What is CPMG condition?

The CPMG (Carr-Purcell-Meiboom-Gill) condition is frequently mentioned in spin-echo-related research papers, yet it's rarely explained in detail.

First off,  Carr, Purcell, Meiboom, and Gill are the researchers who contributed to this technique. According to MRI Questions:

In the early SE (spin echo) experiments by Hahn (1850) and Carr and Purcell (1954) , RF pulses were all applied along the same axis (usually x-direction). In practice, this method resulted in measured T2 values that were too short because of (1) cumulative phase errors from repetitive imperfect 180 pulses, and (2) B1 inhomogeneity effects that spread the magnetization out in a plane containing B1 and B0. In 1958 Meiboom and Gill proposed that such pulse-related errors could be reduced if the 180 pulses in a SE train were phase shifted 90 with respect to the initial 90 pulse. In other words, if the 90 pulse were applied along the x-axis, the 180 pulses would be applied alternately along the +-y-axes. This technique, subsequently known by the acronym CPMG...

 

This raises an important question: why does applying both the 90 and 180 RF pulses along the same axis lead to underestimated T2 values?

 

 

The above figure which came from the original paper by Meiboom and Gill, described the behavior of the nuclear polarization without 90 shift of the first 90 pulse. Therefore, we can conclude that:

• the polarization vector at the time of the echos is alternatively in the +y and -y directions.
• If the 180 pulses deviate from the true 180 amplitude, the corresponding error is cumulative, and successive pulses will rotate the polarization vectors more and more out of the xy plane.  

The modification: