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one wavelength will not fit at another wavelength. In addition, the sizes of the spheres will be much smaller than the characteristic lengths of the actual particles.
Holland and Gagne (1970) measured the scattering matrix for a polydisperse system of silica particles smaller than 1 p.m., m = 1.55. Their data for the matrix elements S11 and S22 at 546 mm are reproduced in figure 3 (Holland, 1969). The solid curve was computed from Mie theory for the observed size distribution. Mie theory fits the data fairly well at small scattering angles, but it predicts a steep rise toward the backscatter direction that is absent in the laboratory data. Data for S12 = S21 indicate that the polarization is positive at 03. 160°, whereas Mie theory predicts negative polarization. There is, however, an indication that the polarization changes sign near 160° at 546 nm and near 150° at 486 mm. The position of the neutral point varies with wavelength in the opposite direction from the shift observed by Weinberg and Mann in the zodiacal light.
Figure 3.-Variation of matrix elements S11(0) and S22(0) with scattering angle 9. Solid line is theoretical curve computed from Mie theory (Holland, 1969, fig. 6).
m = refractive index; Xo = size distribution parameter.
The scattering properties of nonspherical particles also can be studied by microwave scattering from scaled particle models (Greenberg, Pedersen, and Pedersen, 1961). Greenberg, Wang, and Bangs (1971) have found that the measured extinction for particle models with roughened surfaces differs widely from the extinction by smooth spheres. Microwave scattering data over the whole range of scattering angles for many values of a/\ are needed before we can conclude whether the peculiar scattering patterns observed for individual particles average out to resemble scattering by spheres over an extended size distribution.
Scattering functions can be computed analytically for the case of long cylinders (Kerker, 1969; Lind, 1966). Detailed comparison of the scattering functions for spheres and cylinders, and possibly ellipsoids, can provide useful information on the effects of particle shape. For example, there is a significant change in the polarization, even for an extended size distribution, when the angle between the cylinder axis and the incident radiation is varied. However, the polarization by randomly oriented cylinders with n(a) or exp [-5(a|0.5)*] was quite similar to that for spheres with the same size distribution (Hanner, 1969).
The limitations of Mie theory and the importance of computing zodiacal light models for nonspherical particles have been emphasized by Greenberg (1970). Richter (1966) has discussed experimental phase functions and polarization curves for irregular particles over the size range 107° to 10 cm.
The zodiacal light data sample the average properties of the interplanetary dust particles over a large volume of space. Intensity and polarization measurements in the ultraviolet and infrared, together with the wavelength dependence of polarization throughout the visible spectral region, will provide information on the physical nature and size distribution of the dust particles. However, we cannot expect to obtain a complete model of the interplanetary dust from zodiacal light observations alone. The data will be most valuable when combined with the results of particle collections and other methods used to study in detail the physical properties of individual particles.
Giese and Dziembowski (1969) and Giese (1970) have discussed the value of zodiacal light observations from space probes in determining the spatial distribution of the interplanetary dust. Zodiacal light experiments will be included on both the Helios inner solar system probes and the Pioneer F and G asteroid-Jupiter probes.
It is a pleasure to thank Dr. J. L. Weinberg for his interest and his helpful discussions. This research has received support from NSF grant GA-12400 and NASA grant NGR 33-017011.
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BANDERMANN: Purely photometric, spectroscopic, polarimetric observations of the zodiacal light will not lead to definite answers about the physical properties of the particles. One must try to consider all the different types of evidences (zodiacal light as well as impact counts, deep sea sediments, etc.) and then look for collaboration toward an answer.