This paper presents a new reflectance model for rendering computer synthesized images. The model accounts for the relative brightness of different materials and light sources in the same scene. It describes the directional distribution of the reflected light and a color shift that occurs as the reflectance changes with incidence angle. The paper presents a method for obtaining the spectral energy distribution of the light reflected from an object made of a specific real material and discusses a procedure for accurately reproducing the color associated with the spectral energy distribution. The model is applied to the simulation of a metal and a plastic.

A reflectance model for computer graphics

A Reflectance Model for Computer Graphics

X-ray and neutron reflectivity for the investigation of polymers

Concepts, terminology, and symbols are presented for specifying and relating directional variations in reflectance and emissivity of an opaque surface element. Their relationship to more familiar concepts, including those of perfectly diffuse and specular reflectance, is given, and they are applied to illustrative examples. It is shown that, when the usual reciprocity relationship holds, the reflectance for a ray incident on an opaque surface element is related by Kirchhoff's law to the emissivity of that element for a ray emitted along the same line in the opposite sense.

Directional Reflectance and Emissivity of an Opaque Surface

The optical response of coherent thin-film multilayers is often represented with Fresnel coefficients in a 2 x 2 matrix configuration. Here the usual transfer matrix was modified to a generic form, with the ability to use the absolute squares of the Fresnel coefficients, so as to include incoherent (thick layers) and partially coherent (rough surface or interfaces) reflection and transmission. The method is integrated by use of models for refractive-index depth profiling. The utility of the method is illustrated with various multilayer structures formed by ion implantation into Si, including buried insulating and conducting layers, and multilayers with a thick incoherent layer in an arbitrary position.

General transfer-matrix method for optical multilayer systems with coherent, partially coherent, and incoherent interference

Expressions relating the roughness of a plane surface to its specular reflectance at normal incidence are presented and are verified experimentally. The expressions are valid for the case when the root mean square surface roughness is small compared to the wavelength of light. If light of a sufficiently long wavelength is used, the decrease in measured specular reflectance due to surface roughness is a function only of the root mean square height of the surface irregularities. Long-wavelength specular reflectance measurements thus provide a simple and sensitive method for accurate measurement of surface finish. This method is particularly useful for surface finishes too fine to be measured accurately by conventional tracing instruments. Surface roughness must also be considered in precise optical measurements. For example, a non-negligible systematic error in specular reflectance measurements will be made even if the root mean square surface roughness is less than 0.01 wavelength. The roughness of even optically polished surfaces may thus be important for measurements in the visible and ultraviolet regions of the spectrum.

https://apps.dtic.mil/sti/pdfs/AD0262572.pdf

H. E. Bennett

Papers

Relation between Surface Roughness and Specular Reflectance at Normal Incidence