This guest editorial introduces the special section on Light Field and Holographic Displays.

For a multiview three-dimensional (3-D) display system using a two-dimensional (2-D) flat panel display, it is very important to attach accurately an optical plate such as a parallax barrier and a lenticular lens sheet onto a 2-D display panel for the best quality of 3-D images. In most practical cases, however, misalignment occurs since it is too difficult to align perfectly in assembly process. In general, angular misalignment results in the deterioration of 3-D image quality by some increase of crosstalk, so that the resulting 3-D images are even distorted as tilted ones. To correct distorted 3-D images, we propose a method to skew 3-D objects before each image for multiviews is taken by multiple cameras. For this, a formula is derived to determine the amount of skewing 3-D objects. And by using it, some experimental results are shown that distorted 3-D images in a misaligned multiview 3-D display system are completely corrected. Since skewing 3-D objects implies a coordinate transformation of 3-D space, this method can be also used in the manipulation of 3-D image data obtained from a depth camera in order to correct the distorted 3-D images caused by angular misalignment.

Tensor display is an option in glasses-free three-dimensional (3-D) display technology. An initial solution has to be set to decompose the light-field information to be represented by the system. We have analyzed the impact of the initial guess on the multiplicative update rules in terms of peak signal-to-noise ratio, and proposed a method based on depth map estimation from an input light field. Results from simulations were obtained and compared with previous literature. In our sample, the initial values used have a large influence on results and convergence to a local minimum. The quality of the output stabilizes after a certain number of iterations, suggesting that a limit on such numbers should be imposed. We show that the proposed methods outperform the pre-existing ones.

Object tracking is an important problem in computer vision research. Among the difficulties of object tracking, the problem of partial and full occlusion is one of the most serious and challenging problems. To address the problem, we proposed methods to object tracking using plenoptic image sequences. Our methods take advantage of the refocusing capability that plenoptic imaging provides. The proposed methods input the sequences of focal stacks constructed by applying the refocusing algorithm on the plenoptic image sequences. The proposed image selection algorithms select the sequence of optimal images that can maximize the tracking accuracy from the sequence of focal stacks. Focus measure approach and confidence measure approach were proposed as image selection methods and both approaches were validated by the experiments using three groups of plenoptic image sequences that include heavily occluded target objects. The experimental results showed that the proposed methods were promising comparing to the conventional 2-D object tracking algorithms.

Several wavefront printers have been recently proposed. Since the printers can record an arbitrary computer-generated wavefront, they are expected to be useful for fabricating complex mirror arrays used in front projection 3-D screens without using real existing optics. We prototyped two transparent reflective screens using our hologram printer in experiments. These screens could compensate for a spherically distorted reference wave caused by a short projection distance to obtain an ideal reference wave. Owing to the use of the wavefront-printed screen, the 3-D display was simply composed of a normal 2-D projector and a screen without using extra optics. In our binocular system, reflected light rays converged to the left and right eyes of the observer and the crosstalk was less than 8%. In the light field system, the reflected light rays formed a spatially sampled light field and focused a virtual object in a depth range of ±30  mm with a ±13.5-deg viewing angle. By developing wavefront printing technology, a complex optics array may easily be printed by nonprofessionals for optics manufacturing.

We developed a high-resolution active matrix spatial light modulator on a glass substrate. To integrate a switching device on the glass substrate, we designed a high-performance oxide thin-film transistor with a minimum channel length of 1  μm and a maximum processing temperature of 380°C. To drive a large number of data lines, we used multiple source drivers and data drivers as well. For an optical modulation, we optimized a liquid crystal of a high anisotropic refractive index of 0.25 with a cell gap of 2.5  μm, which was effectively operated until pixel pitch is 1.6  μm. Hologram was successfully reconstructed by fabricated SLM with 7-μm pixel pitch. For the other approach for a high-resolution spatial light modulator, we tested a phase change material of Ge2Sb2Te5 [GST]. The variation of refractive index between a polycrystalline phase and an amorphous phase of the GST film is used for a hologram reconstruction. By optimizing the underlying oxide thickness, we can show a color hologram without color filters.

