Little emphasis is put on scanning for birds as an avoidance technique in todays training. I don't fault the Hudson crew for not seeing the birds at all. Dealing with so many of them on a daily basis I had to scan for them or suffer the consequences. Try it some time. First they appear as dots then rapidly get bigger. Use the old constant bearing, decreasing range technique to avoid them. Smooth changes will not alarm your passengers. I always got my FO involved too in case I missed one.
The only bird we hit in over 600 landings there it was the FO flying and at 500 ft on take off we both saw the turkey buzzard in our path following our turn so we reversed the turn and the buzzard did too. We reversed again and the buzzard followed. The FO said they always dive so we pulled up as much as we could and the buzzard did likewise. It hit above my windshield and deflected above us. We flew at a lower altitude to MIA in case it popped some rivets. Just a football size blood smear, no damage.