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The differentiator consists of carefully designed 2D photonic crystal (PhC) slab that can transform an image into its second-order derivative. Based on interference between the direct transmission and low quality factor quasi-guided modes, the PhC slab exhibits angular-dependent transmission for P polarization but remains reflective for S polarization, which avoids polarization mixing in the transmission matrix. Fourier imaging was carried out showing a quadratic transfer function for an NA up to 0.315, which allows one to resolve features on the scale of 1.94λ. To showcase practical applications, the nanophotonic differentiator was directly integrated into an optical microscope and onto a camera sensor demonstrating the ease at which it can be vertically integrated into existing imaging systems. Furthermore, we demonstrate a compound bilayer flat optical by integrating the differentiator with a metalens for realizing a compact and monolithic image processing system. In all cases, the use of the nanophotonic differentiator allows for a significant reduction in size compared to traditional systems as one does not need to pass through the Fourier plane for performing complex image processing. This freedom should open new doors for optical analog image processing in applications involving machine vision.

A heterodyne grating interferometer (HGI) with high stability and low nonlinearity is presented. An optical arrangement with Littrow configuration combined with Wollaston prism is proposed for the HGI. The compact and symmetrical design make it insensitive to environmental disturbances. The optimal separate angle of the Wollaston prism is investigated with rigorous coupled-wave analysis (RCWA), and the value of 44° corresponding to the grating pitch of 845 nm is selected. The approximately equal diffraction efficiencies of 76.54% and 76.64% for TE and TM polarizations are respectively obtained, which is beneficial to the signal-to-noise ratio (SNR) of HGI. Additionally, the nonlinear errors including polarization mixing, frequency mixing and polarization-frequency mixing are analyzed. The polarization mixing error is dramatically decreased owing to the high extinction ratio of Wollaston prism. It reveals that the developed HGI has the potential for nanometric displacement measurement.

A multimode fiber subjected to random mode and polarization mixing represents a complex photonic system with strong coupling of spatial, temporal, spectral and polarization degrees of freedom. By exploiting such coupling, we demonstrate a full control of the polarization state of light transmitted through a multimode fiber by adjusting the spatial profile of incident field. After applying stress to the fiber to induce strong mode and polarization mixing, we measure the polarization-dependent transmission matrices, and find the transmission eigenchannels. By launching light to specific eigenchannnels, we are able to preserve the polarization state despite strong polarization mixing in the multimode fiber, or to convert all transmitted light to the orthogonal polarization state. In addition, we show that the linearly polarized input light can be changed completely to circularly polarized output. Furthermore, arbitrary polarization states can be realized for individual spatial channels at the output by tailoring the incident wavefront of a single polarization. Such global control is possible only in the presence of strong mode mixing in the fiber. Namely, strong polarization mixing itself is not sufficient to generate arbitrary polarization states at the output. Therefore, the strong entanglement of spatial and polarization degrees of freedom is essential to achieve a complete control of polarization. Such global control of the polarization states of all output channels is more challenging than the local control of the polarization state of a single output channel.

This paper reviews ways and means used for reduction or elimination of periodic nonlinearity in heterodyne interferometers. The periodic nonlinearity resulting from polarization mixing or frequency mixing in heterodyne interferometers was modeled into one expression, which included the initial polarization state of the laser source, the rotational alignment of the beam splitter along with different transmission coefficients for polarization states and the rotational misalignment of a receiving polarizer. Three compensation techniques, measuring two orthogonal output signals, Lissajous Compensation and Chu-Ray Algorithm, are described and discussed for reduction of periodic nonlinearity. These algorithms needed at least one fringe of motion or a constant velocity sweep to properly correct the motion. And five types of two spatially separated beam interferometer configurations are described and discussed for elimination of periodic nonlinearity to a picometer level. It is concluded that the main disadvantage of these configurations was their complex architecture with unbalanced long beam paths.

