def overhead_antenna_pattern(right_ascension, declination, polarization):
    """Return the antenna pattern factors F+ and Fx as a function of sky
    location and polarization angle for a hypothetical interferometer located
    at the north pole. Angles are in radians. Declinations of ±π/2 correspond
    to the normal to the detector plane (i.e. overhead and underneath) while
    the point with zero right ascension and declination is the direction
    of one of the interferometer arms.

    Parameters
    ----------
    right_ascension: float
    declination: float
    polarization: float

    Returns
    -------
    f_plus: float
    f_cros: float
    """
    # convert from declination coordinate to polar (angle dropped from north axis)
    theta = np.pi / 2.0 - declination

    f_plus  = - (1.0/2.0) * (1.0 + cos(theta)*cos(theta)) * \
                cos (2.0 * right_ascension) * cos (2.0 * polarization) - \
                cos(theta) * sin(2.0*right_ascension) * sin (2.0 * polarization)

    f_cross =   (1.0/2.0) * (1.0 + cos(theta)*cos(theta)) * \
                cos (2.0 * right_ascension) * sin (2.0* polarization) - \
                cos(theta) * sin(2.0*right_ascension) * cos (2.0 * polarization)

    return f_plus, f_cross
def overhead_antenna_pattern ( right_ascension , declination , polarization ) : theta = np . pi / 2.0 - declination f_plus = - ( 1.0 / 2.0 ) * ( 1.0 + cos ( theta ) * cos ( theta ) ) * cos ( 2.0 * right_ascension ) * cos ( 2.0 * polarization ) - cos ( theta ) * sin ( 2.0 * right_ascension ) * sin ( 2.0 * polarization ) f_cross = ( 1.0 / 2.0 ) * ( 1.0 + cos ( theta ) * cos ( theta ) ) * cos ( 2.0 * right_ascension ) * sin ( 2.0 * polarization ) - cos ( theta ) * sin ( 2.0 * right_ascension ) * cos ( 2.0 * polarization ) return f_plus , f_cross
Return the antenna pattern factors F+ and Fx as a function of sky
    location and polarization angle for a hypothetical interferometer located
    at the north pole. Angles are in radians. Declinations of ±π/2 correspond
    to the normal to the detector plane (i.e. overhead and underneath) while
    the point with zero right ascension and declination is the direction
    of one of the interferometer arms.

    Parameters
    ----------
    right_ascension: float
    declination: float
    polarization: float

    Returns
    -------
    f_plus: float
    f_cros: float