In the computer detection and calculation process, we mainly utilize two image processing techniques[13-14] for the patterns captured by the CCD # 1 and CCD # 2, so that we can obtain the full field measurement from image # 1 and the caustic information from image # 2. This system consists of two CCD cameras to scan the pattern, and is connected to the frame grabbers. The frame grabber is a video digitizer which can digitize video signals from the CCD camera in real time and store the digitized image into the on-board frame memory. The image also can be displayed simultaneously on the analog video monitor. The frame grabber is a plug-in card for the 486 PC. It has 256K bytes of frame memory organized as 512times 512times 8 bits. The incoming video signal has 8 bits resolution at a rate of 30 frames per second. An 8-bits A/D converter quantifies the signal to 256 gray levels. Each pixel in the frame memory may take a value between 0 and 255, with the value 0 corresponding to the black level and 255 to the white level. In image #1 processing we use the noise-suppression step to delete the noise of the digitized image, and then count the number of fringe variations. In image # 2 we use a low pass filter and edge detecting operation to find the distance of the maximum diameter of the caustic curve. The detailed steps of these procedures are explained in the following sections.

Many observers may think that the interference fringes outside the caustic curve lead to no experimental information. But these fringe movements respond to the variations of the thickness of the specimen. The thickness variation due to Poisson's effect and the variation in the refractive index of the constrained material yields the fringes' movement of the outer region in caustics. The variation of the fringes at the vicinity of the crack tip is too fast to be calculated at every instant. Here we also avoid the plastic zone for the fringe movements because this region is difficult to distinguish. We now consider the set-up adjusted for the observation of fringes of equal thickness at the thickness located between front and rear surface of the testing specimen. If the light source is in an oblique incident condition with a small angle theta , the above equation must be written as follows:

m l = 2ndcosq

whered is the thickness of the specimen.

n is the refraction index of the specimen.

lis the wavelength of the light source.

m is the fringe order.

A fringe pattern related to thickness variations in the specimen is obtained by video camera # 1. For the quantitative scalar signal quantization methods[15] let f and f denote the gray level of a real, scalar signal sample and its quantized value, respectively. Because we use a 5 mW He Ne laser as the light source, the noise is manifested from the coherent light in the form of speckle cells, superposed rings, etc.. Furthermore, the electronic noise is also caused by video equipment. Assume that f is constrained in the upper limit a_U and lower limit

We define a set of reconstruction levels r_j and a set of decision levels

d_j such that

if d_j+1 <=f <= d_j, then f =r_j

Thus, we find that the fluctuation of the gray level of a image should not be neglected. The purpose of noise suppression is to delete the fluctuation of the gray level of the image which is due to the noise. Fig.3 is one example of the original image and the distribution profile of gray level along a straight line x-x' of the image. We can judge the fringe motions by counting the variation of the gray level of the pixel. A hysteresis method is introduced to suppress the noise, and we select the high threshold value to be G_high and the low threshold value to be G_low.

The value G_high and G_low depend on a gap value and the average brightness value of the image which is expressed as the following equation :

f_ave =

where ,f_ave is the average brightness value of the image.f(x,y) is the gray level of the pixel (x,y) of the image.n is the total pixel number.

A gap value G_gap is expressed as the following type:

G_gap= | (f'(x,y))-f_ave |

Where, f'(x,y) is the maximum gray level of the pixel (x,y) at a testing duration.Then we define:G_high= f_ave + 3/4 (G_gap)G_low= f_ave - 3/4 G_gapThus if the gray level of a pixel is increasing in magnitude, the counter will remain at the original value until the gray level exceeds the high threshold value. Then the value of the counter adds 1. Subsequently the counter will remain at this value even if the gray level decreases below the high

threshold value. The counter will add 1 only if the gray level is decreased below the low threshold value. This method provides an effective means for rejecting noise.

In other words, the counter of fringe variation is according the following criteria.

if f(x,y)>= G_high and Flag=0 , Then N(x,y) = N(x,y)+1 and

Flag=1.

if f(x,y) <= G_low and Flag=1 , Then Flag=0

where,

Flag is a logical value.

N(x,y) is the counter of fringe variation of the pixel (x,y) of the image.

2.2 Filtering in image # 2

The value of the stress intensity factor is very sensitive to the measurement of the maximum diameter of the caustic curve. In image # 2 the main objective is to obtain the maximum diameter of each caustic and the position of the crack tip. A method to obtain these values is from the distance between respective peaks in the histograms of the image for evaluation of K_c of the cracks. When the direction of the maximum diameter of the caustic curve is along the x or y axis this measurement is usually accurate, since the peaks are very sharp. But if the direction is arbitrary, we must use the filter operation to obtain the value of the maximum diameter. The intention for filtering is to leave out the noise and enhance the signal part of a image. Here we use a low pass mask and Sobel mask of 3times 3 matrix to perform the filtering process. From the concepts of Fourier optics, we define the gray level function of an image in a spatial domain as f(x,y) and an impulse response of a mask as h(x,y). The new image g(x,y) after convolution operation ast can be expressed as follows:

g(x,y)=h(x,y)* f(x,y)In the spatial frequency domain we can obtain:G(f_x,f_y)=H(f_x,f_y)F(f_x,f_y)where G, H, and F are the Fourier transform of g, h, and f. From the above equation we can see the spatial frequency of an original image will be depressed or enhanced only depending on the mask h(x,y). We choose a general low pass mask h_1 :

h_1=

[1/16 1/8 1/16

1/8 1/4 1/8

1/16 1/8 1/16]

Fig.4(A) is a original image and Fig.4(B) is the image after low pass filtering.

To find the edge of a caustic we use a gradient enhancement method. The gradient vector of an image f(x,y) can be defined as:

The magnitude of nabla f(x,y) can be derived from the above equation:

Then we can obtain the gradient along the x axis direction: =

[ f(x-1,y-1) +2f(x,y-1) + f(x+1,y-1)]- [ f(x-1,y+1) +2f(x,y+1) + f(x+1,y+1)]

So the Sobel mask of the y axis direction enhancement can be expressed as:

h_2=

[-1 -2 -1

0 0 0

1 2 1

]

Fig.4(C) is the Image after Sobel operation along the x axis direction. From Fig.4(C) we can obtain the location of the crack tip and the maximum diameter of the caustic curve. We can alternate the Sobel mask for other directions for another different caustic curves.

nextindexback