def brightness_correlate(A, A_w, M, N_b):
    """
    Returns the *brightness* correlate :math:`Q`.

    Parameters
    ----------
    A : numeric
         Achromatic signal :math:`A`.
    A_a: numeric
        Achromatic post adaptation signal of the reference white :math:`A_w`.
    M : numeric
        Overall chromatic response :math:`M`.
    N_b : numeric
         Brightness surround induction factor :math:`N_b`.

    Returns
    -------
    numeric
        *Brightness* correlate :math:`Q`.

    Examples
    --------
    >>> A = 15.506854623621885
    >>> A_w = 35.718916676317086
    >>> M = 0.0082378857872741976
    >>> N_b = 75.0
    >>> brightness_correlate(A, A_w, M, N_b)  # doctest: +ELLIPSIS
    22.2097654...
    """

    N_1 = ((7 * A_w) ** 0.5) / (5.33 * N_b ** 0.13)
    N_2 = (7 * A_w * N_b ** 0.362) / 200

    Q = ((7 * (A + (M / 100))) ** 0.6) * N_1 - N_2
    return Q