def test_grad_echo_Elena():
samples_tmp = 140
tx_dt = 0.1
rx_dt = 3.33 #desired sampling dt
rx_dt_corr = rx_dt *0.5 #correction till the bug is fixed
exp = Experiment(samples=samples_tmp,
lo_freq=14.2375,
tx_t= tx_dt,
rx_t=rx_dt_corr,
instruction_file="grad_echo_elena.txt")
# RF pulse`
tx_time = 20
t = np.linspace(0, tx_time, math.ceil(tx_time/tx_dt)+1) # goes to tx_time us, samples every tx_t us; length of pulse must be adjusted in grad_echo_elena.txt
alpha = 0.46 # alpha=0.46 for Hamming window, alpha=0.5 for Hanning window
Nlobes = 5
ampl = 0.125
#sinc pulse with Hamming window
tx_x = ampl * sinc(math.pi*(t - tx_time/2),tx_time,Nlobes,alpha)
tx_idx = exp.add_tx(tx_x) # add the data to the ocra TX memory
# gradient echo; 190 samples total: 50 for first ramp, 140 for second ramp
grad = np.hstack([
np.linspace(0, 0.9, 10), np.ones(30), np.linspace(0.9, 0, 10), # first ramp up/down
np.linspace(0,-0.285, 20), -0.3 * np.ones(100), np.linspace(-0.285, 0, 20)
])
# Correct for DC offset and scaling
scale = 0.9
offset = 0.0
grad_corr = grad*scale + offset
grad_idx = exp.add_grad(grad_corr, grad_corr, grad_corr)
if False: # set to true if you want to plot the x gradient waveform
plt.plot(grad_corr);plt.show()
data = exp.run()
data_mV = data*1000
# time vector for representing the received data
samples_data = len(data)
t_rx = np.linspace(0, rx_dt*samples_data, samples_data) #us
plt.plot(t,tx_x)
plt.title('sampled data = %i' % samples_data)
# plt.plot(t_rx,np.real(data_mV))
# plt.plot(t_rx,np.imag(data_mV))
# plt.plot(t_rx,np.abs(data_mV))
# plt.legend(['real', 'imag', 'abs'])
# plt.xlabel('time (us)')
# plt.ylabel('signal received (mV)')
# plt.title('sampled data = %i' %samples_data)
plt.show()
def test_grad_echo_Elena():
exp = Experiment(samples=600,
lo_freq=14.2375,
tx_t=0.1,
rx_t=2,
instruction_file="ocra_lib/grad_echo_elena.txt")
# RF pulse
t = np.linspace(
0, 20, 201
) # goes to 20us, samples every 10ns; length of pulse must be adjusted in grad_echo_elena.txt
# sinc pulse
tx_x = np.sinc((t - 10) / 6)
tx_idx = exp.add_tx(tx_x) # add the data to the ocra TX memory
# gradient echo; 190 samples total: 50 for first ramp, 140 for second ramp
grad = np.hstack([
np.linspace(0, 0.9, 10),
np.ones(30),
np.linspace(0.9, 0, 10), # first ramp up/down
np.linspace(0, -0.285, 20),
-0.3 * np.ones(100),
np.linspace(-0.285, 0, 20)
])
# Correct for DC offset and scaling
scale = 0.9
offset = 0.0
grad_corr = grad * scale + offset
grad_idx = exp.add_grad(grad_corr, grad_corr, grad_corr)
if False: # set to true if you want to plot the x gradient waveform
plt.plot(grad_corr)
plt.show()
data = exp.run()
plt.plot(np.real(data))
plt.plot(np.imag(data))
plt.plot(np.abs(data))
plt.legend(['real', 'imag', 'abs'])
plt.show()
def se_2D_v0_RP():
# Experiment parameters
freq_larmor = 2.147 # local oscillator frequency, MHz
sample_nr_echo = 128 # number of (I,Q) USEFUL samples to acquire during a shot
pe_step_nr = 128 # number of phase encoding steps
tx_dt = 0.1 # RF TX sampling dt in microseconds; is rounded to a multiple of clocks (122.88 MHz)
rx_dt = 50 # RF RX sampling dt
