Problem:

I'm trying to construct an anaerobic kitchen-waste digester at home.

The major output from the digester is methane - with a significant component of carbon dioxide. To scrub/reduce the CO2 I was thinking of passing the methane through a freshwater container charged with algae ... then it occurred to me to also think of introducing some bioluminescent algae to drive the photosynthesis & absorb some of the oxygen released by the other algae. Understandably this would be an unbalanced system.

But ... can bioluminescence drive photosynthesis?

Please describe the process of photosynthesis.