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. Author manuscript; available in PMC: 2010 Apr 1.
Published in final edited form as: Magn Reson Med. 2009 Apr;61(4):981–988. doi: 10.1002/mrm.21851

Table 2. Phase noise variance and ratio values of balanced encoding strategies versus simple encoding strategies.

Theoretical values Experimental values

σx2
σy2
σz2
σ2¯
Two-point Balanced
σφ2/2
0.02371 0.02371
Simple
2σφ2
0.09018 0.09018
Bal/Sim 25% 26.3% 26.3%

Three-point Balanced
2σφ2/3
0.03325 0.03061 0.03193
Simple
2σφ2
0.09341 0.09196 0.09269
Bal/Sim 33.3% 35.6% 33.3% 34.4%

Four-point Balanced
3σφ2/4
0.03339 0.03692 0.03690 0.03574
Simple
2σφ2
0.09450 0.09502 0.09157 0.09370
Bal/Sim 37.5% 35.3% 38.9% 40.3% 38.1%