Page 216 - Photodetection and Measurement - Maximizing Performance in Optical Systems

Contamination and Industrial Systems

Contamination and Industrial Systems 209

under the hole is unstable, as surface tension eventually amplifies small diam-
eter variations, causing the thread to narrow down into to a series of drops. A
beautiful description of this process has been given by Boys (1959), along with
drawings of uniform droplet streams, and alternating size streams. (Similar
streams are sometimes seen along spider’s webs. Spiders seem to be the experts
of surface tension).
Although water threads are unstable, with reasonable care in design of the
container’s orifice, avoiding turbulence and carefully minimizing vibration of
the container, surprisingly long threads can be formed in water and other
liquids. The jets also often become electrostatically charged, so grounding of the
apparatus is helpful. In the region above breakup, the thread takes on an eerily
stable glass-like quality, eminently suitable for optical transmission and scat-
tering measurements. The surface tension ensures that the higher spatial fre-
quency components of surface ripples caused by orifice imperfections are rapidly
smoothed out.
In transmission we have to live with the distorted cylindrical surface of the
liquid. In principle this could be corrected with an external glass block, but in
practice it is simpler to use a rectangular-section orifice, and achieve almost flat
liquid surfaces for a few millimeters. Predistortion of the orifice might even move
the optimum region lower down the thread to a more convenient location. Many
products are available that use this falling stream approach, primarily in the
ultraviolet where water absorption is highest, or with strongly absorbing samples
such as waste-water and other effluents. This is just the application where some
protection against fouling is required, so the technology is well suited.
Turbidity measurements on falling streams are also popular. When light
is incident on an ensemble of scattering particles, the angular distribution of
scattering efficiency is a function of the particle’s shape, refractive index dif-
ference from its surrounding, and most importantly of its size. Particles much
larger than the light wavelength predominantly scatter in a forward direction,
while those much smaller than the wavelength typically scatter almost omni-
directionally. The latter case is convenient, as there is then little need to worry
about the distortion caused by water surface shape. For best sensitivity the
detector should be arranged to capture as large a solid angle of the scattered
light as possible. Some applications, for example turbidity measurement of
drinking water, use industrial standards that specify 90° scattering, which
greatly degrades the method’s potential sensitivity. The brewing business typ-
ically does allow small-angle scattering (ª5°), giving much higher sensitivity in
the detection of low concentrations of yeast spores.
Multiple reflections occur between the water surfaces, which can be disturb-
ing in some photometric and imaging applications. Forming antireflection coat-
ings here to reduce the reflected power is likely to be a difficult task, but perhaps
possible with oil films. Reflections are strongest for meridional rays, light trav-
elling almost around the external surface of the fiber in whispering gallery
modes, named after the famous acoustic effect heard in the dome gallery of
Christopher Wren’s St. Paul’s Cathedral in London.

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