Criterion to determine the wave vector range of heterodyne near-field exposure time-dependent spectrum

Recently, image methods for measuring dynamics of nanoparticles have garnered attention; however, the low-speed frame rate of normal image sensors limits their application. Applying a low-speed detector can extract fast dynamic information by the method of an exposure time-dependent spectrum, whereas its accuracy is too sensitive to the wave vector range selection. In this paper, we present a criterion to determine the wave vector range for the image method of heterodyne near-field light scattering, where the hologram of the particles is analyzed to extract the particle dynamics. A normalized instrument factor ratio 𝓇(q) is defined, and the accuracy of results can be guaranteed when the upper limit q_up is selected at the maximum of 𝓇(q_up)=1, and the lower limit q_low is selected according to the optimal goodness of fit R². The experimental results verify the effectiveness of the proposed criterion. Since most image methods for nanoparticle characterizing are related to the wave vector range selection, it is believed that the idea of this criterion can be extended generally.