Integrating Spheres theory and applications - Allied Scientific Pro

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Integrating Sphere Theory and Applications3.2.2 Measurement Geometry 0°/d vs. d/0°The previous examples of reflectance and transmittance geometriesdepicted a directional incident flux and hemisphericalcollection by the integrating sphere after interaction withthe sample material. The geometry is correctly defined asdirectional/hemispherical and commonly abbreviated as0°/d referring to near normal incidence and diffuse collection.The 0° angle should be replaced by the actual angleof incidence when describing a particular integrating sphereinstrument, for example, 8°/d. Reflectance factor is thequantity directly measured in 0°/d geometry.FIGURE 24In order to utilize Eq. 29, the proper sphere design is onethat keeps the average reflectance constant. A comparisonsphere mounts both the sample and the reference simultaneouslyto port openings in the integrating sphere.A reciprocal optical geometry can be used in both reflectanceand transmittance measurements. In the d/0° geometry,the sample irradiation is hemispherical and the sampleis viewed from the near normal direction.FIGURE 26FIGURE 25The comparison sphere features an average sphere wallreflectance that is constant, a function of each materialreflectance. In a single beam instrument, the sphere can berotated to alternately position each material in the incidentbeam. In double beam reflectometers, a baseline is initiallyestablished with a standard reference material mounted atthe sample port opening in order to determine the ratio ofincident flux in each beam.The measurement quantity in the reflectance geometry isproperly termed the radiance factor. The radiance of thesample under diffuse irradiation is compared to the radianceof a reference material. The radiance factor is equivalentto the reflectance factor for reciprocal geometries, i.e.- theétendue and angle from the sample normal is the same forthe directional beams, a hemispherical detector field-of-view(0°/d) is replaced by a hemispherical input flux (d/0°). Instrumentswhich use d/0° often employ an auxiliary integratingsphere source.Substitution error also applies to transmittance measurementssince the sample surface tangential to the port openingwill contribute to the average reflectance of the spherecavity. A comparison sphere is recommended for transmittancemeasurements as well.14
Integrating Sphere Theory and Applicationsto increase the radiance as well as provide a step wisemethod of attenuating the radiance level.Tungsten halogen lamps are most commonly used withintegrating sphere sources. These lamps provide a continuousspectrum, free of emission lines or temporal instabilitywhen operated from a current regulated power supply. Thespectral radiance of the sphere source can be estimatedby combining the sphere radiance equation with blackbodyequations for the spectral radiant flux.There are two main advantages of the d/0° geometry. Theincident flux is significantly greater since integrating spheresprovide total light collection, thus increasing the signaltonoiseratio for the instrument. Polychromatic irradiationwill stimulate photon induced radiance, such as that due tofluorescence, which often needs to be quantified in manycolor and appearance measurements. The main disadvantageof d/0° instruments is sample heating which can inducethermochromic effects. Many commercial color measurementinstruments will utilize flashlamps to reduce thermalmeasurement error.3.3 Uniform SourcesFIGURE 27In the previous applications, the integrating sphere is usedas a collecting device for the measurement of radiant flux,either the absolute amount emitted from a light source itselfor the relative amount of flux transmitted or reflected bymaterials.The open port of an internally illuminated integrating spherecan itself serve as a large area diffuse light source.and,where;EQ. 31EQ. 32r(l) = spectral reflectance of sphere surfaceF i l= spectral radiant fluxF o= rated wattage of the lampl = wavelengthT = temperature of the filament≈ correlated color temperaturec 1, c 2, s = blackbody constantsThe radiance equation is multiplied by the number of lampsif more than one lamp is used.FIGURE 28Lamps are placed inside the integrating sphere around theperimeter of the viewing port. The lamps are usually baffledfrom the port. The radiance of the sphere is a function of thewattage rating of the lamp. Multiple lamps can be used15
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