The nonlinearity of the interferometer is an essential error in nanoscale measurements influenced by anisotropic gain and nonorthogonality of imperfect polarization components. In this paper, polarization error and the corresponding nonlinearity correction method are studied. The paper is divided into two parts, in the first part, main research focuses on the polarization mixing effect of multi-pass interferometer, besides this, polarization beam splitter and retardation plate are also analyzed, then a final synthetic evaluation is obtained through Jones matrix. In the second part, a harmonic separation method of interferometer signals is researched, the method first decomposes signals into Fourier series, then uses least square fitting to estimate coefficients of main terms of series. In the correction process, the primary phase angle is obtained through coefficients of base series and trigonometric formulas; the finer phase angle is obtained through coefficients of harmonics and Taylor expansion. Experimental results demonstrate that the nonlinearity of homodyne interferometer is significantly reduced in nanometer measurements.

We present both simulation and experimental results showing that circularly polarized light maintains its degree of polarization better than linearly polarized light in scattering environments. This is specifically true in turbid environments like fog and clouds. In contrast to previous studies that propagate single wavelengths through broad particle-size distributions, this work identifies regions where circular polarization persists further than linear by systematically surveying different wavelengths through monodisperse particle diameters. For monodisperse polystyrene microspheres in water, for particle diameters of 0.99 and 1.925 microns and varying optical depths, we show that circular polarization’s ability to persist through multiple scattering events is enhanced by as much as a factor of four, when compared to that of linear polarization. These particle diameters correspond to size parameters found for infrared wavelengths and marine and continental fog particle distributions. The experimental results are compared to Monte Carlo simulations for all scattering environments investigated.

Information about the polarization of light is valuable because it contains information about the light source illuminating an object, the illumination angle, and the object material. However, polarization information strongly depends on the direction of the light source, and it is difficult to use a polarization image with various recognition algorithms outdoors because the angle of the sun varies. We propose an image enhancement method for utilizing polarization information in many such situations where the light source is not fixed. We take two approaches to overcome this problem. First, we compute an image that is the combination of a polarization image and the corresponding brightness image. Because of the angle of the light source, the polarization contains no information about some scenes. Therefore, it is difficult to use only polarization information in any scene for applications such as object detection. However, if we use a combination of a polarization image and a brightness image, the brightness image can complement the lack of scene information. The second approach is finding features that depend less on the direction of the light source. We propose a method for extracting scene features based on a calculation of the reflection model including polarization effects. A polarization camera that has micro-polarizers on each pixel of the image sensor was built and used for capturing images. We discuss examples that demonstrate the improved visibility of objects by applying our proposed method to, e.g., the visibility of lane markers on wet roads.

Based on the detailed derivation of the displacement measurement principle with Jones matrix method, the optical system of the heterodyne grating interferometry that we previously proposed was modified. A reflection phase grating with smaller grating pitch was designed with rigorous coupled-wave analysis (RCWA) to improve the measurement performance. The first order diffraction efficiency of 47.35% and 56.24% were obtained for TE and TM polarization, respectively. Therefore the TM polarization was chose to enhance the signal-to-noise ratio (SNR) of the beat signal. Meanwhile, the errors of the optical system resulting from grating non-uniformity, frequency mixing, polarization mixing and polarization-frequency mixing were discussed as well. It was shown that the frequency mixing was the main source of the errors, and the modified heterodyne grating interferometry had the potential to realize nanometer resolution for displacement measurement.

Interferometer is widely used in precise displacement measurement. Nonlinearity of interferometer is one of the major limits when using interferometers in nanometer displacement measurement. Nonlinearity is caused by phase mixing in homodyne interferometers due to the imperfect of polarization optical components. Both the detection part and interferometer part cause nonlinearity. In this study, the polarization mixing effect of multi-pass interferometer caused by the interferometer part is analyzed by Jones matrix. The effects of polarization beam splitter and wave plate on the nonlinearity are studied. The results show that the polarization mixing effect in multi-pass interferometers cause different orders of frequency components. The nonlinearity error is asymmetry with different harmonic components compared to that caused by the detection part.

