Speckle interferometry is an established method for the interferometric characterization of rough objects. By measuring the specimen before and after a force is applied, the deformation of an object under a load can be determined. Alternatively, using two wavelengths, the shape of the object itself can be measured. However, owing to the multiple beam nature of the interference from a rough surface, the resulting phase maps are impaired by the presence of phase singularities, see Fig. 1. Firstly, the phase singularities make the speckle phase noisy. Secondly, in regions where the fringe density is high, the presence of phase singularities makes the fringes dissolve, such that even advanced unwrapping and filtering methods fail.
Therefore, we aim at a physical procedure to reduce the number of phase singularities in the speckle phase. This is achieved by tayloring the spatial coherence in the interferometer via extended (and possibly structured) light sources, realizing an incoherent averaging of different, mutually incoherent speckle fields. Figure 2 shows the relevant part of the setup when using an incoherent light source in the form of a disc.
The speckle phase for a point and the disc source are shown in Fig. 3 for the case of a deformation measurement. The speckle phase is considerably smoother, and the phase singularities are significantly reduced in number.
Using an extended disc source has the disadvantage of limiting the flexibility in the interferometer, because the optical path lengths of object and reference arms have to be matched to achieve high speckle contrast. Other light source shapes can be used to alleviate this restriction, including periodic light sources or ring shaped structures.
The mechanism behind the reduction process involves subtle effects, including a change in the effective speckle size due to the incoherent averaging, while at the same time enhancing phase singularity correlations in the fields between the first and second measurements.