TABLE I.

Performance summary of different scan profiles, optimized by solving (9) subject to scan time constraint T_R,max = 41.9ms. The first column defines each profile. The next four columns describe P^*. The latter three pairs of columns show how worst-case σ̃_T1 σ̃_T2, and Ψ̃ values degrade from tight to broad ranges. Flip angles are in degrees; all other values are in milliseconds.

Scan	${\widehat{\alpha }}_0^{\text{spgr}}$	${\widehat{\alpha }}_0^{\text{dess}}$	${\widehat{T}}_R^{\text{spgr}}$	${\widehat{T}}_R^{\text{dees}}$	${\stackrel{\sim }{\sigma }}_{T_1}^{\mathrm{t}}({\mathbf{P}}^{\ast })$	${\stackrel{\sim }{\sigma }}_{T_1}^{\mathrm{b}}({\mathbf{P}}^{\ast })$	${\stackrel{\sim }{\sigma }}_{T_2}^{\mathrm{t}}({\mathbf{P}}^{\ast })$	${\stackrel{\sim }{\sigma }}_{T_2}^{\mathrm{b}}({\mathbf{P}}^{\ast })$	Ψ̃t(P*)	Ψ̃b(P*)
(2, 1)	(15, 5)°	30°	(12.2, 12.2)	17.5	28	154	1.3	9.1	4.0	17.7
(1, 1)	15°	10°	13.9	28.0	27	169	2.8	8.8	4.9	17.9
(0, 2)	–	(35, 10)°	–	(24.4, 17.5)	21	113	1.5	6.0	3.5	12.2