http://en.wikipedia.org/wiki/Digital_caliper#Digital_caliper

Digital calipers contain a linear encoder. A pattern of bars is etched directly on the Printed circuit board in the slider. Under the scale of the caliper another printed circuit board also contains an etched pattern of lines. The combination of these printed circuit boards forms two variable Capacitors. As the slider moves the capacitance changes in a linear fashion and in a repeating pattern. The two capacitances are out of phase. The circuitry built into the slider counts the bars as the slider moves and does a linear interpolation based on the magnitudes of the capacitors to find the precise position of the slider.