Superconducting gap in the presence of bilayer splitting in underdoped $(\mathrm{P}\mathrm{b},\mathrm{B}\mathrm{i}{)}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$

The clearly resolved bilayer splitting in angle-resolved photoemission spectra of the underdoped Pb-Bi2212 compound raises the question of how the bonding and antibonding sheets of the Fermi surface are gapped in the superconducting state. Here we compare the superconducting gaps for both split components and show that within the experimental uncertainties they are identical. By tuning the relative intensity of the bonding and antibonding bands using different excitation conditions, we determine the precise k dependence of the leading edge gap. Significant deviations from the simple $\cos {(k}_x)-\cos {(k}_y)$ gap function for the studied doping level are detected.