That may depend on the plant species you are working with. I found that with Chenopodium album lowered red to far-red light ratio delayed flowering contrary to other work with other species.
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You may take a general info from George Bernier http://www.ncbi.nlm.nih.gov/pmc/articles/PMC160348/pdf/051147.pdf. As far light dependent quantitative flowering you should take different units (and instruments) as lux is calibrated on human photopic response and has little far red and red in it. A radiometer with extended spectral response (320-1100 nm, like Hamamtsu S 1087-01) is the correct choice. Photoperiodic plants are sensitive to day legth for induction,but expression rates may depend on fluence rate. Red -far red ratios in the open field havre a limited effect.You may see specific infos according to your application, but several olants require a thermoperiod for induction.
In soybean, red : far red ratio causes the different photoperiod reaction depending on genotype. E loci which are responsibe for daylength reaction interact with R:FR ratio.