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Calibration of a Terrestrial Laser Scanner - Institute of Geodesy and ...

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2.1 Distance <strong>and</strong> Reflectance Measurement System 172.1.8 Reflection PrinciplesThe reflection <strong>of</strong> electro-optical waves is based on different types <strong>of</strong> reflection. It is distinguished between:•specular, i.e. mirror-like, reflection• diffuse, i.e. Lambertian, reflectionThe specular or mirror-like reflection is characterized so that the angle <strong>of</strong> reflection 6r is identical to theangle <strong>of</strong> incidence 9t with respect to the surface normal0r = 0t. (2.9)The incoming ray is reflected in only one single direction. The specular reflection appears if the roughness<strong>of</strong> the surface is relatively small in comparison to the wavelength <strong>of</strong> the incoming ray [Gerthsen <strong>and</strong> Vogel,1993]. The specular reflection is illustrated in Figure 2.11 (left). The complement to specular reflectionis the diffuse reflection, as illustrated in Figure 2.11 (middle). The incoming ray fans out as a bundle <strong>of</strong>reflecting rays, covering the hemisphere surrounding the surface <strong>of</strong> the object. This reflection requires thatthe roughness <strong>of</strong> the surface be uneven or granular with respect to the wavelength <strong>of</strong> the incoming ray. Ifa surface is completely non-specular, the reflected light will spread over the hemisphere surrounding thesurface.The combination <strong>of</strong> specularray isreflection <strong>and</strong> diffuse reflection leads to a mixed reflection. Theincomingdivided into several reflecting rays covering the hemisphere surrounding the surface <strong>of</strong> the object.However, the intensity <strong>of</strong> the ray, with its angle <strong>of</strong> reflection equalling the angle <strong>of</strong> incidence, mirrored atthe surface normal, is the largest. One approximation <strong>of</strong> a mixed reflection is shown in Figure 2.11 (right).Some surfaces exhibit retroreflection. The structure <strong>of</strong> these surfaces is such that lightis returned in thedirection from which it came reagardless <strong>of</strong> the angle <strong>of</strong> incidence. Such reflection is caused by prisms,which are used for precisedistance measurements <strong>of</strong> total stations.specular reflection diffuse reflection "mixed" reflectionFigure 2.11: Types <strong>of</strong> reflection: specular reflection (left), diffuse reflection (middle) <strong>and</strong> mixed reflection, consisting<strong>of</strong> combined diffuse-specular reflection (right).2.1.9 Reflectance ModelsSpecular reflection <strong>and</strong> diffuse reflection are simple approximations. In reality, surfaces exhibit varioustypes <strong>of</strong> reflection. Other properties <strong>of</strong> electromagnetic waves, e.g. polarization, influence the way <strong>of</strong>reflection <strong>and</strong> complicate a mathematical description. In computer graphics several models were developedfor describingthe reflectance. Inthe following,three models are introduced: the Lambertian reflectance

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