def lightness_correlate(A, A_w, c, z):
    """
    Returns the *Lightness* correlate :math:`J`.

    Parameters
    ----------
    A : numeric
        Achromatic response :math:`A` for the stimulus.
    A_w : numeric
        Achromatic response :math:`A_w` for the whitepoint.
    c : numeric
        Surround exponential non linearity :math:`c`.
    z : numeric
        Base exponential non linearity :math:`z`.

    Returns
    -------
    numeric
        *Lightness* correlate :math:`J`.

    Examples
    --------
    >>> A = 23.9394809667
    >>> A_w = 46.1882087914
    >>> c = 0.69
    >>> z = 1.9272135955
    >>> lightness_correlate(A, A_w, c, z)  # doctest: +ELLIPSIS
    41.7310911...
    """

    J = 100 * (A / A_w) ** (c * z)
    return J