AbstractAn unidentified quantum fluid designated the pseudogap (PG) phase is produced by electron-density depletion in the CuO₂ antiferromagnetic insulator. Current theories suggest that the PG phase may be a pair density wave (PDW) state characterized by a spatially modulating density of electron pairs. Such a state should exhibit a periodically modulating energy gap ${Δ }_{{{{{{\rm{P}}}}}}}({{{{{\boldsymbol{r}}}}}})$ Δ P ( r ) in real-space, and a characteristic quasiparticle scattering interference (QPI) signature ${Λ }_{{{{{{\rm{P}}}}}}}({{{{{\boldsymbol{q}}}}}})$ Λ P ( q ) in wavevector space. By studying strongly underdoped Bi₂Sr₂CaDyCu₂O₈ at hole-density ~0.08 in the superconductive phase, we detect the 8a₀-periodic ${Δ }_{{{{{{\rm{P}}}}}}}({{{{{\boldsymbol{r}}}}}})$ Δ P ( r ) modulations signifying a PDW coexisting with superconductivity. Then, by visualizing the temperature dependence of this electronic structure from the superconducting into the pseudogap phase, we find the evolution of the scattering interference signature $Λ ({{{{{\boldsymbol{q}}}}}})$ Λ ( q ) that is predicted specifically for the temperature dependence of an 8a₀-periodic PDW. These observations are consistent with theory for the transition from a PDW state coexisting with d-wave superconductivity to a pure PDW state in the Bi₂Sr₂CaDyCu₂O₈ pseudogap phase.