Nanoparticles are small particles whose sizes are less than 100？nm. They have many industrial applications due to their unique properties. Their properties are often size-dependent; thus the accurate determination of nanoparticle sizes is important for quality assurance of nanoparticle production processes. A small angle X-ray scattering technique is a promising method used for characterizing nanoparticle sizes. It has distinctive advantages over other techniques such as electron microscope techniques. In this paper, we review the state-of-the-art methods for determining the sizes of nanoparticles with small angle X-ray experiments and discuss the advantages and limitations of the state-of-the-art methods. 1. Introduction Nanoparticles are tiny particles whose sizes are less than 100？nm and have many industrial applications due to their novel physical and chemical properties, nanobiotechnology [1], drug delivery [2, 3], catalysis [4–7], fluorescent biological labels [8], biodetection of pathogens [9], chemical sensors [10], optical/electronic/magnetic devices [11], and medicine [12]. The physical and chemical properties exhibited by nanoparticles are often size-dependent [13–16]. Therefore, by controlling the size of nanoparticles, we should be able to draw the desired properties of the nanoparticles. In order to control the particle sizes, we should be able to accurately quantify the sizes of the nanoparticles produced from a synthesis process of nanoparticles, because we cannot control what we cannot quantify. Therefore by quantifying the sizes of nanoparticles we can control its synthesis process and its production. The accurate size determination becomes even more important on the industry scale, because it helps install quality assurance of nanoparticle production processes [17, 18]. There are several techniques that obtain the size information of nanoparticles, atomic force microscopy (AFM) [19], transmission electron microscopy (TEM) [20], scanning electron microscopy (SEM) [21], differential mobility analysis, dynamic light scattering (DLS) [22], and small angle X-ray scattering (SAXS). Depending on the material to be characterized, each of these techniques has its own peculiar advantages and disadvantages. The SAXS has the advantage over other techniques of being able to analyze a wide variety of sample types, including aerosols, colloidal suspensions, powders, solids, and thin films. Another advantage of the SAXS over the electron microscopy (EM) methods is that the SAXS often requires very little sample preparation time, in contrast to the
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