The TBT diagram, named after the authors who developed it (Trouille, Barger & Tremonti, 2011), combines rest-frame g-z color with the emission line ratio [NeIII]3869/[OII]3726,3729 in order to disentangle AGN from star-forming galaxies. It was calibrated using low-redshift SDSS galaxies similarly to the approach followed elsewhere when developing alternate diagnostic diagrams (e.g., Blue, DEW, MEx and CEx diagrams described in other pages). The required measurements for the TBT diagram are available out to z~1.4 with optical spectra, extending further the range with respect to diagrams that include [OIII]5007.
The division line on the TBT diagram is as follows:
(g-z)0 = -1.2 x log([NeIII]/[OII]) - 0.4
where (g-z)0 is the rest-frame g-r color, [NeIII] is the line flux of [NeIII]3869 and [OII] is the line flux of the [OII]3726,3729 doublet (sometimes labelled as [OII]3727 when the doublet components are not resolved).
This code assumes that rest-frame g-z colors are in AB magnitudes. In the case of the SDSS prior sample, they were calculated using the kcorrect code (version v4_1_4) from Blanton & Roweis (2007). Also see the kcorrect wiki site here.