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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def rytov_sc(radius=5e-6, sphere_index=1.339, medium_index=1.333, wavelength=550e-9, pixel_size=1e-7, grid_size=(80, 80), center=(39.5, 39.5), radius_sampling=42):
 r"""Field behind a dielectric sphere, systematically corrected Rytov This method implements a correction of :func:`qpsphere.models.rytov`, where the `radius` :math:`r_\text{Ryt}` and the `sphere_index` :math:`n_\text{Ryt}` are corrected using the approach described in :cite:`Mueller2018` (eqns. 3,4, and 5). .. math:: n_\text{Ryt-SC} &= n_\text{Ryt} + n_\text{med} \cdot \left( a_n x^2 + b_n x + c_n \right) r_\text{Ryt-SC} &= r_\text{Ryt} \cdot \left( a_r x^2 +b_r x + c_r \right) &\text{with} x = \frac{n_\text{Ryt}}{n_\text{med}} - 1 The correction factors are given in :data:`qpsphere.models.mod_rytov_sc.RSC_PARAMS`. Parameters radius: float Radius of the sphere [m] sphere_index: float Refractive index of the sphere medium_index: float Refractive index of the surrounding medium wavelength: float Vacuum wavelength of the imaging light [m] pixel_size: float Pixel size [m] grid_size: tuple of floats Resulting image size in x and y [px] center: tuple of floats Center position in image coordinates [px] radius_sampling: int Number of pixels used to sample the sphere radius when computing the Rytov field. The default value of 42 pixels is a reasonable number for single-cell analysis. Returns ------- qpi: qpimage.QPImage Quantitative phase data set """

    r_ryt, n_ryt = correct_rytov_sc_input(radius_sc=radius,
                                          sphere_index_sc=sphere_index,
                                          medium_index=medium_index,
                                          radius_sampling=radius_sampling)

    qpi = mod_rytov.rytov(radius=r_ryt,
                          sphere_index=n_ryt,
                          medium_index=medium_index,
                          wavelength=wavelength,
                          pixel_size=pixel_size,
                          grid_size=grid_size,
                          center=center,
                          radius_sampling=radius_sampling)

    # update correct simulation parameters
    qpi["sim radius"] = radius
    qpi["sim index"] = sphere_index
    qpi["sim model"] = "rytov-sc"

    return qpi