A birefringent twister combines a birefringent element and a cylindrical lens to realize a stable twisting interferometer. We report numerical simulation for a birefringent twister for Gaussian beam and Laguerre-Gaussian beam inputs.
We have generated and propagated both diffracting and non-diffracting speckles using the scattering of perfect optical vortices. The diffracting speckles have been realized in the near field and non-diffracting speckles have been realized in the far field, i.e. after taking the Fourier transform of near-field speckles using a simple convex lens. We found that the experimental results are in good agreement with the theoretical results. These results may find applications in classical cryptography and communication as we have both varying and non-varying random field patterns with propagation distance.
A modified interferometer that introduces position and momentum shifts in mutually orthogonal directions can transform optical modes by raising and lowering radial and azimuthal mode indices. The action of this interferometer can be generalized in the form of a pair of twisting operators, which can be further written in terms of the ladder operators of the 2-dimensional harmonic oscillator. For lower order input modes there is good agreement between theory and experiment, but as the input mode becomes more complex, experimental results start to deviates from first-order theory. This is due to the shifts becoming larger relative to beam structure. We discuss how higher order corrections can be calculated for such cases.
We previously proposed a three-dimensional microscopic imaging system for objects hidden behind scattering media using in-line phase-shift digital holography, which simultaneously captures amplitude and phase information. However, as the thickness of the scattering medium increases, the influence of scattering is enhanced, and the reconstructed image of the object behind the scattering medium deteriorates. In this paper, we report the evaluation of this image using a near-infrared light source with a wavelength of 780 nm that is capable of deep tissue penetration. A favorable microscopic image of the object behind the rat-skin sample of 912 μm-thickness was successfully reconstructed.
Spatially incoherent light can result from nonlinear processes where a group of photons are emitted in entangled states of spatial modes, which results in an incoherent mixture of constituting spatial modes when the photons are assessed one by one. In this paper we explore a method which uses a tilted lens to probe the orbital angular momentum (OAM) spectrum of such a mixture. We examine the general case where the photons are in mixtures of both different OAM and radial modes, resulting in a 2-dimensional random distribution that creates a more difficult challenge compared to mixtures of OAM only.
Anharmonic behavior of coincidence count rate obtained with the hologram shifting method can be used to probe highdimensional effect of orbital angular momentum entangled photon pairs. We perform numerical analysis for the case where the photon pairs are created by spontaneous parametric downconversion, and both photons are observed through singlemode fibers after mode conversion with phase-only holograms. The center of the holograms are shifted by a constant distance from the beam axis and the relative shift direction is scanned. We explore effects of pump beam width and crystal length with respect to the hologram shift distance.
We experimentally generate the Bessel-Gauss coherence functions using the cross-correlations between the two speckle patterns obtained using the perfect optical vortices (POV) of different orders. POV beams are generated using the Fourier transform of Bessel-Gauss beams by displaying the axicon hologram on spatial light modulator. A ground glass plate is used for scattering POV beams and the speckles are recorded. The cross-correlation function of two speckle patterns is Bessel-Gauss functions whose order is given by the difference in the orders of two POV beams used for scattering. The auto-correlation function of these speckles is Bessel-Gauss function of order zero.
In the unfolding process a uniformly polarized optical vortex evolves into a complex polarization distribution within a birefringent crystal. In this paper we introduce the “unfolding region” to characterize this process. This is the real space region over which the polarization state travels half way around the Poincar´e sphere relative to that observed at the center of the beam. Ideally the region is a circle, but it can be distorted into an ellipse by a small tilt between the ordinary and extraordinary rays. We have applied the above analysis to an actual unfolding process observed with a birefringent interferometer.
A relation between vectorial source structure and coherence-polarization of the fluctuating field is established. This
relation connects the source structure to the degree of coherence by Fourier relation, and this is extension of the van
Cittert-Zernike theorem to the vectorial regime. Experimental verification of the proposed theorem is presented by
making use of space averages as replacement of ensemble averages for Gaussian stochastic field. Both experimental and analytical results are obtained for different polarized sources, and good agreements between two justify use of space average as replacement of ensemble average in the spatially fluctuating field.
