def nonlinear_limb_darkening(x, c0=0.0, c1=0.0, c2=0.0, c3=0.0):
    """
    Define non-linear limb darkening model with four parameters c0, c1, c2, c3.
    """
    model = (1. - (c0 * (1. - x ** (1. / 2)) + c1 * (1. - x ** (2. / 2)) + c2 * (1. - x ** (3. / 2)) + c3 *
                   (1. - x ** (4. / 2))))
    return model