What is the working principle of a potentiostat? What role does the reference electrode play?

Question

I am trying to understand the working principle of a potentiostat instrument, which is used as impedance analyzer in a three-electrode cell system setup.

By referring on the circuit below, any current contribution due to redox reaction is compensated controlling the output voltage Vo of the opamp. Indeed, changes of Im involves changes of the voltage drop across the reference electrode and the working electrode. The voltage drop between Re and We is fed to the input of the system, so the output voltage Vo is modified until the sample voltage equals the input voltage Ei. Finally, the current is evaluated using a known resistor Rm where the voltage drop Vm is measured (Im = Vm/Rm). Is that correct?

Why it is necessary to use a reference electrode instead of a polarizable electrode? A reference electrode is characterized by a constant potential between the interface electrode/electrolyte, what involves that condition in the whole system.

Basic scheme of a potentiostat instrument:

Answer 1

There can happen some chemical reaction on the surface of CE which adds some voltage between the liquid and CE, maybe a layer of a gas. It's effectively in series with Vo and hides what happens to be the electric field strength in the liquid. The circuit adjusts Vo so that the voltage between the reference electrode is the same as the input Ei. The electrode system is calibrated so that one knows the electric field strength in the liquid for certain Ei. The voltage drop over Rm tells how much current is caused and the geometry of the cell is selected so that the current presents how high current density is caused in the liquid by certain electric field strength. Current density vs electric field strength probably is the interesting property of the liquid.

Note: This is what a electronic hobbyist with elementary knowledge of electricity can find by pure reasoning. It unfortunately totally skips all electrochemical engineering terminology.