##### Times have to match with "<instruction_file>.txt" ####
T_tx_Rf = 100 # RF pulse length (us)
T_G_ramp_dur = 250 # Gradient ramp time
BW = 20000 # Rf Rx Bandwidth
sample_nr_2_STOP_Seq = 256 + 1000 # Nr. of samples to acquire TO STOP the acquisition
# Correct for DC offset and scaling
scale_G_x = 0.32
scale_G_y = 0.32
scale_G_z = 0.32
offset_G_x = 0.0
offset_G_y = 0.0
offset_G_z = 0.0
# Rf amplitude
Rf_ampl = 0.3 #0.07125 # for Tom
# Centering the echo
echo_delay = 4550 # us; correction for receiver delay
rx_dt_corr = rx_dt * 0.5 # correction factor to have correct Rx sampling time till the bug is fixed
t_G_ref_Area = (
(1 / (BW / sample_nr_echo)) /
2) * 1e6 # The time needed to do half the encoding (square pulse)
T_G_pe_dur = t_G_ref_Area + T_G_ramp_dur # Total phase encoding gradient ON time length (us)
T_G_pre_fe_dur = t_G_ref_Area + (
3 /
2) * T_G_ramp_dur # Total freq. encoding REWINDER ON time length (us)
T_G_fe_dur = 2 * (
t_G_ref_Area + T_G_ramp_dur
) # Total Frequency encoding gradient ON time length (us)
##### RF pulses #####
### 90 RF pulse ###
# Time vector
t_Rf_90 = np.linspace(0, T_tx_Rf,
math.ceil(T_tx_Rf / tx_dt) +
1) # Actual TX RF pulse length
# sinc pulse
alpha = 0.46 # alpha=0.46 for Hamming window, alpha=0.5 for Hanning window
Nlobes = 1
# sinc pulse with Hamming window
# tx90 = Rf_ampl * sinc(math.pi*(t_Rf_90 - T_tx_Rf/2),T_tx_Rf,Nlobes,alpha)
tx90_clean = Rf_ampl * np.ones(np.size(t_Rf_90))
### 180 RF pulse ###
# sinc pulse
tx180 = tx90_clean * 2
tx90 = np.concatenate((tx90_clean, np.zeros(1100 - np.size(tx90_clean))))
tx180 = np.concatenate(
(tx180, np.zeros(2200 - np.size(tx180) - np.size(tx90))))
# For testing ONLY: shot rf to mimic echo for centering the acquisition window
tx90_echo_cent = np.hstack((tx90_clean, np.zeros(100)))
##### Gradients #####
# Phase encoding gradient shape
grad_pe_samp_nr = math.ceil(T_G_pe_dur / 10)
grad_ramp_samp_nr = math.ceil(T_G_ramp_dur / 10)
grad_pe = np.hstack([
np.linspace(0, 1, grad_ramp_samp_nr), # Ramp up
np.ones(grad_pe_samp_nr - 2 * grad_ramp_samp_nr), # Top
np.linspace(1, 0, grad_ramp_samp_nr)
]) # Ramp down
grad_pe = np.hstack([grad_pe, np.zeros(500 - np.size(grad_pe))])
# Pre-frequency encoding gradient shape
grad_pre_fe_samp_nr = math.ceil(T_G_pre_fe_dur / 10)
grad_pre_fe = np.hstack([
np.linspace(0, 1, grad_ramp_samp_nr), # Ramp up
np.ones(grad_pre_fe_samp_nr - 2 * grad_ramp_samp_nr), # Top
np.linspace(1, 0, grad_ramp_samp_nr)
]) # Ramp down
grad_pre_fe = np.hstack(
[grad_pre_fe, np.zeros(500 - np.size(grad_pre_fe))])
# Frequency encoding gradient shape
grad_fe_samp_nr = math.ceil(T_G_fe_dur / 10)
grad_fe = np.hstack([
np.linspace(0, 1, grad_ramp_samp_nr), # Ramp up
np.ones(grad_fe_samp_nr - 2 * grad_ramp_samp_nr), # Top
np.linspace(1, 0, grad_ramp_samp_nr)
]) # Ramp down
sample_nr_center_G_fe = (
((1 / (BW / 128)) / 2) * 1e6 +
T_G_ramp_dur) / 10 # Total phase encoding gradient ON time length (us)
grad_fe = np.hstack([
np.zeros(
np.round(sample_nr_center_G_fe -
np.size(grad_fe) / 2).astype('int')), grad_fe,
np.zeros(np.round(1000 - np.size(grad_fe)).astype('int'))
