To understand fully the underwater light field we need a detailed knowledge of the angular distribution of radiant flux at all depths. Some information on the angular structure of the field can be derived from the measurements of irradiance discussed above. Irradiance reflectance (R = Eu/Ed) is a crude measure of angular structure. More information is contained in the three average cosines: M for the total light field, ~pd for the downwelling stream and Mu for the upwelling stream, all of which can be derived from irradiance and scalar irradiance values
For a complete description, however, we need the value of radiance at all vertical and azimuthal angles, i.e. the radiance distribution. Radiance is a measure of the radiant intensity (per unit projected area) in a specified direction at a particular point in the field, and so should be measured with a meter that can be oriented in that direction and that ideally should have an infinitesimally small acceptance angle. In reality, to ensure that the meter collects enough light to measure with reasonable accuracy, particularly in the dim light fields existing at greater depths, acceptance angles of 4 to 7° may be used. The simplest type of radiance meter is known as a
Gershun tube photometer, after the Russian physicist Gershun, who made notable contributions to our understanding of the structure of light fields in the 1930s. It uses a cylindrical tube to limit the acceptance angle; the photodetector, with a filter in front of it, is at the bottom (Fig. 5.6). To achieve the necessary sensitivity, a photomultiplier would normally be used as the detector.
The most difficult problem encountered in the measurement of underwater radiance is that of accurately controlling the zenith and azimuth angle of the photometer tube: quite complex systems involving built-in compasses, servo mechanisms and propellers to rotate the instrument are required.636,1172,1380 Another problem is that to determine a complete radiance distribution with a radiance meter is likely to take quite a long time, during which the position of the Sun will change. For example, if radiance is measured at intervals of 10° for the zenith angle (0-180°) and 20° for the azimuth angle (0-180° is sufficient, the distribution being symmetrical about the plane of the Sun) then 190 separate values must be recorded. Smith, Austin and Tyler (1970) developed a photographic technique by means of which radiance distribution data can be recorded quickly. Their instrument consists of two cameras placed back to back, each equipped with a 180°-field-of-view lens. One camera photographs the upper and the other photographs the lower hemisphere. By densitometry of the film, the relative radiance values over all zenith and azimuth angles can be determined at whatever degree of resolution is required, at a later time. In a further refinement of the same principle, Voss (1989) developed an electro-optic radiance distribution camera system, in which the radiance distribution is recorded, not on film, but with a 260 x 253 pixel electro-optic charge injection device.
Of particular interest in the context of remote sensing of the ocean is the nadir radiance. This is the upward radiance (Lu) in a small angular interval centred around the vertical, i.e. it is the radiance measured by a radiance meter pointing vertically downward. As noted earlier in the case of irradiance, self-shading by the instrument itself can cause errors. On the basis of Monte Carlo modelling, Gordon and Ding (1992) found that for direct sunlight with the refracted solar beam at a solar zenith angle of 0w, the proportionate error in Lu, defined by r true _ r measured e = L-—u--(5.5)
true Lu is a function of the product of the absorption coefficient (a) and the radius (R) of the instrument in accordance with e « 1 - e-kaR (5.6)
where k = 2/tan 0w. A relationship of the same general form, but with a different k, is obtained for that part of the incident flux contributed by skylight. Field data obtained with radiometers of varying diameter by Zibordi and Ferrari (1995) in the Lago di Varese (Italy) are in good agreement with the Gordon and Ding predictions, and errors can range from a few per cent to several tens of per cent. Aas and Korsb0 (1997) found the relative self-shading error for an instrument radius of 7.5 cm to be in the range 0.04 to 0.18 in average optical conditions in the Oslofjord (Norway).
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