Timo knows his stuff. We generally like to advise to make your back a single growth ring and that is still the best advice, however if you scrape thru a ring on one limb, you can always chase that ring out to the middle of a non bending handle and it will be fine even if the other limb is in a different ring.
_____________|------------- the solid line is one limb in one ring, the verticle line is the center of a non bending handle and the dotted line is another ring in the other limb. A bow laid out this way, or a pair of spliced billets, will be fine.