Pitfalls in normalizing scanning tunneling spectroscopy and how to do it ``right'' (from an experimentalist perspective)

Scanning tunneling spectroscopy is widely used to probe the local density of states (LDOS) by measuring $\mathrm{d}I/\mathrm{d}V$ typically using a lock in amplifier. According to theory, the data has to be normalized by $(I/V)$ to reveal the true LDOS - of cause still convoluted with the tip density of states. This process can induce its own artifacts and has to be done carefully. In our case the algorithm includes finding the true bias offset (if any), correct any offset in the measured current, rescale the measured $\mathrm{d}I/\mathrm{d}V$ curves using the calculated version $(\Delta I/\Delta V)$, replacing $I(V)$ around $V_{\mathrm{bias}}=0$ by a polynomial and finally performing the normalization. The motivation and consequences of each step will be discussed using example data.