The radiative properties of engineering surfaces with microscale surface texture or topography (patterned or random roughness and coating or multi-layer) are of fundamental and practical importance. In the rapid thermal processing or arc/flash-assisted heating of silicon wafers, the control of thermal energy deposition through radiation and the surface temperature measurement using optical pyrometry require in-depth knowledge of the surface radiative properties. These properties are temperature, wavelength, doping level, and surface topography dependent. It is important that these properties can be modeled and predicted with high accuracy to meet very stringent temperature control and monitor requirements. This study solves the Maxwell equations that describe the electromagnetic wave reflection from the one-dimensional random roughness surfaces. The surface height conforms to the normal distribution, i.e., a Gaussian probability density function distribution. The numerical algorithm of Maxwell equations’ solution is based on the well-developed finite difference time domain (FDTD) scheme and near-to-far-field transformation. Various computational modeling issues that affect the accuracy of the predicted properties are quantified and discussed. The model produces the bi-directional reflectivity and is in good agreement with the ray tracing and integral equation solutions. The predicted properties of a perfectly electric conductor and silicon surfaces are compared and discussed.

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Radiative properties of thin films are derived based on the concept of optical coherence theory. Instead of the previous approach of deriving the property formulas based on the degree of coherence, a direct integration approach to obtain the averaged properties over a finite spectral resolution is developed. The analytical results are in excellent agreement with the measured spectra. The formulas are compact in form and easy to use to invert optical properties or film thicknesses with measured reflectance or transmittance. Rigorous criteria for incoherent and coherent limits can be easily reduced from the general formulas and the resulting equations corresponding to those of geometric and wave optics, respectively. These criteria are very useful in determining under what situations simpler wave optics and geometric optics formulas can be applied.

The radiative properties of engineering surfaces with microscale surface textures depend on the incident wavelength, optical properties, and temperature as well as the topography of the reflective surface. In the case of slightly rough surfaces, the traditional Kirchhoff theory on rough surface scattering may be applicable. In this study, a direct numerical solution of Maxwell's equations was developed to understand scattering from weakly to very rough surfaces. The method is the finite-difference time-domain method. The problem of interest is a set of gold surfaces with Gaussian random roughness distributions. Highly accurate experimental data are available from the earlier work of Knotts and O'Donnell in 1994. Due to the negative real component of the complex dielectric constant at the infrared light source wavelengths of 1.152 and 3.392 µm, the convoluted integral was used to convert the frequency domain electrical properties to time-domain properties in order to obtain convergent solutions. The bi-directional reflectances for both normal and parallel polarizations were obtained and compared with experimental data. The predicted values and experimental results are in good agreement. The highly specular peak in the reflectivity was reproduced in the numerical simulations, and the increase of the parallel polarization bi-directional reflectance was found to be due to the effect of a variation in the optical constant from 1.152 to 3.392 µm.