A tunable light source having a temporal coherence length such that interference fringes are detected within the optical path difference of the interferometer is spectrally controlled to produce multiple wavelengths during sequential fractions of the integration time of the detector of the interferometer. The wavelengths are selected so as to produce a visible correlogram at each integration time according to spectrally controlled interferometry (SCI) principles. Such different wavelengths may be produced by stepwise or continuous modulation. The modulation step is repeated sequentially while changing the period of modulation to produce a succession of predetermined spatial patterns of interference fringes, as required for interferometric measurements. The approach enables the practice of SCI with common-path apparatus used for conventional phase shifting, thereby combining the advantages of high-coherence and white-light interferometry. A suitable time-modulated source combines a coherent source with an optical modulator and a waveform generator synchronized with the source.