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88 SMT Magazine • June 2016 With the specular light intensity of each LED light ring, it is possible to draw the calcu- lated specular light reflection for each surface angle Is(∅s) (Figure 6). Since the intensity of light reflection, Is, de- pends only on the surface angle, ∅s, now it will be possible to determine the surface angle by applying the inverse function of Phong (7). The inverse Phong was implemented by us- ing the Manhattan distance between the ob- served specular reflection from the solder joint surface area, Ps(x,y), and each angle from the Phong illumination reflection, Is (17). 17 Since both the observed light reflection, Ps(x,y), and the calculated specular reflection, Is, consist in three plans of RGB components, the equation (17) will be developed to (18). The solder joint surface angle is determined as the minimum index obtained for angles be- tween 0º and 90º, representing all possible an- gles of the solder joint surface. 18 Figure 8 shows the result function, ∅s(x,y), where the variation of solder joint surface an- gle, ∅s, can be seen along P(x,y). 3D Solder Joint Reconstruction The reconstruction of the solder joint sur- face shape, z(x,y), is possible by integrating the solder joint surface angle, ∅s(x,y), along the sol- der profile from the beginning of the solder pad to the component electrode (19). 19 Figure 6: Phong calculated illumination reflection. Figure 7: The observed RGB color variation along the solder joint profile. Figure 8: Surface angles along the solder joint. 3D SOLDER JOINT RECONSTRUCTION ON SMD BASED ON 2D IMAGES