本研究之目的在建立一套位移及應變量測系統，利用數位影像量測試件面內位移及應變，數位影像相關法是一種非接觸式、非破壞性的光學量測方式，原理是比較變形前後兩張影像欲求位置之相關性，藉由相關性最好之對應位置即可求得位移，並可以透過求得之位移場直接或者透過更進一步的運算計算出應變場。
為了避免鏡頭像差造成影像扭曲之誤差影響，利用剛體平面位移之結果及最小平方法來計算影像扭曲參數，進而進行影像扭曲之校正，校正前後最大誤差從18μm降至1μm。
本文利用數位影像相關法以及影像扭曲之校正，建立位移及應變量測系統，並利用剛體平面位移及金屬拉伸試驗探討系統面內位移及應變之準確性，在解析度高時位移量測誤差均能低於11μm，應變量測誤差均能低於10%，最後應用在生物組織拉伸試驗中，利用數位影像相關法量測雞胸肉之變形，並且與羅裕龍老師實驗室之Stoke儀量測之光學參數做比較，找出線偏光像位差與縱向及橫向應變差值有斜率變化上之關係。

關鍵字:數位影像相關法；影像扭曲校正；拉伸試驗；生物組織

SUMMARY

The purpose of this thesis was to develop a system for measuring displacements and strains by digital image correlation (DIC) technology. Digital image correlation is a non-contact, non-destructive optical measuring method. By processing the digital images of test object surface recorded by an imaging device before and after deformation, DIC directly provides full field displacements of the object surface to sub-pixel accuracy, and strain can be calculated directly or by further manipulations of the displacement fields. In order to avoid image distortion which is caused by lens aberrations, distorted displacement results could be applied as they are able to determine the distortion coefficient of the camera lens. After calibrating the image distortion, the maxinmum error is down from 18μm to 1μm. The accuracy of the DIC system is verified through rigid body, in-plane translation tests and tensile tests. In high resolution condition, displacement measuring max error is 11μm, and strain measuring errors are less than 10%. Finally, applying the DIC system in the bio-tissue tensile test to measure the deformation, then compare the result with Prof. Lo’s group’s measured parameters. We found that the difference of longitudinal and lateral strain and linear birefringence parameter have a relationship with slope.

Key words: digital image correlation; image distortion correction; bio-tissue; tensile- test

INTRODUCTION
The theory of biomechanics has provided great contributions to our knowledge about human health. Also, this theory can be applied to understand human’s disease, injury and can provide the suitable treatments. Thus, biomechanics has yet reached its full potential as a consistent contributor to the improvement of health-care delivery. Because of the inherent complexities of the microstructure and biomechanical behavior of biological cells and tissues, there is a need for new theoretical frameworks to guide the design and interpretation of new classes of experiments There are many researches on studying on the stress-optic coefficient, strain-optic coefficient, and Young’s Modulus in optical fibers, because most of the elements of the optical fiber such as the transform between retardation distribution, axial stress, and fiber’s cross-section are known or can be determined easily. But, there are not so many researches in the stress-optic and strain-optic coefficient of bio-tissue because the characteristics are much more difficult to measure and calculate than optical fiber itself. In this thesis, a new optical system which combines the decoupled model developed in Lo’s group with the DIC method in order to locally determine stress, strain, strain-optic relationship. By using this new system, this thesis can extract more detailed parameters in order to locally analyze the bio-tissue. This is a significant advantage and unique difference of this thesis in comparisons with other researches in measurement strain-optic coefficient and other parameters.

DIGITAL IMAGE CORRELATION METHOD

Figure I shows the schematic illustration of a typical experimental setup using an optical imaging device for the DIC method. The specimen surface must have a random gray intensity distribution (i.e. the random speckle pattern), which deforms together with the specimen surface as a carrier of deformation information. The camera is placed with its optical axis normal to the specimen surface, imaging the planar specimen surface in different loading states onto its sensor plane.

Figure I Typical optical image acquisition system for the DIC method [Pan et al., 2009].
The basic principle of DIC is the tracking (or matching) of the same points (or pixels) between the two images recorded before and after deformation as schematically illustrated in Fig. II. In order to compute the displacements of point P, a square reference subsets of (2M+1) × (2M+1) pixels centered at point P(x_0,y_0) from the reference image is chosen and used to track its corresponding location in the deformed image.
 

Figure II Schematic illustration of a reference square subset before deformation and a target (or deformed) subset after deformation [Pan et al., 2009].
A subset of points around a node is mapped from the reference image to the deformed image. Each of these subset points is located in the reference image at (x, y) and is mapped to the deformed image at location (x’, y’) using
x_i^' = x_0 + u (x_0,y_0)
y_i^' = y_0 + v (x_0,y_0) (1)
with u (x_0, y_0) and v (x_0,y_0) being the displacement components of each subset point. The new assumption that u (x_0, y_0) and v (x_0,y_0) can be approximated by a second-order Taylor series expansion around point (x_0,y_0) lead to the mapping functions
x_i^' = x_0 + u_0 + u_x ∆x + u_y ∆y + 1/2 u_xx 〖∆x〗^2 + 1/2 u_yy 〖∆y〗^2 + u_xy ∆x∆y
y_i^' = y_0 + v_0 + v_x ∆x + v_y ∆y + 1/2 v_xx 〖∆x〗^2 + 1/2 v_yy 〖∆y〗^2 + v_xy ∆x∆y (2)
where ∆x=x-x_0 and ∆y=y-y_0.
To evaluate the similarity degree between the reference and deformed subsets, a correlation criterion should be defined in advance before correlation analysis.
Table I Commonly used SSD correlation criterion. [Pan et al., 2009]

The best estimations of the parameters are obtained by minimizing the correlation coefficient using a nonlinear optimization process, usually accompanied by algorithms including coarse-fine method, or Newton-Raphson (NR) method. To achieve subpixel accuracy, bicubic spline interpolation schemes should be implemented to reconstruct a continuous gray value distribution in the deformed images.
RESULTS
Figure III and IV show the DIC and linear birefringence parameter results of chicken breast tensile test. First chicken breast tensile test direction is parallel to the grain direction, and the second one is perpendicular to grain direction. The parameter β is phase retardation of the linear birefringence property which is measured by prof. Lo’s group. The results show that β has a relationship with the stretching direction. Because of Strain-optic law, we compare the difference of the longitudinal strain and transverse strain with β. We found that β also has a relationship with the difference of the longitudinal strain and transverse strain.


Figure III First chicken breast tensile test results.


Figure IV Second chicken breast tensile test results.
CONCLUTION
This thesis combines DIC system with the decoupled model developed in Lo’s group in order to locally determine strain-optic relationship. By using this new system, we measured the chicken breast tensile test successfully. We also found that the difference of the longitudinal strain and transverse strain has a relationship with the linear birefringence parameter.

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