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Multiple Scattering Measurements as a Function of Wavelength by Use of a Dye Laser Ariel Cohen Department of Atmospheric Sciences, Hebrew University, Jerusalem, Israel. Received 14 June 1974. The multiple scattering effects on laser pulses transmit- ted through and scattered by clouds and aerosol layers have been calculated and discussed by many authors. 1-4 Special consideration has been given to the case of double scattering and its effect on lidar returns. 5-6 In contrast to the body of literature on the theory of multiple scattering, few experiments have been conducted under controlled, well-defined conditions. This is espe- cially true for the scattering properties at a given scattering angle as a function of the wavelength. Recently, Querfeld et al. 7 presented scattering measure- ments in two wavelengths and four scattering angles, but no experimental work is known to the author on multiple scattering properties for a continuous range of wavelength or a continuously varying size parameter [a = (27πτ)/λ], in analogy to the well-known Mie scattering curves for single scattering. 8 In this work we present the results of the lab- oratory measurements of multiple scattering as a function of wavelength for various optical depths (measured sepa- rately at one wavelength). The main components of the experimental setup are de- scribed elsewhere. 9 The following modifications were in- troduced: (1) A polarizer was added to the dye laser cavity and a highly polarized output beam was achieved. The rotation of the polarizer enabled measurements of each of the first two Stokes parameters of the scattered beam to be made separately. (2) The wavelength ranges in these measurements were in the green (5100 Å ≤ λ ≤ 5600 A) and in the red (5900 A ≤ λ ≤ 6450 Å). (3) The scattering cell was a rectangular cell having the dimensions: 3.9 cm X 1.9 cm. (4) Six samples of various concentrations of monodis- persed particles were prepared. Their optical depths (τ) measured for λ = 6135 A can be derived from Fig. 1. As can be seen, the ratios are approximately 1:2:4:8:16:32. Note that the values of exp (— τ) are plotted. The output of the laser was directed through a diverging lens and a beam splitter into the glass cell containing the 2.956-μm latex spheres. Light scattered from the cell was detected by a RCA 1P28 photomultiplier. The light re- moved by the beam splitter was directed to a second RCA 1P28 photomultiplier to provide a reference signal. The outputs of both photomultipliers were sampled at the peak of the laser pulse, then integrated, and finally directed to an analog divider, where the signal from the sample cell was divided by the reference signal— thus removing effects of variations in laser output power and spectral response of the photomultipliers. The concentrations of samples 5 and 6 were chosen to produce single scattering alone. This was proven by the similarity of the curves obtained for the two concentra- tions. Thus, Fig. 2 (sample 5) represents the Mie single scattering curve at σ = 90° ±0.3° for Dow latex spheres of radius r = 2.956 μm and 5900 Å ≤ λ ≤ 6450 Å. (See Ref. 9.) As the optical depth increased, the multiple scattering processes affected the scattering curves (see Fig. 2, samples 4-1), the main characteristics of which can be summarized as follows: (1) The maxima and minima are gradually smoothed out (Fig. 2 sample 1), an effect that is more pronounced for the minima (Fig. 2, sample 2). (2) Within a range of τ values, the multiple scattering values can be found by interpolation. This last result is valuable for the determination of the multiple scattering effect for an arbitrary optical depth. Fig. 1. Optical depth measurements for the samples 1-6. The samples are formed by varying the concentration of Dow latex spheres (r = 2.956 μm). The measurements were taken at λ = const = 6135 A. The pairs of plotted lines give the ratios of the laser light intensities after passing through the samples arid before reaching them. Fig. 2. Scattering curves as a function of wavelength, showing the effect of decreasing multiple scatter. The vertical short lines ap- pearing on the curves are calibration points, the values of which are as follows (-2 A): 210 = 5928 A, 200 = 5988 A, 190 = 6047 A, 180 = 6107 A, 170 = 6170 A, 160 = 6229 A, 150 = 6287 A, 140 = 6345 A, and 130 = 6403 A. Sample 1 refers to the highest concen- tration decreases from sarhples 1-5. 268 APPLIED OPTICS / Vol. 14, No. 2 / February 1975
