# Universal Behavior of the Image Resolution for Different Scanning Trajectories
## 1 Introduction
Thus, understanding every aspect of the scanning pattern within the FOV, including the scanning pattern density, the time spent, the signal-to-noise ratio, and the error in each local region, is absolutely essential. It is crucial to consider the importance of the appropriately quantified pixel size or the empty gap between the pattern and its distribution within the FOV. Here, it is important to distinguish between the ideas of image resolution and spatial resolution. Image resolution is primarily determined by the total number of pixels in an image, which is also defined by the size of each pixel in that image. For instance, a fixed size image with many small pixels rather than a few large pixels will have a high image resolution. Hence, image resolution is inversely proportional to pixel size. The amount of detail and sharpness visible in the image is determined by the image resolution. In contrast, spatial resolution refers to the smallest discernible detail in an image, which establishes the level of detail that an imaging system, such as a camera or sensor, is able to differentiate. Spatial resolution is typically expressed by the smallest resolvable feature size, which can be measured in millimeters, micrometers, or even nanometers. In general, to distinguish fine details in an image, the image resolution must be greater than the spatial resolution (i.e., the size of the pixel must be a few folds smaller than the spatial resolution) [21]. As a result, the main emphasis of this paper is on the image resolution generated by different scanning trajectories and how it is related to the selection of scanning parameters. Any trajectory scanning system has a scanning point that sweeps through the FOV in a particular pattern [6; 22]. The image resolution, scan time, or speed may vary depending on the trajectory selected, which can also affect the quality of the to-be-scanned images [8]. Thus, being able to measure image resolution through the pixel size and understand how it relates to the scanning parameters is crucial, especially for the system operators [23]. The primary objective of this work is to establish a theory for determining the minimal image resolution, or maximum pixel size, using all of the trajectory crossing points (indicated by the blue dots on all scanning patterns shown in Figure 1) throughout the whole FOV. The image resolution and its impact on the quality of the reconstructed image are also evaluated for a variety of trajectories that can be utilized in biomedical imaging. There are various scanning trajectories available these days, which include bidirectional Cartesian (BC), triangular Lissajous (TL), sinusoidal Lissajous (SL), radial Lissajous (RL), unidirectional Cartesian, Cartesian improved, spiral, and radial. This paper will concentrate on the first four scanning trajectories, namely BC, TL, SL, and RL, due to their high scan resolution, fairly regular pattern formation, and ability to generate quality reconstructed images with isotropic resolution [8; 24]. To fulfill the aforementioned goals, the following section will first focus on determining the maximum pixel size for all scanning trajectories for a variety of scanning parameters. The relationship between pixel size and scanning parameters will then be established. The effect of scanning parameters on pixel coverage will be investigated next. Finally, the effectiveness and accuracy of image reconstruction for all trajectories will be assessed and compared.