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June 2016 • SMT Magazine 85 Expanding the Phong model, the equation (2) will allow to define the illumination reflec- tion Ir, according to the material characteristics, nShiny, illumination angle, ∅i, observation an- gle, ∅o, and the surface angle, ∅s. The param- eter Ia, Id and Is correspond to ambient light intensity, diffuse light intensity, and specular light intensity. 2 Using the Phong model, it will be clear that the reflection light intensity will depend on several variables shown in equation (3). 3 Since the proposed approach works with metallic surfaces, the diffuse light reflection was neglected and the intensity of light reflection will depend only on the ambient lights and specular reflection (4). 4 To analyze the solder joint surface, a square area, P(x,y), was drawn with limitations of the pad and component localization according to specification [11] (Figure 4). Since the initial im- age is an RGB color image, the square area has the correspondent's three plans (red, green and blue components). 5 The light reflection on the square area could be calculated using the Phong reflection model (6). 6 Considering the following parameters as constants (∅i,∅o,ia,id,is,nShiny), it will be pos- sible to apply the inverse function of the Phong reflection model to obtain the solder joint sur- face angle ∅s(x,y), for each pixel coordinate de- fined in P(x,y) (7). 7 The 3D reconstruction of the solder joint surface can be determined by: 8 To convert the z(x,y) function from pixels to metric dimensions, the CR parameter was used for the camera resolution in µm/pixel. Ambient Light Reflection Since the ambient light reflection doesn't contain any information from the surface an- gle, this light component was removed from the inspection area by (9), keeping only the ob- served specular reflection Ps(x,y) for the follow- ing developments. 9 The ambient light reflections Ia are calcu- lated along the area of solder joint using (10). 10 Figure 4: Solder joint area. 3D SOLDER JOINT RECONSTRUCTION ON SMD BASED ON 2D IMAGES