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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.

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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.

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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.

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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.

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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.

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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.

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Scattering media have always been looked upon as an obstacle in imaging. Various methods, ranging from holography to phase compensation as well as to correlation techniques, have been proposed to cope with this obstacle. We, on the other hand, have a different understanding about the role of the diffusing media. In this paper we propose and demonstrate a 'scatter-plate microscope' that utilizes the diffusing property of the random medium for imaging micro structures with diffraction-limited resolution. The ubiquitous property of the speckle patterns permits to exploit the scattering medium as an ultra-thin lensless microscope objective with a variable focal length and a large working distance. The method provides a light, flexible and cost effective imaging device as an alternative to conventional microscope objectives. In principle, the technique is also applicable to lensless imaging in UV and X-ray microscopy. Experiments were performed with visible light to demonstrate the microscopic imaging of USAF resolution test target and a biological sample with varying numerical aperture (NA) and magnifications.

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Scattering media, such as diffused glass and biological tissue, are usually treated as obstacles in imaging. To cope with the random phase introduced by a turbid medium, most existing imaging techniques recourse to either phase compensation by optical means or phase recovery using iterative algorithms, and their applications are often limited to two-dimensional imaging. In contrast, we utilize the scattering medium as an unconventional imaging lens and exploit its lens-like properties for lensless three-dimensional (3D) imaging with diffraction-limited resolution. Our spatially incoherent lensless imaging technique is simple and capable of variable focusing with adjustable depths of focus that enables depth sensing of 3D objects that are concealed by the diffusing medium. Wide-field imaging with diffraction-limited resolution is verified experimentally by a single-shot recording of the 1951 USAF resolution test chart, and 3D imaging and depth sensing are demonstrated by shifting focus over axially separated objects.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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We experimentally demonstrate control over the group delay of narrow-band (quasi continuous wave) terahertz (THz) pulses with constant amplitude based on optical switching of a metasurface characteristic. The near-field coupling between resonant modes of a complementary split ring resonator pair and a rectangular slit show an electromagnetically induced transparency-like (EIT-like) spectral shape in the reflection spectrum of a metasurface. This coupling induces group delay of a narrow-band THz pulse around the resonant frequency of the EIT-like spectrum. By irradiating the metasurface with an optical excitation pulse, the metasurface becomes mirror-like and thus the incident narrow-band THz pulse is reflected without a delay. Remarkably, if we select the appropriate excitation power, only the group delay of the narrow-band THz pulse can be switched while the amplitude is maintained before and after optical excitation.

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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.

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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.

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We herein present a case of cardiac sarcoidosis with atrioventricular (AV) block that was evaluated using magnetic resonance imaging (MRI) before and after pacemaker implantation. An echocardiogram showed wall thinning in the basal septum. MRI showed late gadolinium enhancement in the interventricular septum and right ventricle. Fluorine-18-fluorodeoxyglucose positron emission tomography (PET) demonstrated abnormal uptake in the same area. An MR-conditional pacemaker was implanted to treat AV block. Steroid treatment resulted in the remission of the cardiac lesions and AV block, as confirmed by PET and MRI. MR-conditional pacemakers are thus considered to have great advantages in treating cardiac sarcoidosis with AV block.

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