We study the density correlation function (DCF) of DPPC lipid bilayers. We compare Molecular Dynamics (MD) results with theoretical predictions obtained with a mesoscopic description, in terms of the lipid membrane elasticity. One key objective of our work is the quantification of the lipid membrane elasticity directly from the DCF, both for the membrane undulations and local membrane thickness. Our method does not require the definition of instantaneous surfaces or internal variables defining lipid orientations. Building on our previous work, here we focus on the intralayer correlations, i.e. the DCF of lipids residing on the same monolayer, by tracking only the position of the phosphorus atoms in a lipid head group. We demonstrate the relevance of the intralayer two-dimensional (2D) correlations to the total DCF. We further show that all-atom (AA) and coarse grained (CG) lipid forcefields, feature distintively different DCFs. The CG forcefield predicts results in good agreement with the mesoscopic predictions, for the entire wavevector range; the AA forcefield (CHARMM36) predict strong peristaltic fluctuations at long wavevectors q≳0.8 nm-1, which are absent in the CG lipid model (MARTINI).