DCIF Room Temp Shim Functions

Shim Function Table:

Shim Function Gradient Order Interaction Order

Z⁰ 1 0 0

Z¹ z 1 0

Z² 2z²-(x²+ y²) 2 1

Z³ z [2z²-3(x²+ y²)] 3 2

Z⁴ 8z² [z²-3(x²+ y²)]+ 3(x²+ y²)² 4 2

Z⁵ 48z³ [z²-5(x²+ y²)]+ 90z(x²+ y²)]² 5 2

X x 1 0

Y y 1 0

ZX zx 2 2

ZY zy 2 2

XY xy 2 1

X²-Y² x²-y² 2 1

Z²X x [4z²- (x²+ y²)] 3 2

Z²Y y [4z²- (x²+ y²)] 3 2

ZXY zxy 3 2

Z(X²-Y²) z (x²- y²) 3 2

X³ x (x²- 3y²) 3 1

Y³ y (3x²- y²) 3 1

Shim	Function	Gradient Order	Interaction Order

Z⁰	1	0	0
Z¹	z	1	0
Z²	2z²-(x²+ y²)	2	1
Z³	z [2z²-3(x²+ y²)]	3	2
Z⁴	8z² [z²-3(x²+ y²)]+ 3(x²+ y²)²	4	2
Z⁵	48z³ [z²-5(x²+ y²)]+ 90z(x²+ y²)]²	5	2
X	x	1	0
Y	y	1	0
ZX	zx	2	2
ZY	zy	2	2
XY	xy	2	1
X²-Y²	x²-y²	2	1
Z²X	x [4z²- (x²+ y²)]	3	2
Z²Y	y [4z²- (x²+ y²)]	3	2
ZXY	zxy	3	2
Z(X²-Y²)	z (x²- y²)	3	2
X³	x (x²- 3y²)	3	1
Y³	y (3x²- y²)	3	1