Monte–Carlo numerical simulation (MCNS) is used to study the characteristics of an underwater scattering channel for an LED source in different types of water. The high scattering effect of turbid water significantly dispersed the signal’s intensity distribution and broadened the half power angle. An empirical path loss model is proposed and was proved effective by simulations in different types of water. In high turbid water, the receiving power is dominated by scattering, while the straight line power is negligible.

An operator-based approach for the study of homogeneous coordinates and projective geometry is proposed. First, some basic geometrical concepts and properties of the operators are investigated in the one- and two-dimensional cases. Then, the pinhole camera model is derived, and a simple method for homography estimation and camera calibration is explained. The usefulness of the analyzed theoretical framework is exemplified by addressing the perspective correction problem for a camera document scanning application. Several experimental results are provided for illustrative purposes. The proposed approach is expected to provide practical insights for inexperienced students on camera calibration, computer vision, and optical metrology among others.

This guest editorial introduces the special section on Long-Range Imaging, which appears in the July 2017 issue of Optical Engineering.

We present a numerical wave propagation method for simulating imaging of an extended scene under anisoplanatic conditions. While isoplanatic simulation is relatively common, few tools are specifically designed for simulating the imaging of extended scenes under anisoplanatic conditions. We provide a complete description of the proposed simulation tool, including the wave propagation method used. Our approach computes an array of point spread functions (PSFs) for a two-dimensional grid on the object plane. The PSFs are then used in a spatially varying weighted sum operation, with an ideal image, to produce a simulated image with realistic optical turbulence degradation. The degradation includes spatially varying warping and blurring. To produce the PSF array, we generate a series of extended phase screens. Simulated point sources are numerically propagated from an array of positions on the object plane, through the phase screens, and ultimately to the focal plane of the simulated camera. Note that the optical path for each PSF will be different, and thus, pass through a different portion of the extended phase screens. These different paths give rise to a spatially varying PSF to produce anisoplanatic effects. We use a method for defining the individual phase screen statistics that we have not seen used in previous anisoplanatic simulations. We also present a validation analysis. In particular, we compare simulated outputs with the theoretical anisoplanatic tilt correlation and a derived differential tilt variance statistic. This is in addition to comparing the long- and short-exposure PSFs and isoplanatic angle. We believe this analysis represents the most thorough validation of an anisoplanatic simulation to date. The current work is also unique that we simulate and validate both constant and varying Cn2(z) profiles. Furthermore, we simulate sequences with both temporally independent and temporally correlated turbulence effects. Temporal correlation is introduced by generating even larger extended phase screens and translating this block of screens in front of the propagation area. Our validation analysis shows an excellent match between the simulation statistics and the theoretical predictions. Thus, we think this tool can be used effectively to study optical anisoplanatic turbulence and to aid in the development of image restoration methods.

We present a block-matching and Wiener filtering approach to atmospheric turbulence mitigation for long-range imaging of extended scenes. We evaluate the proposed method, along with some benchmark methods, using simulated and real-image sequences. The simulated data are generated with a simulation tool developed by one of the authors. These data provide objective truth and allow for quantitative error analysis. The proposed turbulence mitigation method takes a sequence of short-exposure frames of a static scene and outputs a single restored image. A block-matching registration algorithm is used to provide geometric correction for each of the individual input frames. The registered frames are then averaged, and the average image is processed with a Wiener filter to provide deconvolution. An important aspect of the proposed method lies in how we model the degradation point spread function (PSF) for the purposes of Wiener filtering. We use a parametric model that takes into account the level of geometric correction achieved during image registration. This is unlike any method we are aware of in the literature. By matching the PSF to the level of registration in this way, the Wiener filter is able to fully exploit the reduced blurring achieved by registration. We also describe a method for estimating the atmospheric coherence diameter (or Fried parameter) from the estimated motion vectors. We provide a detailed performance analysis that illustrates how the key tuning parameters impact system performance. The proposed method is relatively simple computationally, yet it has excellent performance in comparison with state-of-the-art benchmark methods in our study.

Atmospheric turbulence parameters are estimated for an imaging path based on time-lapse imaging results. Atmospheric turbulence causes frame-to-frame shifts of the entire image as well as parts of the image. The statistics of these shifts encode information about the turbulence strength (as characterized by Cn2, the refractive index structure function constant) along the optical path. The shift variance observed is simply proportional to the variance of the tilt of the optical field averaged over the area being tracked and averaged over the camera aperture. By presuming this turbulence follows the Kolmogorov spectrum, weighting functions, which relate the turbulence strength along the path to the shifts measured, are derived. These weighting functions peak at the camera and fall to zero at the object. The larger the area observed, the more quickly the weighting function decays. One parameter we would like to estimate is r0 (the Fried parameter or atmospheric coherence diameter.) The weighting functions derived for pixel sized or larger parts of the image all fall faster than the weighting function appropriate for estimating the spherical wave r0. If we were to presume that Cn2 is constant along the path, then an estimate for r0 could be obtained for each area tracked, but since the weighting function for r0 differs substantially from that for every realizable tracked area, it can be expected that this approach would yield a poor estimate. Instead, the weighting functions for a number of different patch sizes can be combined through the Moore–Penrose pseudoinverse to create a weighting function that yields the least-squares optimal linear combination of measurements for the estimation of r0. This approach is carried out for one example and is shown to give noisy results. A modified version of this approach that creates larger patches by averaging several smaller patches together solves this noise issue. This approach can also work to estimate other atmospheric para

Accurate simulation and forecasting of over-the-horizon propagation events are essential for various civilian and defense applications. We demonstrate the prowess of a newly proposed coupled mesoscale modeling and ray tracing framework in reproducing such an event. Wherever possible, routinely measured meteorological data from various platforms (e.g., radar and satellite) are utilized to corroborate the simulated results.