A uniformly polarized optical vortex (OV) entering a birefringent crystal is known to unfold into complex polarization structures due to the separation of ordinary and extraordinary rays. The interplay between the topological structures in scalar and vector optics has been studied at the output of finite-length crystals. But the polarization transformation near the unfolding point where the beam initially enters the crystal has not been observed so far. In this paper, we experimentally investigate the spatial polarization structure very near the unfolding point of a uniformly polarized OV beam propagating in a birefringent crystal by constructing a birefringent interferometer. The unfolding point is reconstructed by folding back the two separated beams into a single beam using another identical birefringent crystal, resulting in a birefringent interferometer of Mach-Zehnder type. Small rotation of the second crystal produces output beams with varying separation near the unfolding point. The spatial polarization structure of the output beam is investigated by measuring the Stokes parameters. Such understanding of the connection between defects of scalar optics and vector optics through birefringence will help to shape the spatial polarization states of laser beams for various spectroscopic and microscopic applications.
In this paper, we present an interferometric technique for full field polarization mapping using Fourier fringe
analysis. Uniqueness of the technique lies in its high stability against surrounding vibration and capability of single shot
measurement. Accuracy of the technique is verified by mapping of beam with known state of polarization and
subsequently the technique is used to map polarization for various kinds of sample fields.
We propose a simple scheme for accurate state of polarization (SOP) mapping with an interferometric polarimeter using
Fourier transform method of fringe analysis. In single shot polarimeters that use Fourier transform method of fringe
analysis, a spatial carrier frequency is introduced in the fringes of recorded interferogram either by introducing the
relative tilt between the sample beam under test and a reference beam, as demonstrated by Ohtsuka and Oka or by
passing the sample beam through birefringent optical components such as Wollaston prisms as demonstrated by Oka and
Kaneko. In this technique, the amount of spatial carrier frequency that enabled to filter different terms in the Fourier
spectrum of the recorded interferogram had to be calibrated with the use of light with a known SOP. Even in this case,
the spatial carrier frequency introduced in the recorded interferogram is influenced by the relative tilt of the beam used
for calibration. To eliminate the linear phase introduced by spatial carrier frequency, usually the spectrum around the
carrier frequency location in the Fourier transform is shifted and brought to the centre. During this process an error of a
fraction of a pixel in the shifting of the spectrum after filtering to remove the linear phase introduced by spatial carrier
frequency will drastically change the measured SOP of light. For accurate SOP mapping, it is important that we
eliminate the artifacts and errors due to the spatial carrier frequency in the single shot polarimeter that are otherwise very
promising. In the present work, we propose a Mach-Zehnder interferometric polarimeter that uses a common path
Sagnac interferometer to generate reference beams with orthogonal state of polarization. By taking advantage of the
inherent stability of the proposed common path Sagnac interferometer against surrounding vibrations and air turbulences,
a simple calibration scheme using a light of known state of polarization is used to map the state of polarization with
better accuracy.
In this paper, we propose and demonstrate Stokes holography for recording and reconstructing a object using
polarization fringes. Reconstruction is carried out by scattering the polarization fringes through ground glass, and
replacing the ensemble averages by space averages of the randomly scattered Gaussian field. Object encoded into
polarization fringes are reconstructed into their corresponding elements of generalized Stokes parameters. Experimental
and numerical results of a point object reconstruction are presented.
We propose a simple implementation of off-axis coherence holography with a commercial projector combined with a
Sagnac radial shearing interferometer. The projector functions as a device for display and incoherent illumination of a
coherence hologram, which permits reconstruction of the hologram with a generic spatially-incoherent quasimonochromatic
thermal light source. The Sagnac radial shearing interferometer, with its inherent stability of a common-path
interferometer and controllable magnification introduced by variable shear, functions as a device for correlating
optical fields to detect the 3-D coherence function that represents the object recorded in the coherence hologram. A set of
phase-shifted Fourier transform holograms was displayed sequentially with the projector. The coherence function was
detected by applying the phase-shift technique to the Sagnac radial shearing interferometer, and the object was
reconstructed as the 3-D correlation map of the fields diffracted from the hologram. The technique can be applied for
dispersion-free spatial coherence tomography and profilometry.
