Polarization Fringes Research Articles

Underwater 3D reconstruction based on double N-step orthogonal polarization state phase shift strategy

The nonlinear response of projection equipment and the uneven reflectance of HDR (high dynamic range) object surface pose challenges in underwater 3D reconstruction. As a result, the phase-shifting fringe pattern collected by the camera does not have good sinusoidality, leading to phase errors. Therefore, this paper proposes a double N-step orthogonal polarization state phase-shift strategy (DOPS). This technique uses the degree of linear polarization (DOLP) of polarized light to design a double N-step phase-shifting fringe pattern. The original phase shift fringes are encoded as horizontal polarization fringes, and the additional phase shift fringes are encoded as vertical polarization fringes. Then, the camera captures and extracts the phase information of the two groups of DOLP patterns, which are separately subjected to phase unwrapping. The resulting unwrapped phases are fused to reduce phase error. The experimental results indicate that this method reduces the measurement error by 57 % when dealing with 3D shape measurement of underwater HDR objects, compared to the polarization-encoded phase shift algorithm (PEPS). Additionally, this method is more accurate in measurement accuracy and improves measurement efficiency by 50 % compared to the double N-step phase shift method (DNPS).

Robust structured light 3D measurement method based on polarization-encoded projection patterns.

Fringe projection profilometry (FPP) is widely used in 3D vision measurement because of its high robustness and measurement accuracy. In the case of HDR objects, due to the problem of surface reflectivity, the obtained image will be overexposed. This will cause the sinusoidality of the fringes projected on the surface of the object in the acquired image to be interfered, resulting in a phase error in the calculated wrapped phase. Therefore, a polarization-encoded sinusoidal structured light is proposed to enhance the sinusoidality of the fringe. The phase information contained in the polarized sinusoidal structured light fringe is only related to the polarization state, not to the light intensity. A polarization coding assisted structured light measurement strategy (PASM) is proposed. This method uses polarization coding assisted polarization phase-shifting fringes for phase unwrapping. The angle of the linear polarizer is set to zero in this method, and it does not require rotating the polarizer. It only needs a single exposure to improve the fringe quality and obtain a more stable unwrapping phase. The experimental results show that the obtained polarization fringes have better sinusoidality, and the phase unwrapping can be more accurate. The reconstructed 3D point cloud also does not appear missing and has better accuracy. It is a reliable method for vision measurement of HDR objects.

Interferometric Imaging Ellipsometer for Characterizing the Physical Parameters of a Grown Oxide Layer

Interferometric and ellipsometric techniques are widely used in object characterization, investigation and testing. Both techniques are crucial for industrial sectors in manufacturing and production. In this work, an interferometric imaging ellipsometry method has been developed to measure the ellipsometric parameters Ψ, Δ and thickness t of native oxide layer formed on a copper thin film at wide angle of incidence 57.8–80.2º instantaneously. In this system, Michelson interferometer is illuminated with 45° polarized laser beam of 30 mm diameter. The produced fringes are split by a polarizing beam splitter (PBS) into p- and s- polarization fringes. The interferograms are captured separately by two CCD sensors at the reference and the measurement states without moving any parts in the optical system for each state. The detected p- and s- interferograms are analyzed using ImageJ software for mathematically calculating the values of Ψ, Δ and t of the oxide layer grown on copper thin film surface. The proposed method avoids the offset errors and the probable misalignment resulting from the beam and the optical components. In addition, it gathers the information of the interference pattern with the state of polarization of light for accurate, precise and real time contrast images. The oxide layer thickness is determined under controlled environment with high accuracy and low uncertainty. The results obtained by the proposed technique are consistent with the spectroscopic ellipsometer measurements.

Removal of Spectro-polarimetric Fringes by Two-dimensional Principal Component Analysis

Abstract We investigate the application of two-dimensional Principal Component Analysis (2D PCA) to the problem of removal of polarization fringes from spectro-polarimetric data sets. We show how the transformation of the PCA basis through a series of carefully chosen rotations allows us to confine polarization fringes (and other stationary instrumental effects) to a reduced set of basis “vectors,” which at the same time are largely devoid of the spectral signal from the observed target. It is possible to devise algorithms for the determination of the optimal series of rotations of the PCA basis, thus opening the possibility of automating the procedure of defringing of spectro-polarimetric data sets. We compare the performance of the proposed method with the more traditional Fourier filtering of Stokes spectra.

