With the widespread availability of video digitizers and cheap personal computers, the use of computer vision as an experimental tool is becoming common place. These systems are being used to make a wide variety of measurements that range from simple surface characterization to velocity profiles. The Sub-Pixel Digital Image Correlation technique has been developed to measure full field displacement and gradients of the surface of an object subjected to a driving force. The technique has shown its utility by measuring the deformation and movement of objects that range from simple translation to fluid velocity profiles to crack tip deformation of solid rocket fuel. This technique has recently been improved and used to measure the surface displacement field of an object at high temperature. The development of a PC based Sub-Pixel Digital Image Correlation system has yielded an accurate and easy to use system for measuring surface displacements and gradients. Experiments have been performed to show the system is viable for measuring thermal strain

Mcneill, Stephen R.

Russell, Samuel S.

Sutton, Michael A.

English

NASA Technical Reports Server

N93-13674
DETERMINATION OF HIGH TEMPERATURE STRAINS USING
A PC BASED VISION SYSTEM
Stephen R. McNeill
Michael A. Sutton
Dept. of Mechanical Engineering
University of South Carolina
Columbia SC 29208
Samuel S. Russell
NASA Marshall Space Flight Center
Huntsville, AL
INTRODUCTION
With the widespread availability of video digitizers and cheap personal computers, the use of
compiater vision as a experimental tool is becoming common place. Theses systems are being used to
make a wide variety of measurements that range from simple surface characterization to velocity
profiles. The Sub-Pixel Digital Image Correlation technique t_'2'33has been developed to measure full
field displacement and gradients of the surface of an object subjected to a driving force. The technique
has shown its utility by measuring the deformation t4,s,61and movement of objects that range from
simple translation to fluid velocity profiles t73 to crack tip deformation of solid rocket fuel*. This
technique has recently been improved and used to measure the surface displacement field of an object
at high temperature.
DIGITAL IMAGE CORRELATION
Sub-Pixel Digital Image Correlation uses a digitized image of a random pattern attached to the
surface on an object. The pattern may consist of the natural surface finish, if appropriate, or may be
applied using any method which will produce a random "speckle" pattern. A representative pattern is
shown in Figure 1. After the object is subject to a driving force a second image is acquired. The
movement of the pattern on the surface can be determined by correlating the two image's intensity
patterns. Sub-Pixel accuracy is obtained by interpolation between pixel gray levels. Typical accuracy
for this technique is + 0.02 pixelstSL
The correlation is performed by selecting from the undeformed image a set of neighboring
pixels around the point of interest. The subset must be large enough to contain a unique portion of the
surface's random pattern. A typical subset size is 20 pixels by 20 pixels. The subset chosen is then
compared to subsets of the deformed image to find a match.
* Sutton, M.A., work in progress.
PRECEDING P_GE BLANK NOT FILMED
237
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Because the corresponding subset in the
deformed image will probably not only be
translated but also be deformed, the comparison
of the subsets is done by also deforming the
original subset to find the match. The
deformation across the subset is assumed to be
linear. The deforming of the subset is performed
using
x'=x + u + _u_ + Ou_
ax _ (_)
y"=y +v+ +
ax or
where x and y are the coordinates of a pixel in
the subset before deformation, u and v are the
displacement of the center of the subset, and dx
and dy are the distances from the center of the
subset to the pixel.
The correlation function used is
Figure 1. Representative speckle pattern.
_] a(xi,yj)•B(x:,yf)
C_x OuOuOv_)__l_ _j.l (2)or'ax' l . .
E a<x,,yj)2E
_j-l id.l
where A(xi,yj) is the gray level at in the undeformed image at location (x_,yi), B(x:,yj') is the gray
level in the deformed image at location (:q',y:) which was determined by Equation 1, and n is the
subset size.
When the image is digitized each pixel is assigned a single value representing the intensity
over a finite area of the sensor. The correlation technique was designed assuming that the gray level
value is at the center of the pixel. The mapping of Equation (I) usually maps integer pixel locations of
the undeformed image to non-integer locations in the deformed image. To determine the gray level at
these non-integer locations bi-linear interpolation is used. The formula for this interpolation is