We propose a structure for a layered light-field display composed of high-resolution binary layers and a low-resolution, multibit backlight. This structure aims to increase the upper bound of the spatial frequency while also reducing the total number of bits for the display. The increased layer resolution increases the upper bound of the spatial frequency, meaning that the display can reproduce an object with a large amount of pop-out more clearly than can a conventional light-field display. In contrast, limiting the layers’ transmittance to binary (on/off) levels reduces the total number of bits for the display, thus maintaining the high efficiency of light-field representation. The low-resolution backlight, whose pixels can take multibit values, compensates the number of intensity levels, which would otherwise be quite limited with only the binary layers. Through analytical and experimental results, we show that a display based on the proposed structure can reproduce a light field with high quality and high efficiency as a result of combining the high-resolution binary layers and low-resolution backlight.

We present a technique to record refreshable holographic stereograms continuously. We eliminated the translation stage that shifts the recording beams back and forth and replaced it with an uninterrupted transparent belt holding holographic lenses. The belt is driven along a perimeter, shifting the lens laterally in front of a photorefractive screen without reversing direction. The holographic lenses focus the object beam onto holographic pixels and are permanently recorded in a thin photopolymer. The photopolymer material is flexible enough for the lenses to follow the curvature of the belt when it goes around the tensioning rollers. The hogel data are uploaded sequentially onto a spatial light modulator to form the object beam. The rotation of the belt in one single direction allows for a continuous operation and a much faster recording speed than with a translation stage that needs to reverse direction at the end of its travel span.

Light fields are four-dimensional parametrizations of rays, extensively used for the representation of the rays emitted from three-dimensional objects. With the increasing availability of spectral imagers, conventional light fields can be augmented by the additional spectral information, yielding a five-dimensional ray parametrization referred to as a spectral light field. We demonstrate that utilization of the spectral channel information can improve the profilometric performance of light-field cameras.

We studied highly realistic communication systems using a super multiview three-dimensional (3-D) video system. We propose the developed glasses-free 200-in. 3-D display using ∼200 high-definition (HD) projector units to reconstruct natural life-size 3-D moving objects, such as cars and humans. We also analyzed the optimal arrangement of the multiview camera system for the 3-D display. In the experiments, we developed a prototype super multiview 3-D camera system using compact HD video cameras with real-time convergence compensation circuits that correct the captured images via image processing optimized for the display. We also performed demonstration experiments using the developed 3-D display and camera system in a public area. As a result, we highlight several possibilities for actual applications of the glasses-free super multiview 3-D video system.

We propose a method for arranging multiple projectors in parallel using an image-processing technique and for enlarging the viewing zone in an integral three-dimensional image display. We have developed a method to correct the projection distortion precisely using an image-processing technique combining projective and affine transformations. To combine the multiple viewing zones formed by each projector continuously and smoothly, we also devised a technique that provides accurate adjustment by generating the elemental images of a computer graphics model at high speed. We constructed a prototype device using four projectors equivalent to 4K resolution and realized a viewing zone with measured viewing angles of 49.2 deg horizontally and 45.2 deg vertically. Compared with the use of only one projector, the prototype device expanded the viewing angles by approximately two times in both the horizontal and vertical directions.

Color moirés induced at contact-type multiview three-dimensional and light-field imaging are reviewed, slanted color moirés are introduced, and the reason why they become invisible as the slanting angle increases is explained. The color moirés in the imaging are induced by the structural uniqueness of the imaging, i.e., viewing zone-forming optics (VZFO) on the display panel. The moirés behave differently from those by the beating effect. They are (1) basically chirped, (2) their fringe numbers and phases are also varying according to the changes in viewer’s viewing positions and viewing angles at a given viewing distance, (3) the pattern period of the VZFO is at least more than several times that of the pixel pattern, and (4) they are colored. The color moirés can hardly be eliminated because they are induced structurally, but they can be minimized by either reducing the regularity of the pixel pattern using a diffuser between the panel and the VZFO or aligning VZFO’s pattern to have a certain slanting angle with the pixel pattern in the panel.

