$\alpha'$-corrections to DBI action via T-duality constraint

It is known that D$_p$-brane effective action at the leading order of $\alpha'$ in flat space-time which is given by DBI action, transforms to D$_{p-1}$-brane effective action under standard T-duality transformations of the open string gauge bosons and transverse scalar fields. Extending this duality to order $\alpha'$, one may find corrections to the DBI action which include the second fundamental form $\Omega$ and the covariant derivative of gauge field strength $DF$, as well as the corrections to the T-duality transformations. Using this idea, up to two parameters, we have found all 81 covariant couplings of $D FD F$ and $\Omega\Omega$ with zero, two, four and six $F$'s. The four gauge field couplings that the T-duality constraint fixes are consistent with the known couplings in the literature.