B(x,y) =- a I + fract(x)*a 2 + fract(y),a 3 + fract(x)*pact(y) *a 4 (3)
where
a 1 = B(int(x),int(y))
238
a: = B(int(x+l),int(y)) - B(int(x),int(y))
a 3 = B(int(x),int(y + 1)) - B(int(x),int(y))
a 4 _- B(int(x+l),int(y.l)) ÷ B(int(x),int(y))
fract(x) =fractional part of x
int(x) = integer part of x
The correlation used in the work presented here assumes that all motion of the object is
parallel to the camera's image sensor. When this is true then the displacement of the subsets from the
undeformed image to the deformed image is proportional to the displacement of the object's surface,
and the gradient terms are equal to the gradients of the object's surface. When long focal length lenses
are used small amounts of movement toward the camera can be tolerated without significant error
being introduced. 3-D correlation methods are available t'L§ which can handle large amount of out-
of-plane motion.
PC IMAGE CORRELATION
The program required to perform sub-pixel correlation is memory and CPU intensive. In the
past, the program was run on a VAX 11/780. By running on a machine such as this, there are a host
of problems associated with the transferring of the images between the vision system and the
computation system. Due to the increase in power and memory capabilities of personal computers,
the correlation program has recently been implemented on a PC II. By implementing the program on
the PC, the system which acquires the images can now be used to correlated them. This allows for
ease of implementation and quicker turnaround.
The PC based correlation program runs under Windows 3.0. It was written so that other
applications can be run at the same time. It is user friendly with features which allow it to run
automatically or on a point by point basis. Images from different sources and different formats can be
used. It can display images on the PC monitor (requires a super-VGA monitor card with 1-Mbyte
RAM). Two different correlation schemes are available and user selectable.
The processing times for PC based correlation are, of course, dependent on the machine
configuration. When running a PC configuration of 486, 33Mhz, 8MegRam, 64K CPU cache, and
1"McNeill, S.R., Sutton, M.A., Miao, Z., Ma, J., "Automated Measurement of Surface Shape
by Computer Vision: Part r', submitted for review to IEEE Transactions on Pattern Analysis
and Machine Intelligence, 1992.
:[:McNeill, S.R., Sutton, M.A., Miao, Z., Ma, l., "Automated Measurement of Surface Shape
by Computer Vision: Part rI", submitted for review to IEEE Transactions on Pattern Analysis
and Machine Intelligence, 1992.
§McNeill, S.R., Sutton, M.A., Ma, I., Miao, Z., "Image Correlation for Determination of 3-D
Displacements and Gradients", paper in preparation.
[IWorkdone on contract by S.R.McNeill Services, NAS8-39030.
239
64K Disk Cache the correlation time per point is the same as the program used on the VAX 11/780.
In addition, due to the nature of the PC, when image correlation is being performed on a large
number of points per image, results are obtained faster for the PC than for a multi-user VAX 11/780.
EXPERIENTIAL DETERMINATION OF HIGH TEMPERATURE STRAINS
One application of the systems described above is in the area of high temperature strain
measurement. To test the viability of such a system, an extensive experimental program was initiated
and recently completed to quantify thermal strains by computer vision for temperatures from 0 to
1200°F. The experimental setup,
shown in Figure 2, included a
Lindberg Furnace with radiative
heating elements and a central
open area 250mm X 250 mm X
200mm. The door of the furnace
had a 100ram X 50ram viewing
area. The viewing area contained
two thin panes of high quality
sapphire glass, with the panes
separated by 38ram, to minimize
optical distortion. All of the
specimens were rectangular thin
strips, approximately 25ram X
50ram X 3ram in size. Both
LIgh _
Figure 2 Experimental Setup
aluminum and titanium alloys were used. The surface preparation prior to obtaining the digital
images included spray painting each specimen with a random black and white pattern, using high
temperature paint. The maximum temperature for the paint is approximately 1200°F. After painting,
the specimen was heat cured in the oven to ensure stability of the paint during the tests. For the
strain tests, each specimen was placed on a high temperature ceramic stand in the middle of the
furnace open area. The stand was used to support the specimen during the test and to minimize out-
of-plane motion of the specimen due to expansion of the oven interior. The specimen was
illuminated by white light using a fiber optic lamp placed directly outside of the furnace door. A
video camera was placed approximately 2.2 meters away with various Nikon lenses used to magnify
