Features of Electromagnetic Waves Scattering by Surface Fractal Structures

Abstract

Accurate measurement of surface roughness of machined workpieces is of fundamental importance particularly in the precision engineering and manufacturing industry. This is mainly due to the more stringent demand on material quality as well as the miniaturization of product components in these industries [1-3]. For instance, in the disk drive industry, to maintain the quality of the electrical components mounted on an optical disk, the surface roughness of the disk must be accurately measured and controlled. Hence, the surface finish, normally expressed in terms of surface roughness, is a critical parameter used for the acceptance or rejection of a product. Surface roughness is usually determined by a mechanical stylus profilometer. However, the stylus technique has certain limitations: the mechanical contact between the stylus and the object can cause deformations or damage on the specimen surface and it is a pointwise measurement method and is time consuming. Hence a noncontact and more speed optical method would be attractive. Different optical noncontact methods for measuring surface roughness have been developed mainly based on reflected light detection, focus error detection, laser scattering, speckle and the interference method [4-10]. Some of these have good resolutions and are being applied in some sectors where mechanical measuring methods previously enjoyed clear predominance. Among these methods, the light scattering method [11] which is a noncontact area-averaging technique, is potentially more speedy for surface inspection than other profiling techniques particularly the traditional stylus technique. Other commercially available products such as the scanning tunneling microscope (STM), the atomic force microscope (AFM) and subwavelength photoresist gratings [12-15], which are pointwise techniques, are used mainly for optically smooth surfaces with roughnesses in the nanometer range. In this chapter in the frame of the Kirchhoff method (scalar model) the average coefficient of light scattering by surface fractal structures was calculated. A normalized band-limited Weierstrass function is presented for modeling 2D fractal rough surfaces. On the basis of numerical calculation of average scattering coefficient the scattering indicatrises diagrams for various surfaces and falling angles were calculated. The analysis of the diagrams results in the following conclusions: the scattering is symmetrically concerning a plane of fall; with