def volume_depolarization_cross_parallel(signal_cross, signal_parallel,
    t_cross, t_parallel, r_cross, r_parallel, v_star):
    """    
    Calculate the linear volume depolarization ratio in a lidar system that is
    able to detect the cross-to-parallel depolarization ratio.
    The calibration factor from the delta-90 calibration is being used.
    
    Parameters
    ----------
    signal_cross: vector
       The input vertical profile from the cross channel. Normal measurement (phi=0).
    signal_parallel: vector
       The input vertical profile from the parallel channel. Normal measurement (phi=0).
    t_cross: float
       Transmittance of cross component through transmitted path.
    t_parallel: float
       Transmittance of parallel component through transmitted path.
    r_cross: float
       Transmittance of cross component through reflected path.
    r_parallel: float
       Transmittance of parallel component through reflected path.
    v_star: float
       The calibration constant.
       
    Returns
    -------
    delta_v: vector
       The linear volume depolarization.
    
    Notes
    -----
    The linear volume depolarization ratio is calculated by the formula:
    
    .. math::
       \\delta^V = \\frac{\\frac{\\delta^*}{V^*}T_p - R_p}{R_s - \\frac{\\delta^*}{V^*}T_s}
    
    References
    ----------
    Freudenthaler, V. et al. Depolarization ratio profiling at several wavelengths in pure
    Saharan dust during SAMUM 2006. Tellus, 61B, 165-179 (2008)
    """
    delta_star = signal_cross / signal_parallel
    delta_v = (delta_star * t_parallel / v_star - r_parallel) / (r_cross - 
        delta_star * t_cross / v_star)
    return delta_v