Atmospheric turbulence degrades imagery by imparting scintillation and warping effects that blur the collected pictures and reduce the effective level of detail. While this reduction in image quality can occur in a wide range of scenarios, it is particularly noticeable when capturing over long distances, when close to the ground, or in hot and humid environments. For decades, researchers have attempted to correct these problems through device and signal processing solutions. While fully digital approaches have the advantage of not requiring specialized hardware, they have been difficult to realize in real-time scenarios due to a variety of practical considerations, including computational performance, the need to integrate with cameras, and the ability to handle complex scenes. We address these challenges and our experience overcoming them. We enumerate the considerations for developing an image processing approach to atmospheric turbulence correction and describe how we approached them to develop software capable of real-time enhancement of long-range imagery.

When capturing imagery over long distances, atmospheric turbulence often degrades the data, especially when observation paths are close to the ground or in hot environments. These issues manifest as time-varying scintillation and warping effects that decrease the effective resolution of the sensor and reduce actionable intelligence. In recent years, several image processing approaches to turbulence mitigation have shown promise. Each of these algorithms has different computational requirements, usability demands, and degrees of independence from camera sensors. They also produce different degrees of enhancement when applied to turbulent imagery. Additionally, some of these algorithms are applicable to real-time operational scenarios while others may only be suitable for postprocessing workflows. EM Photonics has been developing image-processing-based turbulence mitigation technology since 2005. We will compare techniques from the literature with our commercially available, real-time, GPU-accelerated turbulence mitigation software. These comparisons will be made using real (not synthetic), experimentally obtained data for a variety of conditions, including varying optical hardware, imaging range, subjects, and turbulence conditions. Comparison metrics will include image quality, video latency, computational complexity, and potential for real-time operation. Additionally, we will present a technique for quantitatively comparing turbulence mitigation algorithms using real images of radial resolution targets.

We introduce a method for creating temporally evolving wavefront distortions that uses Karhunen–Loève (K-L) decomposition and the associated temporal power spectra. We model the single- and multilayer cases for horizontal and vertical paths, for which spherical and plane-wave geometries must be assumed, respectively. Simulation results confirming correct representation of the spatial and temporal statistics are presented. We demonstrate that the method is able to produce dynamic wavefronts that follow the behavior predicted by the theory while introducing key advantages in terms of storage in computer memory.

Computational efficiency and accuracy of wave-optics-based Monte–Carlo and brightness function numerical simulation techniques for incoherent imaging of extended objects through atmospheric turbulence are evaluated. Simulation results are compared with theoretical estimates based on known analytical solutions for the modulation transfer function of an imaging system and the long-exposure image of a Gaussian-shaped incoherent light source. It is shown that the accuracy of both techniques is comparable over the wide range of path lengths and atmospheric turbulence conditions, whereas the brightness function technique is advantageous in terms of the computational speed.

Present space-based optical imaging sensors are expensive. Launch costs are dictated by weight and size, and system design must take into account the low fault tolerance of a system that cannot be readily accessed once deployed. We describe the design and first prototype of the space-based infrared imaging interferometer (SIRII) that aims to mitigate several aspects of the cost challenge. SIRII is a six-element Fizeau interferometer intended to operate in the short-wave and midwave IR spectral regions over a 6×6  mrad field of view. The volume is smaller by a factor of three than a filled-aperture telescope with equivalent resolving power. The structure and primary optics are fabricated from light-weight space-qualified carbon fiber reinforced polymer; they are easy to replicate and inexpensive. The design is intended to permit one-time alignment during assembly, with no need for further adjustment once on orbit. A three-element prototype of the SIRII imager has been constructed with a unit telescope primary mirror diameter of 165 mm and edge-to-edge baseline of 540 mm. The optics, structure, and interferometric signal processing principles draw on experience developed in ground-based astronomical applications designed to yield the highest sensitivity and resolution with cost-effective optical solutions. The initial motivation for the development of SIRII was the long-term collection of technical intelligence from geosynchronous orbit, but the scalable nature of the design will likely make it suitable for a range of IR imaging scenarios.

An atmospheric imaging system based on quantum hyperentanglement has been developed. Hyper-entanglement can increase the maximum detection range of the system by more than a factor of 10, improve the signal-to-noise ratio (SNR) by more than a factor of 10,000, and decrease measurement time. Hyperentanglement refers to entanglement in more than one degree of freedom. A design for creating states hyperentangled in the degrees of freedom polarization, energy-time, orbital angular momentum (OAM), and the radial quantum number is examined. The design helps reduce propagation loss. Figures of merit related to generation and detection efficiencies, the SNR, signal to interference ratio, the measurement time, and phase estimation are provided in closed form. A formula describing how hyperentanglement greatly improves the maximum detection range of the system is derived. Hermite–Gaussian modes, Laguerre–Gaussian (LG) modes, OAM dependence of the LG modes, and mode conversion are discussed. Bell state generation and Bell state measurement, i.e., the ability to distinguish the various Bell states, is discussed. Mathematical and circuit representations of Bell state generation and the Bell state analyzer are provided. Signatures for unique detection of the various Bell states are developed. The formalism permits random noise and entangled or nonentangled sources of interference to be modeled.

Fast steering and quick positioning are prime requirements of the current electro-optical tracking system to achieve quick target acquisition. A scheme has been proposed for realizing these features using two-axis, four-gimbaled sight. For steering the line of sight in the stabilization mode, outer gimbal is slaved to the gyro stabilized inner gimbal. Typically, the inner gimbals have direct drives and outer gimbals have geared drives, which result in a mismatch in the acceleration capability of their servo loops. This limits the allowable control bandwidth for the inner gimbal. However, to achieve high stabilization accuracy, high bandwidth control loops are essential. This contradictory requirement has been addressed by designing a suitable command conditioning module for the inner gimbals. Also, large line-of-sight freedom in pitch axis is required to provide a wide area surveillance capacity for airborne application. This leads to a loss of freedom along the yaw axis as the pitch angle goes beyond 70 deg or so. This is addressed by making the outer gimbal master after certain pitch angle. Moreover, a mounting scheme for gyro has been proposed to accomplish yaw axis stabilization for 110-deg pitch angle movement with a single two-axis gyro.

