Recognition and measurements of nanoparticles in TEM / STEM images by fitting the model grayscale distribution to the real one: new approach for automated statistical analysis

Abstract

The main challenge to manufacture nanoparticles for applications in catalysis, medicine and pharmaceuticals is a mass production of stable nanoparticles with a narrow size distribution to target and control specific effects. Therefore reliable and fast statistical analysis of (nano)particles is of great interest especially for the particle size less than 10 nm due to strong chemical and biological activity associated with high penetrating capabilities through cell membranes. We would like to see these particles, to know their structure and composition, and to measure sizes. The intelligent, fast and reliable program can be a very useful tool for image analysis of “small” nanoparticles in TEM/STEM images. In our work, we show that fitting of the calculated grayscale distribution to the real distribution in (S)TEM images is able to provide the maximum accuracy in measurements of the particle diameters in opposite to algorithms based on image binarization. We apply such fitting to the truth in the vicinity of a nanoparticle image revealing the mass‐thickness, diffraction, and Z‐contrast. In order to describe the dependence of grayscale from thickness of nanoparticles the polynomial g(t) = g 0 +g 1 t+g 2 t 2 +… with sufficiently high power (≥2) and uncertain coefficients was chosen. The high‐degree polynomial is required to take into account the possible non‐monotonic dependence of the grayscale from particle thickness due to the presence of diffraction contrast (in opposite to pure mass‐thickness contrast). Monotonic dependence of the grayscales from specimen thickness is the characteristic of mass‐thickness contrast of particles (amorphous or crystalline particles positioned out of Bragg conditions) in TEM images and Z‐contrast in STEM images. The transfer function of CCD cameras determined the grayscale in the given point of the micrograph through the intensity of the incident wave has also monotonic character. Only the presence of diffraction contrast in the images breaks the monotonic dependence. Thickness of the spherical nanoparticle in a point having (x,y)‐coordinates can be expressed as t(x,y)=((d/2) 2 ‐(x‐x c ) 2 ‐(y‐y c ) 2 )^(1/2). During fitting, the uncertain coefficients g i , coordinates of the particle center (x c ,y c ), and the particle diameter d are computing. Our algorithm for particle recognition and measuring sizes is proposed and realized in the program ANN (Automatic Nanoparticle Numerator). Our algorithm for particle recognition and measuring sizes out of thresholding approach is proposed and realized in the program ANN (Automatic Nanoparticle Numerator). The comparative study of distributions of silver nanoparticle synthesized in different polymer‐water solutions determined manually (about 1000 particles), using ImageJ and ANN was performed (Fig.1 and Fig.2). It shoved a good agreement between results obtained manually and with ANN.