  We discuss how to extract the pomeron-pomeron-$f_2(1270)$ ($\mathbb{P}
\mathbb{P} f_2(1270)$) coupling within the tensor-pomeron model. The general
$\mathbb{P} \mathbb{P} f_2(1270)$ coupling is a combination of seven basic
couplings (tensorial structures). To study these tensorial structures we
propose to measure the central-exclusive production of a $\pi^+ \pi^-$ pair in
the invariant mass region of the $f_2(1270)$ meson. An analysis of angular
distributions in the $\pi^+ \pi^-$ rest system, using the Collins-Soper (CS)
and the Gottfried-Jackson (GJ) frames, turns out to be particularly relevant
for our purpose. For both frames the $\cos\theta_{\pi^{+}}$ and
$\phi_{\pi^{+}}$ distributions are discussed. We find that the azimuthal angle
distributions in these frames are fairly sensitive to the choice of the
$\mathbb{P} \mathbb{P} f_2$ coupling. We show results for the resonance case
alone as well as when the dipion continuum is included. We show the influence
of the experimental cuts on the angular distributions in the context of
dedicated experimental studies at RHIC and LHC energies. Absorption corrections
are included for our final distributions.
