3D Profilometry With a Self-Mixing Interferometer: Analysis of the Speckle Error

We show that the speckle phase error incurred when the laser spot is scanned over the diffusing surface can be made as low as 10– $20~\mu \text{m}$ for object sizes in the range 3–10 cm. This result is new, to the best of our knowledge, because it is usually assumed that when the spot moves of its size, the phase becomes uncorrelated and the measurement cannot be done anymore. We carry out numerical simulations of the process and derive an analytical model to evaluate the phase error and the noise equivalent displacement of the profile measurement by a self-mixing interferometer.