Inverse Hammer-Aitoff projection (deg).

def aitoffImageToSphere(x, y):
    """
    Inverse Hammer-Aitoff projection (deg).
    """
    x = x - 360.*(x>180)
    x = np.asarray(np.radians(x))
    y = np.asarray(np.radians(y))
    z = np.sqrt(1. - (x / 4.)**2 - (y / 2.)**2) # rad
    lon = 2. * np.arctan2((2. * z**2) - 1, (z / 2.) * x)
    lat = np.arcsin( y * z)
    return ((180. - np.degrees(lon)) % 360.), np.degrees(lat)