A single exposure superresolution (SR) restoration algorithm for an optical sparse aperture (OSA) imaging system based on random convolution is proposed. The low-resolution image from the OSA system is restored by adding a set of incoherent measurements taken using random convolution architecture, in which there is a random phase mask in the Fourier plane and a random amplitude mask in the image plane in the conventional optical 4f system. Both masks are generated by chaotic maps. The simulation results show that this algorithm can effectively recover the images degraded by both optical diffraction effect and geometrical limited resolution under noisy and aberrated conditions. The spatial resolution gain factor is above 2.82 without subsampling and 1.26 with subsampling. Moreover, it can obtain a better restoration quality than traditional algorithms by optimizing the initial conditions of chaotic maps.

Satellite remote sensing that utilizes highly accurate cloud detection is important for monitoring natural disasters. The GaoFen-4, China’s first high-resolution stationary satellite, was recently launched and acquires imagery at a spatial resolution of 50 m and a high temporal resolution (up to 10 min). An object-based cloud detection method was conducted for a time series of GaoFen-4 images. The cloudy objects were obtained from the individual images, and the outlier detection of multiple temporal objects was further processed for refinement. In the initial cloud detection, the objects were segmented by the mean-shift algorithm, and their morphological features were extracted by extended attribute profiles. The threshold-detected cloudy objects were trained according to spectral and morphological features, and the initial objects were classified as cloudy or clear by a regularized least-squares classifier. Furthermore, the medians and standard deviations of the classified cloudy and clear objects were calculated and subsequently refined by the outlier detection of multiple temporal images. The clear object features deviated more than a multiple of standard deviations from the medians of the clear objects that were classified as cloudy objects. Additionally, the refined clear objects were obtained by a similar outlier detection method. Flood event monitoring using GaoFen-4 images showed that the average overall accuracy of the initial cloud detection was 83.4% and increased to 93.3% after refinement. This object-based cloud detection method was insensitive to variations in land objects and can effectively improve cloud detection within small or thin areas, which can be helpful for the monitoring of natural disasters.

Alternative approaches to three-dimensional (3-D) reconstruction by employing the concepts of “system identification” and “communication systems” based on structured light patterns are proposed. In addition, a sampling criterion of the light source is derived in the case of using multiple projectors because 3-D reconstruction sometimes employs multiple viewpoints (cameras) and multiple structured light sources (or projectors). To reformulate a reconstruction problem, an input–output (I/O) system theoretic is adopted, and camera(s) and light source(s) that are located at different positions are defined as the output and the input, respectively. Akin to the system identification problem, the ratio of an output to an input, the “system function,” is defined as a 3-D measurement result. Alternatively, the reconstruction work can employ the concept of the “modulation and demodulation theory,” and the reconstruction work can be reinterpreted as an “input estimation problem.” This contribution chiefly deals with approximate reconstruction results that are sufficient for practical applications, such as 3-D object detection, clarification, recognition, and classification, rather than a perfect 3-D reconstruction itself. To that end, the development of an efficient and fast 3-D imaging system framework is proposed.

A pixel mask-based three-dimensional (3-D) display with uniform resolution is proposed. This 3-D display consists of a reflected light source, a pixel mask, a liquid crystal display (LCD) panel, and a lenticular lens. The reflected light source is located on the bottom layer of the proposed 3-D display. It has a reflective structure to improve optical efficiency, so it can make up the brightness loss, which is caused by the pixel mask. The pixel mask is located between the reflected light source and the LCD panel, and is attached on the back surface of the LCD panel. This pixel mask is made of a reflective material, and some transparent areas are etched on it. The pixel mask redefines the pixels of the two-dimensional display panel located in front of it, so the size and location of redefined pixels depend on the transparent area of the pixel mask. The arrangement of the redefined pixels can increase the column numbers of synthetic images. Therefore, the synthetic images can make 3-D images have uniform resolution. A 4-view prototype of this display is developed and the experimental result shows the proposed method can improve resolution uniformity successfully.

An acousto-optic tunable filter (AOTF) is used in the development of hyperspectral imagers from the ultraviolet to the longwave infrared. The spectral response of the transmitted intensity from an AOTF with a rectangular transducer has a sinc²(x) distribution and so far the light leakage from the sidelobes is ignored in hyperspectral imagers. When unpolarized white light is incident on an AOTF, two orthogonally polarized diffracted beams at a specific wavelength with a narrow bandpass filter are transmitted for an applied radio frequency (RF), and an image cube is obtained by tuning the applied RF. We carried out a detailed study of light transmitted through the sidelobes of a TeO₂ AOTF operating in the shortwave infrared region from 0.9 to 1.7  μm to image a scene containing a laser. The AOTF imaging system used telecentric confocal optics that compensate for AOTF aberrations. We used a 16-channel RF driver with independent amplitude and frequency control. By switching off specific RF signals applied to the AOTF, the detailed sidelobe structure for the transmitted intensity was measured and compared with theory. We found that close to 10% of the transmitted light is leaked through the sidelobes. Here, we present our experiment and analysis of the results.

Compared with traditional 3-D shape data, ladar range images possess properties of strong noise, shape degeneracy, and sparsity, which make feature extraction and representation difficult. The slice image is an effective feature descriptor to resolve this problem. We propose four improved algorithms on target recognition of ladar range images using slice image. In order to improve resolution invariance of the slice image, mean value detection instead of maximum value detection is applied in these four improved algorithms. In order to improve rotation invariance of the slice image, three new improved feature descriptors—which are feature slice image, slice-Zernike moments, and slice-Fourier moments—are applied to the last three improved algorithms, respectively. Backpropagation neural networks are used as feature classifiers in the last two improved algorithms. The performance of these four improved recognition systems is analyzed comprehensively in the aspects of the three invariances, recognition rate, and execution time. The final experiment results show that the improvements for these four algorithms reach the desired effect, the three invariances of feature descriptors are not directly related to the final recognition performance of recognition systems, and these four improved recognition systems have different performances under different conditions.