])
# Initialisation of the DAC
exp = Experiment(
samples=
4, # number of (I,Q) samples to acquire during a shot of the experiment
lo_freq=freq_larmor, # local oscillator frequency, MHz
tx_t=tx_dt,
instruction_file="ocra_lib/se_default_vn.txt")
exp.initialize_DAC()
# Loop repeating TR and updating the gradients waveforms
data = np.zeros([sample_nr_2_STOP_Seq, pe_step_nr], dtype=complex)
for idx2 in range(pe_step_nr):
exp = Experiment(
samples=
sample_nr_2_STOP_Seq, # number of (I,Q) samples to acquire during a shot of the experiment
lo_freq=freq_larmor, # local oscillator frequency, MHz
tx_t=
tx_dt, # RF TX sampling time in microseconds; will be rounded to a multiple of system clocks (122.88 MHz)
rx_t=rx_dt_corr, # RF RX sampling time in microseconds; as above
instruction_file="se_2D_LUMC_v0.txt")
###### Send waveforms to RP memory ###########
# Load the RF waveforms
tx_idx = exp.add_tx(tx90) # add 90 Rf data to the ocra TX memory
tx_idx = exp.add_tx(tx180) # add 180 Rf data to the ocra TX memory
tx_idx = exp.add_tx(
tx90_echo_cent
) # add Reference pulse only for measuring acquisition delay
scale_G_pe_sweep = 2 * (idx2 / (pe_step_nr - 1) - 0.5
) # Change phase encoding gradient magnitude
# Adjust gradient waveforms
grad_x_1_corr = grad_pre_fe * scale_G_x + offset_G_x
grad_y_1_corr = grad_pe * scale_G_y * scale_G_pe_sweep + offset_G_y
grad_z_1_corr = np.zeros(np.size(grad_x_1_corr)) + offset_G_z
grad_x_2_corr = grad_fe * scale_G_x + offset_G_x
grad_y_2_corr = np.zeros(np.size(grad_x_2_corr)) + offset_G_y
grad_z_2_corr = np.zeros(np.size(grad_x_2_corr)) + offset_G_z
# Load gradient waveforms
grad_idx = exp.add_grad(grad_x_1_corr, grad_y_1_corr, grad_z_1_corr)
grad_idx = exp.add_grad(grad_x_2_corr, grad_y_2_corr, grad_z_2_corr)
# Run command to MaRCoS
data[:, idx2] = exp.run()
# time vector for representing the received data
samples_data = len(data)
t_rx = np.linspace(0, rx_dt * samples_data, samples_data) # us
plt.figure(1)
plt.subplot(2, 1, 1)
# plt.plot(t_rx, np.real(data))
# plt.plot(t_rx, np.abs(data))
plt.plot(np.real(data))
plt.plot(np.abs(data))
plt.legend(['real', 'abs'])
plt.xlabel('time (us)')
plt.ylabel('signal received (V)')
plt.title('Total sampled data = %i' % samples_data)
plt.grid()
echo_shift_idx = np.floor(echo_delay / rx_dt).astype('int')
rx_sample_nr_center_G_fe = (
((1 / (BW / 128)) / 2) * 1e6 +
T_G_ramp_dur) / 50 # Total phase encoding gradient ON time length (us)
echo_idx = (
rx_sample_nr_center_G_fe - np.floor(sample_nr_echo / 2)
).astype(
'int'
) # np.floor(T_G_fe_dur / (2 * rx_dt)).astype('int') - np.floor(sample_nr_echo / 2).astype('int')
kspace = data[echo_idx + echo_shift_idx:echo_idx + echo_shift_idx +
sample_nr_echo, :]
plt.subplot(2, 1, 2)
# plt.plot(t_rx[echo_idx+echo_shift_idx:echo_idx+echo_shift_idx+sample_nr_echo], np.real(kspace))
# # plt.plot(t_rx, np.imag(data))
# plt.plot(t_rx[echo_idx+echo_shift_idx:echo_idx+echo_shift_idx+sample_nr_echo], np.abs(kspace))
plt.plot(np.real(kspace))
plt.plot(np.abs(kspace))
plt.legend(['real', 'abs'])
plt.xlabel('Sample nr.')
