The RF excitation angle cos qE at which the signal is a maximum for a short-TR steady-state incoherent sequence. The Ernst angle is found from the relation cos ΘE = exp (-TR/T1).

(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.

The incoherent gradient echo (gradient spoiled) type of sequence uses a continuous shifting of the RF pulse to spoil the remaining transverse magnetization. The transverse magnetization is destroyed by a magnetic field gradient. This results in a T1 weighted image. Spoiling can be accomplished by RF or a gradient.
Gradient spoiling occurs after each echo by using strong gradients in the slice-select direction after the frequency encoding and before the next RF pulse. Because spins in different locations in the magnet thereby experience a variety of magnetic field strengths, they will precess at differing frequencies; as a consequence they will quickly become dephased. Magnetic field gradients are not very efficient at spoiling the transverse steady state. To be effective, the spins must be forced to precess far enough to become phased randomly with respect to the RF excitation pulse. In clinical MRI machines, the field gradients are set up in such a way that they increase and decrease relative to the center of the magnet; the magnetic field at the magnet 'isocenter' does not change.
The T1 weighting increases with the flip angle and the T2* weighting increases with echo time (TE). Typical repetition time (TR) are 30-500 ms and TE less than 15 ms.

See also Ernst Angle.

(PFI) A flip angle of less than 90° only partially converts the z-magnetization, leaving a fraction cos a along the longitudinal direction. A flip angle of 90° converts all the z-magnetization into xy-magnetization.
When the repetition time is shorter than T1, the use of a partial flip angle can lead to higher signal intensity. The maximum signal intensity is given by the Ernst angle. For spin echo pulse sequences using an odd number of 180° pulses, an effect similar to the use of a partial flip angle is obtained by using a flip angle greater than 90° to offset the inversion of the remaining longitudinal magnetization by the 180° pulse.

Signal intensity interpretation in MR imaging has a major problem.
Often there is no intuitive approach to signal behavior as signal intensity is a very complicated function of the contrast-determining tissue parameter, proton density, T1 and T2, and the machine parameters TR and TE. For this reason, the terms T1 weighted image, T2 weighted image and proton density weighted image were introduced into clinical MR imaging.
Air and bone produce low-intensity, weaker signals with darker images. Fat and marrow produce high-intensity signals with brighter images.
The signal intensity measured is related to the square of the xy-magnetization, which in a SE pulse sequence is given by
Mxy = Mxy0(1-exp(-TR/T1)) exp(-TE/T2) (1)
where Mxy0 = Mz0 is proportional to the proton or spin density, and corresponds to the z-magnetization present at zero time of the experiment when it is tilted into the xy-plane.

See also T2 Weighted Image and Ernst Angle.