(SE) The most common pulse sequence used in MR imaging is based of the detection of a spin or Hahn echo. It uses 90° radio frequency pulses to excite the magnetization and one or more 180° pulses to refocus the spins to generate signal echoes named spin echoes (SE).
In the pulse sequence timing diagram, the simplest form of a spin echo sequence is illustrated.
The 90° excitation pulse rotates the longitudinal magnetization (Mz) into the xy-plane and the dephasing of the transverse magnetization (Mxy) starts.
The following application of a 180° refocusing pulse (rotates the magnetization in the x-plane) generates signal echoes. The purpose of the 180° pulse is to rephase the spins, causing them to regain coherence and thereby to recover transverse magnetization, producing a spin echo.
The recovery of the z-magnetization occurs with the T1 relaxation time and typically at a much slower rate than the T2-decay, because in general T1 is greater than T2 for living tissues and is in the range of 100-2000 ms.
The SE pulse sequence was devised in the early days of NMR days by Carr and Purcell and exists now in many forms: the multi echo pulse sequence using single or multislice acquisition, the fast spin echo (FSE/TSE) pulse sequence, echo planar imaging (EPI) pulse sequence and the gradient and spin echo (GRASE) pulse sequence;; all are basically spin echo sequences.
In the simplest form of SE imaging, the pulse sequence has to be repeated as many times as the image has lines.
Contrast values:
PD weighted: Short TE (20 ms) and long TR.
T1 weighted: Short TE (10-20 ms) and short TR (300-600 ms)
T2 weighted: Long TE (greater than 60 ms) and long TR (greater than 1600 ms)
With spin echo imaging no T2* occurs, caused by the 180° refocusing pulse. For this reason, spin echo sequences are more robust against e.g., susceptibility artifacts than gradient echo sequences.

See also Pulse Sequence Timing Diagram to find a description of the components.

(GRE - sequence) A gradient echo is generated by using a pair of bipolar gradient pulses. In the pulse sequence timing diagram, the basic gradient echo sequence is illustrated. There is no refocusing 180° pulse and the data are sampled during a gradient echo, which is achieved by dephasing the spins with a negatively pulsed gradient before they are rephased by an opposite gradient with opposite polarity to generate the echo.
See also the Pulse Sequence Timing Diagram. There you will find a description of the components.
The excitation pulse is termed the alpha pulse α. It tilts the magnetization by a flip angle α, which is typically between 0° and 90°. With a small flip angle there is a reduction in the value of transverse magnetization that will affect subsequent RF pulses. The flip angle can also be slowly increased during data acquisition (variable flip angle: tilt optimized nonsaturation excitation). The data are not acquired in a steady state, where z-magnetization recovery and destruction by ad-pulses are balanced. However, the z-magnetization is used up by tilting a little more of the remaining z-magnetization into the xy-plane for each acquired imaging line.
Gradient echo imaging is typically accomplished by examining the FID, whereas the read gradient is turned on for localization of the signal in the readout direction. T2* is the characteristic decay time constant associated with the FID. The contrast and signal generated by a gradient echo depend on the size of the longitudinal magnetization and the flip angle. When α = 90° the sequence is identical to the so-called partial saturation or saturation recovery pulse sequence. In standard GRE imaging, this basic pulse sequence is repeated as many times as image lines have to be acquired. Additional gradients or radio frequency pulses are introduced with the aim to spoil to refocus the xy-magnetization at the moment when the spin system is subject to the next α pulse.
As a result of the short repetition time, the z-magnetization cannot fully recover and after a few initial α pulses there is an equilibrium established between z-magnetization recovery and z-magnetization reduction due to the α pulses.
Gradient echoes have a lower SAR, are more sensitive to field inhomogeneities and have a reduced crosstalk, so that a small or no slice gap can be used. In or out of phase imaging depending on the selected TE (and field strength of the magnet) is possible. As the flip angle is decreased, T1 weighting can be maintained by reducing the TR. T2* weighting can be minimized by keeping the TE as short as possible, but pure T2 weighting is not possible. By using a reduced flip angle, some of the magnetization value remains longitudinal (less time needed to achieve full recovery) and for a certain T1 and TR, there exist one flip angle that will give the most signal, known as the "Ernst angle".
Contrast values:
PD weighted: Small flip angle (no T1), long TR (no T1) and short TE (no T2*)
T1 weighted: Large flip angle (70°), short TR (less than 50ms) and short TE
T2* weighted: Small flip angle, some longer TR (100 ms) and long TE (20 ms)

