Skip to main content
. Author manuscript; available in PMC: 2008 Feb 1.
Published in final edited form as: J Magn Reson. 2006 Oct 27;184(2):207–221. doi: 10.1016/j.jmr.2006.10.002

Table 1.

Parameters of Sampling Patterns. All distances are relative to the spectral width w. A dwell time of Δr= 1/(21/2w) is assumed. The LCRS and RLCRS methods and the parameter α are defined in the text in Section 2.8. For each sampling pattern, Nj indicates the number of sampling points for ring j, which is determined according to the sampling method, while Rj indicates the corresponding artifact-free radius of the point response for that ring. The total number of points for each sampling pattern T = Σ (Nj/2 + 1). The artifact-free radius for the point response of the full sampling pattern is Rcz = min Rj.

Radial Sampling LCRS α = π/2 LCRS α = 1.111 RLCRS α = 1.000 RLCRS α = 0.200
j Nj Rj Nj Rj Nj Rj Nj Rj Nj Rj
1 36 16.21w 4 1.80 w 4 1.80 w 2 0.90 w 2 0.90 w
2 36 8.10 w 8 1.80 w 6 1.35 w 4 0.90 w 2 0.45 w
3 36 5.40 w 10 1.50 w 8 1.20 w 6 0.90 w 2 0.30 w
4 36 4.05 w 14 1.58 w 10 1.13 w 8 0.90 w 2 0.23 w
5 36 3.24 w 16 1.44 w 12 1.08 w 10 0.90 w 2 0.18 w
6 36 2.70 w 20 1.50 w 14 1.05 w 12 0.90 w 4 0.30 w
7 36 2.32 w 22 1.41 w 16 1.03 w 14 0.90 w 4 0.26 w
8 36 2.03 w 26 1.46 w 18 1.01 w 16 0.90 w 4 0.23 w
9 36 1.80 w 30 1.50 w 20 1.00 w 18 0.90 w 4 0.20 w
10 36 1.62 w 32 1.44 w 24 1.08 w 20 0.90 w 4 0.18 w
11 36 1.47 w 36 1.47 w 26 1.06 w 22 0.90 w 6 0.25 w
12 36 1.35 w 38 1.43 w 28 1.05 w 24 0.90 w 6 0.23 w
13 36 1.25 w 42 1.45 w 30 1.04 w 26 0.90 w 6 0.21 w
14 36 1.16 w 44 1.41 w 32 1.03 w 28 0.90 w 6 0.19 w
15 36 1.08 w 48 1.44 w 34 1.02 w 30 0.90 w 6 0.18 w
16 36 1.01 w 52 1.46 w 36 1.01 w 32 0.90 w 8 0.23 w
17 36 0.95 w 54 1.43 w 38 1.01 w 34 0.90 w 8 0.21 w
18 36 0.90 w 58 1.45 w 40 1.00 w 36 0.90 w 8 0.20 w
19 36 0.85 w 60 1.42 w 44 1.04 w 38 0.90 w 8 0.19 w
20 36 0.81 w 64 1.44 w 46 1.04 w 40 0.90 w 8 0.18 w
21 36 0.77 w 66 1.41 w 48 1.03 w 42 0.90 w 10 0.21 w
22 36 0.74 w 70 1.43 w 50 1.02 w 44 0.90 w 10 0.20 w
23 36 0.70 w 74 1.45 w 52 1.02 w 46 0.90 w 10 0.20 w
24 36 0.68 w 76 1.43 w 54 1.01 w 48 0.90 w 10 0.19 w
25 36 0.65 w 80 1.44 w 56 1.01 w 50 0.90 w 10 0.18 w
26 36 0.62 w 82 1.42 w 58 1.00 w 52 0.90 w 12 0.21 w
27 36 0.60 w 86 1.43 w 60 1.00 w 54 0.90 w 12 0.20 w
28 36 0.58 w 88 1.41 w 64 1.03 w 56 0.90 w 12 0.19 w
29 36 0.56 w 92 1.43 w 66 1.02 w 58 0.90 w 12 0.19 w
30 36 0.54 w 96 1.44 w 68 1.02 w 60 0.90 w 12 0.18 w
31 36 0.52 w 98 1.42 w 70 1.02 w 62 0.90 w 14 0.20 w
32 36 0.51 w 102 1.43 w 72 1.01 w 64 0.90 w 14 0.20 w
Rcz 0.51 w 1.41 w 1.00 w 0.90 w 0.18 w
T 608 844 602 528 119