TPDSci Acceptance angle Measuring attenuation of light

Measuring attenuation of light: Acceptance angle of the detector

In a purely light-absorbing medium (Fig. 1 in Attenuation of light: Contributing processes), there is no restriction on the solid angle of acceptance (acceptance angle) of the detector in a transmissometer, i.e. on the range of directions from which the detector accepts light. However, if the medium also scatters light, the acceptance angle of the detector must be restricted to limit the contribution of the scattered light to the power received. Real light sources and detectors are only approximately unidirectional in contrast to ideal sources and detectors shown in Fig. 2 and Fig. 3 in Attenuation of light: Contributing processes. Hence scattered light will contribute to the power received by the detector and a transmission measurement in a light scattering medium will yield a value that is less than the actual attenuation coefficient of the medium, due to the addition of a scattered component to the detected power.

In the single-scattering medium (Fig. 2 in Attenuation of light: Contributing processes) the contribution of the scattered light to the detected power (partially dashed paths) comes primarily from the once-scattered photons and can be made negligible by limiting the acceptance angle of the detector. In a multiple-scattering medium (Fig. 3 in Attenuation of light: Contributing processes) it comes from both once-scattered and multiply-scattered photons, in proportion that depends on the distance between the light source and detector, as well as on the attenuation coefficient and phase function of the medium. Unfortunately, a part of the multiple-scattering contribution cannot be easily reduced by simple limitation of the acceptance angle of the detector because photons forming this part arrive at the detector along the direction of the original beam (Fig. 3, path 5, in Attenuation of light: Contributing processes).

Hence, most researchers restrict the application of the Beer-Lambert law to media with the optical thickness, τ, less than unity. As explained in Transmission, optical density, and thickness, this is the region of single scattering, implying that the multiple-scattered light is unlikely to be detected while making light transmission measurements. However, Swanson NL et al (1999) have shown that this limit can be increased even in the presence of significant multiple scattering (i.e. at optical thickness, τ, of up to about ~10). This has been achieved by both severely restricting the detector acceptance angle in a tranmissometer (thus minimizing the amount of scattered light accepted by the detector) and limiting the contribution of multiple scattered light with an aperture placed near the sample exit window (we discuss the role of such an aperture in more detail in Fig. 1a of Limiting the acceptance angle of the detector). Later, Zaccanti et al (2003) extended this limit to τ ~ 13 with a similar experimental arrangement. A comparably severe limitation of the acceptance angle allows imaging objects hidden in turbid media (see Collimation imaging in turbid media) because the imaging information is carried by non-scattered light and light scattered at small angles.

In the other extreme, when the acceptance angle of the detector approaches 2π, and/or a mechanism is provided for collecting all of the scattered light, then the measurement of the attenuation of light is reduced to the measurement of absorption (for example, Stramski and Reynolds 1993, Nelson NB and Prézelin 1993, Haardt H and Maske 1987, Maske H and Haardt 1987, Shibata K 1959, 1958, Shibata K et al 1954)

CITATION:
Swanson N. L., Jonasz M. 2007. Measuring attenuation of light: Acceptance angle of the detector (www.tpdsci.com/Tpc/AtnCfMsAcptAng.php). In: Top. Part. Disp. Sci. (www.tpdsci.com).

HISTORY:
Published: 21-Nov-2007
Modified: 22-Jan-2008
Peer-reviewed: 22-Dec-2007

Topics in Particle and Dispersion Science