If you get dimming while driving, especially when backing off the gas, it is irritating, but common. Some of us have been chasing this for years. New alternators or new batteries solve the problem for a few months and then it comes back again. Many of us have checked cables and grounds and some - like myself - have even added auxiliary battery cables. (The "big three" mod.) No solution yet. It just seems to be part of our platform.
It almost seems it's part of the PCM, and if the battery is brand new or the alternator is brand new, it stops for a while but then comes back. Check your cable connections and grounds, get the alternator checked out and load test the battery. Also follow the suggestions from other members of this forum, but if everything checks out okay, there might not be a solution.