Potentiometer minimal turning for high resolution
Try this circuit, using 2 pots; its standard method to set coarse, and then fine voltage into ADCs, to examine how the output code bits vary to ensure there are no missing codes







simulate this circuit &ndash; Schematic created using CircuitLab

you may need to insert R8, and use the top node of R8 as your output RTN node, thus allowing testing somewhat below 0volts Vout. 

Make the capacitor as large as possible, electrolytic if you wish. Watch out for
microphonics (vibration sensitivity) of ceramic caps.