Purpose. To observe and explain Vernier acuity and sensitivity to periodic irregularity of edges within a common framework. Methods. Forced-choice thresholds for discriminating smooth, straight edges at 34 different slopes, from edges produced by an algorithm for representing edges by discrete pixels, as exemplified below, were obtained from 3 observers. Note that the upper left example is a classic Vernier acuity pattern; the lower right, a periodic pattern; and the bottom middle, a Vernier acuity pattern superimposed on a periodic pattern. The patterns actually used were 150 pixels across. (Figure Presented) (Graph Presented) Results. The reciprocals of the mean threshold visual angles as a function of slope of the edge are shown in the figure. Each data point (Os) is shown with the corresponding value (Xs) determined by a theory combining (1) the 1-D Fourier transform of the edge shapes, (2) a function describing sensitivity to sinusoidal modulation of edges (Hamerly and Springer, JOSA, 1981), and (3) the oblique effect. Conclusion. Vernier acuity, detection of periodic edge modulation, and combinations of the two can be understood in terms of three simple functions.