Parallel phase-shifting digital holography is a powerful technique for recording motion picture of holograms with an image sensor and numerically reconstructing the motion picture of the high-quality three-dimensional (3-D) images of the object in a computer. This technique provides high-quality images of light intensity and phase of the object at a time instant at arbitrary depth position. Therefore, the technique achieves 3-D motion-picture imaging of a dynamic object. The technique provides not only large depth of field and high temporal resolution at the same time but also a motion picture of an invisible object. It is difficult for other 3-D imaging techniques to achieve these features of parallel phase-shifting digital holography. The authors review two experiments demonstrating the 3-D imaging by the technique and the features of the technique. One experiment demonstrated the motion-picture 3-D imaging of a minute crystal, sinking down in solution, by refocusing the amplitude images of the crystal. The result was obtained for the first time, to the best of our knowledge. The other demonstrated the motion-picture 3-D imaging of refractive indices of dynamic invisible gas flow by applying the Abel inversion to the phase images of the flow obtained by the technique.

A three-dimensional/two-dimensional (3-D/2-D) convertible display was proposed. The display system offers 2-D images via the traditional display technology and offers 3-D images via the computer-generated hologram (CGH) technology. In this system, 2-D and 3-D images are generated from the same amplitude-modulated spatial light modulator (SLM). In the 2-D display mode, the panel displays an amplitude-modulated image and the 2-D image is projected on a polarization-dependent diffuser (PD) screen. In the 3-D display mode, the SLM panel displays CGHs to generate 3-D images. The zero-order diffraction of the amplitude-type CGH will be blocked by a spatial filter (SF), which is designed by a polarizer. Furthermore, a liquid crystal element was employed to modulate the polarization state of the reconstructed light to let the 3-D image quality not to be reduced by the PD. Finally, the proposed system can offer 2-D and 3-D images both clearly. The system suppresses the zero-order diffraction noise of the amplitude-type CGH system successfully.

We analyze 10 cases of noniterative methods for speckle noise reduction in phase-only hologram generation. The analyzed methods are bidirectional error diffusion, random phase-free, double-phase, random displaced phase distribution (RDPD), and complex field encoding (CFE). The first three methods have been used before in the Fresnel hologram display, whereas the last two methods have been used in the area of holographic memory recording and generation of optical fields, respectively. We study the last two methods as alternatives to the generation of a Fresnel hologram without random phase (RP) and compare their results with the first three methods. We found that the RDPD also suffers a high degradation of low frequencies, so we introduce a modification for reducing the degradation effect. This method allows control of the spread angle of the object wave propagation. We also found that the CFE achieves a precise reconstruction of the object in different planes without the addition of any RP, with a very high signal-to-noise-ratio (SNR). We compare the results of 10 cases and discuss the advantages of each one. We include the peak signal-to-noise-ratio and SNR measurements of each case. We present simulated and experimental results.

Light-field optics is used in light-field cameras to alter the focus condition of an image after it is obtained. This unique function implies that information captured with a light-field camera is not a “picture”; rather, it is a real object image. Thus, a two-dimensional (2-D) image of any focus condition can be generated from the acquired data. An explanation is provided on how a light-field camera records or encodes a three-dimensional (3-D) scene onto a 2-D plane as light-field data, and how the data are decoded back into a 3-D image with a light-field display. Other unique applications based on light-field optics are discussed. Unlike conventional optical systems, light-field optics does not require optical conjugation between the display plane and image plane. Thus, light-field optics can provide an effective means of advancement for conventional optical instruments. To demonstrate the potential applications of light-field optics, we developed a light-field camera and display.

