Optical vortex metrology based on the core structures of phase singularities in Laguerre-Gauss transform of a speckle pattern

Abstract

A new technique for displacement measurement is proposed that makes use of phase singularities in the complex signal generated by a Laguerre-Gauss filter operation applied to a speckle pattern. The core structures of phase singularities are used as unique fingerprints attached to the object surface, and the displacement is determined by tracing the movement of registered phase singularities with their correspondence being identified by the fingerprints. Experimental results for translational and rotational displacement measurements are presented that demonstrate large dynamic range and high spatial resolution of the proposed optical vortex metrology.

Riesz transforms in statistical signal processing and their applications to speckle metrology: a review

“…The rotation angle was found to be −518milli-radians with the standard deviation 2milli-radians. We have also demonstrated optical vortex metrology for displacement measurement with nanometric resolution 11,12 , and for random flow measurements In addition to the information about the anisotropic core structure for an individual singularity in azimuthal angle map as its unique fingerprint for reliable identification, we detected a group of optical vortices (singularity clusters) with specific mutual spatial structure to further strengthen an unambiguous tracking over the entire field of view 14 . To demonstrate the performance of the proposed technique, a swimming fugu fish with a speckle-like intensity pattern on its body surface, as seen in Fig.6 (a) and (b), was used as a biological specimen.…”

“…Among all these attempts with proposed filters and generated signals, the signal obtained from Riesz transform has become the most promising one as the attempt for the natural extension of concept of 1-D analytic signal 5,8,10 . Although Riesz transforms have found successes in many applications such as fringe analysis 8 , pattern recognition 5,7 and optical metrology [11][12][13][14][15] , little work has been done to apply such transforms to statistically analyze random signal like speckle patterns. No knowledge has been obtained about the statistical properties of the associated signals when the Riesz transform is applied.…”

“…Some correlation properties associated with the vector representation of a real-valued 2-D speckle pattern have been presented, which share the formal analogy to the statistics of the 1-D analytic signal and may serve as a mathematical foundation for the statistical analysis of 2-D signal 17 . Under the framework of the vector signal representation generated by Riesz transforms, the principle and applications of several techniques, such as Optical Vortex Metrology [11][12][13][14] and Pseduo-Stokes vector correlation [15][16] , which we proposed recently for displacement and flow measurements will be revisited to demonstrate the unique capability of Riesz transform.…”

Analytical Model of the Optical Vortex Scanning Microscope with a Simple Phase Object

“…The first system (named SUPHIM-SUperresolution PHase Image Microscope) was proposed and tested by V. Tychynsky [1,2]. Although the solution proposed by Tychynsky was not successful [3], the phase singularities are still believed to constitute a potential solution for new imaging microscopic systems [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] (not all of which were focused on superresolution [7,8,13,14]). Presently, the most successful superresolution system using optical vortices is the STED microscope [9], where the vortex beam is used as a depletion beam.…”

Generation of Optical Vortex Arrays Using Single-Element Reversed-Wavefront Folding Interferometer

“…An interesting aspect of a vortex beam is that it possesses orbital angular momentum (OAM). Optical vortices play significant role for studying OAM of light fields [2,3] and have been widely used in the area of optical tweezers [4], singular optics [5], optical solitons [6], and optical metrology [7,8]. The most commonly used methods for generating OVs with single or multiple charge are synthetic holograms [9], spiral phase plates [10], liquidcrystal cells [11], dielectric wedge [12], and higher-order laser beams [13].…”