Simulate scattering at a sphere

    Parameters
    ----------
    radius: float
        Radius of the sphere [m]
    sphere_index: float
        Refractive index of the object
    medium_index: float
        Refractive index of the surrounding medium
    wavelength: float
        Vacuum wavelength of the imaging light [m]
    grid_size: tuple of ints or int
        Resulting image size in x and y [px]
    model: str
        Sphere model to use (see :const:`available`)
    pixel_size: float or None
        Pixel size [m]; if set to `None` the pixel size is
        chosen such that the radius fits at least three to
        four times into the grid.
    center: tuple of floats or None
        Center position in image coordinates [px]; if set to
        None, the center of the image (grid_size - 1)/2 is
        used.

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

def simulate(radius=5e-6, sphere_index=1.339, medium_index=1.333,
             wavelength=550e-9, grid_size=(80, 80), model="projection",
             pixel_size=None, center=None):
    """Simulate scattering at a sphere

    Parameters
    ----------
    radius: float
        Radius of the sphere [m]
    sphere_index: float
        Refractive index of the object
    medium_index: float
        Refractive index of the surrounding medium
    wavelength: float
        Vacuum wavelength of the imaging light [m]
    grid_size: tuple of ints or int
        Resulting image size in x and y [px]
    model: str
        Sphere model to use (see :const:`available`)
    pixel_size: float or None
        Pixel size [m]; if set to `None` the pixel size is
        chosen such that the radius fits at least three to
        four times into the grid.
    center: tuple of floats or None
        Center position in image coordinates [px]; if set to
        None, the center of the image (grid_size - 1)/2 is
        used.

    Returns
    -------
    qpi: qpimage.QPImage
        Quantitative phase data set
    """
    if isinstance(grid_size, numbers.Integral):
        # default to square-shape grid
        grid_size = (grid_size, grid_size)
    if pixel_size is None:
        # select simulation automatically
        rl = radius / wavelength
        if rl < 5:
            # a lot of diffraction artifacts may occur;
            # use 4x radius to capture the full field
            fact = 4
        elif rl >= 5 and rl <= 10:
            # linearly decrease towards 3x radius
            fact = 4 - (rl - 5) / 5
        else:
            # not many diffraction artifacts occur;
            # 3x radius is enough and allows to
            # simulate larger radii with BHFIELD
            fact = 3
        pixel_size = fact * radius / np.min(grid_size)

    if center is None:
        center = (np.array(grid_size) - 1) / 2

    model = model_dict[model]
    qpi = model(radius=radius,
                sphere_index=sphere_index,
                medium_index=medium_index,
                wavelength=wavelength,
                pixel_size=pixel_size,
                grid_size=grid_size,
                center=center)

    return qpi