A method of displaying a multiview image set prepared by a computer on an electronic display device based on integral photography has been formulated. With the device, accommodation response was measured and the result that the accommodation response linearly changed within and outside the range of depth of focus was obtained. In contrast, in the measurement of the accommodation response using the stereoscopic image, the accommodation response showed a linear change within and outside the depth of focus at the spatial resolution of three cycle per degree (cpd) or less. Therefore, it can be considered that the measurement result of the accommodation response for integral photography with a spatial resolution of 3 cpd or less cannot be used to determine whether it is influenced by the integral photography display method or spatial resolution reduction. From these results, we found that spatial resolution is required to be 3 cpd or more when outside of the range of depth of focus in the measurement of the accommodation response for integral photography.

Many consumers are interested in three-dimensional (3-D) technologies that make display images as real as possible. In response, a number of fairly mature 3-D technologies have already been introduced in various studies. Among them, we reviewed the integral imaging system and the multiview system, which can realize 3-D, from the past to the present. Those systems, however, suffer from problems such as depth range, two-dimensional (2-D) and 3-D conversions, and 3-D resolution. Therefore, a liquid lens is proposed as a technique to resolve the drawbacks. Using a liquid lens with variable focal length, the depth range was enhanced using a time-division multiplexing technique in an integral imaging system, and the function of 2-D and 3-D switching was enabled in a multiview system. Furthermore, methods were introduced to solve the problems of 3-D resolution reduction in multiview systems and vergence–accommodation conflicts in VR systems.

We developed a holographic head-mounted display with a see-through structure that enables the user to view augmented reality scenes binocularly. It has right and left optical systems for each eye that have horizontal sliding structures to adapt the interdistance to each observer’s different interpupillary distances. Reconstructed images are colorized using the field sequential color method and are enlarged using a Fourier transform optical system. This paper describes a calibration method to correct installation errors arising from the optical elements. The results of objective and subjective evaluations show that the reconstructed images locate at the correct depths and provide correct accommodation and vergence as well.

A reconstruction method of axially moving lenslet array (AMLA) was proposed. First, the dot-pattern reconstructed image was generated from a set of AMLA-recorded EIs using pixel-to-pixel mapping. Then, the empty pixels of dot-pattern reconstructed image can be filled by the average of the intensity values of all pixels that are corresponding to the empty pixels in each EI and determined through back projection. Using this proposed method, not only can the empty pixels be eliminated, but also the image quality is higher than conventional interpolation. Moreover, the axially moving gap can also be arbitrary, which breaks the limitation of the strict interpolation-free condition of the conventional reconstruction method. The feasibility of this method was verified by simulations and optical experiments.

Electroholography enables the projection of three-dimensional (3-D) images using a spatial-light modulator. The extreme computational complexity and load involved in generating a hologram make real-time production of holograms difficult. Many methods have been proposed to overcome this challenge and realize real-time reconstruction of 3-D motion pictures. We review two real-time reconstruction techniques for aerial-projection holographic displays. The first reduces the computational load required for a hologram by using an image-type computer-generated hologram (CGH) because an image-type CGH is generated from a 3-D object that is located on or close to the hologram plane. The other technique parallelizes CGH calculation via a graphics processing unit by exploiting the independence of each pixel in the holographic plane.

We experimentally verified the depth perception and accommodation-convergence conflict in viewing integral photography. For comparison, the same measurements were performed with binocular stereoscopic images and real objects. First, the depth perception in viewing an integral three-dimensional (3D) target was measured at three display resolutions: 153, 229, and 458 ppi. The results showed that the depth perception was dependent on the display resolution. The results were also evaluated in a statistical test at a significance level of 5%. The results showed that the recognized depth perception ranges were 180, 240, and 330 mm when the display resolutions were 153, 229, and 458 ppi, respectively. The results were also analyzed in terms of image resolution. This suggested that depth perception occurred at over 1.0 cpd. The accommodation and convergence responses in viewing an integral 3D target displayed on a 3D display with 458 ppi were measured using PowerRef 3. The experimental results were evaluated with a multiple comparison test. It was found that 6 of the 10 observers did not have an accommodation-convergence conflict when viewing the integral 3D target inside and outside the depth of field. In conclusion, integral photography can provide a natural 3D image that looks like a real object.

