Optimum acquisition times of two spin echoes for MR image synthesis

Spin-echo images can be synthesized at arbitrary values of echo time TEs if two images are acquired at the same repetition time and two different echo times TE1 and TE2. Depending on the value of TEs, the noise in the synthetic images can either be greater or less than the acquisition noise. This note shows that if the time between the acquired echoes TE2 - TE1 is equal to T2, the noise level in the synthetic images is no larger than the acquisition noise for TEs greater than or equal to TE1. This is the lowest possible noise bound for two-echo acquisition. Also, the noise bound for images synthesized with O less than or equal to TEs less than or equal to TE1 is minimized by making TE1 as short as possible.