Periodic nonlinearity is a systematic error limiting the accuracy of displacement measurements at the nanometer level. It results from many causes such as the frequency mixing, polarization mixing, polarization-frequency mixing, and the ghost reflections. An interferometer having accuracy in displacement measurement of less than one-nanometer is necessary in nanometrology. To meet the requirement, the periodic nonlinearity should be less than deep sub-nanometer. In this paper, a nonlinearity-reduced interferometry has been proposed. Both the linear- and straightness-interferometer were tested. The developed interferometer demonstrated of a residual nonlinearity less than 25 pm.

We present a new high-index-contrast material system to realize ridge waveguides and PhC waveguides made of a thin silicon slab embedded in two silica layers. Hence fully symmetrical structures can be etched and two important conditions for low-loss guiding of light can be matched: The symmetry properties of the material avoid polarization mixing and the high index contrast leads to strong confinement of light. Because of operating completely below the lightcone the PhC waveguides allow theoretically lossless guiding of light.

This paper reports an experiment that demonstrated the functionality of a commercial heterodyne interferometer with an oblique-angle fold mirror in the laser feed path. The key issue investigated is whether the oblique angle fold mirrors introduce unacceptable levels of polarization mixing. The manufacture's specifications recommend that only orthogonal fold mirrors be used to control polarization mixing. However, this constraint limits the use of the interferometer for applications such as the measurement of structural dynamics. In the experiment, an orthogonally-fed interferometer was compared to an oblique angle interferometer at roughly 45°. The result indicated a linear relationship between the two measurements to within 0.5 percent. As a result, no evidence of the λ/2 wavelength sinusoidal bias characteristic of polarization mixing errors was found. A 9 percent error did however exist between the intended and observed scaling between the two measurements. While hardware alignment errors are a likely cause of this disagreement, a third axis of measurement is recommended for future investigations.

Sea surface salinity (SSS) has been recognized as a key parameter in climatological studies. SSS can be measured by passive microwave remote sensing at L band, where the sensitivity of the brightness temperatures shows a maximum and the atmosphere is almost transparent. To provide global coverage of this basic parameter with a 3-day revisit time, the SMOS mission was recently selected by ESA within the frame of the Earth Explorer Opportunity Missions. The SMOS mission will carry the MIRAS instrument, the first 2D L-band aperture synthesis interferometric radiometer. To address new challenges that this mission presents, such as incidence angle variation with pixel, polarization mixing, effect of wind and foam and others, a measurement campaign has been sponsored by ESA under the name of WISE 2000 and it is scheduled for October-November 2000. Two L-band radiometers, a video, a IR and a stereo-camera and four oceanographic and meteorological buoys will be installed in the oil platform 'Casablanca' located at 40 Km off the coast of Tarragona, where the sea conditions are representative of the Mediterranean open sea with periodic influence of the Ebro river fresh water plume.

Projectors that use LCOS lightvalves face special contrast requirements. Most configurations for reflective light valves employ tilted beam-dividing coatings that see both bright and dark polarization states. The optics must then be designed to eliminate polarization mixing at these coatings, which ordinarily arises when the S and P planes for different rays are non-parallel. We show how phase- controlled coatings can exploit the double-pass symmetry of the Plumbicon tri-prism geometry to correct this effect, reducing cross-polarized reflectivity to approximately 1E-3 when the light valve is mirror-like in black-state. Though contrast in different rays varies as a function of both ray skew component and coating angle of incidence, we show that for NA

The techniques of stabilizing and linearizing the output of a fiber-optic magnetometer are analyzed both theoretically and experimentally. Results show that the modified phase sensitivity detection system can eliminate the affects of variations due to laser coupling, polarization mixing efficiency, and magnetic feedback and the affects of hysteresis and irregular magnetostrictive response.© (1991) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.