A special set-up was fabricated as a method to test the accuracy of the DIC set-up. Even though there are generalized statements of accuracy regarding DIC systems [14], our intention was to firmly establish error bounds for our particular set-up. Figure17.5 shows the apparatus used to quantify the error in the DIC measurements. The micrometer was positioned on the right side and the beam on top was hinged on the left side. As the micrometer moved up and down, it lifted the tip of the beam. The vertical Fig. 17.4 Horizontal, U, and vertical, V, displacements for the plastic tooth (a) reference image (b–h) series of dental composite applications and curing (i) 72 h after final curing
Fig. 17.3 Horizontal, U, and vertical, V, displacements for the second tooth examined (a) reference image (b) post bonding agent application and cure (c–i) series of dental composite applications and curing
122 B.W. LaCroix et al.
displacement, for small displacements, was linearly proportional to the distance from the hinge. The white portion on the left side shown in the figure is a speckle pattern applied to the surface.
The apparatus was operated by adjusting the micrometer position by rotating the dial. The smallest measurable movement of the micrometer was 0.01 mm. The micrometer was positioned 300 mm from the hinge and a mark was placed on the DIC surface at 30 mm from the hinge. Therefore, through a linear relation, the displacement at this point on the apparatus was 1/10 of the displacement of the micrometer. Consequently, 0.01 mm on the micrometer corresponds to 1mm on the apparatus at the point of interest. Figure17.6shows the point of interest as viewed through the DIC camera system. A length scale with millimeter increments is also included in the figure to provide a sense of scale.
Two variations of measurements were taken with the camera system. The first measurement was the in-plane displace- ment measurement where the camera system was aligned perpendicular to the plane of motion, as shown in Fig.17.7a. The second experiment examined the out-of-plane accuracy of the DIC system by aligning the system parallel to the direction of displacement. This system set-up is shown in Fig.17.7b. The cameras were positioned with similar angles as they were for measuring the displacements identified in the teeth. Both the camera system and the accuracy apparatus were firmly secured to the table.
Table 17.1 Summary of the relative cusp displacements during the testing of the first tooth. Negative values indicate that the cusp tips are moving toward one another
Step Step description
Horizontal cusp relative displacement (mm)
Left cusp vertical displacement (mm)
Right cusp vertical displacement (mm)
a Reference image 0.0 0.0 0.0
b Bonding agent applied 1.7 7.1 8.8
c Bonding agent cured 0.3 7.8 9.2
d Dental composite added 2.6 9.6 12.4
e Immediately post cure 10.5 7.6 12.5
f Successive curing cycles 8.9 4.5 9.0
g 24 h post cure 10.3 8.6 16.6
h 48 h post cure (24 h hydrated) 31.6 37.7 36.1
i 96 h post cure (72 h hydrated) 31.5 33.7 31.7
Table 17.2 Summary of the relative cusp displacements during the testing of the second tooth. Negative values indicate that the cusp tips are moving toward one another
Step Step description
Horizontal cusp relative displacement (mm)
Left cusp vertical displacement (mm)
Right cusp vertical displacement (mm)
a Reference image 0.0 0.0 0.0
b Post bonding agent and cure 4.8 5.3 5.0
c Dental composite added and cured (Part 1) 11.7 5.6 6.2
d Dental composite added and cured (Part 2) 13.2 6.0 7.1
e Dental composite added and cured (Part 3) 16.5 7.6 8.2
f Dental composite added and cured (Part 4) 17.4 8.5 9.5
g Dental composite added and cured (Part 5) 17.4 8.7 9.6
h Dental composite added and cured (Part 6) 16.9 8.8 10.0
i Dental composite added and cured (Part 7) 19.3 9.9 11.0
Table 17.3 Summary of the relative cusp displacements during the testing of the plastic tooth. Negative values indicate that the cusp tips are moving toward one another
Step Step description
Horizontal cusp relative displacement (mm)
Left cusp vertical displacement (mm)
Right cusp vertical displacement (mm)
a Reference image 0.0 0.0 0.0
b Dental composite added and cured (Part 1) 6.0 7.4 9.5
c Dental composite added and cured (Part 2) 7.8 5.3 7.6
d Dental composite added and cured (Part 3) 11.1 5.9 9.1
e Dental composite added and cured (Part 4) 11.5 4.4 7.4
f Dental composite added and cured (Part 5) 12.2 3.1 6.6
g Dental composite added and cured (Part 6) 12.7 1.9 5.7
h Dental composite added and cured (Part 7) 13.7 0.8 4.6
i 72 h post cure 19.3 8.6 2.9
17 Utilizing Digital Image Correlation to Capture Strains in Dental Applications 123
Fig. 17.5 Device used for measuring the accuracy of the DIC set-up
Fig. 17.6 Point of interest on the accuracy measurement device as viewed through the DIC system with a millimeter length scale included for sense of scale
Fig. 17.7 The two system set-ups to determine the accuracy of measurements (a) In-plane displacement set-up (b) Out-of-plane displacement set-up
