The principle of stroboscopic motion freezing of oscillating objects extends directly to interference microscopes that use coherence as part of the measurement principle. Analysis shows, however, that the fringe contrast loss for out-of-plane motion in stroboscopic interferometry is a wavelength-dependent phenomenon, which can alter the apparent nominal center wavelength of the white-light source. As in monochromatic systems, the key adjustable parameter is the duty cycle, equal to the product of the vibrational frequency and the pulse width. This theoretical study provides detailed graphs of expected errors as a function of the duty cycle, including fringe contrast loss, apparent wavelength shift, and measurement error.