Microscopic images of both the structures and surface potential of held emitter arrays were measured by scanning Maxwell-stress microscopy (SMM) in air. Results of the SMM measurements clearly showed nanometer-scale irregularities in the structures and structure-related surface potential distributions. The surface potential of Si was rather flat even at the emitter tip apex. From these results, the work-function values for various emitter materials such as Si, Cr, Mo, W, etc. have been derived by using an Au film as the reference material; the work function of Au was assumed to be 5.1 eV. Experimental procedures and results are described in detail.