Measurement of scattering Beam transmissometers

In the absence of absorption, the scattering coefficient could in principle be determined by measuring the loss of intensity of a narrow parallel beam passing through a known pathlength of medium. If absorption as well as scattering occurs, then the parameter measured by the instrument would in fact be the beam attenuation coefficient, c, rather than the scattering coefficient. If it is possible also to measure the absorption coefficient,a, of the water at the appropriate wavelength, then the scat-tering coefficient,b, may be calculated (b¼ca).

Beam attenuation meters – or beam transmissometers as they are more commonly called – for the in situ measurement of c have long been important tools in hydrologic optics. In principle all they have to do is measure the proportion,c, of the incident beam that is lost by absorption and scattering in a pathlength,r, the beam attenuation coefficient being equal to –[ln(1 –C)]/r(}1.4). In practice, the construction of instruments that accurately measure c is difficult. The problem is that most of the scattering by natural waters is at small angles. Therefore, unless the acceptance angle of the detector of the transmissometer is very small (<1), significant amounts of scattered light remain in the beam and so attenuation is underestimated.

The principles of design of beam transmissometers and the variation of the size of the error with the design parameters have been discussed by Austin and Petzold (1977). One possible optical system is shown sche-matically inFig. 4.4. Most beam transmissometers are monochromatic, but spectral instruments also exist.¹³⁵One of the simpler monochromatic instruments is the WET Labs C-Star, which uses an LED light source to provide a narrow bandwidth centred on 650 nm. This is focused and collimated with an aperture and a lens to produce a parallel beam, which passes through a pathlength of either 10 cm or 25 cm in the water. At the receiver end the light is brought to a focus with another lens, and its intensity measured with a silicon photodiode. The acceptance angle in water is 1.2.¹⁴¹Laser light sources have the advantage for beam trans-missometry that the beam is already highly collimated. The Sequoia Scientific LISST-100X, which is a multi-angle scattering meter used for measuring particle size distribution, and the volume scattering function (see below), uses a laser light source at 670 nm and provides values of beam attenuation coefficient in addition to the other data. Its pathlength is 5 cm and it has an acceptance angle in water of 0.0269.¹⁴¹

The WET Labs ac-9 instrument package includes a spectral beam transmissometer, together with an absorption meter.⁶Both instruments operate at nine wavelengths over the range 412 to 715 nm. Light from an incandescent source passes through a 1 mm aperture, and is then colli-mated with a 38 mm lens followed by a 6 mm aperture. Approximate monochromaticity is achieved by passing the beam through a rotating wheel containing nine 10-nm full width half maximum (FWHM) filters.

The collimated monochromatic beam passes through a flow tube 25 cm (or 10 cm) long, containing the surrounding water in which the instrument

Fig. 4.4 Beam transmissometer optical system (adapted from Austin and Petzold, 1977). To confine measurements to a narrow spectral waveband, a filter can be included in the light path within the receiver.

4.2 Measurement of scattering 105

is immersed. Whereas in the absorption meter the tube is, as discussed earlier (}3.2), a reflective quartz cylinder surrounded by an air layer which ensures that most sideways-scattered photons are not lost, in the trans-missometer the tube has a blackened surface so that sideways-scattered photons are removed. At the receiving end a 30 mm lens re-focuses the light onto a detector behind a 1 mm aperture. The acceptance angle in water is 0.93. Another WET Labs instrument, the ac-s, is broadly similar to the ac-9 but uses a linear variable filter to achieve spectral coverage over the range 400 to 730 nm with 80 wavebands of 15.5 nm FWHM.¹⁴⁹⁸The acceptance angle is 0.75in water.

Althoughin situmeasurements ofcare to be preferred, it is possible to measure the beam attenuation coefficient in the laboratory with a spec-trophotometer, provided that a very small acceptance angle and long-pathlength cells are used.

If, in any water body, the vertical attenuation coefficient for downward irradiance, Kd, and the beam attenuation coefficient are both measured for the same spectral waveband, then using certain empirical relations that have been found to exist betweenKd, bandc,¹³⁶⁹orKd, aand c,¹⁰⁵³it is possible to estimateband thus determinea(fromc¼aþb), or estimate a and thus determine b. Gordon (1991) has described a calculation procedure by means of which, from near-surface measurements ofc, Kd

and irradiance reflectance (R), it is possible to estimate a, b and the backscattering coefficient,bb. This method, like the others, makes use of empirically established relationships between these quantities, but has the advantage that it makes no assumption about the shape of the scattering phase function.

