The spatial coherence function has proven to be a highly effective tool for light field manipulation. Although there has been considerable research on the spatial statistics of light, further exploration is needed to understand the phase variations within the coherence function. This study employs theoretical analysis and experimental investigations to gain insights into the phase modulations of far-field spatial coherence that are solely due to the modulations of the spatially incoherent source. We could modify the phase of the coherence function at different rates between different pairs of points without changing its magnitude. A square-wave amplitude grating is used and moved parallel to its plane to modulate the source intensity distribution. The proposed scheme is experimentally verified using a common-path Sagnac radial-shearing interferometer. This source-modulated phase shift technique has potential applications in optical interferometry schemes that employ incoherent light.
In conventional interferometry, the intensity of the superposed field is observed to study the phase information of object / sample field. The schemes like Weak measurement scheme, spectral switching observes the intensity of the output field for enhancing the sensitivity of the phase measurements. A scheme to enhance the sensitivity in the measurement of path delays through spectral interferometry by observing the phase accumulated by the superposed field with respect to an additional reference beam is presented. Through the interference with additional reference beam maintained at out-of-phase condition near zero optical path delay with respect to the sample probe beam, it is shown to introduce nonlinearity in phase change measured. In the experimental demonstration, the classic low coherence spectral interferometry is used. The three-beam interference is achieved by a modified Michelson interferometer. According to the setting of initial path delay and amplitude ratio of the interfering fields, the intensity of superposed field shows spectral modulations. Spectral phase is measured from the modulations in the recorded spectral interference using Fourier transform method of fringe analysis. In the Fourier domain, a linear path delay between in the interfering beams gives a linear shift in the position of secondary peak. By filtering the secondary peak from the Fourier domain, and taking the Inverse Fourier transform, the amplitude and phase information of the interfering fields can be obtained. The proposed method maps the linear path delay to highly nonlinear phase accumulation and has the potential to enhance sensitivity of phase measurements.
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.
Digital holography is one of the most powerful methods used in metrological applications for non-destructive testing of various components as it provides higher precision up to several nanometres at high speed. As there are many industrial applications such as gear metrology, surface tracing of planar components and so on, which involve dynamic objects, and holographic measurements on such objects is a challenging task. The interference pattern is no longer stable, resulting in low contrast and resolution of the recorded hologram thus degrading the recorded information. In this paper, lensless Fourier transform digital holography is used for analysing the interference contrast as a function of velocity for planar moving objects. Numerical simulations have been carried out to study how the size of reference source and the exposure time of camera affects the contrast of the interference pattern of a moving object. Experimentally, lensless Fourier transform holographic geometry is realised via Sagnac interferometer which provides robustness and immunity against the external vibrations during the recording. The maximum extent of velocity is estimated by analysing the variations in contrast such that there is minimal loss of information from the recorded hologram.
Extracting information of an object which is hidden behind a translucent obstacle is a difficult task. When the obstacle is a diffusing or scattering medium, it becomes much more complicated. The scattering medium makes the phase random, which cannot be retrieved or undone by simple techniques. Many approaches based on interference have been proposed to realise this goal. These approaches have produced good results meanwhile are also very expensive and complex in nature due to the requirement of a separate reference beam to form the interference pattern. We hereby, propose a novel method in which we are illuminating a hidden object with shifted dual beams simultaneously and these two beams are then reflected from the object to produce an interference pattern. This method does not require any separate reference beam to form the interference pattern. The purpose of using dual beam illumination is to eliminate the need of any shearing device to give shear between the object’s fields thus making our technique much more simpler and cost-effective. To validate our technique, a simulation is performed. In this work, we extract the information about the deformation of the object due to loading. In addition, various parameters and their effects on the extraction of information are also mentioned. This technique takes advantage of the merit of Shearography hence the gradient information of the hidden object can also be detected.