plt.ylabel('signal received (V)')
plt.title('Echo time in acquisition from = %f' %
t_rx[echo_idx + echo_shift_idx])
plt.grid()
plt.figure(2)
plt.subplot(1, 2, 1)
Y = np.fft.fftshift(np.fft.fft2(np.fft.fftshift(kspace)))
img = np.abs(Y)
plt.imshow(np.abs(kspace), cmap='gray')
plt.title('k-Space')
plt.subplot(1, 2, 2)
plt.imshow(img, cmap='gray')
plt.title('image')
plt.show()
# Loop repeating TR and updating the gradients waveforms
data = np.zeros([sample_nr_2_STOP_Seq, TR_nr], dtype=complex)
for idxTR in range(TR_nr):
exp = Experiment(
samples=
sample_nr_2_STOP_Seq, # number of (I,Q) samples to acquire during a shot of the experiment
lo_freq=freq_larmor, # local oscillator frequency, MHz
tx_t=
tx_dt, # RF TX sampling time in microseconds; will be rounded to a multiple of system clocks (122.88 MHz)
rx_t=rx_dt_corr, # RF RX sampling time in microseconds; as above
instruction_file="TSE_2D_tests.txt") # TSE_2D_tests.txt
###### Send waveforms to RP memory ###########
tx_length = np.zeros(1).astype(int)
# Load the RF waveforms
tx_idx = exp.add_tx(
tx90.astype(complex)) # add 90x+ Rf data to the ocra TX memory
tx_length = np.hstack([tx_length, tx_length[-1] + tx90.size])
tx_idx = exp.add_tx(
tx180.astype(complex)) # add 180x+ Rf data to the ocra TX memory
tx_length = np.hstack([tx_length, tx_length[-1] + tx180.size])
tx_idx = exp.add_tx(tx180.astype(complex) *
1j) # add 180y+ Rf data to the ocra TX memory
tx_length = np.hstack([tx_length, tx_length[-1] + tx180.size])
tx_idx = exp.add_tx(tx180.astype(complex) *
(-1j)) # add 180y- Rf data to the ocra TX memory
tx_length = np.hstack([tx_length, tx_length[-1] + tx180.size])
# Adjust gradient waveforms
# Echo nr | 1 | 2 |
# Block | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
# Mem | 0 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
def se_2D_v0_RP():
sample_nr = 1100 # number of (I,Q) samples to acquire during a shot of the experiment
pe_step_nr = 32 # number of phase encoding steps
tx_dt = 0.1 # RF TX sampling time in microseconds; will be rounded to a multiple of system clocks (122.88 MHz)
rx_dt = 1 # desired sampling dt
rx_dt_corr = rx_dt * 0.5 # correction factor till the bug is fixed
sample_nr_echo = 32
##### Times in "<instruction_file>.txt" #####
TR = 0.02e6 # Repetition time (us)
TE = 0.001e6 # Echo time (us)
T_tx_Rf = 10 # RF pulse length (us)
T_G_pe_trig = 50 # Phase encoding gradient starting time (us)
T_G_pe_dur = 200 # Phase encoding gradient ON time length (us)
T_G_ramp_dur = 50 # Gradient ramp time
T_G_fe_dur = 2 * T_G_pe_dur # Frequency encoding gradient ON time length (us)
t = np.linspace(0, TR, math.ceil(TR / tx_dt) + 1) # 90 TX instruction length
seq = np.array([[0, T_tx_Rf], # 90 Rf pulse
[T_G_pe_trig, T_G_pe_trig + T_G_pe_dur], # Phase encoding gradient
[TE / 2, TE / 2 + T_tx_Rf], # 180 Rf pulse
[TE + T_tx_Rf / 2 - T_G_fe_dur / 2,
TE + T_tx_Rf / 2 + T_G_fe_dur / 2]]) # Frequency encoding gradient
idx_tmp = np.zeros([np.size(seq, 1), np.size(seq, 0)])
for idx in range(np.size(seq, 0)):
idx_tmp[0, idx] = np.argmin(t <= seq[idx, 0]) # Instruction Start times
idx_tmp[1, idx] = np.argmin(t <= seq[idx, 1]) # Instruction Stop times
