It is indeed true that 90°and 180° pulses do not have to be used to generate a spin echo. In fact, pulses with any flip angles can be used. In his original description of spin echoes, Hahn employed a 90°-90° pair of RF-pulses. When pulses other than 90°-180° are used, the resultant spin echo is sometimes differentiated by calling it a

The reason 90°-180° pairs are most commonly used is that this combination produces the maximum possible echo signal. The maximum SE intensity of a 90°-90° pair is only half as large as that produced by a 90°-180° pair. In general, if the first RF-pulse has flip angle α1 and the second has flip angle α2, the maximum signal intensity of the Hahn echo will be smaller than the conventional (90°-180°) echo by a factor of (sin α1)•(sin² α2/2).

**(though many authors consider***Hahn echo**all*echoes to be Hahn echoes).The reason 90°-180° pairs are most commonly used is that this combination produces the maximum possible echo signal. The maximum SE intensity of a 90°-90° pair is only half as large as that produced by a 90°-180° pair. In general, if the first RF-pulse has flip angle α1 and the second has flip angle α2, the maximum signal intensity of the Hahn echo will be smaller than the conventional (90°-180°) echo by a factor of (sin α1)•(sin² α2/2).

The diagram to the below provides an introduction as to some of the interesting phenomena occurring during a 90°-90°-echo sequence.

The first two drawings in the left column show the expected effect of the initial 90°-pulse and T2*-dephasing. For illustrative purposes we have selected four spins (

The third drawing (bottom left) shows the effect of the second 90°-pulse. We will first focus our attention on spins

The first two drawings in the left column show the expected effect of the initial 90°-pulse and T2*-dephasing. For illustrative purposes we have selected four spins (

**,***a***,***b***, and***c***) that have slightly dephased due to local field inhomogeneities. Spins***d**a*and**are in local fields lower than***c***Bo**, are precessing slightly slower than the Larmor frequency, and are losing phase. Spins**and***b**are in local fields higher than***d****Bo**, precessing faster, and gaining phase. Moreover, we have picked the spin pairs (**) and (***a-b***) to have local field offsets of the same magnitude but opposite polarities, so they gain or lose phase relative to their partner at the same relative rates.***c-d*The third drawing (bottom left) shows the effect of the second 90°-pulse. We will first focus our attention on spins

**and***a***which, by chance, have just reached the −***b**x*and +*x*axes at the time of the second 90°-pulse. By virtue of their unique positions along the ±*x*axes, these spins will not be affected by the second 90°-pulse. They will continue precessing in the transverse plane and at the expected time (TE = 2 x the interpulse delay) will completely rephase and form a tiny echo along the −*y axis.*But what about spins

After the second 90°-pulse, spins

At the time of the second 90°-pulse the

**and***c***that were lagging***d***and***a***and didn't make it all the way to the ±***b**x*axes at the time of the second 90°-pulse? In fact, nearly all of the spins in the sample will be more like**and***c***(rather than the special case of***d***and***a***lying along the***b**x*-axes).After the second 90°-pulse, spins

**and***c***now lie in the vertical (***d**xz*-) plane. Each can be considered to have independent vector components along the*x*- and*z*-axes respectively that will be denoted by*, and***cx**,**cz**,**dx***. Note that each component will be smaller than***dz****and***c***though their vector sum will be of the same magnitude.***d*At the time of the second 90°-pulse the

*x*-components (**and***cx***) are aligned along the ±***dx**x*axes, just like**and***a***Over time***b.***and***cx***will continue to precess in the horizontal (***dx**xy*-) plane and eventually rephase. But because they are precessing more slowly than**and***a***this rephasing will occur at a time later than the time when***b***and***a**b*rephase. The magnitude of the**"mini-echo" will also be smaller than the***cx-dx***mini-echo, because***a-b***and***cx***are smaller than***dx***and***a***.***b*Because most paired spins (like

**and***c***) are precesing in planes***d**parallel*to the main (xy-plane) after the second 90°-pulse and come back into phase at sligtly different times depending on their phase shifts, Hahn referred to this refocusing pattern as the**.***"eight-ball" echo*Finally, whatever happened to the z-components (

*and***cz****)? Because, by definition, these are perfectly aligned with the z-axis (and***dz***Bo**field) they do not precess but remain locked in their vertical positions and are considered "stored". If a third RF-pulse were applied,*and***cz****would have components tipped back into the transverse plane where they would again precess, rephase, and generate an echo. This is the origin of the***dz***discussed in the next Q&A.***stimulated echo (STE)*### Advanced Discussion (show/hide)»

Although I have stated a Hahn echo can be produced by any two pulses for simplicity of explanation, this is obviously not necessarily the case, in that the first pulse cannot be a multiple of 180 degrees.

**References**

Hahn EL. Spin echoes. Phys Rev 1950;80:580-594. (The original duly famous paper where Hahn describes spin echoes).

Hennig J. Echoes — how to generate, recognize, use or avoid them in MR-imaging sequences. Part I: Fundamental and not so fundamental properties of spin echoes. Concepts Magn Reson 1991; 3:125-143.

Scheffler K. spinZoo website. (A great site from the University of Tübingen containing animations of spins subjected to various RF-pulse combinations with some basic discussion about how they form.)