Coaxial differential dynamic microscopy for measurement of Brownian motion in weak optical field

Weak optical fields cause less damage to active cells and are easier to realize than traditional and tightly focused optical fields. While these fields are promising for biomedical science and particle manipulation applications, they lack a method for precise particle diffusion measurement because the weak fields cause the small changes in particle motion caused by weak fields. In this paper, we present a coaxial differential dynamic microscopy (CDDM) technique that uses a differential dynamic microscopy system, combined with an adjustable optical field. We use this technique to study Brownian motion of colloidal particles in weak optical fields. CDDM can quantitatively measure both the intensity and the pattern of the weak optical field and the diffusion coefficient of the particles. While the light paths of both the weak optical field and the illumination are coaxially incident on the sample cell, they remain independent. The optical field can be designed to have any pattern and adjusted to any intensity, while the measurements' sample illumination requirements are also satisfied. To verify the accuracy of the technique, we measured particle diffusion in weak Gaussian optical fields of different strengths. The diffusion coefficient was found to decrease with increasing field strength. These experimental results agree well with those results predicted using the Fokker-Planck equation and Euler algorithm simulations. This technique is expected to provide an efficient tool for research into particle manipulation by using weak optical fields, particularly for delicate systems, such as colloidal particles and biological cells.