##### RF pulses #####
### 90 RF pulse ###
# Time vector
t_Rf_90 = np.linspace(0, T_tx_Rf, math.ceil(T_tx_Rf / tx_dt) + 1) # Actual TX RF pulse length
# sinc pulse
alpha = 0.46 # alpha=0.46 for Hamming window, alpha=0.5 for Hanning window
Nlobes = 1
Rf_ampl = 0.125
# sinc pulse with Hamming window
tx90 = Rf_ampl * sinc(math.pi*(t_Rf_90 - T_tx_Rf/2),T_tx_Rf,Nlobes,alpha)
# tx90 = Rf_ampl * np.ones(np.size(t_Rf_90))
### 180 RF pulse ###
# sinc pulse
tx180 = tx90 * 2
tx180 =np.concatenate((tx180, np.zeros(1000-np.size(tx180)-np.size(tx90))))
# For testing ONLY: echo centering
acq_shift = 0
tx90_echo_cent = np.hstack((
np.zeros(np.floor(T_G_fe_dur/(2*tx_dt)).astype('int')- np.floor(np.size(tx90)/2).astype('int')-acq_shift),
tx90 ,
np.zeros(np.floor(T_G_fe_dur/(2*tx_dt)).astype('int')- np.floor(np.size(tx90)/2).astype('int')+acq_shift)))
# tx90_echo_cent = tx90_echo_cent * 0
##### Gradients #####
# Phase encoding gradient shape
grad_pe_samp_nr = math.ceil(T_G_pe_dur / 10)
grad_ramp_samp_nr = math.ceil(T_G_ramp_dur / 10)
grad_pe = np.hstack([np.linspace(0, 1, grad_ramp_samp_nr), # Ramp up
np.ones(grad_pe_samp_nr - 2 * grad_ramp_samp_nr), # Top
np.linspace(1, 0, grad_ramp_samp_nr)]) # Ramp down
grad_pe = np.hstack([grad_pe, np.zeros(100 - np.size(grad_pe))])
# Frequency encoding gradient shape
grad_fe_samp_nr = math.ceil(T_G_fe_dur / 10)
grad_fe = np.hstack([np.linspace(0, 1, grad_ramp_samp_nr), # Ramp up
np.ones(grad_fe_samp_nr - 2 * grad_ramp_samp_nr), # Top
np.linspace(1, 0, grad_ramp_samp_nr)]) # Ramp down
grad_fe = np.hstack([grad_fe, np.zeros(100 - np.size(grad_fe))])
# Correct for DC offset and scaling
scale_G_x = 0.1
scale_G_y = 0.1
scale_G_z = 0.1
offset_G_x = 0.05
offset_G_y = 0.05
offset_G_z = 0.0
# Loop repeating TR and updating the gradients waveforms
# data = np.zeros([np.size(grad_fe_corr),pe_step_nr])
data = np.zeros([sample_nr, pe_step_nr], dtype=complex)
exp = Experiment(samples=sample_nr, # number of (I,Q) samples to acquire during a shot of the experiment
lo_freq=5, # local oscillator frequency, MHz
tx_t=tx_dt,
# RF TX sampling time in microseconds; will be rounded to a multiple of system clocks (122.88 MHz)
rx_t=rx_dt_corr, # RF RX sampling time in microseconds; as above
instruction_file="ocra_lib/se_default_vn.txt")
exp.initialize_DAC()
for idx2 in range(pe_step_nr):
exp = Experiment(samples=sample_nr, # number of (I,Q) samples to acquire during a shot of the experiment
lo_freq=5, # local oscillator frequency, MHz
tx_t=tx_dt,
# RF TX sampling time in microseconds; will be rounded to a multiple of system clocks (122.88 MHz)
rx_t=rx_dt_corr, # RF RX sampling time in microseconds; as above
instruction_file="se_2D_v0_RP.txt")
###### Send waveforms to RP memory ###########
# Load the RF waveforms
tx_idx = exp.add_tx(tx90) # add the data to the ocra TX memory
tx_idx = exp.add_tx(tx180) # add the data to the ocra TX memory
tx_idx = exp.add_tx(tx90_echo_cent)
scale_G_pe_sweep = 2 * (idx2 / (pe_step_nr - 1) - 0.5)
grad_x_pe_corr = grad_pe * scale_G_x + offset_G_x
grad_y_pe_corr = grad_pe * scale_G_y * scale_G_pe_sweep + offset_G_y
grad_z_pe_corr = np.zeros(np.size(grad_x_pe_corr))+ offset_G_z
