Analysis on Spatial Spectrum of Magnetic Flux Leakage Using Fourier Transform

As an efficient non-destructive testing method, magnetic flux leakage (MFL) has been widely used for damage detection in ferromagnetic materials. The magnetic dipole theory is a traditional method to calculate the magnetic leakage field. In this paper, the magnetic leakage field functions of a slot in a 2-D infinity plate are obtained using the magnetic dipole theory. Equations of the magnetic leakage field are converted into the convolution of two other functions. Spatial spectral equations of the MFL are developed according to the convolution theorem using the Fourier transform (FT) method. The results are analytical functions different from other numerical methods, such as the discrete FT and fast FT methods, and the calculation speed is fast. The results show that the $y$ -component of the magnetic leakage field has 90° phase shift with the $x$ -component. This result has clear physical significance compared with the traditional MFL equations using the magnetic dipole theory. Different spatial spectral curves for different defects are presented in this paper. Since there is a sinc function for the width value in the equation, the width value can be deduced from the first zero-crossing point in the spatial spectrum curves. A new method is proposed to determine the width value using the relationship $w =1/f_{s}$ , where $f_{s}$ is the first zero cross point. Two specimens with different cracks are investigated, and the experimental results show this method can be used as an inverse MFL data interpretation technique.