  We apply the principle of maximum conformality (PMC) to the
Balitsky-Fadin-Kuraev-Lipatov (BFKL) Pomeron intercept at the next-to-leading
logarithmic (NLL) accuracy. The PMC eliminates the conventional renormalization
scale ambiguity by absorbing the non-conformal $\{\beta_i\}$-terms into the
running coupling, and a more accurate pQCD estimation can be obtained. After
PMC scale setting, the QCD perturbative convergence can be greatly improved due
to the elimination of renormalon terms in pQCD series, and the BFKL Pomeron
intercept has a weak dependence on the virtuality of the reggeized gluon. For
example, by taking the Fried-Yennie gauge, we obtain $\omega_{\rm MOM}^{\rm
PMC}(Q^{2},0)\in [0.149,0.176]$ for $Q^2\in[1,100]\;{\rm GeV}^2$. This is a
good property to apply to the high-energy phenomenology. Further more, to
compare with the data, it is found that the physical ${\rm MOM}$-scheme is more
reliable than the $\overline{\rm MS}$-scheme. The ${\rm MOM}$-scheme is gauge
dependent, which can also be greatly suppressed after PMC scale setting. We
discuss the MOM-scheme gauge dependence for the Pomeron intercept by adopting
three gauges, i.e. the Landau gauge, the Feynman gauge and the Fried-Yennie
gauge, and we obtain $\omega_{\rm MOM}^{\rm PMC}(Q^{2}=15\;{\rm GeV}^2,0) =
0.166^{+0.010}_{-0.017}$; i.e. about $10\%$ gauge dependence is observed. We
apply the BFKL Pomeron intercept to the photon-photon collision process, and
compare the theoretical predictions with the data from the OPAL and L3
experiments.