Variable-angle scattering meters

The scattering properties of natural waters are best determined by directly measuring the scattered light. The general principle is that a parallel beam of light is passed through the water, and the light scattered from a known volume at various angles is measured. In the ideal case, the volume scattering function, b(y), is measured from 0 to 180: this provides not only the angular distribution of scattering for that water but also, by integration, the total, forward and backward scattering coefficients (}1.4).

Such measurements are in reality difficult to carry out and relatively few natural waters have been completely characterized in this way. The prob-lem is that most of the scattering occurs at small angles (typically 50%

between 0 and 2–6) and it is hard to measure the relatively faint

scattering signal so close to the intense illuminating beam. We shall considerin situscattering meters first.

An instrument developed by Petzold (1972) for very low angles (Fig. 4.5) uses a highly collimated beam of light traversing a 0.5 m pathlength in water and then being brought to a focus by a long-focal-length lens. Light that has been neither scattered nor absorbed comes to a point in this plane. Light that has been caused to deviate by scattering arrives at this plane displaced a certain distance (proportional to the scattering angle) to one side. A field stop is placed in the focal plane, opaque except for a clear annular ring that allows only light corresponding to a certain narrow (scattering) angular range to pass through and be detected by a photomultiplier behind the stop.

Three such field stops are used, each with the annular ring a different radial distance from the centre: these correspond to scattering angles of 0.085, 0.17 and 0.34. To measure the intensity of the incident beam a fourth stop is used, which has a calibrated neutral-density filter at the centre.

Kullenberg (1968) used a He–Ne laser to provide a collimated light beam traversing a pathlength of 1.3 m in water. At the receiving end of the instrument, the central part of the beam was occluded with a light trap and a system of conical mirrors and annular diaphragms was used to isolate the light that had been scattered at 1, 2.5 or 3.5.

Bauer and Morel (1967) used a central stop to screen off the collimated incident beam and all light scattered at angles up to 1.5. Light scattered between l.5 and 14was collected by a lens and brought to a focus on a photographic plate: b(y) over this angular range was determined by densitometry.

The LISST-100X particle size analyzer, referred to earlier, measures light scattering at 32 forward angles over a range depending on which

Fig. 4.5 Optical system of low-angle scattering meter (after Petzold, 1972).

The vertical dimensions of the diagram are exaggerated.

4.2 Measurement of scattering 107

version of the instrument is used. In the Type B instrument the range is 0.1 to 18. The light source is a solid-state laser operating at 670 nm over a 5 cm pathlength, and there are 32 ring detectors whose radii increase logarithmically.⁸¹⁶

Instruments for measuring scattering at larger angles are constructed so that either the detector or the projector can rotate relative to the other.

The general principle is illustrated in Fig. 4.6. It will be noted that the detector ‘sees’ only a short segment of the collimated beam of light in the water, and the length of this segment varies with the angle of view.

Instruments of this type have been developed by Tyler and Richardson (1958; 20–180), Jerlov (1961; 10–165), Petzold (1972; 10–170) and Kullenberg (1984; 8–160). The recently described volume scattering meter, developed at the Marine Hydrophysical Institute at Sevastopol (Ukraine) in collaboration with Satlantic in Canada, measures the volume scattering function over the range 0.6 to 177.3, with an angular reso-lution of 0.3.⁷⁸⁶ This instrument differs from the normal design in that the positions of the light source and detector are fixed. The measure-ment angle is modified by rotation of a special periscope prism. The initial version was monochromatic, but there is now a multispectral model, operating at seven wavelengths – 443, 490, 510, 532, 555, 590 and 620 nm.¹⁰⁴

The scattering properties of natural waters can be measured in the laboratory but, at least in cases in which scattering values are low, as in many marine waters, there is a real danger that the scattering properties may change in the time between sample collection and measurement. In the case of the more turbid waters commonly found in inland, estuarine and some coastal systems, such changes are less of a problem but it is still

Scattering volume

Receiver

Field of view of receiver

Projector q

Fig. 4.6 Schematic diagram of optical system of general-angle scattering meter (after Petzold, 1972).

essential to keep the time between sampling and measurement to a minimum and to take steps to keep the particles in suspension. Commer-cial light scattering photometers were developed primarily for studying macromolecules and polymers in the laboratory, but have been adapted by a number of workers for the measurement of b(y), in natural waters.^83,1278 The water sample is placed in a glass cell illuminated with a collimated light beam. The photomultiplier is on a calibrated turntable and can be positioned to measure the light scattered at any angle within the range of the instrument (typically 20 to 135). Laboratory scattering photometers for very small angles have been developed^40,1281 and com-mercial instruments are available.

