Optical EngineeringTotal integrated scattering from transparent substrates in the infrared region: validity of scalar theory
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Integrated light scattering, from thin, transparent silicon wafers with different front and backside surface roughness is investigated. The measurements are made at near normal incidence in the IR wavelength region 5 to 20 xm using an integrating sphere. A method to separate the scattering contribution from each interface for measurements on transparent samples is introduced. Scalar scattering theory is used to calculate the effective root mean square roughness from reflectance and transmittance measurements, and these values are compared to profilo- meter data, correcting for the different bandwidth limits. Scattering measurements are performed with both the rough and the smooth surface of the wafer oriented toward the light source, which results in additional knowledge. The maximum ratio between the root mean square roughness and the wavelength of the light, to be used in scalar theory, is found to be considerably higher for the transmittance case than for the reflectance case. In agreement with theory, the calculated root mean square roughness is found to be proportional to the refractive index of incident medium in reflectance, and to the difference in refractive indices of incident and refracting medium for the transmittance case.