124 B.W. LaCroix et al.
Additionally, a third set of measurements were also obtained from the first set-up. Since the bottom portion of the accuracy measurement device was held stationary throughout the course of the experiment, the in-plane and out-of-plane noise could be calculated by evaluating the bottom surface.
In both tests, the micrometer is adjusted in increments of 0.01 mm from 0 to 0.25 mm and then returned to the initial position. At each increment, three pictures were taken, generating a total of 153 positions for each data point. Each DIC test generates thousands of data points describing the surface. The position of these data points can be plotted as a function of the micrometer position. Figure17.8shows the in-plane and out-of-plane displacements for a single point in the DIC area of interest followed throughout the experiment.
The linear fit was applied to each DIC data point within the area of interest and the standard error was calculated between the linear fit and the data point’s position throughout the experiment. The standard error can be calculated as follows.
^
s2¼ eTe
nynb (17.1)
Whereeis composed of the errors for a particular fit (arranged in a vector),nyis the number of points, andnbis the number of coefficients in the linear fit. Since each point moves a different amount than its neighboring points, the linear fit is reapplied for each point. The standard error was calculated for each DIC point and the average and standard deviation were calculated and presented in Table17.4. The maximum error, with respect to the linear fit, is also presented. Finally, the 95%
confidence bounds were calculated for in-plane and out-of-plane displacements. The error for all measurements can be calculated with 95% confidence bounds as shown in Eq.17.2.
95%CI¼displacement ð1:96 s^Þ (17.2) The same results can be calculated for the stationary portion of the accuracy measurement device (bottom portion of Fig.17.6) as a way to estimate the noise. These results are presented in the final three columns of Table17.4.
From these results, it is apparent that any in-plane measurements made with this system can be trusted with 95%
confidence to 1.7mm. Additionally, out-of-plane measurements can be trusted with 95% confidence to 2.4mm. The maximum in-plane error of a single point in a standard set-up would be slightly more than 2mm and slightly more than 5mm for out-of-plane measurements. However, these points tend to be isolated and are easily discernible as noise.
Sensor noise accounts for roughly a third of the in-plane errors and the remaining two-thirds could potentially be from the accuracy measurement device. A majority of the out-of-plane error is due to noise in the system, which is most likely due to the cameras being so close to one another and positioned at such a small angle. Generally, the cameras should be Fig. 17.8 (a) In-plane displacement of a single point on the surface of the accuracy apparatus as a function of micrometer position with a linear polynomial fit to the data (b) Out-of-plane displacement of a single point on the surface of the accuracy apparatus as a function of micrometer position with a linear polynomial fit to the data
17 Utilizing Digital Image Correlation to Capture Strains in Dental Applications 125
positioned with an angle between them of 45–90. The larger the angle, the smaller observable angle one can achieve on a cylindrical-like object, due to the overlapping area from the two cameras. Out-of-plane accuracy was sacrificed in this case in order to maximize the observable area in this experiment.
The generalized calculation of uncertainty [14] for a typical DIC set-up can be used to formulate a comparison. From Fig.17.6, it can be found that there is 1 pixel per 0.0059 mm. Generally, DIC set-ups can achieve an uncertainty of 0.015 pixels. This converts to 0.8mm when multiplied out. Therefore, the generalized expression supports our calculations.