Mie-simulated field behind a dielectric sphere

    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]
    focus: float
        .. versionadded:: 0.5.0

        Axial focus position [m] measured from the center of the
        sphere in the direction of light propagation.
    arp: bool
        Use arbitrary precision (ARPREC) in BHFIELD computations

    Returns
    -------
    qpi: qpimage.QPImage
        Quantitative phase data set

def mie(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), focus=0, arp=True):
    """Mie-simulated field behind a dielectric sphere

    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]
    focus: float
        .. versionadded:: 0.5.0

        Axial focus position [m] measured from the center of the
        sphere in the direction of light propagation.
    arp: bool
        Use arbitrary precision (ARPREC) in BHFIELD computations

    Returns
    -------
    qpi: qpimage.QPImage
        Quantitative phase data set
    """
    # simulation parameters
    radius_um = radius * 1e6  # radius of sphere in um
    propd_um = radius_um  # simulate propagation through full sphere
    propd_lamd = radius / wavelength  # radius in wavelengths
    wave_nm = wavelength * 1e9
    # Qpsphere models define the position of the sphere with an index in
    # the array (because it is easier to work with). The pixel
    # indices run from (0, 0) to grid_size (without endpoint). BHFIELD
    # requires the extent to be given in µm. The distance in µm between
    # first and last pixel (measured from pixel center) is
    # (grid_size - 1) * pixel_size,
    size_um = (np.array(grid_size) - 1) * pixel_size * 1e6
    # The same holds for the offset. If we use size_um here,
    # we already take into account the half-pixel offset.
    offset_um = np.array(center) * pixel_size * 1e6 - size_um / 2

    kwargs = {"radius_sphere_um": radius_um,
              "refractive_index_medium": medium_index,
              "refractive_index_sphere": sphere_index,
              "measurement_position_um": propd_um,
              "wavelength_nm": wave_nm,
              "size_simulation_um": size_um,
              "shape_grid": grid_size,
              "offset_x_um": offset_um[0],
              "offset_y_um": offset_um[1]}

    background = np.exp(1j * 2 * np.pi * propd_lamd * medium_index)

    field = simulate_sphere(arp=arp, **kwargs) / background

    # refocus
    refoc = nrefocus.refocus(field,
                             d=-((radius+focus) / pixel_size),
                             nm=medium_index,
                             res=wavelength / pixel_size)

    # Phase (2PI offset corrected) and amplitude
    amp, pha = field2ap_corr(refoc)

    meta_data = {"pixel size": pixel_size,
                 "wavelength": wavelength,
                 "medium index": medium_index,
                 "sim center": center,
                 "sim radius": radius,
                 "sim index": sphere_index,
                 "sim model": "mie",
                 }

    qpi = qpimage.QPImage(data=(pha, amp),
                          which_data="phase,amplitude",
                          meta_data=meta_data)
    return qpi