Presence of vortices/phase singularities has been demonstrated in instantaneous generalized Stokes parameters (IGSP) of
the field generated by illuminating a random phase screen with a polarization structured beam. Polarization structuring is
achieved by focusing the vector beam with tilt in one of the orthogonal polarization components with respect to other.
Spatially structured polarized beam is scattered by non-birefringent random phase screen placed at the focal plane of
focusing lens. Field distribution of orthogonal polarization components are evaluated at the focal plane of second lens,
and subsequently IGSPs are evaluated. Evaluations of the IGSPs are performed by varying one observation point r2 with
respect to a fixed reference point r1. Distribution of phase singularities is displayed in the phase map of IGSP. These
singularities disappear in the spatially averaged generalized stokes parameters.
A new image reconstruction scheme for coherence holography using a modified Sagnac-type radial shearing
interferometer with geometric phase shift is proposed and experimentally demonstrated. The reconstruction of off-axis
objects placed at different depths makes this proposed technique the most generic one. A reconstructed image,
represented by a coherence function, can be visualized with a controllable magnification, which opens up a new
possibility for a coherence imaging microscope.
We raise an issue whether phase singularities are foes or friends in optical metrology, and give an answer by introducing
the principle and applications of a new technique which we recently proposed for displacement and flow measurements.
The technique is called optical vortex metrology because it makes use of the unique characteristics of phase singularities
as markers or tracers for the displacement and flow measurements. The phase singularities are created in the complex
signal representation of a speckle-like random pattern, which is generated by means of a vortex filer operating a Riesz or
Laguerre-Gauss transform to the random pattern.
We review the principle and the applications of unconventional holography, called coherence holography1,2, which we recently proposed as a general technique for the synthesis and the control of 3-D spatial coherence function. An object recorded in a hologram is reconstructed as the three-dimensional distribution of a complex spatial coherence function, rather than as the complex amplitude distribution of the optical field itself that usually represents the reconstructed image in conventional holography. We introduce a newly proposed simple optical geometry for the direct visualization of the reconstructed coherence image, along with the experimental results validating the proposed principle. We also show that coherence holography has potential applications in optical coherence tomography and profilometry3 as well as in basic science of coherence vortices4.
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.
Based on the fringe formation in the k-vector space, we proposed an angular spectrum scanning technique for absolute interferometry. Instead of sweeping the optical frequency over a wide range of spectrum, we tune the angular spectrum by changing the incident angle of a monochromatic plane wave with a spatial light modulator (SLM). In the experiment, we built an equivalent spatially incoherent "ring source" to realize the angular spectrum scanning, and applied an algorithm to compensate the offset fluctuation of the fringe intensity.
A technique of imaging with a spatial coherence function, referred to as coherence holography, is proposed. A hologram
of a three-dimensional object is recorded with coherent light in the same manner as in conventional holography, but the
hologram is illuminated with spatially incoherent light to reconstruct the object as the three-dimensional distribution of
a spatial coherence function, rather than as the amplitude or the intensity distribution of the optical field. A simple
optical geometry for direct visualization of the reconstructed coherence image is proposed, and the results of
preliminary experiments of a computer-generated coherence hologram (CGCH) are presented, which demonstrate the
potential of CGCH as a means for optical coherence tomography and profilometry.
A novel scheme of an interferometric microscope is proposed to visualize a geometrical spin-redirection phase image that represents the local inclination of micro surface structures of an object. The observed phase depends on the state of polarization and optical constants of the object material, which enables one to distinguish the spin-redirection phase from the conventional dynamical phase. A preliminary experiment was performed, and the phase images obtained were found to be consistent with those predicted by computer simulation based on a theoretical model.
By controlling the irradiance of an extended quasi-monochromatic, spatially incoherent source with a spatial light modulator, we generated a special optical field that exhibits a high degree of coherence with phase singularities for a specific pair of points at specified locations along the axis of beam propagation. Some local properties associated with coherence vortices, such as the Berry anisotropy ellipse describing the anisotropic degree of coherence close to a vortex core and the Dennis angular momentum rule for its associated phase, are also investigated experimentally.
