White-light interferometry—Envelope detection by Hilbert transform and influence of noise

Abstract White-light interferometry is an established method for the measurement of the geometrical shape of objects. It can also be used for the measurement of the shape of objects with rough surfaces. Because of the rough surface, the phase of the white-light interferogram is not evaluated, the height information is obtained from the interferogram envelope. Hilbert transform is a classical method to calculate the envelope. In a real measurement, the interferogram is affected by the noise. We look for the answer to following questions: how does the noise of the calculated envelope look like? How does the noise influence the measurement uncertainty?