From the definition of volume scattering function (}1.4) it follows that to calculate the value ofb(y) at each angle it is necessary to know not only the radiant intensity at the measuring angle, but also the value of the scattering volume ‘seen’ by the detector (this varies with angle as we noted above), and the irradiance incident upon this scattering volume. In the case of laboratory scattering meters, scattering by a water sample can be related to that from a standard scattering medium such as pure benzene.⁹³⁷

Once the volume scattering function has been measured over all angles, the value of the scattering coefficient can be obtained by summation (integration) of 2pb(y) siny in accordance with eqn 1.40. The forward and backward scattering coefficients,bfandbb, are obtained by integra-tion from 0 to 90, and from 90 to 180, respectively.

Fixed-angle scattering meters

As an alternative to measuring the whole volume scattering function in order to determineb,b(y) can be measured at one convenient fixed angle, and by making reasonable assumptions about the likely shape of the volume scattering function in the type of water under study (see below), an approximate value of b can be estimated by proportion. In marine waters, for example, the ratio of the volume scattering function at 45to the total scattering coefficient (b(45)/b) is commonly in the range 0.021 to 0.035 sr¹.⁶³⁶From an analysis of their own measurements ofb(y) and bin the Pacific and Indian Oceans and in the Black Sea, Kopelevich and Burenkov (1971) concluded that the error in estimating b from single-angle measurements of b(y) is lower for angles less than 15: 4 was considered suitable. A linear regression of the type

4.2 Measurement of scattering 109

logb¼c1logðÞ þc2 ð4:3Þ wherec1andc2are constants, was found to give more accurate values for b than a simple proportionality relation such as b¼constantb(y). On the basis both of Mie scattering calculations, and analysis of literature data on volume scattering functions for ocean waters, Oishi (1990) con-cluded that there is an approximately constant ratio between the back-scattering coefficient and the volume back-scattering function at 120, so that bbcan be calculated from a scattering measurement at 120, using the relationship

bb7 ð120Þ ð4:4Þ

As a function of the volume scattering function, the backscattering coef-ficient can be expressed (}1.4) in the form

bb ¼ 2 ð

=2ðÞsind which for any given value ofycan be replaced with

bb¼2 ðÞðÞ ð4:5Þ

where w(y) is a dimensionless constant, sometimes referred to as the conversion factor, which makes this equality true at angley.⁸⁴⁹Equation 4.5 can be regarded as a more general form of eqn 4.4, and so for backscattering meters using the Oishi principle (which in fact works quite well over a wide angular range) but operating at an angle other than 120, w(y) is determined empirically.Equation 4.4corresponds tow(120)1.1.

Single-angle estimates of bb are often carried out at 140. For coastal shelf waters off New Jersey (USA), Boss and Pegau (2001) found an average value of 1.18 for w(140); for Black Sea coastal waters Chami et al. (2006a) obtained an average value of 1.21.

As can readily be verified,eqn 4.4works very well for the two volume scattering functions listed in Table 4.2. On the basis of Mie theory calculations, Oishi concluded that this relationship should be unaffected by wavelength. Field measurements of b(y) by Chami et al. (2006a) confirm that this is the case in coastal waters of the Black Sea.

The WET Labs ECO BB scattering meter makes use of this principle to measure bb. The light from an LED, modulated at 1 khz, is emitted into the water and scattered light is received by a detector positioned where the acceptance angle forms a 117 intersection with the source beam.¹¹⁷⁹ Versions of the instrument operating at 470, 532 or 660 nm

are available; another version incorporates all three wavelengths. The HOBI Labs HydroScat-2 Backscattering Sensor^{849, 605}also uses a modu-lated LED as a light source and measures light back-scattered at an angle centred on 140. It operates at two wavelengths, 420 and 700 nm: versions with other pairs of wavelengths are available. The HydroScat-4 measures backscattering at four wavelengths.⁶⁰⁴ These instruments also measure chlorophyll fluorescence.

If, for a given water, the beam attenuation coefficient and the absorp-tion coefficient can both be measured, then the scattering coefficient can be obtained by difference (b¼c–a). This indirect approach is in principle less accurate since the estimate ofb must combine the separate errors in the determination ofc and a. To obtain b by a direct measurement of scattered light is preferable. Nevertheless, when both c and a data are available from, for example, an instrument such as the ac-9, then it is worth while collecting values ofbas well.

