We present phase-sensitive absolute amplitude measurements of surface acoustic wave fields obtained using a stroboscopic white-light interferometer. The data analysis makes use of the high resolution available in the measured interferometric phase data, enabling the characterization of the out-of-plane surface vibration fields in electrically excited microstructures with better than 100 pm amplitude resolution. The setup uses a supercontinuum light source with tailored spectral properties for obtaining the high amplitude resolution. The duration of the light pulses is less than 300 ps to allow the detection of high frequencies. These capabilities enabled a detailed measurement of the focusing of surface acoustic waves by an annular interdigital transducer structure operating at 74 MHz, featuring a maximum vibration amplitude of 3 nm.