OCR Text |
Show The uniformity of the response for different particle trajectories is determined by the uniformity of I" over the measurement volume. (As shown in Figure 2, the measurement volume is elongated in shape because the scattering angle Is near 180°.) Since the intensity of the laser beam, I", is not uniform over its cross section but has a gaussian intensity distribution, S is a function of the particle trajectory through the measurement volume. Thus, a stream of monodisperse particles flowing through the measurement volume would produce a distribution of signal intensities. This distribution is determined both by the laser intensity distribution in the measurement volume, and by the directional trajectories of the particle through the measurement volume. (The distributions of both the integrated signals and the peak signals will be different depending on the angle the trajectory makes with the laser beam.) This nonuniformity of the response is accounted for in the data analysis procedure by the solution of an N x N matrix equation which relates the distribution of peak signal intensities (having N intensity bins) to the distribution of particle sizes (having N size bins). The N x N transformation matrix can be determined either experimentally by using monodisperse particles, or analytically by calculating the beam intensity distribution and the particle trajectory probability distribution for the measurement volume (as was used here). The function in the above equation which relates the scattered signal intensity to the particle size is the differential scattering cross section. The cross section is a function of the diameter and complex refractive index of the particle or droplet, the wavelength and polarization of the incident laser light, and the scattering angle. For our optical setup, the laser wavelength and polarization were fixed, and the complex index of refraction of the sulfuric acid droplets (the particles of major interest) was known. The scattering geometry for the individual measurements was also fixed, although the collection lens accepted light which was scattered over a small range of scattering angles. Thus, the differential scattering cross section for an individual measurement is a function only of the particle diameter (spherical particles have been assumed, which is a good approximation for liquid droplets). A graph of the differential scattering cross section for our measurement is shown in Figure 3. The graph has been 24-7 |