Approaches to control the moiré effect are discussed. To improve the image quality, especially in the autostereoscopic three-dimensional displays, the minimization of the moiré effect is considered, including the minimization by angle, by period, by distance, etc. Also, less known nontraditional but effective approaches, such as spectral trajectories, statistical treatment, convolution-based minimization, and the amplitude of the moiré patterns, are at issue. On the other hand, the maximum moiré can be useful in displays. A proposed “2.5-D” display represents a new type of displays, the displays based on the moiré effect as on the main physical principle. As of today, binary black-and-white images are displayed, but this is not a principal limit and color imaging is also possible. A positive usage of the moiré effect to show images instead of its removal may be considered as an approach in displaying.

One-dimensional 1-μm-pitch light modulation was achieved experimentally using a liquid crystal (LC) device for wide viewing-zone angle holographic displays. When the pixel pitch of the LC device is 1  μm, individual pixel driving is extremely difficult due to electric field leakage and penetration of the elastic force of the LC from adjacent pixels. To overcome these problems, a dielectric shield wall structure is suggested, with dielectric walls between pixels. An LC cell with a dielectric shield wall structure was fabricated using nanoimprint technology; the individuality of the light modulation and diffraction pattern produced by the LC cell was evaluated. Our results showed that the dielectric shield wall structure achieved individual 1-μm-pitch light modulation and a diffraction angle of 19 deg at a wavelength of 633 nm. The remaining layer of the dielectric resin, which is surplus dielectric resin under the dielectric walls produced by the nanoimprint procedure, should be reduced as it tends to increase the driving voltage and electric field leakage from adjacent pixels.

Traditional Hough transform-based methods detect objects by casting votes to object centroids from object patches. It is difficult to disambiguate object patches from the background by a classifier without contextual information, as an image patch only carries partial information about the object. To leverage the contextual information among image patches, we capture the contextual relationships on image patches through a conditional random field (CRF) with latent variables denoted by locality-constrained linear coding (LLC). The strength of the pairwise energy in the CRF is measured using a Gaussian kernel. In the training stage, we modulate the visual codebook by learning the CRF model iteratively. In the test stage, the binary labels of image patches are jointly estimated by the CRF model. Image patches labeled as the object category cast weighted votes for object centroids in an image according to the LLC coefficients. Experimental results on the INRIA pedestrian, TUD Brussels, and Caltech pedestrian datasets demonstrate the effectiveness of the proposed method compared with other Hough transform-based methods.

Dual-view transport of intensity equation (TIE) method is an ideal way for quantitative live cell imaging as it has advantages such as real-time imaging, multimode observations, compact setup, and large field of view (FoV). However, due to the image recorder installation error, the inevitable FoV mismatch between the captured under- and over-focus intensities reduces the accuracy in both amplitude and phase retrievals. Here, to eliminate this undesired FoV mismatch, the phase correlation-based digital FoV correction is adopted to recognize and compensate the rotation, scale, and translation between the under- and over-focus images. Both the numerical simulations as well as the experiments in standard sample detection and quantitative live cell imaging prove that the digital FoV correction combined dual-view TIE method can maintain the consistence of the dual FoVs, thus guaranteeing the high-accurate amplitude and phase computations, proving the proposed method is a promising quantitative live cell imaging tool in various applications such as biological observations and medical diagnostics.

The performance of differential synthetic aperture ladar (DSAL) processing versus phase-gradient autofocus (PGA) technique in SAL image formation is demonstrated experimentally using phase history data (PHD) with large random phase errors and various target returns generated from a laboratory DSAL setup operating at 1550-nm wavelength. Results show that at strong return levels, both DSAL and PGA are very robust in focusing high-resolution images from the PHD; whereas, as target returns become weak and PHD is dominated by noise, the iterative PGA performs less effectively than the DSAL does. It is concluded that, on the whole, the DSAL technique is possibly more robust than PGA in both effectiveness and efficiencies.

