We have shown that the three dimensional read head field from a perpendicular recording medium can be calculated by using Fourier components of the field[1]. According to the method the magnetic potential components Φ can be obtained from the medium charge after spacing loss correction σ{sub}0 and the head characteristic matrix K by using the equation Φ≈K{sup}(-1)σ{sub}0, or eq. (1) in Fig. 1, where Φ{sub}n (k{sub}z) is the component of Φ corresponding to base function sin(nπx/G{sub}s)exp(ik{sub}xx). The components of the matrix K can be calculated with using a numerical integration. Aharoni[2] pointed out that certain numerical integration encountered in two dimensional field calculations with soft under-layer[3,4] can be transformed into an infinite sum thus speeding up the calculation significantly. Here we show that the transformation can be generalized to three dimensional cases, and be applied to the calculation of the components of the head characteristic matrix K. We will also show that the head characteristic matrix can be physically interpreted in terms of self energy of the field.
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