## 1 Introduction  
Fluorescent magnetic particle inspection (MPI) is one of the most widely used nondestructive testing (NDT) technologies for the detection of surface cracks on ferromagnetic material workpieces, due to its simple operation and high sensitivity [1, 2]. In traditional methods, cracks are inspected manually; hence, the visual limitation of inspectors is the bottleneck for detection efficiency, reliability, and consistency. With the unprecedented applications of industrial cameras and machine learning, the automated fluorescent MPI technology based on machine vision has attracted tremendous attention in comparison to manual fluorescent MPI based on human vision, due to its high efficiency [3, 4]. For example, [PERSON] et al. have improved the crack clarity and recognition rate by optimizing the hardware of fluorescent MPI equipment. However, this process still does not involve automatic detection technology, such as computer image processing algorithms [5], charge-coupled device (CCD) cameras, or optical scanning, or optical scanning together with light reception by a photomultiplier tube to collect image of the cracks, computer technology to perform image processing, and pattern recognition for crack identification [6]. In addition, [PERSON] et al. proposed an algorithm that uses the fractal dimension of crack recognition to automatically identify specific types of crack defects [7]. Although automatic discrimination systems and related algorithms based on image processing have been continuously proposed, there are still few mature industrial applications [8; 9; 10; 11]. Currently, the development of fluorescent MPI technology is focusing on an automatic inspection system that can record crack images and analyze the images accordingly. However, there are few works regarding the underlying working principle of the automatic inspection system and no theoretical studies on this topic were found. During a cycle of fluorescent MPI, the workpiece is sprayed with magnetic particle suspension and simultaneously energized by a magnetic field. The magnetic field at cracks leaks outside the workpiece surface, thus magnetic particles in the suspension accumulate on the cracks (this phenomenon is displayed as a crack indication under 365 nm UV light). The magnetic particle suspension for fluorescent MPI is a mixture of an aqueous carrier liquid and fluorescent magnetic particles which are evenly suspended in the carrier. The concentration of magnetic particles in the suspension has a direct effect on the results of fluorescent MPI [12]. When the magnetic particle concentration in the suspension and the magnetic field imposed on the workpieces are consistent, the developed crack indications are also consistent [13]. However, in the process of fluorescent MPI, the variation of the magnetic particle concentration is very complicated. The workpiece continuously consumes magnetic particles in the suspension; thus, the magnetic particle concentration in the suspension decreases with the increase of the number of inspected parts. The changing concentration of fluorescent magnetic particles present in the suspension causes crack indications formed by magnetic particles to change continuously, thus it directly affects the reliability, stability, and consistency of the obtained results [14; 15]. Existing crack indications formed by magnetic particles have no quantitative evaluation standards, which is not conducive to the development of automated fluorescent MPI technologies [16; 17]. Furthermore, there is a lack of quantitative studies that investigate the effect of magnetic particle concentration in the suspension on magnetic particle crack imaging. Therefore, in the present study, in order to quantitatively determine the quality of the crack images, a comparison of different parameters of crack indication images was presented and a set of effective quantitative evaluation parameters of crack images, such as indication gray scale value, background gray scale value, and indication/background contrast ratio, was proposed.