The role of electron-lattice interaction in pair formation in high-Tc superconductivity has been under debate for twenty years. One thing which strongly distinguishes copper-oxides is that pairing appears to occur at atomic scale. Thus it is at atomic scale where electron-lattice interactions need to be examined. Using newly developed atomic resolution d2I/dV2-imaging technique with other well established spectroscopic imaging methods, three major experiments are performed to investigate lattice impact on superconductivity.

The first experiment reveals intense disorder of mode energy at nanometer scale. d2I/dV2 exhibits modulation along Cu-O bond direction and signatures interaction of antinodal quasiparticle with the bosonic mode. The average mode energy has minimal change with changing hole density. Substitution of 16O for 18O throughout the crystal exhibits the classic isotope shift in mode energy. Moreover, the local gap disorder and mode energy are anti-correlated.

The second experiment reveals the impact of periodic unit cell distortion on local superconductivity. The periodic unit cell distortion manifests itself as the incommensurate bulk crystalline modulation (called supermodulation). A technique called phase map is developed to accurately determine local supermodulation phase phi. Superconducting gap is found to vary co-sinusoidally with phi, indicating that the local pairing strength is modulated by Cu-Oapical bond length dA. Therefore a non random out-of-plane effect of lattice on superconductivity is identified.

In the last experiment, omega is found to vary co-sinusoidally with phi, similar to pairing gap, but almost 180 degree out of phase. This means delta and omega are both modulated by periodic distortion of CuO5 cage. Experiments on 16O/18O isotope samples at the same doping level are performed. Careful comparison of superconducting electronic structure of the isotope samples shows no detectable change. The only change is that the omega(phi) is systematically shifted by several mV while the delta(phi) remains unchanged.

Thorough studies presented in this thesis on r- and k-space electronic structure with atomic resolution, as well as impact of unit cell dimension change on pairing and lattice vibration mode, provide a complete set of microscopic experimental description of isotope effects in Cuprates, which any theoretical model should be consistent with.