As an alternative to correlation-based techniques widely used in conventional speckle metrology, we propose a new technique that makes use of phase singularities in the complex analytic signal of a speckle pattern as indicators of local speckle displacements. The complex analytic signal is generated by vortex filtering the speckle pattern. Experimental results are presented that demonstrate the validity and the performance of the proposed optical vortex metrology with nano-scale resolution.
The Laguerre-Gaussian (LG) beam is an optical beam with a phase singularity that propagates along its axis. We have studied the effect of astigmatnic aberration on LG beams through numerical simulation and experiment. An LG beam with astigmatic aberration can undergo various transformations. An LG beam with astigmatic aberration can be expanded in terms of Hermite-Gaussian (HG) beams whose horizontal and vertical axes are aligned with the axes of the astigmatism. By redefining the expansion coefficients to include the Gouy phase of the HG beams, the coefficients can be reduced to a single parameter that depends on the propagation distance. It can be shown that the various transformations of the LG beam is governed by this parameter. This presents us with a simple method of estimation the beam profile and positions of the split phase singularities at any given propagation distance. The estimations show good agreement with intensity and phase distributions calculated with the angular spectrum method.
A new technique is proposed that enables reconstruction of phase-shift digital holograms with unknown phase shifts. The technique is based on the phase-shift technique combined with the Fourier transform technique to have the advantages of these two techniques. First the unknown phase shifts are determined by the Fourier transform technique, and then the complex field recorded in the digital hologram is obtained by the phase shift technique using the knowledge of the phase shifts. Experimental results are presented that demonstrate the validity of the principle.
The Laguerre-Gaussian (LG) beam is an optical beam with a phase singularity that propagates along its axis. We have previously reported the fabrication of blazed transmission phase holograms to generate beams with phase singularities. A common problem encountered in the generation of a phase singularity with high charge is that the singularity tends to split into m individual charge 1 singularities, where m is the charge of the original singularity. We have found through numerical simulation that astigmatic aberration can cause a higher-charge phase singularity to split. We have also found that strong astigmatic aberrations make the resulting beam close to a Hermite-Gaussian beam rather than an LG beam. Experimental investigation of these phenomena agree with the numerical simulation.
The Laguerre-Gaussian beam is an optical beam with a phase singularity that propagates along its axis. We have fabricated blazed phase holograms to generate these beams using electron- beam lithography techniques. The resulting holograms were illuminated with a Gaussian beam, and the phase distribution of the resulting beams were examined by analyzing interference fringes with the Fourier-transform method.
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