Integrating Spheres theory and applications - Allied Scientific Pro

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Integrating Sphere Theory and ApplicationsIn either design, the angular response does not perfectlycorrespond to the cosine function since certain incident rayswill first impose on the baffle before being distributed to thesphere wall. The true angular response is usually determinedexperimentally and then applied as a correction factorin high accuracy irradiance measurements.3.2 Reflectance and Transmittance of MaterialsFIGURE 18The centrally located baffle prevents direct irradiation of thedetector. The entrance port becomes the effective measuringaperture of the device. For regular irradiance measurements,the cosine angular response is required. Theirradiance of a flat surface E, is proportional to the cosine ofthe angle of incidence, q.EQ. 28For spectral irradiance measurements in which a monochromatoris used, a 90° port geometry can be more accommodating.This design is commonly used for global irradiancemonitors since the integrating sphere provides good spectralresponse from the UV to the NIR regions of the atmosphericsolar spectrum. A quartz weather domeguards against environmental contaminants.The single largest application for integrating spheres is themeasurement of the reflectance and transmittance of diffuseor scattering materials. The measurements are almostalways performed spectrally, as a function of wavelength.The one exception may be the measurement of luminousreflectance or transmittance using a photopic responsedetector.In the ultraviolet, diffuse transmittance is used to determinethe UV resistance of pharmaceutical containers, sunprotective clothing, and automotive paints. In the visiblespectrum, the color of materials is quantified and controlledin industries such as paints, textiles and the graphic arts. Inthe infrared, the total hemispherical reflectance determinessurface emissivities applied to radiant heat transfer analysisof thermal control coatings and foils used in spacecraftdesign.A transmittance measurement places a material sample atthe entrance port to the sphere (as shown in Figure 20).FIGURE 20In reflectance measurements, the sample is placed at aport opening opposite the entrance port. The incident flux isreflected by the sample. The total hemispherical reflectance,both the diffuse and specular components, is collected bythe integrating sphere.FIGURE 1912
Integrating Sphere Theory and ApplicationsCalibration of the reflectance scale is performed by comparingthe incident flux remaining in the sphere after reflectingfrom a standard reference material.FIGURE 21The angle of incidence in reflectance measurements is usuallyslightly off normal up to 10°. The specular componentcan be excluded from the measurement by using normal(0°) incidence or by fitting another port in the specular pathand using a black absorbing light trap to extinguish thespecular flux.Reflectance measurements at larger or variable incidentangles are performed by placing the sample at the center ofthe sphere and rotating it about a fixed input beam.Baffles are placed to prevent the photodetector on thesphere from directly viewing the irradiated sample in eithermeasurement. In the reflectance geometry, a baffle isusually placed between the portion of the sphere wall thatreceives the specular component as well. It is best to use aphotodetector with a hemispherical field-of-view to reduceany sensitivity to the scatter distribution function of thesample.3.2.1 Substitution vs. Comparison SpheresA unique integrating sphere error is attributed to the designsdepicted in Figure 20 and Figure 21 due to the sample effectivelyaltering the average reflectance of the sphere wall.Calibration of the transmittance scale is usually performedby initially measuring the incident flux before the sample isplaced against the entrance port.FIGURE 23The ideal measurement relationship is for the ratio of radianceproduced inside the sphere to be equal to the ratio ofthe reflectance for each material.where; r r= the reflectance of the reference materialEQ. 29The sample measurement quantity, r s, is properly knownas the reflectance factor. The term refers to the fact that theincident flux was not directly measured as the reference.However, in the substitution sphere of Figure 23, the averagereflectance of the sphere changes when the sample issubstituted for the reference material. The true measurementequation in a substitution sphere is, therefore;EQ. 30where; r s= average wall reflectance with sampler r= average wall reflectance with referenceFIGURE 22The average reflectance with the sample material in place,r s, cannot be easily determined since it is also dependenton r s. The magnitude of this error can be plotted for a typicalSpectraflect integrating sphere with 5% port openingsand a 1% sample port opening. The reference material isSpectralon.13
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