(FISP) A fast imaging sequence, which attempts to combine the signals observed separately in the FADE sequence, generally sensitive about magnetic susceptibility artifacts and imperfections in the gradient waveforms. Confusingly now often used to refer to a refocused FLASH type sequence.
This sequence is very similar to FLASH, except that the spoiler pulse is eliminated. As a result, any transverse magnetization still present at the time of the next RF pulse is incorporated into the steady state. FISP uses a RF pulse that alternates in sign. Because there is still some remaining transverse magnetization at the time of the RF pulse, a RF pulse of a degree flips the spins less than a degree from the longitudinal axis. With small flip angles, very little longitudinal magnetization is lost and the image contrast becomes almost independent of T1. Using a very short TE (with TR 20-50 ms, flip angle 30-45°) eliminates T2* effects, so that the images become proton density weighted. As the flip angle is increased, the contrast becomes increasingly dependent on T1 and T2*. It is in the domain of large flip angles and short TR that FISP exhibits vastly different contrast to FLASH type sequences. Used for T1 orthopedic imaging, 3D MPR, cardiography and angiography.

(SFP or SSFP) Steady state free precession is any field or gradient echo sequence in which a non-zero steady state develops for both components of magnetization (transverse and longitudinal) and also a condition where the TR is shorter than the T1 and T2 times of the tissue. If the RF pulses are close enough together, the MR signal will never completely decay, implying that the spins in the transverse plane never completely dephase. The flip angle and the TR maintain the steady state. The flip angle should be 60-90° if the TR is 100 ms, if the TR is less than 100 ms, then the flip angle for steady state should be 45-60°.
Steady state free precession is also a method of MR excitation in which strings of RF pulses are applied rapidly and repeatedly with interpulse intervals short compared to both T1 and T2. Alternating the phases of the RF pulses by 180° can be useful. The signal reforms as an echo immediately before each RF pulse; immediately after the RF pulse there is additional signal from the FID produced by the pulse.
The strength of the FID will depend on the time between pulses (TR), the tissue and the flip angle of the pulse; the strength of the echo will additionally depend on the T2 of the tissue. With the use of appropriate dephasing gradients, the signal can be observed as a frequency-encoded gradient echo either shortly before the RF pulse or after it; the signal immediately before the RF pulse will be more highly T2 weighted. The signal immediately after the RF pulse (in a rapid series of RF pulses) will depend on T2 as well as T1, unless measures are taken to destroy signal refocusing and prevent the development of steady state free precession.
To avoid setting up a state of SSFP when using rapidly repeated excitation RF pulses, it may be necessary to spoil the phase coherence between excitations, e.g. with varying phase shifts or timing of the exciting RF pulses or varying spoiler gradient pulses between the excitations.
Steady state free precession imaging methods are quite sensitive to the resonant frequency of the material. Fluctuating equilibrium MR (see also FIESTA and DRIVE)and linear combination SSFP actually use this sensitivity for fat suppression. Fat saturated SSFP (FS-SSFP) use a more complex fat suppression scheme than FEMR or LCSSFP, but has a 40% lower scan time.
A new family of steady state free precession sequences use a balanced gradient, a gradient waveform, which will act on any stationary spin on resonance between 2 consecutive RF pulses and return it to the same phase it had before the gradients were applied.
This sequences include, e.g. Balanced Fast Field Echo - bFFE, Balanced Turbo Field Echo - bTFE, Fast Imaging with Steady Precession - TrueFISP and Balanced SARGE - BASG.

See also FIESTA.

(GRASS) This sequence is very similar to FLASH, except that the spoiler pulse is eliminated. As a result, any transverse magnetization still present at the time of the next RF pulse is incorporated into the steady state. GRASS uses a RF pulse that alternates in sign. Because there is still some remaining transverse magnetization at the time of the RF pulse, a RF pulse of a degree flips the spins less than a degree from the longitudinal axis. With small flip angles, very little longitudinal magnetization is lost and the image contrast becomes almost independent of T1. Using a very short TE eliminates T2* effects, so that the images become proton density weighted. As the flip angle is increased, the contrast becomes increasingly dependent on T1 and T2*. It is in the domain of large flip angles and short TR that GRASS exhibits vastly different contrast to FLASH type sequences.

(SFP or SSFP) Steady state free precession is any field or gradient echo sequence where the TR is shorter than the T1 and T2 times of the tissue.
The flip angle and the TR maintain the steady state. The flip angle should be 60-90° if the TR is 100 ms, if the TR is less than 100 ms, than the choice of the flip angle for steady state is 45-60°. The T1 weighting is controlled by TR and flip, the T2 weighting increases with the TE. Common TR is between 20 - 50 msec.

In simple ultrafast GRE imaging, TR and TE are so short, that tissues have a poor imaging signal and - more importantly - poor contrast except when contrast media enhanced (contrast enhanced angiography). Therefore, the magnetization is 'prepared' during the preparation module, most frequently by an initial 180° inversion pulse.
In the pulse sequence timing diagram, the basic ultrafast gradient echo sequence is illustrated. The 180° inversion pulse is executed one time (to the left of the vertical line), the right side represents the data collection period and is often repeated depending on the acquisition parameters.
See also Pulse Sequence Timing Diagram, there you will find a description of the components.
Ultrafast GRE sequences have a short TR,TE, a low flip angle and TR is so short that image acquisition lasts less than 1 second and typically less than 500 ms. Common TR: 3-5 msec, TE: 2 msec, and the flip angle is about 5°. Such sequences are often labeled with the prefix 'Turbo' like TurboFLASH, TurboFFE and TurboGRASS.
This allows one to center the subsequent ultrafast GRE data acquisition around the inversion time TI, where one of the tissues of interest has very little signal as its z-magnetization is passing through zero.
Unlike a standard inversion recovery (IR) sequence, all lines or a substantial segment of k-space image lines are acquired after a single inversion pulse, which can then together be considered as readout module. The readout module may use a variable flip angle approach, or the data acquisition may be divided into multiple segments (shots). The latter is useful particularly in cardiac imaging where acquiring all lines in a single segment may take too long relative to the cardiac cycle to provide adequate temporal resolution.
If multiple lines are acquired after a single pulse, the pulse sequence is a type of gradient echo echo planar imaging (EPI) pulse sequence.

See also Magnetization Prepared Rapid Gradient Echo (MPRAGE) and Turbo Field Echo (TFE).