We demonstrate that the recent observations of spatial oscillations in the energy position of the superconducting coherence peaks in the cuprate, transition metal dichalcogenide, iron-based, and heavy-fermion superconductors are consistent with the possible presence of a pair-, charge-, or spin-density-wave phase. We show that for all three cases, the spatial oscillations of the superconducting order parameter, $\mathrm{\Delta }\left(\mathbf{r}\right)$ can be imaged via the critical Josephson current, $I_c\left(\mathbf{r}\right)$ measured in Josephson scanning tunneling spectroscopy experiments. Finally, we show that the spatial oscillations of the density waves and of $\mathrm{\Delta }\left(\mathbf{r}\right)$ exhibit relative phase shifts of $\mathrm{\Delta }\varphi =0$ or $\pi$ for a charge-density wave, and $\mathrm{\Delta }\varphi =\pi /2$ for the spin-density wave.

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• Charge density waves
• Pair density wave
• Spin density waves
• Superconductivity
• Scanning tunneling spectroscopy