Polarization modeling and predictions for DKIST part 3: focal ratio and thermal dependencies of spectral polarization fringes and optic retardance

Data products from high spectral resolution astronomical polarimeters are often limited by fringes. Fringes can skew derived magnetic field properties from spectropolarimetric data. Fringe removal algorithms can also corrupt the data if the fringes and object signals are too similar. For some narrow-band imaging polarimeters, fringes change the calibration retarder properties and dominate the calibration errors. Systems-level engineering tools for polarimetric instrumentation require accurate predictions of fringe amplitudes, periods for transmission, diattenuation, and retardance. The relevant instabilities caused by environmental, thermal, and optical properties can be modeled and mitigation tools developed. We create spectral polarization fringe amplitude and temporal instability predictions by applying the Berreman calculus and simple interferometric calculations to optics in beams of varying F/ number. We then apply the formalism to superachromatic six-crystal retarders in converging beams under beam thermal loading in outdoor environmental conditions for two of the world’s largest observatories: the 10-m Keck telescope and the Daniel K. Inouye Solar Telescope (DKIST). DKIST will produce a 300-W optical beam, which has imposed stringent requirements on the large diameter six-crystal retarders, dichroic beamsplitters, and internal optics. DKIST retarders are used in a converging beam with F/ ratios between 8 and 62. The fringe spectral periods, amplitudes, and thermal models of retarder behavior assisted DKIST optical designs and calibration plans with future application to many astronomical spectropolarimeters. The Low Resolution Imaging Spectrograph with polarimetry instrument at Keck also uses six-crystal retarders in a converging F / 13 beam in a Cassegrain focus exposed to summit environmental conditions providing observational verification of our predictions.

Principle analysis of snapshot Mueller matrix imaging polarimeter using birefringent crystal

Conventional Muller matrix imaging polarimeter (MMIP) with several rotating elements suffers mechanical complexity, vibration noise, heat generation, and other unwanted problems. To overcome those shortcomings, we present a snapshot Muller matrix imaging polarimeter (SMMIP) using a birefringent crystal with high extinction ratio. The snapshot imaging polarimeter allows a single image to be used to measure the polarization of a scene without electronic control units or moving mechanical components. This new polarimeter combines the technique of Muller matrix spectropolarimetry with a snapshot imaging polarimeter through using modified Savart polariscope (MSP-SMMIP). It contains both a generator and an analyzer module. Spatial polarization fringes are localized on a sample by incorporating modified Savart polariscope into a polarization generator module. These fringes modulate the Mueller matrix components of the sample, which are subsequently isolated with modified Savart polariscope in an analyzer module, and the analyzer and the imaging lens combine with 16 beams to create interference, resulting in spatial modulation on the two-dimensional CCD camera. Expressions for interference intensities, optical system analysis, theory of calibration and method of reconstruction are presented. Finally, the numerical simulation is used to demonstrate theoretical analysis and the feasibility of MSP-SMMIP. The layout is very easy to calibrate and the reference target is only a linear polarizer at 22.5°. Moreover, the remarkable advantages of the proposed instrument, compared with conventional Muller matrix imaging polarimeter, are that it is also simple, compact, snapshotted, and static (no moving parts). Therefore we believe that the proposed snapshot imaging polarimeter will be very useful in many applications, such as biomedical imaging and remote sensing.

Polarization modeling and predictions for DKIST part 2: application of the Berreman calculus to spectral polarization fringes of beamsplitters and crystal retarders

We outline polarization fringe predictions derived from an application of the Berreman calculus for the Daniel K. Inouye Solar Telescope (DKIST) retarder optics. The DKIST retarder baseline design used six crystals, single-layer antireflection coatings, thick cover windows, and oil between all optical interfaces. This tool estimates polarization fringes and optic Mueller matrices as functions of all optical design choices. The amplitude and period of polarized fringes under design changes, manufacturing errors, tolerances, and several physical factors can now be estimated. This tool compares well with observations of fringes for data collected with the spectropolarimeter for infrared and optical regions at the Dunn Solar Telescope using bicrystalline achromatic retarders as well as laboratory tests. With this tool, we show impacts of design decisions on polarization fringes as impacted by antireflection coatings, oil refractive indices, cover window presence, and part thicknesses. This tool helped DKIST decide to remove retarder cover windows and also recommends reconsideration of coating strategies for DKIST. We anticipate this tool to be essential in designing future retarders for mitigation of polarization and intensity fringe errors in other high spectral resolution astronomical systems.

Snapshot imaging Mueller matrix polarimeter using polarization gratings

A snapshot imaging Mueller matrix polarimeter (SIMMP) is theoretically described and empirically demonstrated through simulation. Spatial polarization fringes are localized onto a sample by incorporating polarization gratings (PGs) into a polarization generator module. These fringes modulate the Mueller matrix (MM) components of the sample, which are subsequently isolated with PGs in an analyzer module. The MM components are amplitude modulated onto spatial carrier frequencies which, due to the PGs, maintain high visibility in spectrally broadband illumination. An interference model of the SIMMP is provided, followed by methods of reconstruction and calibration. Lastly, a numerical simulation is used to demonstrate the system's performance in the presence of noise.

Stokes holography

A new technique, referred to as Stokes holography, is proposed and experimentally demonstrated for controlled synthesis of generalized Stokes parameters in 3D space using Stokes fringes. Stokes fringes are polarization fringes which permit to record and reconstruct complete wavefront. Full use of Stokes fringes in a single step is realized by scattering complex field and subsequently reconstructing using spatial averaging of the randomly scattered field. Mathematical formulations are derived and supported by experimental results of 3D object reconstruction in generalized Stokes parameters.

