Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement

Rather than regarding the phase singularities as obstacles or nuisances in phase unwrapping, we explore new possibilities of making use of the phase singularities in optical metrology. Instead of intensity correlation techniques used in conventional speckle metrology, we propose a new technique of displacement measurement that makes use of the density of phase singularities in the complex analytic signal of the speckle pattern, which is generated by Hilbert filtering. Experimental results and theoretical analysis are presented that demonstrate the validity of the proposed technique.