We designed and developed a control circuit for a three-dimensional (3-D) light-emitting diode (LED) array to be used in volumetric displays exhibiting full-color dynamic 3-D images. The circuit was implemented on a field-programmable gate array; therefore, pulse-width modulation, which requires high-speed processing, could be operated in real time. We experimentally evaluated the developed system by measuring the luminance of an LED with varying input and confirmed that the system works appropriately. In addition, we demonstrated that the volumetric display exhibits different full-color dynamic two-dimensional images in two orthogonal directions. Each of the exhibited images could be obtained only from the prescribed viewpoint. Such directional characteristics of the system are beneficial for applications, including digital signage, security systems, art, and amusement.

An improved multiple circular array (MCA) configuration is proposed for sparse aperture (SA) optical imaging systems. Using genetic algorithms, the practical cutoff frequency (PCOF), based on the modulation transfer function for the array, is selected as the fitness function. Moreover, the parameters, such as diameters of aperture sets, spacing between the aperture sets, and relative rotation angles between aperture sets on different concentric circles, are calculated. Improved MCA configurations, with aperture numbers of 6, 9, 12, 10, 15, 11, and 13, are given. Golay arrays, MCAs, a single annular aperture, and improved arrays with the same fill factor are compared. The results show that the improved array has highest PCOF of all the SA arrays, smoother coverage in Fourier space, and better midfrequency contrast than MCAs. Consequently, the improved array is a promising aperture configuration that can approximate a single annular aperture.

A method is proposed for depth extraction of low-texture region with a light field (LF) camera, which expands the application. Based on the analysis of LF data, it is proven that the depth information can be estimated from a single LF image. Furthermore, as the lenslet LF data can be decoded into a subimages array, and the relationship among subimages is proven to be affine transformation, we used the geometry relationship, which is represented by partition ratio of triangle grids area, to replace the unreliable gray value of low-texture region for stereo matching. In addition, to obtain accurate ratio values, preset points are projected to enrich the texture with a projector, which is convenient and reliable. The proposed method improves the accuracy of the depth extraction obviously at low-texture region compared with the traditional state-of-the-art LF method, and results are validated by experiments.

Calibration is a critical step for the projector-camera-based structured light system (SLS). Conventional SLS calibration means usually use the calibrated camera to calibrate the projector device, and the optimization of calibration parameters is applied to minimize the two-dimensional (2-D) reprojection errors. A three-dimensional (3-D)-based method is proposed for the optimization of SLS calibration parameters. The system is first calibrated with traditional calibration methods to obtain the primary calibration parameters. Then, a reference plane with some precisely printed markers is used for the optimization of primary calibration results. Three metric error criteria are introduced to evaluate the 3-D reconstruction accuracy of the reference plane. By treating all the system parameters as a global optimization problem and using the primary calibration parameters as initial values, a nonlinear multiobjective optimization problem can be established and solved. Compared with conventional calibration methods that adopt the 2-D reprojection errors for the camera and projector separately, a global optimal calibration result can be obtained by the proposed calibration procedure. Experimental results showed that, with the optimized calibration parameters, measurement accuracy and 3-D reconstruction quality of the system can be greatly improved.

This paper presents our research findings on high-speed high-accuracy three-dimensional shape measurement using digital light processing (DLP) technologies. In particular, we compare two different sinusoidal fringe generation techniques using the DLP projection devices: direct projection of computer-generated 8-bit sinusoidal patterns (a.k.a., the sinusoidal method), and the creation of sinusoidal patterns by defocusing binary patterns (a.k.a., the binary defocusing method). This paper mainly examines their performance on high-accuracy measurement applications under precisely controlled settings. Two different projection systems were tested in this study: a commercially available inexpensive projector and the DLP development kit. Experimental results demonstrated that the binary defocusing method always outperforms the sinusoidal method if a sufficient number of phase-shifted fringe patterns can be used.

Extractions of particle positions from inline holograms using a single coefficient of Wigner–Ville distribution (WVD) are experimentally verified. WVD analysis of holograms gives local variation of fringe frequency. Regardless of an axial position of particles, one of the WVD coefficients has the unique characteristics of having the lowest amplitude and being located on a line with a slope inversely proportional to the particle position. Experimental results obtained using two image sensors with different resolutions verify the feasibility of the present method.

The magnetic-field-compensation optical vector magnetometer based on the nonlinear Hanle effect in alkali metal vapor allowing two-axis measurement operation has been further elaborated for three-axis performance, along with significant reduction of measurement time. The upgrade was achieved by implementing a two-beam resonant excitation configuration and a fast maximum searching algorithm. Results of the proof-of-concept experiments, demonstrating 1  μTB-field resolution, are presented. The applied interest and capability of the proposed technique is analyzed.

Single diamond turning is usually used to fabricate multilayer diffractive optical elements (MLDOEs). The choice of diamond tools directly influences the profile error and surface roughness error of MLDOEs. Those two errors will cause the shadowing effect and scattering effect, which decrease the diffraction efficiency of MLDOEs. The relationship among diffraction efficiency, cutting tool radius, feed rate, and microstructure periods was presented. A model to find the optimal cutting tool radius and feed rate before the fabrication was put forward to balance the influence of shadowing effect and scattering effect, which can maximize the polychromatic integral diffraction efficiency. The effect of diamond cutting tool radius and feed rate in the manufacturing process of MLDOEs is discussed and analyzed numerically, and the results will be intended as guidelines for manufacture of MLDOEs to achieve diffractive surface-relief profile with high quality.

The mid-infrared (mid-IR) is a spectral region (≈2 to 20  μm) that is of key importance in astronomy for applications such as exoplanet imaging and spectroscopic analysis. Long baseline stellar interferometry is the only imaging technique that offers the possibility to achieve milli-arcsecond angular resolution in the mid-IR. At the heart of such an interferometer is the beam combining instrument, which enables coherent beam combination of the signals from each baseline. In comparison to bulk-optic beam combiners, beam combiners that utilize photonic planar light wave circuits for interferometry provide a more scalable and stable platform. The current generation of beam combination circuits are fabricated using conventional fabrication technologies, using silica-based materials, and are thus not suitable for operation in the mid-IR. There is, therefore, a need to explore more unconventional waveguide fabrication technologies, capable of enabling the fabrication of low-loss mid-IR waveguides and photonic beam combining circuits. We report on the development of low-loss single-mode waveguides in a gallium lanthanum sulfide glass using ultrafast laser inscription. The optimum waveguides are found to exhibit a propagation loss of 0.25±0.05  dB cm−¹.

