Plants do not perceive R:FR ratio. They perceive the phytochrome photostationary state (PSS), or the ratio between the two forms of phytochrome: Pr and Pfr. Basically, each wavelength has a certain conversion effect on these two forms. For example, red light strongly converts Pr to Pfr, farred light strongly converts Pfr to Pr. Blue (yes, blue) light also converts Pr to Pfr, although not as strong as red light. So, if you grow plants in monochromatic blue light, plants would also perceive it as there's some red light around. All the light combined will create an equilibrium of Pr-Pfr in the plants, i.e. the PSS.
Sager et al. (1988, doi: 10.13031/2013.30952) made an excellent paper in which they measured the phytochrome conversion efficiency of each wavelength. Using their data and formula and the spectrum of the light you use, you can calculate the PSS of your light environment. And you should use this instead of the purely red:farred intensity ratio in your study.