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| Measuring attenuation of light: Limiting acceptance angle of the detector with a lens-aperture system | Parent topic |
Fig. 1. Limiting of the detector acceptance angle in a transmissometer by a lens-aperture system. Abbreviations: A - aperture, B - collimated light beam, D - detector with a response insensitive to the direction of radiation within the left-hand side hemisphere, L - lens (note the orientation of the lens), pp - principal plane of the lens, S - sample, Vi – elementary scattering volumes of the sample (a short arrow from V1 to V2 represents schematically illumination of volume V2; in reality, V2 receives illumination from the entire sample), W - window, θ1/2 - the acceptance angle of the detector (this angle is the same for every scattering volume within the sample as long as the window and lens diameters are sufficiently large to prevent vigneting).
Top panel: optical schematics. In the paraxial approximation (for example: http://scienceworld.wolfram.com/physics/ParaxialApproximation.html), the half-angle, θ1/2, of the acceptance cone is defined by the aperture radius, r, and the focal length, f, of the lens as follows, θ1/2 = atan(r / f), assuming that the refractive indices of the media on the object and image sides of window W are the same, otherwise refraction at the window needs to be taken into account. For small aperture radii, θ1/2 = ~ r / f [radians]. By moving the detector away from the focal plane of the lens, one increases the beam footprint at the detector surface, and thus minimizes the effect of local variations in the responsivity across the active area of the detector (for example, Campos J et al 1988) on the transmissometer signal.
Bottom panel: the outlines of bundles of rays scattered by two arbitrarily selected volume elements, V1 (single and multiple scattering) and V2 (multiple scattering) of the sample, which are accepted by the detector. See the traces of rays that are rejected by aperture A (Fig. 1a). Note that by adding, just behind window W, another aperture with a diameter equal to that of the beam and coaxial with A, the contribution of multiple scattering by the parts of the sample located outside the beam-illuminated volume (for example, V2) can be reduced (bottom panel of Fig. 1a).
See also a lensless acceptance angle limiting system (Fig. 2).
| CITATION: Swanson N. L., Jonasz M. 2007. Measuring attenuation of light: Limiting acceptance angle of the detector with a lens-aperture system (www.tpdsci.com/Tpc/AtnCfMsAcptAngLimFigLA.php). In: Top. Part. Disp. Sci. (www.tpdsci.com). |
HISTORY: Published: 21-Nov-2007 Modified: 15-Jan-2008 Peer-reviewed: 22-Dec-2007 |
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