“…Within this effectivemedium approach our samples are optical bi-layers in which a thin film, described by an effective complex refractive index n 1 + ik 1 , covers a partially transparent thick substrate, described by a true complex refractive index n 2 + ik 2 where k 2 n 2 . For this structure, analytical calculation of the reflectance R and transmittance J using well-known method is possible [19], which gives R = 01 + 12 e 2i 1 + ( 01 12 + e 2i 1 ) 20 e 2i 2 1 + 01 12 e 2i 1 + ( 12 + 01 e 2i 1 ) 20 (4)…”
Section: Theorymentioning
confidence: 99%
“…The reason for that is the scattering by imperfections in the bulk, which breaks down the coherence of the light waves reflected from the interfaces back into the substrate. If one describes this scattering by random fluctuations of n 2 , the statistical average of R and J is equivalent to their average over the optical-path phase˚= Re( 2 ), which is mathematical idea behind the multiple-reflection approximation [20]. For one thick slab in the air, the well known apparent transmittance formula obtained [17] by an incoherent summation of the multiply reflected rays, indeed follows from such an averaging.…”
“…Within this effectivemedium approach our samples are optical bi-layers in which a thin film, described by an effective complex refractive index n 1 + ik 1 , covers a partially transparent thick substrate, described by a true complex refractive index n 2 + ik 2 where k 2 n 2 . For this structure, analytical calculation of the reflectance R and transmittance J using well-known method is possible [19], which gives R = 01 + 12 e 2i 1 + ( 01 12 + e 2i 1 ) 20 e 2i 2 1 + 01 12 e 2i 1 + ( 12 + 01 e 2i 1 ) 20 (4)…”
Section: Theorymentioning
confidence: 99%
“…The reason for that is the scattering by imperfections in the bulk, which breaks down the coherence of the light waves reflected from the interfaces back into the substrate. If one describes this scattering by random fluctuations of n 2 , the statistical average of R and J is equivalent to their average over the optical-path phase˚= Re( 2 ), which is mathematical idea behind the multiple-reflection approximation [20]. For one thick slab in the air, the well known apparent transmittance formula obtained [17] by an incoherent summation of the multiply reflected rays, indeed follows from such an averaging.…”
A method of surface temperature measurement by infrared thermography in a lubricated contact has been developed. The capabilities of the camera are examined. The analysis, which needs the determination of global radiometric coefficients and leads to radiometric equations is presented. The calibration of emissivity and transmittivity coefficients of the involved materials is reported. The validity of the method is tested and discussed.Nomenclature E global coefficient of emission L radiant intensity M radiative power R global coefficient of reflection
“…where R(λ) is the reflectance at the window surface and L(λ, T b ) is the spectral radiance of the blackbody [4]. The first term represents the radiation from the blackbody, and the second one from the window itself.…”
Section: Mathematical Model Of Thermal Image Degradationmentioning
Optical windows are indispensable for monitoring industrial processes under vacuum or high pressure by using thermal imagers and radiation thermometers. When a thermal imager observes a sample through an infrared window at elevated temperatures, the window emits additional thermal radiation and increases the background signal of the thermal images, which results in image degradation. Standard four-bar images with various radiance temperature differences were measured using a thermal imager with a spectral band from 3 µm to 5 µm through a UV-grade sapphire window. The four-bar images are given by a blackbody collimator with various image patterns. The window was indirectly heated in a furnace and then rapidly placed on the optical path between the collimator and the thermal imager. The four-bar image degradation was measured as a function of the window temperature and the radiance temperature difference of the four-bar pattern. A simple equation which describes the contrast of the four-bar image by using the transmittance and reflectance of the sapphire window was proposed. It was confirmed that the model can properly predict the window temperature when the appearance of the four-bar pattern cannot be determined.Keywords Aerodynamic heating · Emissivity · Infrared window · Minimum resolvable temperature difference (MRTD) · Noise equivalent temperature difference (NETD) · Thermal imager
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