The Design and simulation of diffuse lambertian surfaces with Matlab

There are many practical situations in which it would be desirable to have optical diffusers whose light scattering properties could be controlled. In particular, a non absorbing diffuser that scatters light uniformly within a range of angles and produces no scattering outside this range would be an attractive and useful optical element. We will call this a band-limited uniform diffuser. Such as element would have applications, for example, in projection systems, where it is important to produce even illumination without wasting light [1].Optical devices that give rise to a scattered intensity that is proportional to the cosine of the scattering angle are frequently used in the optical industry, e.g. for calibrating scatter meters. Such diffusers have the property that their radiance or luminance is the same in all scattering directions. Due to this angular dependence such devices are often referred to as Lambertian diffusers. In the visible region of the optical spectrum volume disordered media, e.g. compacted powdered barium sulfate, and freshly smoked magnesium oxide are used as Lambertian diffusers. However, this type of diffuser is inapplicable in the infrared region due to its strong absorption and the presence of a specular component in the scattered light, in this frequency range. The design of a random surface that acts as a Lambertian diffuser, especially in the infrared region of the optical spectrum is therefore a desirable goal [2].For simulation and fabrication diffuser surfaces, we should modele them with a method. For this, we present four methods in this study: The Kirchhoff Approximation Method, The Small perturbation Method (SPM), The Integral Equation Method (IEM) and The Small Slope Approximation (SSA) [3]. The Kirchhoff Method and the SPM represent early approaches to scattering which are still much used and the latter two represent moe modern approaches which have larger domains of validity. With regard to simplicity of Kirchhoff method and relative accuracy of it, we use it for simulation diffuse surface.