Classification of GRE sequences can be made into four categories:

• T1 weighted or incoherent/(RF or gradient) spoiled GRE sequences
• T1/T2* weighted or coherent/refocused GRE sequences
• T2 weighted contrast enhanced GRE sequences
• ultrafast GRE sequences

See also Gradient Recalled Echo Sequence, Spoiled Gradient Echo Sequence, Refocused Gradient Echo Sequence, Ultrafast Gradient Echo Sequence.

(IR) The inversion recovery pulse sequence produces signals, which represent the longitudinal magnetization existing after the application of a 180° radio frequency pulse that rotates the magnetization Mz into the negative plane. After an inversion time (TI - time between the starting 180° pulse and the following 90° pulse), a further 90° RF pulse tilts some or all of the z-magnetization into the xy-plane, where the signal is usually rephased with a 180° pulse as in the spin echo sequence. During the initial time period, various tissues relax with their intrinsic T1 relaxation time.
In the pulse sequence timing diagram, the basic inversion recovery sequence is illustrated. The 180° inversion pulse is attached prior to the 90° excitation pulse of a spin echo acquisition. See also the Pulse Sequence Timing Diagram. There you will find a description of the components.
The inversion recovery sequence has the advantage, that it can provide very strong contrast between tissues having different T1 relaxation times or to suppress tissues like fluid or fat. But the disadvantage is, that the additional inversion radio frequency RF pulse makes this sequence less time efficient than the other pulse sequences.

Contrast values:
PD weighted: TE: 10-20 ms, TR: 2000 ms, TI: 1800 ms
T1 weighted: TE: 10-20 ms, TR: 2000 ms, TI: 400-800 ms
T2 weighted: TE: 70 ms, TR: 2000 ms, TI: 400-800 ms

See also Inversion Recovery, Short T1 Inversion Recovery, Fluid Attenuation Inversion Recovery, and Acronyms for 'Inversion Recovery Sequence' from different manufacturers.

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).

Contrast enhanced GRE sequences provide T2 contrast but have a relatively poor SNR. Repetitive RF pulses with small flip angles together with appropriate gradient profiles lead to the superposition of two resonance signals.
The first signal is due to the free induction decay FID observed after the first and all ensuing RF excitations.
The second is a resonance signal obtained as a result of a spin echo generated by the second and all addicted RF-pulses.
Hence it is absent after the first excitation, it is a result of the free induction decay of the second to last RF-excitation and has a TE, which is almost 2TR. For this echo to occur the gradients have to be completely symmetrical relative to the half time between two RF-pulses, a condition that makes it difficult to integrate this pulse sequence into a multiple slice imaging technique. The second signal not only contains echo contributions from free induction decay, but obviously weakened by T2-decay. Since the echo is generated by a RF-pulse, it is truly T2 rather than T2* weighted. Correspondingly it is also less sensitive to susceptibility changes and field inhomogeneities.
Companies use different acronyms to describe certain techniques.
Different terms (see also acronyms) for these gradient echo pulse sequences:
CE-FAST Contrast Enhanced Fourier Acquired Steady State,
CE-FFE Contrast Enhanced Fast Field Echo,
CE-GRE Contrast Enhanced Gradient-Echo,
DE-FGR Driven Equilibrium FGR,
FADE FASE Acquisition Double Echo,
PSIF Reverse Fast Imaging with Steady State Precession,
SSFP Steady State Free Precession,
T2 FFE Contrast Enhanced Fast Field Echo (T2 weighted).
In this context, 'contrast enhanced' refers to the pulse sequence, it does not mean enhancement with a contrast agent.