Artis-Zeego is an advanced interventional imaging system that can provide the three-dimensional (3-D) reconstruction of the coronary artery in real time. However, the mechanical accuracy will degenerate after long-time use. The inaccurate geometry will affect the spatial resolution of the 3-D reconstruction. We propose a calibration algorithm to tackle this problem. There are three steps of our algorithm. First, we propose a geometry estimation algorithm that is based on the classical helical phantom. Second, we transfer the geometry to the nominal C-arm coordinate system. Third, we propose the posteriori movement models at three imaging work positions. The contributions include three parts. First, the proposed geometry estimation algorithm is more robust and easier to implement than other algorithms that are based on the helical phantom. Second, the geometry parameters can be transferred to the nominal C-arm system. Therefore, the calibration work will be independent of the phantom placement. Third, the movement models can estimate and predict the geometries at any acquisition angle. The clinical experiments demonstrate that the proposed method can estimate and predict the acquisition geometry with accuracy. The acquisition trajectories can be modeled as a rigid motion at head and left work positions. The acquisition trajectory should be modeled as a rigid motion with a residual translation at Table30 work position.

Multicamera arrays are increasingly employed in both consumer and industrial applications, and various passive techniques are documented to estimate depth from such camera arrays. Current depth estimation methods provide useful estimations of depth in an imaged scene but are often impractical due to significant computational requirements. This paper presents a framework that generates a high-quality continuous depth map from multicamera array/light-field cameras. The proposed framework utilizes analysis of the local epipolar plane image to initiate the depth estimation process. The estimated depth map is then refined using total variation minimization based on the Fenchel–Rockafellar duality. Evaluation of this method based on a well-known benchmark indicates that the proposed framework performs well in terms of accuracy when compared with the top-ranked depth estimation methods and a baseline algorithm. The test dataset includes both photorealistic and nonphotorealistic scenes. Notably, the computational requirements required to achieve an equivalent accuracy are significantly reduced when compared with the top algorithms. As a consequence, the proposed framework is suitable for deployment in consumer and industrial applications.

Single point active alignment method is a widely used calibration method for optical-see-through head-mounted displays (OST-HMDs) since its appearance. It always requires high-accuracy alignment for data acquisition, and the collected data affect the calibration accuracy to a large extent. However, there are often many kinds of alignment errors occurring in the calibration process. These errors may contain random errors of manual alignment and system errors of the fixed eye-HMD model. To tackle these problems, we first leverage a random sample consensus approach to recurrently decrease the random error of the collected data sequence and use a region-induced data enhancement method to reduce the system error. We design a typical framework to enhance the data acquisition for calibration, sequentially reducing the random error and the system error. Experimental results show that the proposed method can significantly make the calibration more robust due to the elimination of sampling points with large errors. At the same time, the calibration accuracy can be increased by the proposed dynamic eye-HMD model that takes the eye movement into consideration. The improvement about calibration should be significant to promote the applications based on OST-HMDs.

Fresnel zone lens (FZL) telescope is attracting increasing attention owing to its small volume and light weight. However, depending on the fabrication method of FZL, the linewidth and etch depth of FZL may deviate from the set value. It must be considered that the performance of the FZL is influenced by aberrations generated during manufacture. We simulate the effect of fabrication errors on optical performance of FZL and find that the linewidth error of FZL structure is the main cause of image degradation. In addition, we provide a method for correcting aberrations of FZL telescope with adaptive optics system (AOS). This method is verified by the experimental system. The results show that the image resolution is successfully improved after AO correction. The full-width, half-maximum value of a far-field image is improved from 0.065 to 0.038λ. The peak value of image energy after correction has increased by 4.23 times.

