Acoustic foam is used to help dampen first order reflection of higher frequency sound. The noise emitted by the LT-150 is more a upper mid-range (say 500Hz) tone. I would think the the 1 1/2" space that open celled foam like that occupies could be better served with something else.
I am also building a hush box and planned on using the following:
First 1/2" MDF, then 1/8th acoustic dampening vinyl (often sold as Dynamat), 1/2" artificial jute carpet padding from Home Depot, and finally 1/8th" duct insulation tape (1/8" foamed rubber with thick aluminum front face).
I really, really doubt that much sound will be making it's way out of the solid portions of this box. I expect that most sound leakage will be from the HEPA covered air vents and the lens opening (fitted with FLD filter).
The benefit to the multilayer approach is that every material provides it's best sound absorption at a specific frequency. By alternating materials and densities, you can get a more total sound barrier.
I think the aluminum face may resonate the sound so that when it does leak through the air vents it would sound louder. Plus the reflected light from light spill may worsen contrast of your PJ. I'd recommend having 2 half-inch MDF sandwhich together using screws with Dynamat ( www.partsexpress.com has generic version for less). Dynamat blocks the resonation and vibration and the 2 layer of MDF should work better at deadening the sounds. I guess you could mount the aluminum tape backward but I don't think it'll stick without glueing which is a lot of trouble. For even more sound absorbtion, add a thin layer of fiberglass (carcinogen) or polyfill (fibers may get into optics). I went with polyfill and covered it with black cotton sheet to contain the fibers and absorb the light spill.
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