Phase Cycling with Opencore NMR

1 Aug 2019 minor revision by Kazuyuki Takeda 20 July 2018 Kazuyuki Takeda

Let me explain the difference between phase modulation and phase cycling.
For simplicity, suppose a sequence in which we apply a single pulse:
```
pulse(pw; F1Amp(a), F1Phase(ph1), F1_Gate, F1_Unblank)
```
With this, the spectrometer emits a pulse with a width pw, amplitude a, and phase ph1. In addition, gate F1_Unblank is activated in this example for power amplifier operation.
Gate F1Phase is used to modulate the phase.
That is, phase modulation is used to change the phase of rf pulses.
Conversely, the idea of phase cycing is to make a shift, in addition to phase modulation, to the rf phase according to the current count of sequence repetition.
To implement phase cycling with Opencore NMR, we need to declare phaselist in the preample:
```
phaselist pl1=(ch1;x,y,-x,-y);
```
Here, we have defined, as an example, a phaselist pl1 acting in channel 1 (ch1) with 4 items (x,y,-x,-y), which are equivalent to (0,90,180,270), respectively.

Then, we are able to use it in the pulse command as follows:

pulse(pw; F1Amp(a), F1Phase(ph1), pl1, F1_Gate, F1_Unblank)

When we perform repetition of the sequence, the phase of the pulse for the first count of repetition is ph1 (=ph1+0). That for the second time is ph1+90, the third, ph1+180, and the fourth, ph1+270.
When we come to the last item of the phaselist, the next time we will be starting with the first item.
It is allowed to specify the phaselist alone, i.e., without phase modulation, as follows:
```
pulse(pw; F1Amp(a), pl1, F1_Gate, F1_Unblank)
```
No F1Phase appearing in the pulse command is equivalent to F1Phase(0).
It would be important to specify the cycled acquisition phase in the preample of the pulse program, as follows:
```
acqphase=x,y,-x,-y;
```

Phase cycling of 2D NMR with Opencore NMR

2D DARR experiment

version=2.0;

// defaultGates.gate is located in the "gates" folder in the application directory.
uses = defaultGates.gate;

transform F1Freq=#+180;
transform F1Amp=2.885
 +1.008*#
 -0.003488*pow(#,2)
 +1.137e-4*pow(#,3)
 -1.506e-6*pow(#,4)
 +6.825e-9*pow(#,5);

transform F3Freq=#-180;
transform F3Amp=
   2.73427712298906
 + 1.89853477788022*#
 - 0.0332935019246977*#*#
 + 0.000440209448828365*pow(#,3)
 - 2.95191768378146e-06*pow(#,4)
 + 7.90382924566022e-09*pow(#,5);

//------  PPG Clock frequency
CLK=160;

//---------- frequency variable ----------
freq f1=75.782798;
freq f1_offset=0.00471;
freq f3=301.3719;
freq f3_offset=0;

//---------- amplitude variable ----------
double aXScale=1;
amp aX90=50;
amp aXCP=50;
amp aXRamp=0;
double aHScale=0.9551;
amp aHDARR=11;
amp aH90=100;
amp aHCP=60;
amp aHRamp=5;
amp aHDec=100;

//---------- phase variable ----------
phase phDec1=0;
phase phDec2=15;

//----------- time variables ------------
time pw90X=5u;
time t1=0u;
time tMix=5m;
time pw1=2.5u;
time ct=1m;
time pw_tppm=5u;
time rd=5u(receiver delay);
time ad=5u(acquisition delay);

//----- loop variables -----

//----- int variable -----
int nCP=11;

// This is not going to be altered, and thus is declared with "const".
const int AD9858_2GHZ_DISABLE=16472;

//-----  aux parameters  -----
aux PD=2s(Pulse Delay);
aux NA=16(Number of Accum);
aux DW=10u(DWell time);
aux AL=4096(Acquisition Length);
aux ND=0(Number of Dummy scans);

phaselist plc1=(ch1; -y,x,-y,x);
phaselist plc2=(ch1; x,x,-x,-x);
acqphase=x,x,-x,-x;

start

pulse(50n; F1FreqRST,F2FreqRST,F3FreqRST)
pulse(50n; F1Freq(setup;AD9858_2GHz_DISABLE),
           F2Freq(setup;AD9858_2GHz_DISABLE),
           F3Freq(setup;AD9858_2GHz_DISABLE))

delay(1m)
pulse(5000n; F1Freq(f1+f1_offset),F3Freq(f3+f3_offset))
delay(1m)

Init
  pulse(10u;                     F1_Unblank, F3_Unblank)
  pulse(pw1;                     F1_Unblank, F3Amp(aHScale*aH90), F3Phase(90), F3_Gate, F3_Unblank)
  pulse[nCP](ct; F1Amp( aXScale*(aXCP+(#/nCP-0.5)*aXRamp) ), F1_Gate, F1_Unblank,
                F3Amp( aHScale*(aHCP+(#/nCP-0.5)*aHRamp) ), F3Phase(0), F3_Gate, F3_Unblank)
  // asynchronous TPPM decouple
  async(tppm)
  // evolution in the indirect (t1) dimension
  pulse(t1; F1_Unblank)
  // 1H channel is restored to synchronous operation
  sync(3)
  // Transverse 13C magnetization is flipped to the z axis
  pulse(pw90X; plc1, F1Amp(aX90), F1_Gate, F1_Unblank)
  // 13C-13C exchange under DARR irradiation.
  // 1H nutation frequency should be adjusted to the MAS frequency for rotary resonance recoupling
  pulse(tMix-10u;        F3Amp(aHDarr), F3_Gate, F3_Unblank)
  pulse(10u; F1_Unblank, F3Amp(aHDarr), F3_Gate, F3_Unblank)
  // Finally, 13C magnetization is observed under TPPM decoupling
  pulse(pw90X; plc2, F1Amp(aX90), F1_Gate, F1_Unblank)
  async(tppm)

  //
  pulse(rd)
  pulse(ad;         RG)
  pulse(dw*al;  ST, RG)
  //
  sync(3)
relax

async(3;TPPM)
  pulse(pw_tppm; F3Amp(aHScale*aHDec), F3Phase(phDec1), F3_Gate, F3_Unblank)
  pulse(pw_tppm; F3Amp(aHScale*aHDec), F3Phase(phDec2), F3_Gate, F3_Unblank)
continue

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