Phase Cycling and Gradient Pulses - The James Keeler Group

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φ sig , is measured anti-clockwise from the x-axis. The dot shows the axis along which the receiver is aligned; this phase, φ rx , is also measured anti-clockwise from the x-axis. If the vector and receiver are aligned along the same axis, Φ = 0, and the real part of the spectrum shows the absorption mode lineshape. If the receiver phase is advanced by π/2, Φ = 0 – π/2 and, from Eq. [1] S( ω)= B[ A( ω)+ iD( ω) ] exp( −iπ 2) = B − iA( ω)+ D( ω) [ ] This means that the real part of the spectrum shows a dispersion lineshape. On the other hand, if the magnetization is advanced by π/2, Φ = φ sig – φ rx = π/2 – 0 = π/2 and it can be shown from Eq. [1] that the real part of the spectrum shows a negative dispersion lineshape. Finally, if either phase is advanced by π, the result is a negative absorption lineshape. y x φ rx φ 9.2.6 CYCLOPS The CYCLOPS phase cycling scheme is commonly used in even the simplest pulse-acquire experiments. The sequence is designed to cancel some imperfections associated with errors in the two phase detectors mentioned above; a description of how this is achieved is beyond the scope of this discussion. However, the cycle itself illustrates very well the points made in the previous section. There are four steps in the cycle, the pulse phase goes x, y, –x, –y i.e. it advances by 90° on each step; likewise the receiver advances by 90° on each step. The figure below shows how the magnetization and receiver phases are related for the four steps of this cycle 9–6
y –x x –y pulse x y –x –y receiver x y –x –y Although both the receiver and the magnetization shift phase on each step, the phase difference between them remains constant. Each step in the cycle thus gives the same lineshape and so the signal adds on all four steps, which is just what is required. Suppose that we forget to advance the pulse phase; the outcome is quite different pulse x x x x receiver x y –x –y y –x x –y Now the phase difference between the receiver and the magnetization is no longer constant. A different lineshape thus results from each step and it is clear that adding all four together will lead to complete cancellation (steps 2 and 4 cancel, as do steps 1 and 3). For the signal to add up it is clearly essential for the receiver to follow the magnetization. 9.2.7 EXORCYLE EXORCYLE is perhaps the original phase cycle. It is a cycle used for 180° pulses when they form part of a spin echo sequence. The 180° pulse cycles through the phases x, y, –x, –y and the receiver phase goes x, –x, x, –x. The diagram below illustrates the outcome of this sequence 9–7
Page 1 and 2: 9 Coherence Selection: Phase Cyclin
Page 3 and 4: We can go further with this interpr
Page 5: that the cosine and sine modulated
Page 9 and 10: phase cycling of many two- and thre
Page 11 and 12: ( ) ( )= ( ) exp −iΩtIz I± exp
Page 13 and 14: t 1 t 2 p 2 1 0 -1 -2 ∆p=±1 ±1,
Page 15 and 16: simply because cos(Ωt 1 ) = cos(-
Page 17 and 18: A A + A A 1 1 4 1+ 2 4 1− 2 which
Page 19 and 20: [ ] 1 S+ ( F1, F2)= 2 A1+ + iD1+ A2
Page 21 and 22: pulse goes x, -x and the receiver g
Page 23 and 24: step pulse phase phase shift experi
Page 25 and 26: As the cycle has four steps, a path
Page 27 and 28: dimensional spectra. This is consid
Page 29 and 30: doubles the length of the phase cyc
Page 31 and 32: t 1 τ mix t 2 1 0 -1 If we group t
Page 33 and 34: magnetic field is made spatially in
Page 35 and 36: 1.0 M x 0.5 0.0 10 20 30 40 50 γGr
Page 37 and 38: ∑ sp i iγ iBg,iτi = 0 . i With
Page 39 and 40: We start out the discussion by cons
Page 41 and 42: The sequence below shows the gradie
Page 43 and 44: stronger the gradient the more rapi
Page 45 and 46: discrimination in the F 1 dimension
Page 47 and 48: I ∆ 2 ∆ 2 ∆ 2 ∆ 2 t 2 S t 1
Page 49: y the gradient at the edges of the

Phase Cycling and Gradient Pulses - The James Keeler Group

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