I always keep my CF filter separate from my hood because the way you have it won't maximize the cooling of the grow space because you are cooling the lamp with heated air from the grow space, not with actual cool air that should come from the outside of the grow space. I do mine like so.... on one side of the hood I run a vent / ducting to one of the tents 6" - 8" openings, then I put a filter on that end, I use one of those thin brown Frost king filters, then on the other side of the hood I put my cheap 240 CFM booster fan sucking air outward from the hood, then I vent that to the outside, as that is the best way to maximize the cooling of your grow area when using a enclosed hood!