All-Optical Control of Gigahertz Acoustic Resonances by Forward Stimulated Interpolarization Scattering in a Photonic Crystal Fiber

We report the observation of a novel nonlinear optoacoustic phenomenon, that we name forward stimulated interpolarization scattering. When two frequency-offset laser signals are colaunched into orthogonally polarized guided modes of a birefringent small-core (1.8 μm diameter) photonic crystal fiber, a pattern of axially moving polarization fringes is produced, with a velocity and spacing that depends on the frequency offset. At values of frequency offset in the few-GHz range, the pattern of moving fringes can perfectly match the phase velocity and axial wavelength (3.9 mm) of the torsional-radial acoustic mode tightly guided in the core. An intense optoacoustic interaction ensues, leading to efficient nonlinear exchange of power from the higher frequency (pump) mode to the orthogonally polarized lower frequency (Stokes) mode. A full-vectorial theory is developed to explain the observations.

Edge-emitting electroluminescence polarization investigation of InGaN/GaN light-emitting diodes grown by metal-organic chemical vapor deposition on sapphire (0001)

The edge-emitting electroluminescence (FL) state of polarization of blue and green InGaN/GaN light-emitting diodes (LEDs) grown in EMCORE’s commercial reactors was studied and compared to theoretical evaluations. Blue (∼475 nm) LEDs exhibit strong EL polarization, up to a 3:1 distinction ratio. Green (∼530 nm) LEDs exhibit smaller ratios of about 1.5:1. Theoretical evaluations for similar InGaN/GaN superlattices predicted a 3:1 ratio between light polarized perpendicular (E⊥c) and light polarized parallel (E‖c) to the c axis. For the blue LEDs, a quantum well-like behavior is suggested because the E⊥c mode dominates the E‖c mode 3:1. In contrast, for the green LEDs, a mixed quantum well (QW)-quantum dot (QD) behavior is proposed, as the ratio of E⊥c to E‖c modes drops to 1.5:1. The EL polarization fringes were also observed, and their occurrence may be attributed to a symmetric waveguide-like behavior of the InGaN/GaN LED structure. A large 40%/50% drop in the surface root mean square (RMS) from atomic force microscopy (AFM) scans on blue/green LEDs with and without EL fringes points out that better surfaces were achieved for the samples exhibiting fringing. At the same time, a 25%/10% increase in the blue/green LED photoluminescence (PL) intensity signal was found for samples displaying EL interference fringes, indicating superior material quality and improved LED structures.

Edge‐Emitting Photoluminescence/Electroluminescence Polarization Studies of InGaN/GaN Structures Grown by MOCVD on (0001) Sapphire

This paper compares results from different sets of typical blue/green InGaN/GaN structures (MQWs, LEDs) grown in EMCORE's commercial reactors (EMCORE GaNzilla and SpectraGaN) on (0001) sapphire. Edge-emitting photoluminescence (PL) and electroluminescence (EL) were used to characterize representative samples from each set. The PL/EL state of polarization was investigated and compared to theoretical evaluations. Blue (∼475 nm) structures exhibit strongest polarizations, up to a 3:1 TE to TM ratio. Green (∼520 nm) structures exhibit smaller polarizations, about a 1.5:1 ratio. Polarization of luminescence in edge geometry also enables a clear distinction between quantum well (QW) and quantum dot (QD) cases in supperlattice structures. For the blue samples a QW-like behavior is observed since the TE mode dominates the TM mode 3:1. In contrast, for the green samples a mixed QW-QD behavior is suggested, as the TE:TM ratio drops to 1.5:1. PL/EL polarization fringes were also observed and a possible correlation with interfaces quality suggested. The implications of these results for high power optoelectronic and electronic devices will be addressed.

Coupling of orthogonally polarized eigenwaves in BaTiO_3 by light-induced parametric scattering

Efficient indirect recording of space-charge gratings by two orthogonally polarized light waves is shown to be possible in crystals with diffusion charge transport when pronounced light-induced scattering is involved. The recorded grating is π/2 shifted with respect to the polarization fringes and therefore leads to a unidirectional intensity transfer between the pump waves; the direction of transfer depends on the sign of photoexcited carriers. The relatively strong coupling effects between ordinary and extraordinary waves, detected experimentally in BaTiO3, are reasonably explained within the proposed model.

Use of the Babinet Compensator for Anomalous Dispersion Measurements

Reorientation of the optical elements in a standard experimental setup that utilizes a Babinet compensator to measure the anomalous dispersion of a birefringent mediumn results in a useful trade-off between the intensity and visibility of the polarization fringes produced by the apparatus. The fringe pattern is analyzed and numerical results are presented that illustrate the nature of the trade-off and its application to measurements near the center of a strong absorption line.

Scalar Polarization Fringes Produced by the Superposition of Crystalline Plates

Scalar Polarization Fringes Produced by the Superposition of Crystalline Plates