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 'Frequency Encoding Gradient' 
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Flat TopForum -
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The flat top is the area at the top of the frequency encoding gradient where the data sampling occurs. By increasing the BW the amount of time the flat top is on is reduced. Shortening the duration of the flat top shortens the echo spacing and also geometric distortions. The area under the frequency gradient determines the FOV, while the flat top determines the number of samples to be collected.
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Fractional Echo
 
Fractional echo (also called asymmetric or partial echo) is used to shorten the echo time in a sequence, by acquiring partial echoes in the frequency direction. The reduction of echo time is possible because if the first part of the echo is not received, the dephasing lobe of the frequency encoding gradient is not to be on for quite as long, and this saves time.

See also Partial Fourier Technique, Read Conjugate Symmetry, Single Side View and acronyms for 'fractional echo' from different manufacturers.
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RARE
Monday, 3 December 2012   by www2.warwick.ac.uk    
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Multi Echo Data Image CombinationInfoSheet: - Sequences - 
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(MEDIC) MEDIC is a heavily T2* weighted spoiled gradient echo sequence with multiple echoes. MEDIC uses a series of identically phase encoded gradient echoes, sampled per line in k-space. Unipolar frequency encoding gradients are used to achieve flow compensation and to avoid off resonance effects. For each echo the magnitude images are reconstructed and postprocessed by using a sum of squares algorithm to improve the signal to noise ratio. The increased receiver bandwidth reduces the T2* effects and impairment of the spatial resolution.
The multi echo data image combination sequence is potentially useful in imaging of cartilage in joints.
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Phase Encoding Gradient
 
(Gφ) The phase encoding gradient is a magnetic field gradient that allows the encoding of the spatial signal location along a second dimension by different spin phases. The phase encoding gradient is applied after slice selection and excitation (before the frequency encoding gradient), orthogonally to the other two gradients. The spatial resolution is directly related to the number of phase encoding steps (gradients).
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Further Reading:
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RARE
Monday, 3 December 2012   by www2.warwick.ac.uk    
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Principles of Magnetic Resonance Imaging
Friday, 21 December 2001   by www.mikepuddephat.com    
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Pulse Sequence Timing DiagramInfoSheet: - Sequences - 
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Spin Echo Timing Diagram The schematic figures of a pulse sequence timing diagram illustrate the steps of basic hardware activity that are incorporated into a pulse sequence. Time during sequence execution is indicated along the horizontal axes. Each line belongs to a different hardware component. One line is needed for the radio frequency transmitter and also one for each gradient (Gs = slice selection gradient x, Gf = phase encoding gradient y, Gf = frequency encoding gradient z, also called readout gradient).
In picture 1, a timing diagram for a 2D pulse sequence is shown.
Slice selection and signal detection are repeated in duration, relative timing and amplitude, each time the sequence is repeated. A single phase encoding component is present each time the sequence is executed.
Additional lines are added for ADC (Analog to Digital Converter) and sampling. A gradient pulse is shown as a deviation above or below the horizontal line. Simultaneous component activities such as the RF pulse and slice selection gradient are indicated as a non-zero deviation from both lines at the same horizontal position. Simple deviations from zero show constant amplitude gradient pulse. Gradient amplitudes that change during the measurement, e.g. phase encoding are represented as hatched regions.

Spin Echo Timing Diagram The second picture shows a timing diagram for a 3D pulse sequence.
Volume excitation and signal detection are repeated in duration, relative timing and amplitude, each time the sequence is repeated. Two phase encoding components are present, one in the phase encoding direction and the other in slice selection direction (irrespectively incremented in amplitude) in each time the sequence is executed. A description of the comparison of hardware activity between different pulse sequences.
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