Matrix-based integral transformations for Stokes imaging with partially polarized and partially coherent light.

With the aid of the matrix-based integral transforms called matrix convolution and matrix direct correlation, we provide a simplified expression for the space- and frequency-domain calculations of polarization imaging with partially polarized and partially coherent light. As an example of practical interest, a formula for Stokes imaging, based on the generalized Stokes parameters, is presented, in which a hypermatrix-based transmission cross-coefficient matrix is introduced to represent the combined effects of diffraction and aberrations of a polarization-dependent imaging system and a partially polarized, partially coherent illumination system. The coherent and incoherent limits in Stokes imaging are discussed with the optical transfer matrix, along with its frequency response for a diffraction-limited incoherent polarization imaging system. A generalized concept of the apparent transfer matrix is introduced to deal with the nonlinearity inherent in the polarization imaging system under partially coherent illumination.

Functionally integrated waveguide illuminator for common-path digital holographic microscopy through random media.

We designed and fabricated a functionally integrated optical waveguide illuminator specially for common-path digital holographic microscopy through random media. The waveguide illuminator creates two point sources with desired phase shifts, which are located close to one another so that the common-path condition of the object and reference illumination is satisfied. Thereby, the proposed device permits phase-shift digital holographic microscopy free from bulky optical elements such as a beam splitter, an objective lens, and a piezoelectric transducer for phase shifting. Using the proposed device, microscopic 3D imaging through a highly heterogeneous double-composite random medium was experimentally demonstrated by means of common-path phase-shift digital holography.

Autocorrelation functions and power spectral densities of the Stokes parameters in a polarization speckle pattern.

The concept of ensemble-average polarization and coherence has been applied to studying fluctuating Stokes parameters in a polarization speckle observed when coherent light is passed through a birefringent polarization scrambler. With the aid of the ensemble-average van Cittert-Zernike theorem for the propagation of ensemble-average polar-coherence, we invesitgate the autocorrelation functions and power spectra of the Stokes parameters to expose the dependence of the polarization-related scale-size distributions on the optical geometries in which the polarization speckle arises. A generalized concept of the Stokes ensemble-average coherence areas is introduced to deal with the polarization-related average areas associated with polarization speckle.

3D imaging through a highly heterogeneous double-composite random medium by common-path phase-shift digital holography.

A method is proposed for 3D imaging through a highly heterogeneous double-composite random medium made of a thick mildly inhomogeneous medium followed by a thin strongly scattering layer. To realize the immunity to the heterogeneous random medium, a system of common-path phase-shift digital holography is designed in such a manner that the wavefront distortion caused by the first inhomogeneous medium is canceled out by the common-path geometry, and the influence of the random phase introduced by the second scattering layer is removed by the intensity-based recording of the digital hologram on the thin scattering layer. The validity of the method was confirmed by experiments.

Enhanced Fourier-transform method for high-density fringe analysis by iterative spectrum narrowing.

We propose a model-based fringe analysis technique that enables the Fourier transform method to analyze dense fringe patterns with large phase variations. The conventional Fourier-transform method has a limited dynamic range of measurable phase because the Fourier spectra broadened by large phase variations cannot be separated by the spatial carrier frequency. Our model-based iterative technique effectively narrows the broad spectrum and reduces phase errors. Results of simulations and experiments are presented that demonstrate the validity of the proposed spectrum-narrowing technique for high-density fringe patterns.

Three-dimensional microscopic imaging through scattering media based on in-line phase-shift digital holography.

Microscopic three-dimensional imaging and phase quantification for objects hidden behind a scattering medium by using in-line phase-shift digital holography are proposed. A spatial resolution of 1.81 µm and highly accurate quantitative phase imaging are demonstrated for objects behind a scatter plate. Three-dimensional imaging was confirmed using objects with a depth difference of 1.32 mm. Further, imaging was performed using rat skin as a demonstration for imaging through a complex multilayer scattering medium, where a spatial resolution close to the theoretically predicted value was achieved by experiment.

Dynamically Babinet-invertible metasurface: a capacitive-inductive reconfigurable filter for terahertz waves using vanadium-dioxide metal-insulator transition.

