cpp/python/spectrum.py

import numpy as np
import matplotlib.pyplot as plt

from python.helpers import read_parameter_file

# parameter for spectrum simulations
lb = 2e3
pulse_length = 2e-6


def dampening(x: np.ndarray, apod: float) -> np.ndarray:
    """
    Calculate additional dampening to account e.g. for field inhomogeneities.

    :param x: Time axis in seconds
    :param apod: Dampening factor in 1/seconds
    :return: Exponential dampening
    """

    return np.exp(-apod * x)


def pulse_attn(freq: np.ndarray, t_pulse: float) -> np.ndarray:
    """
    Calculate attenuation of signal to account for finite pulse lengths.

    See Schmitt-Rohr/Spieß, eq. 2.126 for more information.

    :param freq: Frequency axis in Hz
    :param t_pulse: Assumed pulse length in s
    :return: Attenuation factor.
    """
    # cf. Schmitt-Rohr/Spieß eq. 2.126; omega_1 * t_p = pi/2
    pi_half_squared = np.pi**2 / 4
    omega = 2 * np.pi * freq

    numerator = np.sin(np.sqrt(pi_half_squared + omega**2 * t_pulse**2 / 2))
    denominator = np.sqrt(pi_half_squared + omega**2 * t_pulse**2 / 4)

    return np.pi * numerator / denominator / 2


def post_process_spectrum(parameter_file, apod, tpulse):
    parameter = read_parameter_file(parameter_file)

    # files have form ste_arg=0.000000e+01_parameter.txt, first remove ste part then parameter.txt to get variables
    varied_string = str(parameter_file).partition('_')[-1].rpartition('_')[0]

    # make evolution times
    tevo = np.linspace(parameter['techo_start'], parameter['techo_stop'], num=int(parameter['techo_steps']))

    if varied_string:
        raw_data = np.loadtxt(parameter_file.with_name(f'timesignal_{varied_string}.dat'))
    else:
        raw_data = np.loadtxt(parameter_file.with_name(f'timesignal.dat'))

    t = raw_data[:, 0]
    timesignal = raw_data[:, 1:]

    timesignal *= dampening(t, apod)[:, None]
    timesignal[0, :] /= 2

    # FT to spectrum
    freq = np.fft.fftshift(np.fft.fftfreq(t.size, d=parameter['dwell_time']))
    spec = np.fft.fftshift(np.fft.fft(timesignal, axis=0), axes=0).real
    spec *= pulse_attn(freq, t_pulse=tpulse)[:, None]

    #
    #
    # reduction_factor[i, :] = 2*timesignal[0, :]


    plt.plot(freq, spec)
    plt.gca().set_title(varied_string)
    plt.show()
    #
    # plt.semilogx(taus, reduction_factor, '.')
    # plt.show()