grad_x_fe_corr = grad_fe * scale_G_x + offset_G_x
grad_y_fe_corr = np.zeros(np.size(grad_x_fe_corr)) + offset_G_y
grad_z_fe_corr = np.zeros(np.size(grad_x_fe_corr)) + offset_G_z
grad_idx = exp.add_grad(grad_x_pe_corr , grad_y_pe_corr , grad_z_pe_corr)
grad_idx = exp.add_grad(grad_x_fe_corr , grad_y_fe_corr , grad_z_fe_corr)
# grad_idx = exp.add_grad(np.zeros(np.size(grad_fe_corr)), grad_fe_corr, np.zeros(np.size(grad_fe_corr)))
data[:, idx2] = exp.run()
# data = exp.run()
data_mV = data * 1000 # data = np.zeros([sample_nr, pe_step_nr])
# time vector for representing the received data
samples_data = len(data)
t_rx = np.linspace(0, rx_dt * samples_data, samples_data) # us
plt.plot(t_rx, np.real(data_mV))
# plt.plot(t_rx, np.imag(data_mV))
plt.plot(t_rx, np.abs(data_mV))
plt.legend(['real', 'imag', 'abs'])
plt.xlabel('time (us)')
plt.ylabel('signal received (mV)')
plt.title('sampled data = %i' % samples_data)
plt.grid()
echo_delay = 96.5 # ms
echo_shift_idx = np.floor(echo_delay/rx_dt).astype('int')
echo_idx = np.floor(T_G_fe_dur / (2 * rx_dt)).astype('int') - np.floor(sample_nr_echo/ 2).astype('int')
kspace = data[echo_idx+echo_shift_idx:echo_idx+echo_shift_idx+sample_nr_echo, : ]
# Y = np.fft.fftshift(np.fft.fft2(np.fft.fftshift(kspace)))
plt.figure(2)
plt.plot(t_rx[echo_idx+echo_shift_idx:echo_idx+echo_shift_idx+sample_nr_echo], np.real(kspace))
# plt.plot(t_rx, np.imag(data_mV))
plt.plot(t_rx[echo_idx+echo_shift_idx:echo_idx+echo_shift_idx+sample_nr_echo], np.abs(kspace))
plt.legend(['real', 'imag', 'abs'])
plt.xlabel('time (us)')
plt.ylabel('signal received (mV)')
plt.title('sampled data = %i' % samples_data)
plt.grid()
Y = np.fft.fftshift(np.fft.fft2(np.fft.fftshift(kspace)))
img = np.abs(Y)
plt.figure(3)
plt.imshow(img, cmap='gray')
plt.title('image')
plt.show()
# Loop repeating TR and updating the gradients waveforms
data = np.zeros([sample_nr_2_STOP_Seq, pe_step_nr], dtype=complex)
for idx2 in range(pe_step_nr):
exp = Experiment(
samples=
sample_nr_2_STOP_Seq, # number of (I,Q) samples to acquire during a shot of the experiment
lo_freq=freq_larmor, # local oscillator frequency, MHz
tx_t=
tx_dt, # RF TX sampling time in microseconds; will be rounded to a multiple of system clocks (122.88 MHz)
rx_t=rx_dt_corr, # RF RX sampling time in microseconds; as above
instruction_file="se_2D_I3M_v1.txt")
###### Send waveforms to RP memory ###########
# Load the RF waveforms
tx_idx = exp.add_tx(tx90) # add 90 Rf data to the ocra TX memory
tx_idx = exp.add_tx(tx180) # add 180 Rf data to the ocra TX memory
tx_idx = exp.add_tx(
tx90_echo_cent
) # add Reference pulse only for measuring acquisition delay
scale_G_pe_sweep = 2 * (idx2 / (pe_step_nr - 1) - 0.5
) # Change phase encoding gradient magnitude
# Adjust gradient waveforms
grad_x_1_corr = grad_pre_fe * scale_G_x + offset_G_x
grad_y_1_corr = grad_pe * scale_G_y * scale_G_pe_sweep + offset_G_y
grad_z_1_corr = np.zeros(np.size(grad_x_1_corr)) + offset_G_z
grad_x_2_corr = grad_fe * scale_G_x + offset_G_x
grad_y_2_corr = np.zeros(np.size(grad_x_2_corr)) + offset_G_y
grad_z_2_corr = np.zeros(np.size(grad_x_2_corr)) + offset_G_z
