Fourier-domain filtering analysis for color-polarization camera demosaicking: publisher's note.

This publisher's note includes corrections to Appl. Opt.63, 2314 (2024) APOPAI0003-693510.1364/AO.516696.

Fourier-domain filtering analysis for color-polarization camera demosaicking.

We review Fourier-domain methods for demosaicking Bayer-filter color cameras and monochrome polarization cameras, and then generalize the approach for the quad-Bayer-filter mosaic and for color-polarization cameras. For each of these four mosaic filter types, we provide theoretical expressions for the sampling functions, the Fourier-domain channels, and the linear combination of reconstructed channels (the demosaicking algorithm) needed to estimate the input (presampled) image. A useful advantage of the Fourier-domain approach is that it provides a direct means of visualizing and quantifying when aliasing is likely or unlikely to be present. For the Bayer and quad-Bayer-filter types, we provide simulated images, while for the polarization camera types we provide experimental images and videos to illustrate the algorithm and analyze crosstalk error.

Differences between the geometric phase and propagation phase: clarifying the boundedness problem.

We show white light interferometer experiments that clearly demonstrate the basic differences between geometric and propagation phases. These experimental results also suggest a way to answer the "boundedness problem" in geometric phase-whether geometric phase is unbounded (i.e., can take on any values without limit) or bounded (i.e., limited to values between -π and +π). We show why the answer to this question is not as easy as it seems, from both a theoretical and an experimental perspective, and explain how the answer depends on one's choice of phase convention. We also hope that the videos provided will be pedagogically useful for explaining geometric phase.

Deciphering Pancharatnam's discovery of geometric phase: retrospective.

While Pancharatnam discovered the geometric phase in 1956, his work was not widely recognized until its endorsement by Berry in 1987, after which it received wide appreciation. However, because Pancharatnam's paper is unusually difficult to follow, his work has often been misinterpreted as referring to an evolution of states of polarization, just as Berry's work focused on a cycle of states, even though this consideration does not appear in Pancharatnam's work. We walk the reader through Pancharatnam's original derivation and show how Pancharatnam's approach connects to recent work in geometric phase. It is our hope to make this widely cited classic paper more accessible and better understood.

Wave description of geometric phase.

Since Pancharatnam's 1956 discovery of optical geometric phase and Berry's 1984 discovery of geometric phase in quantum systems, researchers analyzing geometric phase have focused almost exclusively on algebraic approaches using the Jones calculus, or on spherical trigonometry approaches using the Poincaré sphere. The abstracted mathematics of the former and the abstracted geometry of the latter obscure the physical mechanism that generates geometric phase. We show that optical geometric phase derives entirely from the superposition of waves and the resulting shift in the location of the wave maximum. This wave-based model provides a way to visualize how geometric phase arises from relationships between waves, and from the transformations induced by optical elements. We also derive the relationship between the geometric phase of a wave by itself and the phase exhibited by an interferogram, and provide the conditions under which the two match one another.

Apophyllite waveplates.

We investigate the polarization characteristics of apophyllite crystals in an attempt to evaluate their potential use for achromatic waveplates. Among the 50 plates that we extracted and polished from natural apophyllite crystals, a few show the sought-for characteristic of birefringence that increases linearly with the wavelength. However, we also find that the crystals among our samples exhibit a sectored structure in their polarization properties, as well as an undesirable degree of spatial nonuniformity.

Gaussian profile estimation in one dimension: erratum.

This erratum corrects errors in Appl. Opt.46, 5374 (2007)APOPAI0003-693510.1364/AO.46.005374.

Design of channeled spectropolarimeters.

I present design and tolerancing guidelines for constructing channeled spectropolarimeter systems employing high-order retarders. The discussion includes how to select appropriate retarder thicknesses, how to accurately align the elements, how to tolerance the retarders, and how to analyze the effect of different polarizer types on the system performance.

Minimizing scattering-induced phase errors in differential interference contrast microscopy.

SIGNIFICANCE: Differential interference contrast (DIC) microscopes allow noninvasive in vivo observation of transparent microstructures in tissue without the use of fluorescent dyes or genetic modification. We show how to modify a DIC microscope to measure the sample phase distribution accurately and in real-time even deep inside sample tissue. AIM: Our aim is to improve the DIC microscope's phase measurement to remove the phase bias that occurs in the presence of strong scattering. APPROACH: A quarter-wave plate was added in front of the polarization camera, allowing a modified phase calculation to incorporate all four polarization orientation angles (0 deg, 45 deg, 90 deg, and 135 deg) captured simultaneously by the polarization camera, followed by deconvolution. RESULTS: We confirm that the proposed method reduces phase measurement error in the presence of scattering and demonstrate the method using in vivo imaging of a beating heart inside a medaka egg and the whole-body blood circulation in a young medaka fish. CONCLUSIONS: Modifying a polarization-camera DIC microscope with a quarter-wave plate allows users to image deep inside samples without phase bias due to scattering effects.

Dynamic calibration for enhancing the stability of a channeled spectropolarimeter.

Channeled spectropolarimeters are optical instruments that measure the spectral dependence of the polarization of light without any mechanically moving parts. An important factor in achieving stable and accurate measurements is the calibration process, especially in dynamic environments where temperature fluctuations or other factors affect the retardance of the components in the polarimeter. In previous research, a self-calibration algorithm that accounts for these variations was developed, without any additional reference measurements. In this paper, we identify an ambiguity in the self-calibration phase, which limits the allowed temperature changes to surprisingly small ranges. We show how to adaptively estimate and correct for the phase ambiguity using a polynomial curve-fitting algorithm, extending the temperature range to virtually all practical scenarios. Lastly, we demonstrate the ability of the modified self-calibration algorithm to provide stable reconstruction of the Stokes vector for a temperature range >40∘C, using an experimental channeled spectropolarimeter.

