. 2011 Mar 22;66(3):669–677. doi: 10.1002/mrm.22849

Table 1.

Numerically Derived Settings for Minimal Noise Propagation

N	σ²_ρ1 × A²/ρ₁²/ σ²_S^a	τ_1opt/τ_E	τ_2opt/τ_E	σ²_A × ρ₁²/ σ²_S^a	τ_1Aopt/τ_E	τ_2Aopt/τ_E
2	4.000	0.4142	2.4142	5.6133	0.4903	3.1461
3	2.9313	0.3718	2.2108	2.9886	0.4633	2.7927
		0.3718			0.4633
3	2.9313	0.4520	2.6939
			2.6931
4	2.0000	0.4142	2.4141	2.8067	0.4904	3.1721
		0.4142	2.4141		0.4903	3.1495
4				2.0841	0.4456	2.6310
					0.4456
					0.4456
5	1.6532	0.3898	2.2885	1.6203	0.4323	2.5303
		0.3898	2.2892		0.4323
		0.3898			0.4323
					0.4323
5	1.6532	0.4370	2.5664
		0.4371	2.5656
			2.5633
6	1.3333	0.4142	2.4142	1.8711	0.4903	3.1483
		0.4142	2.4142		0.4905	3.1471
		0.4142	2.4142		0.4904	3.1471
6				1.3360	0.4217	2.4590
					0.4217
					0.4217
					0.42165
					0.42165

Normalized unit-free variances and normalized τ as defined in (16). The left side of the look-up table pertains to noise propagation into the normalized maps of ρ₁ (relaxation), the right side to normalized maps of A (amplitude).

Variation in the last digits is due to the cut-off condition of the algorithm and rounding.

Note that the unit-free normalized variances for the symmetric schemes (boldface) are proportional 1/N, because the dual angle settings are replicated.