Structured-light systems consisting of a camera and projector are powerful and cost-effective tools for three-dimensional (3-D) shape measurements. However, most commercial projectors are unable to generate distinct patterns due to defocusing and shallow focusing issues. We propose a hybrid method for enhancing the calibration and scanning features of the defocusing structured-light 3-D scanning system. Instead of using conventional sequential binary patterns, we replace the highest-level binary pattern by a high-order sinusoidal pattern. In our proposed system, a pan-tilt stage carrying a checkerboard is used to assist the simultaneous calibration of the camera and projector. Initially, the camera is calibrated to obtain the extrinsic positions of the stage. In addition, we utilize the multiplication of vertical and horizontal stripe patterns to enhance the corresponding features between the camera and projector. The projector is then calibrated using the extrinsic features determined from the calibrated camera. The experimental results show that the use of the high-order sinusoidal pattern significantly improves reprojection error. Our proposed method can easily be incorporated in the defocusing projector for scanning various types of objects.

A diagonal-based heterodyne grating interferometer (HGI) for two-dimensional displacement measurement is presented. It can simultaneously realize the high signal contrast and signal-to-noise ratio (SNR) with the specially designed cross grating. Meanwhile, an eightfold optical subdivision can be acquired with the proposed phase decoupling method. The signal contrast of 96.55% and SNR of 50 dB are obtained with laser power of 0.45 mW. Several tests including linear displacement, planar displacement, and stability are conducted in the experiments. The theoretical resolution of 0.125 nm, the short-range repeatability of 2.35 and 3.24 nm under round-trip movement of 10  μm, and the system stability better than   ±  4 and   ±  6  nm over 10 min are achieved for the X- and Y-directions, respectively. In addition, the measurement errors including geometric, nonlinear, and noncommon-path errors are analyzed. The results demonstrate that the proposed diagonal-based configuration combined with cross gratings is extremely suitable for HGIs, which has the potential to simultaneously improve the performance and practicability of HGIs.

A model is presented to analyze the effect of chromatic aberration of the spatial filter lenses on the compressed pulse duration. The parameters of the SHENGUANG (SG) II 5 PW laser system are demonstrated as examples. The numerical simulation results show that the compressed pulse duration with full aperture is increased by 3 times compared with the ideal compressed pulse duration in the case of chromatic aberration of the lenses. The result of full-aperture measurement at the SG II 5 PW laser system is in good agreement with the theoretical calculation. In the case of full-aperture measurement, the shortest compressed pulse duration is obtained by adjusting the compressor to compensate for the phase aberration introduced by the chromatic aberration of the spatial filter lenses at the SG II 5 PW laser facility. These results are helpful in finding an optimized pulse duration, considering the chromatic aberration of lenses in the femtosecond laser facility, and in obtaining a deep understanding of the effect of chromatic aberration of lenses on the pulse contrast ratio and pulse duration in ultrashort laser systems.

To better address the temperature interference problem of fiber Bragg grating (FBG) strain-based anemometer sensors, based on the FBG sensor theory, the cross-sensitivity mechanism of the fiber grating during wind speed and temperature measurement is analyzed, and the relations between the central wavelength variation of dual Bragg gratings and that of the temperature and wind speed are derived. Two Bragg gratings with different periods are created in the same fiber for wind speed and temperature measurements. The temperature detection grating is encapsulated in a stainless-steel capillary tube single-end fixed support structure to shield the device from wind pressure, achieve a rapid thermal response, and improve the real-time performance of wind speed compensation. To further improve the wind speed temperature compensation results, modification of the surface of the temperature detection grating is proposed via an aluminium coating with a high linear thermal expansion coefficient to improve the temperature detection resolution and thus improve the compensation precision. Additionally, to improve the stability of the anemometer sensor in a wind field, a concave windward baffle structure is proposed. Flow field simulation via the ANSYS software FLUENT shows that this structure is superior to the existing plate structure. The anemometer sensor is evaluated using temperature detection and wind pressure simulation experiments, and the results are as follows: the wind speed detection range is 0 to 35  m  /  s, the linear sensitivity is 2.4261  ×  10  −  1  pm  /  v2, the temperature detection range is 0°C to 50°C, and the linear sensitivity of the temperature detection grating with aluminium coating modification is increased to 33.9  pm  /    °  C. In the wind speed range of 0 to 25.4  m  /  s, the maximum error after temperature compensation is 0.39  m  /  s.