The efficiency of sunlight collection systems is related to the optical element used as a collector. On this subject, the design of a nontracking solar collector that consists of a segmented nonimaging Fresnel dome is presented. It is formed by the conjunction of different zones for solar collection, where each one is a nonimaging Fresnel lens that collects a specific angular range (θ_in) of sunlight received in the northeast of Mexico, but the methodology presented can be easily extended to other geographic locations. The final design is a semistationary segmented collector with a 100-cm diameter and 50-cm focal length that needs a 180-deg rotation over the XY-plane in each equinox. The numerical simulations show that the nontracking segmented collector has a combined acceptance semiangle of θ_in=±105  deg with an average efficiency of over 67% from 9:00 to 18:00 h. The spatial and angular distributions of the sunlight collected are also included. This design has a collection area equal to that of a single nonimaging Fresnel lens with an acceptance semiangle of θ_in=±45  deg. These results are reproducible and provide valuable data for designing nontracking solar collectors based on nonimaging Fresnel lens.

We have explored double-layer-coated fiber optics using two-phase immiscible non-Newtonian fluid as a polymeric material. We have considered two layers, the first layer is assumed of soft material and the second consists of hard material. Resin flows are driven by fast-moving glass fiber and the pressurization at the coating die inlet. Two cases of temperature linearly varying at the boundaries have been discussed. The assumption of fully developed flow of non-Newtonian fluid permits an exact solution to the Navier–Stokes equations. The thickness of the secondary coating resin and the shear stress on the glass fiber, which are two basic output variables of practical concern, have been examined by several input parameters: two geometric parameters, i.e., radius of the glass fiber R_w and radius of the coating die R_d; two operational parameters, i.e., the velocity ratio U and power indices n_1,2; the non-Newtonian parameter S_1,2; and the nondimensional parameters H and ϕ. The comparison of the present work with published result predicts the close agreement.

In long-distance, high-speed underwater laser communication, because of the strong absorption and scattering processes, the laser pulse is stretched with the increase in communication distance and the decrease in water clarity. The maximum communication bandwidth is limited by laser-pulse stretching. Improving the communication rate increases the intersymbol interference (ISI). To reduce the effect of ISI, the Viterbi equalization (VE) algorithm is used to estimate the maximum-likelihood receiving sequence. The Monte Carlo method is used to simulate the stretching of the received laser pulse and the maximum communication rate at a wavelength of 532 nm in Jerlov IB and Jerlov II water channels with communication distances of 80, 100, and 130 m, respectively. The high-data rate communication performance for the VE and hard-decision algorithms is compared. The simulation results show that the VE algorithm can be used to reduce the ISI by selecting the minimum error path. The trade-off between the high-data rate communication performance and minor bit-error rate performance loss makes VE a promising option for applications in long-distance, high-speed underwater laser communication systems.

A theoretical study of coherently coupled spatial soliton pairs propagating along the same line in biased two-photon photorefractive crystals is presented. Our results show that coherently coupled bright–bright and dark–dark soliton pairs propagating collinearly can be supported in a steady-state regime under appropriate conditions. Moreover, the effects of the intensity ratio, the initial phase difference between two incident coherent beams, and various external bias fields on the existence conditions and properties of these soliton pairs have been discussed in detail. The stability of these soliton pairs has also been discussed by means of beam propagation methods. Finally, the temperature dependence of the dark irradiance and diffusion process on the intensity profiles and self-deflection of coherently coupled bright–bright soliton pairs are also analyzed.

An iterative algorithm is proposed and investigated for phase noise estimation of discrete Fourier transform spread (DFT-S) orthogonal frequency division multiplexing (OFDM). Compared with common phase estimation (CPE), significant improvement of tolerance to laser bandwidth is obtained and 2.7 dB improvement at BER of 3.8×10⁻³ is found using the CPE-iter scheme in 103.3  Gb/s coherent polarization-division-multiplexed DFT-S OFDM system over 480-km transmission through simulation.

A strain sensing element in a high temperature environment is presented and experimentally demonstrated. The proposed strain sensing element consists of polyimide-coated fiber Bragg grating (FBG) and double rhombus metal structure. The polyimide-coated FBG was fabricated on the double rhombus metal structure by a modulated low softening glass process. The double rhombus metal structure was made of high temperature constant modulus alloy. The sensitivity of the strain sensing element is enhanced by two times of strain amplification and could be adjusted by selecting the angle and the dimension of the double rhombus metal structure appropriately. It is experimentally demonstrated that the proposed strain sensing element could be used at the high temperature of 300°C, and the average wavelength sensitivity of the strain sensing element at 300°C is 3.049 and 3.259  pm/μϵ for the compressed and stretched states, respectively.

The relatively unsatisfactory performance of optical wireless communication (OWC) with respect to WiFi and millimeter-wave communications has formed a key issue preventing its commercialization. We experimentally demonstrate an OWC technology using a combination of positive real-valued orthogonal frequency-division multiplexing (OFDM) and optical beamforming (OB). Due to the intensity-modulation and direct-detection aspects of OWC systems, a positive real-valued OFDM signal can be suitably utilized to maximize the OWC data rate. Further, the OB technique, which can focus laser light on a desired target, can be utilized to increase the OWC data rate and transmission distance. Our experimental results show that the received optical signal power and electrical signal increase by up to 42 and 25 dB, respectively. Further, the data rate increases by a factor of 200 with OB over the conventional approach.