Turbidimeters

A specialized and simplified laboratory form of the fixed-angle scattering meter is the nephelometric turbidimeter. The word ‘turbidity’ is used in a general sense to indicate the extent to which a liquid lacks clarity, i.e.

scatters light as perceived by the human eye. In the most common type of instrument, a beam of light is directed along the axis of a cylindrical glass cell containing the liquid sample under study. Light scattered from the beam within a rather broad angle centred on 90 is measured by a photomultiplier located at one side of the cell (Fig. 4.7). The ‘turbidity’

(Tn) of the sample in nephelometric turbidity units (NTU) is measured relative to that of an artificial standard with reproducible light-scattering properties. The standard can be a suspension of latex particles, or of the polymer formazin, made up in a prescribed manner. Turbidimeters, as at present constituted, do not attempt to provide a direct estimate of any fundamental scattering property of the water and the nephelometric turbidity units are essentially arbitrary in nature. Nevertheless, the tur-bidity measured in this way should be directly related to the average volume scattering function over an angular range centred on 90, and so for waters of given optical type (e.g. waters with moderate to high turbidity due to inorganic particles) should bear an approximately linear relation to the scattering coefficient. Since turbidimetric measurements are so easily made, and since there already exist a large amount of turbidimetric data on inland water bodies, comparative studies on a

4.2 Measurement of scattering 111

variety of natural waters to determine the empirical relation between nephelometric turbidity and scattering coefficient would be valuable.

Some existing indirect measurements (see below) suggest that for turbid waters, by a convenient coincidence, b/Tnis about 1 m^lNTU^l. Turbi-dimeters are, however, not well suited for characterizing waters with very low scattering values, such as the clear oceanic types.

Indirect estimation of scattering properties

While few aquatic laboratories carry out measurements of the funda-mental scattering properties of natural waters, many routinely measure underwater irradiance (}5.1). Since irradiance at any depth is in part determined by the scattering properties of the water, there is the

Fig. 4.7 Schematic diagram of optical system of nephelometric turbidimeter.

possibility that information on the scattering properties might be derived from the measured irradiance values. For water with a speci-fied volume scattering function and with incident light at a given angle, then at any given optical depth (see}1.6for definition), the irradiance reflectance,R, and the average cosine,, of the light are functions only of the ratio, b/a, of scattering coefficient to absorption coefficient.

Conversely, if the value of reflectance at a certain optical depth is given, then the values ofandb/aare fixed, and in principle determin-able. Kirk (1981a, b) used Monte Carlo numerical modelling (}}5.5 and 6.7) to determine the relations between b/a for the medium and R and at a fixed optical depth, for water with a normalized volume scattering function identical to that determined by Petzold (1972) for the turbid water of San Diego harbour. It was considered that these relations would be approximately valid for most natural waters of mod-erate to high turbidity. Using the computer-derived curves it is possible, given a measured value of irradiance reflectance at a specified optical depth, such as z¼2.3 (irradiance reduced to 10% of the subsurface value), to read off the corresponding values of andb/a. The irradiance values are used to estimateKE, the vertical attenuation coefficient fornet downward irradiance (}1.3), and the value of a is calculated from the relationa¼KE (}1.7). Knowinga andb/a, the value ofb may then be obtained.

As a test of the validity of this procedure, Weidemann and Bannister (1986) compared, for Irondequoit Bay, L. Ontario, estimates ofaderived from irradiance measurements as indicated above, with estimates obtained by summing the measured absorption coefficients due to gilvin, particulate matter and water: agreement was good. Furthermore, esti-mates ofread off from the¼fðRÞcurve agreed with those obtained from the measured ratio of net downward, to scalar, irradiance (eqn 1.15):

a similar finding was made by Oliver (1990) for a range of river and lake waters in the Murray Darling basin, Australia.

Values of scattering coefficient obtained in this way by Kirk (1981b) for various bodies in Southeastern Australia were found to correlate very closely with the values of nephelometric turbidity, (Tn), a parameter that (see above) we might reasonably expect to be linearly related to the scattering coefficient: the average ratio of b to Tn

was 0.92 m^lNTU^l. Using literature data for Lake Pend Oreille in Idaho, USA,¹⁰⁷⁶ the method was found to give a value of b differing by only 5% from that derived from the beam attenuation and absorp-tion coefficients.

4.2 Measurement of scattering 113

With the help of a separately derived expression (eqn 6.11) forKas a function ofa, band m0(the cosine of the refracted solar beam beneath

With the help of a separately derived expression (eqn 6.11) forKas a function ofa, band m0(the cosine of the refracted solar beam beneath