Speckle-based techniques have noteworthy applications in the field of material science, surface characterization, determining mechanical displacements, biological activity in diffuse layer, imaging through turbid layer etc. The passage of coherent light through a diffuse layer generates a random speckle pattern, which have the inherent feature of carrying information associated with the diffuse layer. Dynamic laser speckle associated with the displacements of scattering surface has prominent impacts in the study of biological activity inside the diffuse layer. Investigations are progressing in the direction of exploring the dynamical properties associated with speckled speckles and its applications in imaging and characterization scenarios. In this work, we theoretically and experimentally study the dynamical properties of speckles through a static scattering layer using intensity correlation. The displacement (transverse or angular) produced in the concealed scatterer generates the dynamic speckle pattern which is observed through a second static diffuser. We expect to find applications of this investigation into the tracking objects hidden in the diffuse layer, measuring biological activity in diffuse layer, displacement measurements, etc.
That a paraxial light beam with spin angular momentum (SAM,σ ) propagating in a helical trajectory leads to the appearance of Rytov-Vladimirsky-Berry (RVB) phase has been a topic of extensive research for the past several decades. Recently, using geometrical optics approximation, it was shown that variations in the beam propagation direction leads to generic parallel transport law – a beam with intrinsic orbital angular momentum (IOAM, l ) behaves topologically similar to polarized beam containing only SAM but of magnitude proportional to the total angular momentum TAM = l ± σ . By considering the interaction of a beam with IOAM, propagating in a non-planar trajectory and hence with extrinsic orbital angular momentum (EOAM), in an inhomogeneous medium we study the parallel transport of fiber mode structure as a manifestation of orbit-orbit interaction. The resulting rotation of the transverse beam structure due to the parallel transport of the LP fiber mode propagating along non-planar ray direction is attributed to the ‘orbital’ Berry phase. The mode transformation is simulated based on the interference of the vector-vortex modes excited in the TMF. The LP mode rotation angle calculated as a function of the beam position at the fiber input is expected to show topological features that can be mapped onto orbital Poincaré sphere.
We propose a fast and precise optical 3D measurement method. The principle is similar to that of white-light
interferometry. The broad-band light source of white-light interferometry is replaced by two lasers with different
wavelengths. The object to be measured is placed into one arm of a Michelson interferometer and moved along the
optical axis. The intensity measured at the output of the interferometer is equal to the field autocorrelation. In the case of
two wavelengths, the autocorrelation is a periodical function with peaks as a result of their beating. The period can be
adjusted by the choice of the wavelength difference. By choosing a short period, a fast and precise measurement is
performed in the range of a single beat. However, such a measurement is ambiguous if the object has structures deeper
than the beat period. The ambiguity is removed by a fast auxiliary measurement with a long beat period covering the
whole depth range of the object. The auxiliary measurement need not be precise and can be completed quickly with a
large sampling step.
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.
We propose and demonstrate the recording of hologram of an incoherently illuminated object by using a Sagnac radial shearing interferometer, a Pockels cell and an 8 bit CCD camera. An approach based on statistical optics is used for understanding the concept of recording of an incoherent-object as complex spatial coherence function. The Sagnac radial shearing interferometer is used for the correlation of optical fields and the Pockels cell is used to shift the phase of the interfering fields. The fringe contrast and fringe phase that jointly represent the complex spatial coherence function are measured by applying a 5-step phase shifting algorithm while recording the interferograms. The results of recording and reconstruction of an object illuminated using a light emitting diode, Luxeon Star LXHL-MMID, having spectral width at half maximum of about 35nm at wavelength 530nm, are presented. Due to the implementation of the phase shift by using a Pockels cell, the system is mechanics free and has the potential for automated fast measurement which can be applied for the investigation of dynamic situations. Moreover, the interference of the optical field even with low temporal coherent light is achieved without using any interference filter and a reliable 3-D object reconstruction can be achieved even in an outdoor environment due to the inherent stability provided by the common path interferometer. By changing the shearing parameter, we can tailor the range of the measured coherence function depending on object under test. This could enable one to use it as coherence zooming microscope.
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.
We review two techniques of unconventional holography, coherence holography and photon-correlation holography,
which we recently proposed and experimentally demonstrated. We will emphasize the importance of noticing
mathematical analogies in optics and physical phenomena, which give insights into the methodology for developing new
techniques.
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.
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