stable speckle patterns were observed for an oxidized superalloy specimen
at temperatures up to 750 "C. The total time required to rotate the goniometer to the
three orientations and record the six speckle patterns was 10 seconds. This data acquisition
time is too long for dynamic applications such as standard elevated temperature tension
tests.
The ability to measure the principal strains from the three linear strains depended
to a great extent on the performance of the goniometer. The alignment, positioning, and
repeatability requirements were all very stringent. Measurement error could have been
introduced if extreme care had not been exercised.
Excessive speckle displacement can lead to decorrelation. When the displacement is
so great that the areas of the speckles in the reference pattern move off the array then
correlation is lost. Yamaguchi [5] defined the correlation limit of the perpendicular
displacement A Y, zz (equation (4)) as the sum of the array height H (Fig. 1) and the mean
speckle height. Because of the small A Y, zz limit, the system experienced decorrelation
perpendicular to the direction of the array.
Similarly, the correlation limit of Ax, zz (equation (3)) is the sum of the array
length L and the mean speckle length. When the correlation limit is large, however, the
actual decorrelation depends on many practical factors such as specimen movement,
material, and surface topology. This was observed in the direction of the array.
3. SHEAR STRAIN SYSTEM WITH AREA DETECTOR ARRAY
The system described in the above section suffered from long data acquisition times,
stringent alignment requirements, and decorrelation perpendicular to the direction of the
array. To overcome these disadvantages, the goniometer is now replaced by additional
beam steering optics and an area array is substituted for the linear array. Extending the
three element rosette configuration would require three pairs of beam positions for three
angular orientations and six two-dimensional (2-D) cross---correlations. A novel
implementation is proposedin this sectionwhich simplifies the systemby eliminating one
of the angular orientations and two 2-D cross---correlations.
3.1 Speckle Displacement Relations
An alternative to the three element rosette method of determining two---dimensional
surface strain is to measure two linear strains along orthogonal axes and the shear strain
between those axes. As noted by Yamaguchi [1], the shear strain component Exy as well as
rigid body components are contained in the perpendicular displacement A Y, zz (equation
(4)). Direct implementation of the symmetrical beam position concept, however, does not
lead to complete rigid body cancellation. An important summation operation is required
before the desired result is achieved.
Figure 4, the optical geometry of the system, is the same as figure 1 except for the
replacement of the linear array by the area array and the addition of two source points S.
The sides of the rectangular array are aligned parallel to the X and Y axes.
For 0s in the z-z plane, the Ax, zz and A Y, xz components of A are the same as
equations (3) and (4), respectively. Both speckle displacements are measured by 2-D
cross--correlation of the reference and the shifted patterns using any appropriate means [6].
To eliminate the dependency of Ax, zz and reduce the dependency of A y, xz on the
components of rigid body motion, the difference between the speckle displacements for the
angles 0s and -0 s is calculated. Thus, AAx, zz is the same as equation (5), _xx is the same
as equation (6), and
AA Y, zz = A y, zz ( Os) - A y, zz(-Os) = - 2Lo(EzySin 0s - flsin 0s). (10)
Equation (10) retains the shear strain component but f2z is not canceled by using the
symmetrical beam positions.
Beam steering optics now change the plane of incidence by 90". For 0s in the y---z
plane (Fig. 4), Is = (0, sin 8s, cos 0s), and the components of A are given by
AX, y z = a z -Lo[EzySin Os -fly(cos 0s + 1) + flzSin 0s] (11)
Ay, yz= ay- Lo[Eyysin 0s + az(cos 0s + 1)]. (12)
,For this orientation, the perpendicular displacement is AX, yz. Taking the difference
between the speckle displacements for the angles 0s and -0 s yields the equations,
AAx,_z= Ax, yz(es)-AX,_z(-0s)=-2to(%Sin es + az_in0s)
AAZ,yz = A y,yz(Os)- A y,yz(-Os)= - 2LoEyySin0s.
(13)
(14)
Finally, the shear component is completely separated by combining the difference between
the perpendicular displacements for each orientation. Summing equations (10) and (13),
AA Y, zz + AAx, yz = - 4LoCxySin 0s"
The linear strain cyy and the shear strain 7zy
¢ = - AAY_yz
YY 2L o sin 0s
are found from
(15)
(16)
AA y, zz + AAx, yz (17)
"TzY- 2L sin 0
O S
where czy in equation (15) has been replaced by 7zy/2. Thus, equations (6), (16), and (17)
represent the desired two linear strains along orthogonal axes and the shear strain between
those axes.
The magnitude and direction of the principal strains are found from the equations
1[ j 1¢1 = _ czz + %y + (¢zz - Cyy)2 + ._zy2 (is)
1 I yy)2 2]¢2=2 ¢xz + ¢yy- (¢xz - ¢ + 7xy (19)
tan 2¢ = ?zY (20)
¢ -- 8
xz yy
where the two solutions of equation (20) differ by 90" [4].
7
3.2 Area Array Results
A commercial frame transfer charge-coupled device has been selected for the area
array of the proposed system. It consists of 739 photosites on 8.5 #m centers parallel to the
X axis and 484 photosites on 9.875 #m centers parallel to the Y axis. Synchronization and
timing follow the EIA RS-170 standard operating at a frame rate of 30 Hz.
