# Particle and Particle Agglomerate Size Monitoring by Scanning Probe Microscope
## 3 Size-Monitoring Method with the Use of the SPM  
The nanoparticle-size monitoring with the use of the SPM can be described as follows. Firstly, a surface area is selected (for example, with the help of a video camera); after that, the selected area is scanned several times at high resolution. Let us consider the case when the size of the studied area exceeds the microscope field; it is rather common considering that the resolution of an optical microscope is 1 \(\upmu\)m and the size of high-resolution scanners is 1-3 \(\upmu\)m. Traditionally, the scanning of surface areas exceeding the field is performed using overlapped scans and a sample displacement. Before the displacement, the probe is taken away from the surface and brought back after the displacement. The scanning process is performed until there are a required number of particles on the acquired images, the sizes of which form the statistics for monitoring. The scans can be uniformly arranged over the specified area with a fixed overlap (uniform scanning, Figure 1a) or along the line with an increased concentration of controlled particles (tracking scan, Figure 1b). For example, when particles are deposited on the HOPG surface, the most probable site of their allocation is the boundaries of terraces. In this case, the tracking scan provides a considerable decrease in the monitoring time. At such scanning, the displacement of scans is performed by a scanner or motorized sample platform. Here it is necessary to consider that the error in the positioning by a motorized platform is significantly bigger than that in the case with a scanner. The acquired scans (images) are stitched into a single image before processing or are processed separately while the repeating results in the overlap regions are excluded. The uniform scanning of a studied area is sufficiently elaborated by the microscope and software manufacturers. In the present study, we turn our attention to tracking scans. Tracking scanning allows to significantly save the time of scanning. The amount of savings provided in [25] amounted to up to 67% of the scanning time [25]. For example, in the case shown in Figure 1, the time savings is 5/9 or 55%. It should be noted that significant time savings are also achieved by automating the pre-processing of images and the selection of the trajectory of the displacement of the field of view, carried out by the experimenter manually. Our approach to particle size monitoring, founded on tracking scan, is based on solving the following tasks:  
1. Particle detection: image segmentation, particle allocation, the determination of the particle sizes and coordinates;
2. Computation of the sample displacement value providing the coordinate coupling of two overlapping images and the continuation of the particle-size data acquisition;
3. Computation of the \"global\" coordinates of the particle centres for excluding repeating measurements in the areas of the image overlapping. To solve the first task, the modern SPM software contains the tools for particles detection and determination of their sizes, or such tools are in specialized software. For example, the NT-MDT microscopes (the software ImageAnalysis) contain a GrainAnalysis function, and in the specialized software MountainsSPIP there is a Grain/Pore Analysis function. The drawback of the above tools is the necessity of manual adjustment. In addition, these tools are based on the standard tools for image binarization and segmentation (Watershed [26], [PERSON]'s method [27]), which decreases the accuracy of the size determination for superimposing particles and particles with different degrees of brightness. The difference in brightness is possible even when particles are deposited from a liquid solution on atomically smooth substrates. This is due to nano- and microparticles that tend to form polydisperse agglomerates and a surface with an irregular relief.