## Abstract

We describe a method for quickly and easily measuring the size of small particles in suspensions. This method uses a self-mixing laser Doppler measurement with a laser-diode-pumped, thin-slice LiNdP_{4}O_{12} laser with extremely high optical sensitivity. The average size of the particles in Brownian motion is determined by a Lorentz fitting of the measured power spectrum of the modulated self-mixing laser light resulting from the motion. The dependence of the measured power spectra on particle size and concentration was quantitatively identified from the results of a systematic investigation of small polystyrene latex particles with different diameters and concentrations. The sizes and ratios of particles with different diameters mixed in water were accurately measured. An application of this self-mixing laser method for estimation of the average size of plankton in seawater showed that it is a practical method for characterizing biological species.

© 2006 Optical Society of America

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### Equations (9)

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(1)
$$I\left(k,\omega \right)=A\frac{\Gamma}{\left[{\left(\omega -2\pi {f}_{\mathrm{AOM}}\right)}^{2}+{\Gamma}^{2}\right]},$$
(2)
$$\Gamma ={k}^{2}D,\text{}$$
(3)
$$D=\frac{{k}_{B}T}{3\mathrm{\pi \eta d}},$$
(4)
$$\text{k}\left(\theta \right)=\left(\frac{4\mathrm{\pi n}}{\lambda}\right)\mathrm{sin}\left(\frac{\theta}{2}\right),$$
(5)
$$I\left(\theta \right)\propto {V}^{2}\mathrm{NP}\left(\theta \right),$$
(6)
$$P\left(\theta \right)={\mid \frac{3\left(\mathrm{sin}x-x\mathrm{cos}x\right)}{{x}^{2}}\mid}^{2},$$
(7)
$$x=\frac{d}{2}\left(\frac{4\mathrm{\pi n}}{\lambda}\right)\mathrm{sin}\left(\frac{\theta}{2}\right)=\frac{\mathrm{dk}\left(\theta \right)}{2},$$
(8)
$$I\left(\omega \right)={A}_{1,\mathrm{mix}}\frac{{\Gamma}_{1,\mathrm{mix}}}{\left[{\left(\omega -2\pi {f}_{\mathrm{AOM}}\right)}^{2}+{{\Gamma}_{1,\mathrm{mix}}}^{2}\right]}+{A}_{2,\mathrm{mix}}\frac{{\Gamma}_{2,\mathrm{mix}}}{\left[{\left(\omega -2\pi {f}_{\mathrm{AOM}}\right)}^{2}+{{\Gamma}_{2,\mathrm{mix}}}^{2}\right]},$$
(9)
$${N}_{i,\mathrm{mix}}=\frac{{N}_{i,\mathrm{sin}\mathrm{gle}}{A}_{i,\mathrm{mix}}}{{A}_{i,\mathrm{sin}\mathrm{gle}}},$$