A new method of white-light fringes analysis called multi-spectral phase-crossing detection is presented. The technique is based on analysis of phase distributions of at least two white-light interferograms recorded simultaneously by detectors with mutually different spectral sensitivities. The analysis of the phase crossing of multiple white-light interferograms with different spectral bands gives us the possibility to find the position of zero optical path difference without ambiguity. The theoretical background and measurement results are presented.
An interferometer based on the spatial coherence detection has been developed for absolute height measurement. The location of a coherence peak resulting from the illumination of an extended quasi-monochromatic spatially incoherent light source with zone-plate-like spatial structure gives the longitudinal depth information. Besides simplifying the control of the light source structure, LCD-SLM eliminates the mechanical movement. Experiments of step height detection and profilometry of an object with a rough surface are presented that demonstrate the validity of the principle.
As an alternative to the intensity correlation technique used in conventional speckle metrology, we propose a new technique of displacement measurement based on spatial signal-domain phase-only correlation that makes use of the pseudo phase of the complex analytic signal generated from a Hilbert-filtered speckle pattern. Experimental results are presented that demonstrate the validity and the advantage of the proposed signal-domain phase-only correlation technique over the conventional intensity correlation technique.
A new technique, called spatio-spectral digital holography, is proposed. The technique is based on the combination of the principles of a spectral interference microscope and digital holography, where the spectral interferometry provides the function of full-field tomographic imaging, and digital holography gives a microscope objective the function of adaptive numerical focusing. Experimental results are presented that demonstrate the validity of the proposed principle.
We address the basic issue of the observation condition in a synthetic coherence function applied to optical tomography and profilometry, which has not been made clear in previous papers. We present a more general theory for interference fringe formation for spatial coherence control with a synthetic source. The generalized theory predicts the existence of the observation condition that can make the measurement insensitive to the tilt of the object, which will open the new possibility of measuring objects with rough surfaces. We present experimental results that quantitatively verify the validity of the principle and the prediction.
Under the assumption of Gaussian random process, we discuss the first and the second order statistical properties of the complex amplitude of analytic signal of the white-light speckle pattern. We derive the autocorrelation function of the pseudo phase. Based on these results, we show mathematically that the proposed signal domain phase-only correlation (SD-POC) has advantage over the conventional intensity-based correlation techniques in its performance of micro-displacement measurement. We also present experimental results that support the theory.
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.
Instead of the intensity information used in conventional speckle metrology, we explore new possibilities of making use of the phase information of speckle patterns. We propose a new technique of displacement measurement that makes use of the phase singularities in the analytic signal of the speckle pattern, which is generated by Hilbert filtering. Experimental results are presented that demonstrate the validity and the limitation of the proposed technique.
A new depth-from-defocus type co-axial 3-D sensor is proposed that permits shade-free absolute 3-D shape measurement from the contrast information of a frequency-multiplexed single fringe pattern. The Fourier transform method is used for spatial frequency demultiplexing and extracting the fringe contrast. 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.
For the absolute and shade-free shape measurement of 3D objects with large height discontinuities, a co-axial optical sensor system with a common image plane for pattern projection and observation was proposed. Experimental results are presented that demonstrate the shape measurements of objects with a deep hole and large discontinuities.
To enable unified analysis and simultaneous evaluation of geometrical spin-redirection phase and Pancharatnam phase, conventional 2 X 2 Jones matrix calculation is generalized and a new scheme of 3 X 3 matrix calculation is proposed. By the proposed algorithm one can trace the polarization state changes and the geometric phase shifts caused by the beam propagation along an arbitrary optical path that involves both reflection and refraction at surfaces with Fresnel shift and birefringence.
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.
Noting the analogy between electro-magnetic fields and the vector fields of phase gradients obtained by heterodyne techniques, we propose a new algorithm for least-squares phase unwrapping. Instead of solving a Poisson equation for the unwrapped phase map or using the Green's formulation, we directly remove singular points or residues from the measured phase map by superposing sign-reversed vortex fields which cancel out the rotational vector fields associated with the phase singular points.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.