Determining Surface Roughness and Shape of Specular Diffuse Lobe Objects Using Photometric Sampling Device

The photometric sampling method extracts shape and reflectance properties of surfaces by using multiple illumination directions and a single viewing direction. We have previously proposed a recovering algorithm for smooth surfaces. One of the limitations of the previous algorithm is that it cannot recover the shape and roughness of specular lobe dominant surfaces. Surface reflection consists of three components: specular spike, specular lobe, and Lambertian. Among these three components, the previous method only can handle surfaces of the specular spike and the Lambertian. This paper proposes a novel algorithm to recover surface shape and roughness of specular lobe dominant surfaces. An extraction algorithm uses the set of image brightness values measured at each surface point. Each brightness value reflecting surfilcc provides one non-linear image irradiant equation, containing unknown parameters for surface orientation, reflectance and Figure 1: Three component reflection model. surface roughness. The algorithm iteratively solves the set of image irradiant non-linear equations with respect to these parameters. The experiments conducted on several rough surfaces show high accuracy in estimated orientations, and good estimation in surface roughness. We have demonstrated the ability of our method to detect surfacedefects on the rough gold surface of LSI package. INTRODUCTION device and developed an algorithm to determine surface orientation based on a two component model: the Lambertian diffuse component and the specular spike component. The algorithm can be applied to smooth surfaces such as silicon wafers or transparent plastic lenses. However, since the algorithm ignored the specular diffuse lobe component, it can not be applied to rough surfaces such as solder joints or sand-b1a.t finished surfaces. This paper describes a method to determine surface oriSurface shape and roughness are important inspection crientation and roughness of specular diffuse lobe dominant teria in industrial applications. For example, surface defects on a silicon wafer can be detected as points with non-mirror surfaces. like reflection properties. A solder joint can be inspected from its appearance without electronic or mechanical methSPECULAR DIFFUSE REFLECTION MODEL ods. It can be judged good if its surface looks smooth and wet, and if its shape has gentle slopes. In many cases, the surface inspection of industrial products can be performed by comparing actual values and design values of shape and surface roughness. Therefore, we have developed an algorithm called the photosampler which can determine the shape and reflectance of a limited class of objects 121. A set of images of the object are taken sequentially activating light sources whose locations and distributions are known. From this image sequence, surface reflectance and orientation can be calculated using a reflectance model. Sato, Nayar and Lkeuchi [4] have built a 3D photosampling 'This research was sponsored in part by the Avionics Laboratory. Wright Research and Development Center, Aeronautical Systems Division (AFSC). U.S. Air Force. Wright-Patterson AFB, Ohio 45433-6543 under Contract F.1.1615-90-C-1465 Order No. 7597. Out surface reflection model consists of three components: Lambertian diffuse, specular spike and specular diffuse lobe 131. See Figure 1. For a very smooth surface, the spike component dominates, and the surface looks like a mirror. As a surface becomes rougher, the mirror-like spike component shrinks rapidly, and the specular diffuse lobe component begins to dominate. Qpical specular diffuse lobe dominant surfaces include: a "cold" solder joint which has been melted and resolidified, or metal finished by sand-blasting. The Lambertian diffuse component is considered to be body reflection which originates from inside a dielectric material like a plastic or a ceramic. The three component model is useful for describing material type and surface finish. The specular diffuse lobe component is also a function of surface roughness. Surface roughness is a statistical function. The appearance of a specular diffuse lobe dominant surface can vary from shiny to blurred. Our model for the specular diffuse lobe component is based on the BeckmannSpizzichino physical optics model [I] and the TorranceSparrow geometrical optics model 151. Lirrdu; a2 L,d = cGexp T, cos 8, 2a,, where G and a,, represent the geometric attenuation factor and the surface roughness parameter, respectively. The angle, a is measured as the difference betweeen the surface orientation and the bisector of the viewing and the light source direction. This model corresponds to the second term of the Beckmann-Spizzichino model; the specular diffuse lobe component. Although, the model is very simple, we have confirmed that it provides a good approximation of the specular diffuse lobe component of the Beckmann-Spizzichino model. See [5] for more details. PHOTOSAMPLER APPARATUS Figure 2 shows a photograph of the experimental device. The photosampler has lamps and a sphere made of lightdiffusing material. The spherical diffuser is illuminated by an outside lamp, and generates an extended light source toward its inside. The object is placed at the center of the spherical diffuser, and is viewed by a TV camera through a hole at the top of the diffuser. The process of measuring image brighmess for different source directions is_equivalent to_sampling the image irradiance equation, I f ( S ) , at various S;. We distribute an array of extended sources around the object such that each source illuminates the object from a different direction. The entire array of extended sources may be scanned by sequentially activating each source one at a time and taking an image. Therefore, the scanning process results in a set of brightness, I, : i = 1,. . . , M, measured at each point on the object surface. M equals the number of extended light sources. Figure 2: the photosampler device