Displacement measurement with multi-level spiral phase filtering in speckle interferometry

A multi-level spiral phase filter is proposed in electronic speckle pattern interferometry (ESPI) for out-of-plane displacement measurements. This filter generates a particular kind of speckle pattern that results from the convolution of standard speckles with the filter point spread function (Fourier transform). We shall refer to it as a vortex-filtered speckle pattern (VF-SP). It is shown here that if unresolved and fully developed VF-SPs are generated, then each speckle contains embedded phase terms which can be controlled by the multi-level spiral filter rotation. This mechanism effectively allows the application of standard phase extraction procedures for displacement measurements. Numerical simulations of an interferometer working with VF-SPs were done to verify this technique. Experimental validation was achieved with an out-of-plane electronic speckle pattern interferometer, in which an Liquid Crystal on Silicon (LCoS) was used to generate the multi-level spiral phase filters.