The problem of spatial tracking for Hermite–Gaussian free-space optical (HG-FSO) links is addressed. Since HG waveforms allow for the simultaneous presence of orthogonal spatial channels, FSO-HG has the potential of offering a considerable increase in system capacity as compared with the standard FSO systems. To harness this capacity gain, the problem of spatial tracking becomes of paramount importance as the presence of spatial error significantly impacts the orthogonality of the HG waveforms. We, then, consider spatial tracking using a standard quad-detector arrangement and assume that the background noise and/or receiver thermal noise are large enough to warrant a Gaussian detection statistics. The performance is assessed in terms of the probability density function of the spatial tracking error for HG order of up to 3. In assessing performance, it is assumed that the impact of the cross-talk among the spatial modes is negligible under the steady-state condition. Numerical results are presented to assess the viability of the tracking loop. Numerical results show that among the HG waveforms with orders ranging from 1 to 3, the second-order HG waveform offers the best tracking performance and, hence, must be selected for the purpose of tracking in HG-FSO systems.

The features of the supercontinuum generation (SCG) using intense femtosecond pulses are systematically investigated in condensed mediums [sapphire, BK7 glass, ultraviolet (UV)-fused silica, and fluoride crystals]. By optimizing the experimental conditions and choosing suitable mediums, the bandwidth of the SCG can be extended to the UV regime with good spectral stability. This study demonstrates that materials with high bandgap present high efficiency for SCG, particularly in the short wavelength region. The achievable short wavelength and low power-density threshold of the SCG exhibit complicated correlations with the bandgap of condensed mediums.

This paper proposed an analytical approach to evaluate the timing jitter’s impairment to the ergodic capacity and outage performance of an on-off keying wireless optical link, where the compound channel consists of Gamma–Gamma turbulence and pointing errors. Due to the complexity in deducing ergodic capacity, the closed-form bounds are developed, as well as the asymptotic limit. Meanwhile, the Gaussian–Hermite polynomial approximation is exploited to obtain the closed-form expression of outage probability in series. It has been verified by both theoretical results and the Monte-Carlo simulations that the timing jitter leads to a restriction of the ergodic capacity, even with tremendous transmitting power. In the meantime, small timing jitters could be endurable in the analysis of outage probability, whereas the large timing jitters diverge from the lower ones.

In visible light communication (VLC) networks, light-emitting diodes (LEDs) as transmitters are densely deployed so that the interference between cells is serious. A variety of methods about interference management have been proposed to improve the signal-to-interference-plus-noise ratio (SINR). However, the achievable SINR has not been studied yet. We obtain the achievable signal-to-interference ratio and improve the SINR with the derived results. A simple analytic solution is provided to show the achievable SINR of two cells under a linear model. Furthermore, we discuss the effect of different parameters of the SINR distribution under the linear model.

We develop an optical ring resonator with tunable coupling coefficients for use in wavelength division multiplexing routers. The coupling coefficients of the resonator are precisely tuned by the utilization of an electrostatic comb drive microelectromechanical system (MEMS) actuator. The MEMS actuator has the ability to accurately adjust gap spacing between cavity and waveguide. Moreover, integration of MEMS actuator with optical ring resonators overcomes the optical lithography challenges for patterning the small gap between cavity and waveguide. Different finite-element (FE) method simulations have been carried out in order to study the mechanical and optical operating characteristics of the ring resonator. The movable microring resonator can be displaced 1.33  μm with less than 3 V actuation voltage in 850  μs to control the transferred optical power and bandwidth of the resonator. Optical simulations show extinction ratios as high as 17 dB for the device with 90-nm gap spacing and 21.5 dB for the device with 60-nm gap spacing, respectively. In addition, the bandwidth of the filter is adjustable from 0.3 to 0.65 nm.

Elastic software-defined optical networks greatly improve the flexibility of the optical switching network while it has brought challenges to the routing and spectrum assignment (RSA). A multilayer virtual topology model is proposed to solve RSA problems. Two RSA algorithms based on the virtual topology are proposed, which are the ant colony optimization (ACO) algorithm of minimum consecutiveness loss and the ACO algorithm of maximum spectrum consecutiveness. Due to the computing power of the control layer in the software-defined network, the routing algorithm avoids the frequent link-state information between routers. Based on the effect of the spectrum consecutiveness loss on the pheromone in the ACO, the path and spectrum of the minimal impact on the network are selected for the service request. The proposed algorithms have been compared with other algorithms. The results show that the proposed algorithms can reduce the blocking rate by at least 5% and perform better in spectrum efficiency. Moreover, the proposed algorithms can effectively decrease spectrum fragmentation and enhance available spectrum consecutiveness.

Compared with optical network-on-chip (ONoC) with single wavelength, ONoC adopting wavelength division multiplexing (WDM) technology possesses a very prominent advantage—higher bandwidth. Therefore, WDM-based ONoC has been considered one of the most promising ways to relieve the rapidly increasing traffic load in communication systems. A WDM-based router, as the core equipment of WDM-based ONoC, is influenced by crosstalk noise, especially the nonlinear crosstalk noise generated by the four-wave mixing effect. Thus, to explore the performance of the N-port nonblocking optical router using WDM, we propose a universal analytic model to analyze the transmission loss, crosstalk noise, optical signal-to-noise ratio (OSNR), and bit error ratio (BER). The research results show that crosstalk noise varies along with signals at different wavelengths in the same channel. For signals with the same wavelength, the noises generated in the different transmission paths are obviously different from each other. For research of transmission loss, OSNR, and BER, similar results can be obtained. Based on the eye diagrams, we can learn that crosstalk noise will cause signal distortion to a certain extent. With this model, capability of this kind of multiport optical router using WDM can be understood conveniently.

Minimum-shift keying (MSK) has the advantages of constant envelope, continuous phase, and high spectral efficiency, and it is applied in radio communication and optical fiber communication. MSK modulation of coherent detection is proposed in the ground-to-satellite laser communication system; in addition, considering the inherent noise of uplink, such as intensity scintillation and beam wander, the communication performance of the MSK modulation system with coherent detection is studied in the uplink ground-to-satellite laser. Based on the gamma–gamma channel model, the closed form of bit error rate (BER) of MSK modulation with coherent detection is derived. In weak, medium, and strong turbulence, the BER performance of the MSK modulation system is simulated and analyzed. To meet the requirements of the ground-to-satellite coherent MSK system to optimize the parameters and configuration of the transmitter and receiver, the influence of the beam divergence angle, the zenith angle, the transmitter beam radius, and the receiver diameter are studied.

