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Polar nephelometers can typically measure the VSF down to a scattering angle of ~3° to 5° degrees, albeit a polar nephelometer, measuring the VSF down to θ ~ 0.7°, has been described by Lee and Lewis (2003). A specialized small-angle nephelometer (see Volume scattering function of seawater), using a lens to convert angular deviations of light (due to scattering) in the object space to radial deviations in the lens focal plane (i.e. performing an optical Fourier transform), can measure the VSF at a much smaller scattering angle, on the order of 0.1° and less (for example, Agrawal 2005, Forand et al 1993, Spinrad RW et al 1978, Petzold T 1972). A variable-angular aperture version of this type of nephelometer for moderate scattering angles (2, 5, 10, 21°) was developed by Latimer (1984c) for use in particle sizing. R. J. V. Zaneveld and C. Moore (WET Labs) developed a similar device, called the Variable Angle Beam Attenuation Meter (VABAM) in the mid-1990's that measured small-angle scattering between 0.1° and 3° in 24 increments (M. Twardowski, personal communication).
The VSF is linked to the point spread function (PSF) and the modulation transfer function (MTF) (for example, Mertens and Replogle 1977) of a turbid medium through radiative transfer theory. Thus, the VSF can be measured at the small angles by inverting results of the PSF or MTF measurements (for example, Hodara 1973).
A method of measuring the VSF at θ = 0° and at angles near 0° (θ ≤ ~0.05°) has also been proposed (Padmabandu and Fry 1990) but has not gained a following, presumably because of its complexity. That method utilizes the interference in a photorefractive crystal (BaTiO3) of a reference light beam with a beam passing through a turbid medium sample to attenuate the transmitted part of the sample beam while amplifying the scattered part of that beam.
More recently Brogioli et al (2003) have described another unconventional method for measuring the VSF at an arbitrarily small scattering angle. Their method, based on the schlieren technique (for example, Settles GS 2001), is an improvement of their earlier method (Brogioli et al 2002) in which a plane located a short distance behind a sample illuminated by a coherent parallel beam of light is imaged onto a detector to produce essentially a speckle pattern. Irradiance at each point in that pattern results from interference of the illuminating light and light scattered by particles in the sample. Light scattered at all angles smaller than certain angle determined by the system geometry and the wavelength of light participates in the interference. The angular distribution of the scattered light intensity is proportional to the power spectrum of that two-dimensional irradiance pattern. By inserting a knife edge (in their schlieren-based method) into a focus of the imaging lens, Brogioli et al (2003) have eased a problem caused by the vanishing of the phase difference between the scattered and illumination rays when a scattering angle of 0 is approached. This is achieved by the knife edge blocking a ray in each pair of rays scattered symmetrically about the incident beam axis. This preserves the interference pattern due to rays scattered at very-small-angles.
Note that the scattering function of a turbid medium at the small angles may be dominated by turbulence. In particular, Bogucki et al (1998) suggest that at the scattering angles ≤~0.1°, turbulence may dominate the scattering function of seawater. See also VSF at the small angles for natural dispersions.
| CITATION: Jonasz M., Boss E. 2006. Volume scattering function: Small-angle measurement techniques (www.tpdsci.com/Tpc/ScaFnMsSmlAng.php). In: Top. Part. Disp. Sci. (www.tpdsci.com). |
HISTORY: Published: 07-Sep-2006 Modified: 05-Dec-2006 Peer-reviewed: 21-Sep-2006 |
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