71 lines
1.9 KiB
Python
71 lines
1.9 KiB
Python
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import numpy
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import numpy as np
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from matplotlib import pyplot
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# parameter for spectrum simulations
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lb = 2e3
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pulse_length = 2e-6
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def dampening(x: np.ndarray, apod: float) -> np.ndarray:
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"""
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Calculate additional dampening to account e.g. for field inhomogeneities.
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:param x: Time axis in seconds
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:param apod: Dampening factor in 1/seconds
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:return: Exponential dampening
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"""
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return np.exp(-apod * x)
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def pulse_attn(freq: np.ndarray, t_pulse: float) -> np.ndarray:
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"""
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Calculate attenuation of signal to account for finite pulse lengths.
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See Schmitt-Rohr/Spieß, eq. 2.126 for more information.
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:param freq: Frequency axis in Hz
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:param t_pulse: Assumed pulse length in s
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:return: Attenuation factor.
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"""
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# cf. Schmitt-Rohr/Spieß eq. 2.126; omega_1 * t_p = pi/2
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pi_half_squared = np.pi**2 / 4
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omega = 2 * np.pi * freq
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numerator = np.sin(np.sqrt(pi_half_squared + omega**2 * t_pulse**2 / 2))
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denominator = np.sqrt(pi_half_squared + omega**2 * t_pulse**2 / 4)
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return np.pi * numerator / denominator / 2
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def post_process_spectrum(taus, apod, tpulse):
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reduction_factor = np.zeros((taus.size, 5)) # hard-coded t_echo :(
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for i, tau in enumerate(taus):
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try:
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raw_data = np.loadtxt(f'fid_tau={tau:.6e}.dat')
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except OSError:
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continue
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t = raw_data[:, 0]
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timesignal = raw_data[:, 1:]
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timesignal *= dampening(t, apod)[:, None]
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timesignal[0, :] /= 2
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# FT to spectrum
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freq = np.fft.fftshift(np.fft.fftfreq(t.size, d=1e-6))
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spec = np.fft.fftshift(np.fft.fft(timesignal, axis=0), axes=0).real
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spec *= pulse_attn(freq, t_pulse=tpulse)[:, None]
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reduction_factor[i, :] = 2*timesignal[0, :]
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plt.plot(freq, spec)
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plt.show()
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plt.semilogx(taus, reduction_factor, '.')
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plt.show()
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