This paper proposes a reconfigurable planar metamaterial that can be switched between capacitive and inductive responses using local changes in the electrical conductivity of its constituent material. The proposed device is based on Babinet's principle and exploits the singular electromagnetic responses of metallic checkerboard structures, which are dependent on the local electrical conductivity. Utilizing the heating-induced metal-insulator transition of vanadium dioxide (VO2), the proposed meta-material is designed to compensate for the effect of the substrate and is experimentally characterized in the terahertz regime. This reconfigurable metamaterial can be utilized as a switchable filter and as a switchable phase shifter for terahertz waves.

Enhanced intensity variation for multiple-plane phase retrieval using a spatial light modulator as a convenient tunable diffuser.

In the multiple-plane phase retrieval method, a tedious-to-fabricate phase diffuser plate is used to increase the axial intensity variation for a nonstagnating iterative reconstruction of a smooth object wavefront. Here we show that a spatial light modulator (SLM) can be used as an easily controllable diffuser for phase retrieval. The polarization modulation at the SLM facilitates independent formation of orthogonally polarized scattered and specularly reflected beams. Through an analyzer, the polarization states are filtered enabling beam interference, thereby efficiently encoding the phase information in the axially diverse speckle intensity measurements. The technique is described using wave propagation and Jones calculus, and demonstrated experimentally on technical and biological samples.

Coherence and polarization of polarization speckle generated by a rough-surfaced retardation plate depolarizer.

The coherence and polarization of polarization speckle, arising from a stochastic electromagnetic field with random change of polarization, modulated by a depolarizer are examined on the basis of the coherence matrix. The depolarizer is a rough-surfaced retardation plate with a random function of position introducing random phase differences between the two orthogonal components of the electric vector. Under the assumption of Gaussian statistics with zero mean, the surface model for the depolarizer of the rough-surfaced retardation plate is obtained. The propagation of the modulated fields through any quadratic optical system is examined within the framework of the complex ABCD matrix theory to show how the degree of coherence and polarization of the beam changes on propagation, including propagation in free space.

Statistics of the derivatives of complex signal derived from Riesz transform and its application to pseudo-Stokes vector correlation for speckle displacement measurement.

As an improvement of the well-known intensity correlation used in conventional electronic speckle photography, we have proposed a new technique, to the best of our knowledge, for displacement measurement referred to as pseudo-Stokes vector correlation (PSVC). To provide a theoretical background for the superiority of the proposed PSVC technique, we study the statistical properties of the spatial derivatives of the complex signal representation generated from the Riesz transform. Under the assumption of a Gaussian random process, a theoretical analysis for the pseudo Stokes vector correlation has been provided. Based on these results, we show mathematically that PSVC has a performance advantage over conventional intensity-based correlation technique.

Looking through a diffuser and around an opaque surface: a holographic approach.

Retrieving the information about the object hidden around a corner or obscured by a diffused surface has a vast range of applications. Over the time many techniques have been tried to make this goal realizable. Here, we are presenting yet another approach to retrieve a 3-D object from the scattered field using digital holography with statistical averaging. The methods are simple, easy to implement and allow fast image reconstruction because they do not require phase correction, complicated image processing, scanning of the object or any kind of wave shaping. The methods inherit the merit of digital holography that the micro deformation and displacement of the hidden object can also be detected.

Crossover from capacitive to inductive electromagnetic responses in near self-complementary metallic checkerboard patterns.

Transmission spectra of near-self-complementary metallic checkerboard patterns (MCPs) exhibit a drastic change when the metal squares are brought into contact with each other from a noncontact state. Transmission spectra of near-self-complementary samples, which are fabricated by printing technology, show rather gradual systematic change with changing the nominal metal square size while keeping the period because of randomness naturally introduced by the limited accuracy of the printer. The spectra have transmission-invariant frequencies, which means that the spectra are a superposition of two types of spectra, the ratio of which depends on the nominal square size. The correlation seen in the real and imaginary parts of the complex amplitude spectra can be interpreted based on the Kramers-Kronig relation. As an application of the sensitiveness of the transmission spectrum of the MCPs to connectivity of the metal squares, the revealing of an optically hidden pattern by a terahertz beam is demonstrated.

Spectrally resolved incoherent holography: 3D spatial and spectral imaging using a Mach-Zehnder radial-shearing interferometer.

Spatial and spectral information holds the key for characterizing incoherently illuminated or self-luminous objects, as well as for imaging fluorescence. We propose spectrally resolved incoherent holography using a multifunctional Mach-Zehnder interferometer that can introduce both a radial shear and a variable time delay between the interfering optical fields and permits the measurement of both spatial and temporal coherence functions, from which a 3D spatial and spectral image of the object is reconstructed. We propose and demonstrate the accurate 3D imaging of the object spectra by in situ calibration.

