The Spatial Structures of Pseudophase Singularities in the Analytic Signal Representation of a Speckle Pattern and Their Application to Biological Kinematic Analysis

Abstract

Over the past decades, optical vortices or phase singularities have come to attract more and more attentions in the fields of applications such as optical metrology and photon manipulation. Recently, we proposed a new technique of micro-displacement measurement, called Optical Vortex Metrology (OVM) [1, 2]. The key idea of this technique is to make use of the phasesingularities in the pseudophase information of the complex analytic signal obtained from partial Hilbert transform, Riesz transform or Laguerre-Gauss transform of speckle patterns. Although we have experimentally demonstrated the validity of the proposed OVM in displacement measurement with both large dynamic range and high spatial resolution, the application of the proposed technique was restricted because the distortions of the morphology for the phase singularities stemming from speckle decorrelation enhance the difficulty in the unique search and identification of the registered marker phase singularity for calculation of their coordinate difference. In this paper, we propose a new technique that substantially improves the OVM technique in its ability of uniquely identifying the matching phase singularities under large distortions. In addition to the information about the location and the core structures of the phase singularities, we also detect the spatial structures of a group of the pseudophase singularities. This spatial structure can serve as a “constellation” that uniquely characterizes the mutual position relation between the individual phase singularities, and can be used for the purpose of the unique identification of a cluster of the phase singularities. Experimental results have been demonstrated that support the proposed principle.