WATER JET CONFERENCE - Waterjet Technology Association

APPROACH
Most photographic techniques operate by measuring the scattering or absorption
of light from a subject. In the case of water, scattering is enhanced by the presence of an
uneven surface or the occurrence of droplets. Absorption seemed to be a more promising
process because it increases with increasing density of the subject such as that associated
with the core itself. The absorption spectrum of water (Fig. 1, Washburn, 1929) shows
that water absorbs light in the infrared and ultraviolet regions of the spectrum very well.
Visible light is absorbed quite poorly. For photographic purposes, the infrared region is
often more convenient to use than the ultraviolet portion because photographic materials
are more readily available and glass lenses, etc. do not absorb infrared light as easily as
ultraviolet.
Over 200 years ago, Lambert (1760),discovered that when a parallel beam of
monochromatic light of wavelength X and intensity l o enters a homogeneous absorbing
material, the light which is transmitted through a layer of thickness t will have the
intensity
I( ) = I o ( )e − k( ) l (1)
where k is a positive constant called the absorption coefficient of the material.
Lambert's law can be derived by assuming that each infinitesimally thin layer of the
absorbing material absorbs an amount of light which is proportional to the thickness of
the layer and to the intensity of the monochromatic radiation reaching it. This relation is
shown schematically (Fig. 2) for a typical jet.
Usually, strictly monochromatic light is not employed. However, equation 1 is
also valid over a region of the spectrum when the absorption coefficient is a weak
function of wavelength or in a reasonably small region of the spectrum for which the
incident light is continuous (Nebeker, 1965). Problems sometimes arise if equation 1 is
applied in regions where the absorption spectrum is discrete and not continuous.
However, the experimental circumstances can often be adjusted so that this equation is an
adequate representation of the observations.
Differentiating equation 1 with respect to thickness t (k and I o are constants)
dI
dl
k
= e
Io −kl (2)
Hence, the rate of change of transmitted light intensity is proportional to the
absorption coefficient k. Figure 1 shows that the absorption coefficient is two or three
orders of magnitude greater in the infrared region of the spectrum than the visible.
Therefore, equation 2 indicates that this infrared approach will yield results which are
much more sensitive to variations in width and size of the central core of the jet than one
would expect using light in the visible region of the spectrum.
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