the image. Typically, the image-camera resolution was 40 pixels per mm on the object surface. The
images were obtained during the high temperature test and stored in the computer for detailed analysis
after the test was completed.
After several experiments were completed, it was determined that thermal oscillations in the air
outside of the sapphire windows were the primary source of noise in the optical images. To reduce
this noise, several approaches were tried. The most successful was the use of a steady flow of air
over the surface of the sapphire windows. This was accomplished by using a small fan to blow room
air over the windows. Images obtained using this procedure at temperatures of 0, 400, 800 and"
1200°F were obtained. Results for the displacement field on the specimen surface were determined to
be relatively free of large variations due to the thermal convective air currents.
240
To obtain the surface strain fields, the displacement fields at each temperature were first
smoothed _91. By averaging approximately I000 derivatives of the smoothed displacement fields over
the surface of the specimen, and using small strain-displacement gradient theory, the surface strains
could be estimated. Results of several tests indicate that (a) the point to point variation in optically
measured strain (this is important if the strain field is not uniform) is on the order of 300 microstrain,
(b) the average strains, obtained by comparing several composite images obtained at one temperature,
vary by 10-30 microstrain, (c) the thermal oscillations in the air outside the window are almost solely
responsible for the errors in the strain data and (d) comparison of the optically estimated thermal
coefficient of expansion to data obtained from the literature indicates that the optical values are within
the scatter in available data.
EXPERIMENTAL RESULTS
A representative sample of the data obtained is shown in Figure 3 and Figure 4. The +0.02
pixel error can be seen in the data.
-i
I"
1
i
Figure 3 V-Displacement at 800°F Figure 4 U-Displacement at 800°F
The data was smoothed and is shown in Figure 5 and Figure 6.
It is emphasized that the images shown in Figures 3 and 4 were obtained using the small fan to
"randomize" the effect of the convective currents. If the fan is not used, the effects of these currents
can be seen in Figures 7 and 8. Figs. 7 and 8 are correlation results from two images that were taken
at the same temperature but different times. If a fan is used to circulate the air then the plots would
have been essentially flat.
241
SUMMARY
In summary, the development of a PC based Sub-Pixel Digital Image Correlation system has
yielded an accurate and easy to use system for the measuring surface displacements and gradients.
Experiments have been performed to show the system is viable
.1@_')
,d)
in use of measuring thermal strain.
!
.),
II
Figure 5 Smoothed V-Displacement at Figure 6 Smoothed U-Displacement at
800°F. 800°F.
)
)
,2
Figure 7 V-Displacements due
convective current.
to Figure 8 U-Displacements due to
convective currents.
242
REFERENCES
o
,
°
°
°
6_
°
Peters, W.H. and Ranson, W.F. "Digital Imaging Techniques in Experimental Stress
Analysis", Opt. Eng., 21,427-431, May 1982.
Sutton, M.A., Cheng, M., Peters, W.H., Chao, Y.J., and McNeill, S.R. "Determination of
Displacements Using an Improved Digital Correlation Method", Computer Vision, 133-139,
Aug. 1983.
Bruck, H.A., McNeill, S.R., Sutton, M.A., and Peters, W.H. "Digital Image Correlation
Using Newton-Raphson Method of Partial Differential Correction", Experimental Mechanics,
Vol.29, No.3, pp.261-267, Sept. 1989.
Chu, T.C., Peters, W.H., Ranson, W.F., and Sutton, M.A. "Application of Digital
Correlation Methods to Rigid Body Mechanics", Proc. 1982 Fall Meeting of SESA, 73-77,
Nov. 1982.
Sutton, M.A., Cheng, M., Peters, W.H., Chao, Y.J., and McNeill, S.R. "Application of an
Optimized Digital Correlation Method to Planar Deformation Analysis", Image and Vision
Computing, 4 (3), 143-150, Aug. 1986.
McNeill, S.R., Peters, W.H., and Sutton, M.A. "Estimation of Stress Intensity Factor by
Digital Image Correlation", Eng. Fracture Mechanics, Vol 28, No.I, 101-112, 1987.
He, Z.H., Sutton, M.A., Ranson, W.F., Peters, W.H., "Two-dimensional Fluid-velocity
Measurements by Use of Digital-speckle Correlation Technique", Experimental Mechanics,
Vol 24, No.2, 117-121, 1984.
Q Sutton, M.A., McNeill, S.R., Jang, J., Babai, M., "Effects of Subpixel Image Restoration
on Digital Correlation, Error Estimates", Optical Engineering, Vol.27, No.10, 870-877, 1988.
° Sutton, M.A., "Full-field Representation of Discretely Sampled Surface Deformation for
Displacement and Strain Analysis", Experimental Mechanics, June, 168-177, 1991.
243
,_ LI,


Determination of high temperature strains using a PC based vision system

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