Recent advances in digital holography [invited].

This article presents an overview of recent advances in the field of digital holography, ranging from holographic techniques designed to increase the resolution of microscopic images, holographic imaging using incoherent illumination, phase retrieval with incoherent illumination, imaging of occluded objects, and the holographic recording of depth-extended objects using a frequency-comb laser, to the design of an infrastructure for remote laboratories for digital-holographic microscopy and metrology. The paper refers to current trends in digital holography and explains them using new results that were recently achieved at the Institute for Applied Optics of the University Stuttgart.

Spatial stationarity of statistical optical fields for coherence holography and photon correlation holography.

The spatial stationarity of scattered optical fields constitutes a basic premise of coherence holography and photon correlation holography. Nevertheless, spatial stationarity seems to have attracted less attention and still remains a less familiar concept than temporal stationarity because it has been a common practice in statistical optics to assume temporal ergodicity and replace the ensemble average with the time average, rather than the space average. To form the theoretical basis for coherence holography and photon correlation holography, an investigation is made into the spatial stationarity of the statistical optical field, and combinations of a light source and an optical system are identified that can create spatially stationary scattered fields. The result justifies the principles of coherence holography and photon correlation holography, and the previously reported experiments.

Vectorial van Cittert-Zernike theorem based on spatial averaging: experimental demonstrations.

The van Cittert-Zernike theorem is extended to the vectorial regime based on spatial averaging over the observation plane, and experimental demonstrations are presented. The theorem connects complex vectorial source structure to the degree of coherence and polarization of the spatially fluctuating vectorial field in the far field. Experimentation is carried out by making use of the space averages as a replacement of ensemble averages for the Gaussian stochastic field. For quantitative comparison with the theorem, analytical and experimental results are presented for a rectangular aperture with different vectorial source structures.

Fourier fringe analysis and its application to metrology of extreme physical phenomena: a review [Invited].

The paper reviews a technique for fringe analysis referred to as Fourier fringe analysis (FFA) or the Fourier transform method, with a particular focus on its application to metrology of extreme physical phenomena. Examples include the measurement of extremely small magnetic fields with subfluxon sensitivity by electron wave interferometry, subnanometer wavefront evaluation of projection optics for extreme UV lithography, the detection of sub-Ångstrom distortion of a crystal lattice, and the measurement of ultrashort optical pulses in the femotsecond to attosecond range, which show how the advantages of FFA are exploited in these cutting edge applications.

Coherence holography by achromatic 3-D field correlation of generic thermal light with an imaging Sagnac shearing interferometer.

We propose a new technique for achromatic 3-D field correlation that makes use of the characteristics of both axial and lateral magnifications of imaging through a common-path Sagnac shearing interferometer. With this technique, we experimentally demonstrate, for the first time to our knowledge, 3-D image reconstruction of coherence holography with generic thermal light. By virtue of the achromatic axial shearing implemented by the difference in axial magnifications in imaging, the technique enables coherence holography to reconstruct a 3-D object with an axial depth beyond the short coherence length of the thermal light.

Interferometer setup for the observation of polarization structure near the unfolding point of an optical vortex beam in a birefringent crystal.

We propose a novel birefringent interferometer setup for the study of unfolding points, and obtain for the first time to our knowledge the spatial polarization structure very near the unfolding point of a uniformly polarized optical vortex beam propagating in a birefringent crystal. The unfolding point is reconstructed by folding back the two separated eigen-beams at the output of the birefringent crystal into a single beam using another identical birefringent crystal, resulting in a birefringent interferometer of Mach-Zehnder type. We also demonstrate that the separation near the unfolding point can be varied by a small rotation of the second crystal.

Single-shot full-field interferometric polarimeter with an integrated calibration scheme.

A simple interferometric polarimeter with an integrated calibration scheme is proposed for accurate and fast mapping of the state of polarization (SOP). Conventional single-shot polarimeters that detect the amplitude and phase of orthogonally polarized field components by interferometry using Fourier fringe analysis suffers from errors caused by the imperfect reference beam and ambiguity in the spatial carrier frequency in the fringe pattern. In the proposed system, the integrated calibration scheme eliminates those error sources and enables accurate measurement of SOP without prior knowledge of the reference beam and the spatial carrier frequency.