We demonstrate a photonic crystal fiber with near-zero flattened dispersion, ultralower effective material loss (EML), and negligible confinement loss for a broad spectrum range. The use of cyclic olefin copolymer Topas with improved core confinement significantly reduces the loss characteristics and the use of higher air filling fraction results in flat dispersion characteristics. The properties such as dispersion, EML, confinement loss, modal effective area, and single-mode operation of the fiber have been investigated using the full-vector finite element method with the perfectly matched layer absorbing boundary conditions. The practical implementation of the proposed fiber is achievable with existing fabrication techniques as only circular-shaped air holes have been used to design the waveguide. Thus, it is expected that the proposed terahertz waveguide can potentially be used for flexible and efficient transmission of terahertz waves.

A hybrid suboptimum channel separation (S-CS) scheme is presented. The distinct feature of the scheme is that it selectively minimizes the four-wave mixing (FWM) effect on the worst-affected channels and enhances the performance and spectral bandwidth efficiency in a controlled way. The scheme is helpful in the precise adjustment of tradeoff between immunity from FWM and spectral bandwidth requirement. The simulative comparison of the S-CS with optimum unequal channel separation (OUCS) and equal channel separation (ECS) schemes is performed to show its effectiveness. A dense wavelength division multiplexed system having a total capacity of 1.64  Tb/s in C band is implemented using the presented scheme. A maximum of 82 channels spaced at minimum CS of 50 GHz operating at a data rate of 20  Gb/s for each of the channels is realized using a S-CS (n=12) hybrid scheme. The simulations are performed in the presence of all the linear and nonlinear impairments and noises. A maximum of 480- and 300-km distances using SSMF and ITUT.G655 fibers, respectively, is realized using dispersion-compensating fibers for 82 channels. The ECS and hybrid OUCS can be realized to cover the same distances but with 73 and 79 channels, respectively, due to the realization problem and bandwidth inefficiency.

The wide range power dependence of vector stimulated Brillouin scattering (SBS) gain is theoretically and experimentally characterized by a mathematical model and measurement system based on the heterodyne pump–Stokes technique. The results show that SBS phase shift is much more tolerant of pump depletion than SBS amplitude gain, hence the performance improvement of the SBS-based distributed sensing system can be achieved by measuring the SBS phase shift spectrum. The discussion about the measured Brillouin spectrum width versus pump power at different Stokes powers reveals that the occurrence of nonnegligible pump depletion imposes a restriction on the determination of pump and Stokes powers in an SBS amplitude gain-based application system. The amplitude gain and phase shift of vector SBS gain increase with the increase of pump power and decrease with the increase of Stokes power, which indicates that the design strategy with smaller Stokes power and higher pump power is reasonable. And the measured center-asymmetry of the SBS phase shift spectrum is mainly caused by the nonlinear refractive index, which puts a limitation on the maximum pump power. The obtained results can provide a useful basis for the optimal design of practical vector SBS gain-based application systems.

With the development of nanotechnology, nanocomposite materials based on renewable resources are the focus of this research. Nanocellulose was prepared using sulfuric acid to swell cotton pulp, following with extensive ultrasonication. Nanocellulose/polyaniline (NC/PANI) and nanocellulose/poly(3,4-ethylenedioxythiophene) (NC/PEDOT) nanocomposites with core/shell structure were manufactured by in situ polymerization. The film-forming properties and electrochromic properties of PANI and PEDOT were significantly improved using the nanocellulose as matrix. NC/PANI and NC/PEDOT composite films were studied in single and dual electrochromic devices (ECDs). A viscous gel electrolyte (GE) was used in ECDs. The architectural design of single and dual device was ITO/NC-PANI/GE/ITO or ITO/NC-PEDOT/GE/ITO and ITO/NC-PANI/GE/NC-PEDOT/ITO, respectively. The dual ECD based on NC/PANI and NC/PEDOT composite films exhibited a higher color contrast (30.3%), shortest response time (1.5 s for bleaching and 1.9 s for coloring), largest coloration efficiency (241.6  C/cm^2[/sup]), and best cycling stability (over 150 cycles) compared with the single devices.

A tunable-focus liquid crystal (LC) lens is prepared. The orientation of the LC is controlled using a homeotropic polyimide (PI) layer and a homogeneous PI layer. The homeotropic PI layer has a concave shape. The LC in the concave space presents a hybrid alignment and has a convex shape. As a result, the LC has a lens character with the shortest focal length in the voltage-off state. The focal length can be tuned from 9 to 15 cm when an applied voltage is changed from 0 to 8 V_rms. Our LC lens has no threshold voltage, and the fabrication procedure is relatively simple.

The refractive index of fully dense, infrared-transparent polycrystalline alumina (PCA) with a mean grain size of ∼0.6  μm is reported for the wavelength range 0.85 to 5.0  μm over the temperature range T=296 to 498 K. The temperature-dependent Sellmeier equation is n²−1=(A+B[T²−T_o²])λ²/[λ²−(λ₁+C[T²−T_o²])²]+Dλ²/(λ²−λ₂²), where λ is expressed in μm, T_o=295.15  K, A=2.07156, B=6.273×10−⁸, λ₁=0.091293, C=−1.9516×10−⁸, D=5.62675, λ₂=18.5533, and the root-mean square deviation from measurements is 0.0002. This paper describes how to predict the refractive index of fully dense isotropic PCA with randomly oriented grains using the ordinary and extraordinary refractive indices (n_o and n_e) of sapphire spatially averaged over the surface of a hemisphere. The refractive index of alumina at 296 and 470 K agrees within ±0.0002 with the predicted values. Similarly, the ordinary and extraordinary optical constants k_o and k_e are used to predict the absorption coefficient of alumina. The refractive indices n_o and n_e of sapphire grown at Rubicon Technologies by the Kyropoulos method were measured at 295 K and agree with published Sellmeier equations for sapphire grown by other methods within ±0.0002.

