Biplanar Shim Coil Design for 1.5 T Permanent Magnet of In Vivo Animal MRI

This paper presents an approach of designing biplanar shim coils for a 1.5 T permanent magnet of in vivo animal MRI. The 1.5 T permanent magnet used in the system has two confronting circular poles, the diameter of which is only 200 mm. Active shimming method is applied to improve the magnetic field generated by the magnet. A series of biplanar shim coils are designed which degenerate magnetic field in the form of certain spherical harmonic terms. In this approach, to restrict the current distribution on the coil plane within a finite radius, the current density is described by a summation of trigonometric functions which are similar to the Fourier series. The undetermined coefficients of these trigonometric functions can be obtained through a regularization approach based on the target-field method. Then the current density distribution is transformed to the winding pattern of the coils using the stream function method. The magnetic fields generated by the shim coils are verified via Biot-Savart law which shows that this approach of designing shim coils is practical.