Patent ID: 7193417

Claim:
A bi-planar coil assembly for producing a magnetic field which comprises one or more specified spherical harmonics in a specified volume, said coil assembly comprising: (I) a first coil assembly, said assembly comprising one or more windings that (i) define a first plane and (ii) have an outer perimeter in said first plane, said outer perimeter defining a first rectangle having four sides each of which is tangent to the outer perimeter, said first rectangle having (a) the smallest area A of any rectangle which encloses the one or more windings and (b) two diagonals which intersect at a centroid (the centroid of the first rectangle); and (II) a second coil assembly, said assembly comprising one or more windings that (i) define a second plane and (ii) have an outer perimeter in said second plane, said outer perimeter defining a second rectangle having four sides each of which is tangent to the outer perimeter, said second rectangle having (a) the smallest area of any rectangle which encloses the one or more windings and (b) two diagonals which intersect at a centroid (the centroid of the second rectangle); wherein: (1) the first and second planes are parallel and spaced from one another; (2) a line through the centroids of the first and second rectangles defines an x-axis of an x,y,z-coordinate system, the origin of which lies at a point on said x-axis that is equidistant from the first and second planes; (3) the bi-planar coil assembly produces a magnetic field, the x-component of which, in general form, can be written as: B ⁡ ( r , θ , ϕ ) = ∑ n = 0 ∞ ⁢ ⁢ ∑ m = 0 m = n ⁢ ⁢ r n ⁡ [ A n ⁢ ⁢ m ⁢ cos ⁡ ( m ⁢ ⁢ ϕ ) + B n ⁢ ⁢ m ⁢ sin ⁡ ( m ⁢ ⁢ ϕ ) ] ⁢ P n ⁢ ⁢ m ⁡ ( cos ⁢ ⁢ θ ) where A nm and B nm are the amplitudes of spherical harmonics, P nm (cos θ) are associated Legendre polynomials, n is the order and m the degree of the polynomial, and r,θ, and φ are polar co-ordinates of a polar coordinate system that has an origin that (a) lies in the y-z plane of the x,y,z-coordinate system and (b) is offset from the origin of the x,y,z-coordinate system; (4) the specified volume lies between the first and second planes and has a center that lies at the origin of the polar coordinate system; and (5) at least one of the one or more specified spherical harmonics has a degree m′ and an order n′ which satisfy the relationships: (i) m′≧0, and (ii) n′=0 or n′≧2.