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where θ is the angle of propagation of the incoming beam. The projection in figure 8 is typical. The phase shift is evident in the shape of the line profile across the crack. The leftmost line profile is the attenuation-only projection (t = 4.1 ns, R1 = 6.7 m, t/R1 = 0.037), the centre line profile is for the optimal combination (t = 8.8 ns, R1 = 10.6 m, t/R1 = 0.035) and the rightmost profile (t = 17.4 ns, R1 = 20.1 m, t/R1 = 0.026) has a phase shift of about 10 degrees. In practice, with a given mechanical setup, the best phase contrast can be achieved by carefully adjusting the source to detector distance (t/R1), thereby adjusting the amount of phase shift occurring in the propagation. The projected line profiles in figure 8 were all from the same crack on the same projection, so the phase contrast can be plotted directly as a function of t/R1. In this case, the data from scans 1, 2, 3 and 4 were plotted in figure 9. The dashed line is the average phase contrast for different source to detector distances and it is clear that the optimal phase contrast is achieved with t/R1 = 0.035, which corresponds to the dotted line in figure 8. Thus, the reason for the poor visibility of the crack in scan 1 is the low t/R1 value in scan 4. The phase contrast at scan 7 and 8 are higher than at scan 4 and the reason for the increased visibility of the crack is the higher t/R1 value in scan 7 and 8. Thus, both phase contrast and t/R1 improve the visibility of cracks.
In this study, all of the high-speed optics were mounted on a rotary table. This is a simple and convenient way to access a variety of different parameters. However, with this arrangement, the alignment of the specimen, the focal length of the optics, and the focal plane on the specimen all change with rotation. The alignment must be readjusted whenever the specimen is replaced, which can be time consuming. As a result, most microscope manufacturers have come up with their own, custom, more convenient and rigid support system.
The problem with this system is that it covers the whole house. It is very slow in its detection and can miss some cracks, and its offline mode does not have a good scan for cracks, it always fails to detect cracks. I will continue to work on this and update this if i am able to find a better one. 827ec27edc