We examined infrared transmission characteristics of a sol–gel derived zirconia film and the antireflective(AR) effect of this film for an Si substrate in the midinfrared region. The surface reflection loss of an Siplate is high (∼30%) because of the high refractive index (3.42) in the infrared region. We employed zirconiananoparticle dispersion with 15 wt. % (1-butanol solvent) as starting sol solution. Then, the dispersion wascoated with Si substrate at a spin-coating speed of 2000 rpm, and the substrate was heated to 150°C. Thenumber of coatings was repeated seven times. As a result, the transmittance at 5.6-μm wavelength wasenhanced to 66.2%, and we found that the coated film worked efficiently as the AR film up to 10-μm wavelength.Additionally, by heating the substrate to 800°C, the large absorptions at 2.9-, 6.4-, and 6.9-μm wavelengths couldbe suppressed because the hydroxy group in the film was reduced. Its peak transmittance was 67.9% at 4.9-μmwavelength.

A conformal encapsulation material for use in high-power, thermally stable ultraviolet (UV) light-emitting diodes was successfully developed. For silicone, thermal degradation started at ∼ 200°C , and the transmittance was 85.5% at 365 nm. The transmittance decreased by 55% after thermal aging at 250°C for 72 h and it decreased further by 2.5%, even at room temperature, under continuous exposure to UV light at 365 nm for 72 h. By contrast, for the sol–gel material, thermal degradation started at ∼ 300°C , and the transmittance was 90% at 365 nm. The transmittance decreased negligibly after thermal aging at 250°C for 72 h and it did not decrease further even at 75°C under continuous exposure to UV light at 365 nm for 72 h.

Lead selenide (PbSe) has been studied as a promising material for room temperature midwave infrared detection. We have investigated pure PbSe, as well as tin (Tn) and cadmium (Cd)-doped PbSe, nanocrystalline materials produced using physical vapor transport methods on glass and high-resistivity silicon substrates. The morphologies were investigated by scanning electron microscopy and energy-dispersive x-ray analysis. Pure PbSe layers consisted of nanocrystals that change into cubes and cuboids upon annealing. Cuboids generally grew in [100] orientation and ultimately developed in nanorods. Growth on silicon and glass substrates showed different morphologies of pure PbSe material. Parabolic and elongated morphologies resulted in nanowires on the top of thin layers of PbSe nanofilm, which acted as the substrate. Under low gradient annealing conditions (<20  K/cm), elongated morphologies grew into nanorods. Annealing of these samples resulted in coarse nanomorphologies with higher resistivity. In the case of Tn-doped PbSe, annealing dissolved a Tn-rich phase observed in as-grown films. Cd- and iodine-doped films produced through the addition of Cd selenide and Cd iodide, respectively, showed higher resistivity than similarly treated pure PbSe films. Annealing of as-grown materials in the presence of oxygen or iodine showed increased resistivity and significant changes in optical characteristics.

A structure of polarization beam splitter based on a symmetrical metal-cladding waveguide (SMCW) was demonstrated. The light beam energy can be coupled into the SMCW directly through free space without additional coupler. By introducing anisotropic material into the guided layer, different excitation conditions for transverse-electric and transverse-magnetic modes are obtained, which results in polarization-dependent reflection. The propagation loss that is mainly caused by the metal absorption is <2  dB.

A tunable single polarization filter based on high-birefringence photonic crystal fiber with silver wires symmetrically filled into cladding air holes is designed. The confinement loss of the unwanted polarized mode (x-polarized mode) at 1310- and 1550-nm bands are 371 and 252  dB/cm, whereas another mode confinement loss (y-polarized mode) at the corresponding wavelength as low as 14 and 10  dB/cm, respectively. Moreover, the 20-dB bandwidth can reach 179 (at the 1310-nm band) and 71 nm (at the 1550-nm band) for a propagation distance of 1 mm. The dispersion relations and polarization characteristics are analyzed in detail utilizing the finite element method. Numerical results show that by adjusting the pitch between two adjacent air holes, the diameters of cladding air holes or silver wires near the fiber core, the resonance wavelength and resonance strength can be tuned effectively, which is beneficial for tunable polarization filter devices in the communication wave bands.

Laser dicing with tightly focused nanosecond pulsed laser light inside a semiconductor wafer is a dry, debris-free dicing method achieved by the generation of thermal microcracks. This method has two practical issues: a dicing speed that is limited by the repetition rate of the pulsed laser and potential damage to integrated circuits on the wafer from excessive laser intensity due to insufficient beam divergence. By correcting aberrations and generating multiple beams via wavefront modulation, multiple focused beams inside the wafer will become sufficiently divergent to avoid undesirable potential laser damage. We confirmed these improvements by dicing sapphire wafers with a pulsed laser and a high-numerical-aperture objective lens.

To restrain the infrared radiation from high temperature objects to decrease the probability of being discovered by infrared detectors operating in the mid- and far-infrared atmospheric windows, we design a one-dimensional heterostructure photonic crystal (PC) using low-cost coating materials Te and ZnSe, and test its reflection spectra and radiant temperature. The tested results show that this PC has high average reflectance in 3- to 5-μm and 8- to 14-μm wavebands, which is 86.72% and 72.91%, respectively, and the corresponding emissivity is 0.072 and 0.194, respectively. The radiant temperatures of the PC are always lower than those of the background, with the maximal difference of the radiant temperature being 31.97°C corresponding to a background radiant temperature of 75.64°C. The study confirms that the deposited PC can effectively decrease the infrared radiation in mid- and far-infrared bands.

This article [Opt. Eng. 54(11), 115104 (2015)] was originally published on 3 November 2015 with an error in the name of the first author. The name “Jin Lin” has been corrected to “Jing Lin.” The paper was corrected online on 22 June 2017.

This article [Opt. Eng. 53(5), 051405 (2014)] was originally published on 6 December 2013 with an error in Eqs. (1) and (9). The refractive index n should be in the denominator rather than the numerator in the first term on the right hand side of these equations. The corrected equations are printed below:

This erratum details corrections made to the published article http://dx.doi.org/10.1117/1.OE.56.7.071508.