Compensating for nonlinear dispersion in channeled spectropolarimetry.

All common waveplate materials exhibit nonlinear dispersion of retardance, producing an unwanted chirp in the interference fringes that channeled spectropolarimeters use for heterodyning polarization data. After showing how to quantify this nonlinearity, we survey the common waveplate materials and find that MgF2 has significantly lower nonlinearity than any other available material. We also quantify the degree of crosstalk caused by dispersion nonlinearity and show that, unlike in linear dispersion, the degree of crosstalk depends on the sequence of how the phase calibration is implemented. Regardless of how the calibrated phases have been obtained, shifting each channel to baseband prior to windowing minimizes crosstalk error.

Single shot 3D profilometry by polarization pattern projection.

We demonstrate a uniaxial 3D profilometry system illuminating the sample with a linear polarization pattern and measuring a polarization camera. The linear polarization pattern is generated by a spatial light modulator and a quarter-wave plate in the optical system. The system can measure four different fringe patterns with a phase difference of 90 deg simultaneously in the polarization camera. Therefore, we can measure three-dimensional shapes in a single shot. We present the measurement principles of the system and show the results of a real-time 3D profilometry experiment.

Angularly selective microstructured surface for tuning seasonal sunlight interaction.

In the temperate latitudes, high-reflectivity exterior surfaces save energy spent on ventilation and cooling during summer, but cost energy on heating in winter. Angularly selective surfaces that adjust their reflectivities by sun position allow beneficial effects in both seasons - high reflectivity in summer and high absorption in winter. Here we show how a planar microstructured surface can produce such an angularly selective behavior and estimate its energy efficiency under direct solar irradiance at 35° N. Results show that such an ideal angularly selective surface has the potential to improve efficiency by up to 43.2% compared to a conventional concrete surface. Numerical results for an aluminum one-dimensional periodic structure indicate that it achieves a 25.7% improvement of efficiency. Finally, we validate the designed structure by measuring the reflectivity of the fabricated surface at a series of angles.

Alignment precision of polarization components.

Recent research publications in the polarization literature have discussed methods of correcting for azimuthal alignment errors of optical elements in postprocessing. However, we show that high angular precision is not difficult to achieve during system alignment, so that postprocessing correction should be unnecessary. We estimate the alignment precision achievable for linear polarizers and waveplates in polarization systems. This shows that using an optical signal model for alignment allows a precision limited by the quality of the optics and detectors rather than the quality of the mechanics, rendering millidegree alignment precision possible with ordinary rotational mounts.

Compact and high-speed Stokes polarimeter using three-way polarization-preserving beam splitters.

We present a new real-time Stokes parameter measurement technique using three polarized beam splitters without mechanical motion or electrical tuning. This system can analyze the polarization state of light at 30 kHz, limited only by the speed of the detector analog to digital converters. The optical system is also compact (52×30×25 mm) because it consists only of small volume optical devices. We show that the system can measure arbitrary polarization states with an accuracy of better than 0.006 in the normalized Stokes parameters. We also demonstrate the ability to measure fast dynamic polarization states by analyzing the state produced by a fast rotating quarter-wave plate and the time-dependent stress induced in a PMMA block by hitting the block with a hammer.

Quantitative discrimination of biological tissues by micro-elastographic measurement using an epi-illumination Mueller matrix microscope.

We propose a method for estimating the stiffness of bio-specimens by measuring their linear retardance properties under applied stress. For this purpose, we employ an epi-illumination Mueller matrix microscope and show the procedures for its calibration. We provide experimental results demonstrating how to apply Mueller matrix data to elastography, using chicken liver and chicken heart as biological samples. Finally, we show how the histograms of linear retardance images can be used to distinguish between specimens and quantify the discrimination accuracy.

Erratum: Video-rate quantitative phase analysis by a DIC microscope using a polarization camera: errata.

[This corrects the article on p. 1273 in vol. 10, PMID: 30891345.].

Video-rate quantitative phase analysis by a DIC microscope using a polarization camera.

This paper describes how to take advantage of the replacement of an intensity camera with a polarization camera in a standard differential interference contrast (DIC) microscope. Using a polarization camera enables snapshot quantitative phase analysis so that real-time imaging of living transparent tissues become possible. Using our method, we quantify the phase measurement accuracy using a phantom consisting of glass beads embedded in lacquer. In order to demonstrate these advantages, we image the pumping heart and blood flow in a living medaka egg.

Robust full Stokes imaging polarimeter with dynamic calibration.

We present a full Stokes imaging polarimeter using a rotating retarder in combination with a polarization camera-a detector array on which a pixelated polarizer array is attached. By itself, a polarization camera cannot capture the full Stokes parameters, but we add a rotating retarder in front and show how it can be used to provide full Stokes images. In addition, we demonstrate the advantage that it can be recalibrated dynamically while taking measurements, allowing accurate measurements even in environments where the retardance in changing.

Stokes polarimeter performance: general noise model and analysis: erratum.

We correct two errors in Appl. Opt.57, 4283 (2018)APOPAI0003-693510.1364/AO.57.004283.