@@ -33,11 +33,11 @@ def sinc_pulse(flip_angle, duration, bandwidth, dt, phase_angle=0, window='hann'
3333
3434 .. math::
3535
36- \\ theta = \\ gamma \\ int B_1 dt
36+ \\ theta = \\ gamma \\ int_0^T B_1 dt
3737
38- where :math:`\\ theta` is the flip angle, :math:`\\ gamma` is the gyromagnetic
39- ratio, and :math:`B_1 ` is the pulse amplitude. The sinc pulse is normalized
40- to achieve the desired flip angle.
38+ where :math:`\\ theta` is the flip angle in rads , :math:`\\ gamma` is the gyromagnetic
39+ ratio in rads/s/T, :math:`T ` is the pulse duration is s, and :math:`B_1` is the pulse
40+ amplitude in T. The sinc pulse is normalized to achieve the desired flip angle.
4141
4242 """
4343 theta , alpha = np .deg2rad (phase_angle ), np .deg2rad (flip_angle )
@@ -73,14 +73,13 @@ def adiabaticity(pulse_am, pulse_fm, dt):
7373
7474 .. math::
7575
76- K = \\ frac{\\ left | \\ gamma B_{\\ mathrm{effective}} \\ right |}{\\ left | \\ dv{\\ varphi}{t} \\ right |} = \\ frac{\\ gamma\\ sqrt{A^2(t) + \\ left ( B_0 - \\ frac{\\ omega (t)}{\\ gamma } \\ right )^2}}{\\ dv{}{t}\\ left ( \\ arctan(\\ frac{A(t)}{B_0 - \\ frac{ \\ omega (t)}{ \\ gamma}} ) \\ right )}
76+ K = \\ frac{\\ left | \\ gamma B_{\\ mathrm{effective}} \\ right |}{\\ left | \\ dv{\\ varphi}{t} \\ right |} = \\ frac{\\ gamma\\ sqrt{A^2(t) + \\ left (\\ frac{f (t)}{\\ gammabar } \\ right )^2}}{\\ left| \\ dv{}{t}\\ left ( \\ arctan(\\ frac{\\ gammabar A(t)}{f (t)}) \\ right ) \\ right| }
7777
78- where :math:`A(t)` and :math:`\\ omega(t)` are the amplitude and frequency
79- modulation waveforms, respectively, and :math:`B_0` is the static magnetic
80- field. The adiabaticity is a measure of the ability of the pulse to drive
81- the magnetization to follow the instantaneous effective magnetic field in
82- the rotating frame. When the adiabaticity is much greater than 1, for all
83- time, the pulse is considered adiabatic.
78+ where :math:`A(t)` and :math:`f(t)` are the amplitude and frequency
79+ modulation waveforms, respectively. The adiabaticity is a measure of the
80+ ability of the pulse to drive the magnetization to follow the
81+ instantaneous effective magnetic field in the rotating frame. When the
82+ adiabaticity is much greater than 1, for all time, the pulse is considered adiabatic.
8483
8584 """
8685 Bz_eff = pulse_fm / bloch .GAMMA_BAR
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