A work function study based on the onset shift (i.e., following low energy cut-off) of secondary electron spectra has been used for the last four decades to monitor the deposition and adsorption in real time, measure the dipole momentum and polarizability of the surface layer, and determine the lateral distribution of the work function. In this work, we show that the onset shift depends on both the coverage of adsorbed species that change the work function and the size of low work function patches. Additionally, the extraction field, which is always applied in these measurements, may also influence the onset shift. Numerical calculations of the potential distributions above different non-uniform surfaces were performed in order to quantitatively determine each of these influences. Depending on the patch size, we define three measurement regimes in which the onset position is related to either the surface average of the work function (small patches), the minimum local work function (large patches), or a value in-between (intermediate size patches). Experimental data have corroborated these findings and demonstrated that manipulating the extraction field intensity enables transition between the measurement regimes. Typical misinterpretations due to neglecting the patch size contribution and the surface non-uniformity to the onset shift are analyzed. Additionally, possible application of work function study for determination of the growth mode in the case of submonolayer deposition was discussed.