By steering the laser beams during the transfer gate period (about 30 _) of vertical
blanking, the total time to acquire the four speckle patterns is reduced to 4/30 or 0.13
seconds. This is a 75 fold improvement in the acquisition time over the optical rosette
system.
The area array reduces decorrelation caused by excessive speckle displacement.
Extending the results of the optical rosette system, the correlation limits still apply except
that L and H are now the area array length and height, respectively (Fig. 4). The larger
value of H (4.78 mm compared to 0.3 ram) greatly extends the correlation limit in the
direction parallel to the Y axis. In spite of the smaller value of L (6.28 mm compared to
30.7 mm), from a practical point of view the correlation limit in the direction parallel to
the X axis suffers only slightly.
4. CONCLUDING REMARKS
Compared to the earlier implementation, the use of the area array reduces data
acquisition times, eliminates the stringent alignment of the goniometer, and reduces
decorrelation effects. Moreover, this method employs two pairs of beam positions rather
than three and reduces the number of two-dimensional cross---correlation calculations from
six to four. These features simplify the optical system and improve the speed of response.
5.0 REFERENCES
1. Yamaguchi, I., A Laser-Speckle Strain Gauge. J. Phys. E. Sci. Instrum., vol. 14,
no. 11, pp. 1270-1273, Nov. 1981.
2. Yamaguchi, I., Speckle Displacement and DecorreIation in the Diffraction and
Image Fields for Small Object Deformation. Optica Acta, vol. 28, no. 10, pp. 1359-1376,
Oct. 1981.
3. Lant, C.T., Two-Dimensional High Temperature Optical Strain Measurement
System - Phase II. NASA CR-185116, 1989.
8
4. Kobayashi,A.S., Ed., Handbook on Ezperimental Mechanics, Prentice-Hall, Inc.,
pp. 113-115, 1987.
5. Yamaguchi, I., Simplified Laser-Speckle Strain Gauge. Optical Engineering, vol.
21, no. 3, p. 437, May/June 1982.
6. Takai, N.; Asakura, T., Vectorial Measurements of Speckle Displacement by the
2-D Electronic Correlation Method. Appl. Opt., vol. 24, no. 5, pp. 660--665, 1 March 1985.
S
Unear
array
_.....,,_ L o LsJ
Observation
plane
Figure 1.- Optical geometry of optical strain rosette system with linear
detector array.
X
Object
plane
Ec
_4)5o Eb
Ea
Figure 2. - Angular orientation of optical
strain rosette.
X
• -_ Acousto-optic
Mirror ,-" modulator
At* laser<
Waist positioning
,' lenses
t
,' ,-- Beam
; ,; stops ,"
=_,' r#oTa_£a'tion "-"
t I , ,
._, i beamsplt_ng
I c_lbe _
;" I ,L. Pockels cell
Rotating assembly
Specimen
,--- Line
[_ D" pass
filter
Line scar]
camera
Figure 3. - Optical system configuration.
0 m
"L S
Area array Lo
J
Observation
plane
Figure 4. - Optical geometry of shear strain system with area detector array.
Object
plane
10
Report Documentation PageNational Aeronautics and
Space Administration
1. Report No. 2. Government Accession No. 3. Recipient's Catalog No.
NASA TM-103162
5. Report Date4. Title and Subtitle
Two-Dimensional Surface Strain Measurement Based on a Variation
of Yamaguchi's Laser-Speckle Strain Gauge
7. Author(s)
John P. Barranger
9. Performing Organization Name and Address
National Aeronautics and Space Administration
Lewis Research Center
Cleveland, Ohio 44135-3191
12. Sponsoring Agency Name and Address
National Aeronautics and Space Administration
Washington, D.C. 20546-0001
6. Performing Organization Code
8. Performing Organization Report No.
E-5530
10. Work Unit No.
582-01-11
11. Contract or Grant No.
13. Type of Report and Period Covered
Technical Memorandum
14. Sponsoring Agency Code
15. Supplementary Notes
Prepared for the Conference on Optical Testing and Metrology III sponsored by the Society of Photo-Optical
Instrumentation Engineers, San Diego, California, July 8-13, 1990.
16. Abstract
A novel optical method of measuring two-dimensional surface strain is proposed. Two linear strains along
orthogonal axes and the shear strain between those axes is determined by a variation of Yamaguchi's laser-
speckle strain gage technique. It offers the advantages of shorter data acquisition times, less stringent alignment
requirements, and reduced decorrelation effects when compared to a previously implemented optical strain rosette
technique. The method automatically cancels the translational and rotational components of rigid body motion
while simplifying the optical system and improving the speed of response.
17. Key Words (Suggested by Author(s))
Laser applications
Nondestructive testing
Sensors and transducers
Optics
18. Distribution Statement
Unclassified- Unlimited
Subjcct Category 36
19. Security Classif. (of this report) [ 20. Security Classif, (of this page) I 21. No. of pages
Unclassified [ Unclassified [ 12
NASAFORM1626OCT86 * For sale by the National Technical Information Service, Springfield, Virginia 22161
22. Price*
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Two-dimensional surface strain measurement based on a variation of Yamaguchi's laser-speckle strain gauge

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