Digital holographic particle image velocimetry: eliminating a sign-ambiguity error and a bias error from the measured particle field displacement

In a typical digital holographic PIV recording set-up, the reference beam and the object beam propagate towards the recording device along parallel axes. Consequently, in a reconstructed volume, the real image of the recorded particle field and the speckle pattern that originates from the virtual image of the recorded particle field overlap. If the recorded particle field experiences a longitudinal displacement between two recordings and if the two reconstructed complex-amplitude fields are analysed with a 3D correlation analysis, two separate peaks appear in the resulting correlation-coefficient volume. The two peaks are located at opposite longitudinal positions. One peak is related to the displacement of the real image and the other peak is related to the displacement of the speckle pattern that originates from the virtual image. Because both peaks have a comparable height, a sign ambiguity appears in the longitudinal component of the measured particle field displacement. Additionally, the measured longitudinal particle field displacement suffers from a bias error. The sign ambiguity and the bias error can be suppressed by applying a threshold operation to the reconstructed amplitude. The sign ambiguity, characterized by Gamma, is suppressed by more than a factor of 60. The dimensionless bias error is reduced by a factor of 5.