Fringe projection profilometry is commonly used for three-dimensional (3-D) shape measurement. The gamma effect caused by nonlinear intensity response of projector-camera system makes ideal sinusoidal waveforms nonsinusoidal, leading to phase and 3-D shape errors. The existing phase-error compensation methods or gamma correction methods are complicated and time-consuming. An exponential fringe projection method is proposed based on principal component analysis to alleviate phase error without requiring any complicated prior and post data. The experimental results demonstrate that the proposed method decreases the phase error effectively with high quality in the measured surfaces and needs low computational cost by comparing with the existing state-of-the-art methods.

A theoretical model is introduced to determine the thermocapillary force acting on a microbubble, which adheres to the wall of a container filled with a liquid, during trapping using a focused continuous-wave (CW) laser beam. The model is developed by considering all possible forces acting on the microbubble, which also includes the optical force, the viscous force, and the friction force. The thermocapillary force, estimated from the relative velocity of the trapped microbubble with respect to the container, compares favorably with theoretical predictions based on the temperature gradient induced by the focused laser beam. The proposed experiment can be also used to determine the contact angle and/or the coefficient of friction of the microbubble at the microbubble–container interface. Our results should be useful in the design of efficient systems using microbubbles for drug delivery and water treatment systems.

Wavefront measurements were performed in-flight for a hemispherical turret on the Airborne Aero-Optics Laboratory-Transonic (AAOL-T). For turret side-looking angles near 90 deg, upstream-propagating optical distortions over the turret aperture were observed. These distortions were contributed to acoustic waves originating from the engine downstream of the turret. The acoustical waves were modeled by combining a potential flow solution for a single-frequency moving acoustic source and a potential flow around a sphere. The model was shown to properly predict the spatial statistics and convective speeds of the experimentally observed wavefronts. The model also correctly explained the viewing-angle dependence of the acoustic-related optical distortions. It was shown that for side-viewing angles between 90 deg and 100 deg, these acoustical distortions can be a significant contributor to the overall aero-optical distortions.

To evaluate the intermediate-frequency error of a precision optical surface, a method for more accurate separation and identification of the intermediate-frequency error is proposed. This method is based on the Hilbert spectrum and the instantaneous frequency separation method. Experimental results show that the intermediate-frequency error spectrum can be obtained using the method of instantaneous frequency separation based on the Hilbert spectrum. This method separates only the intermediate-frequency error component (0.03  mm^−  1  ≤  f  ≤  8.33  mm^−  1). Also, the method accurately identifies the nonqualified component distribution (at sampling points 200, 840, and 1000). Therefore, this algorithm is a useful guide for deterministic processing of optical components.

An improved k-means algorithm is proposed to enhance the stability and dynamic measurement accuracy of high-frequency small angle measurement using a dynamic autocollimator. The improved algorithm incorporating an optimized initialization scheme is used to determine the accurate position of the light spot for angle calculation. Simulations executed on different datasets demonstrate the effectiveness of the algorithm. Experimental results indicate that the 30-min stability of 0.58 and 0.69 arc sec at the measurement frequencies of 5 and 10 kHz can be achieved by the improved algorithm, respectively. Also, the dynamic measurement accuracy of 0.99 and 1.25 arc sec under the rotation speeds of 1 and 20  deg  /  s, respectively, at the measurement frequency of 10 kHz can be obtained. It is confirmed that the improved algorithm is necessary and effective for the autocollimator.

The problem of optimizing the distribution of integration time for the degree of linear polarization (DOLP) polarimetry with different types of noise statistics (Gaussian additive, Poisson shot, and gamma speckle) is investigated, in order to decrease the variance of estimator. It is found that if the total integration time of intensity measurements is fixed, the variance of DOLP estimator depends on the distribution of integration time in the presence of Gaussian noise and Poisson shot noise, whereas for the gamma noise, the variance does not depend on the distribution of integration time. We deduce the closed-form solutions of the optimal distribution of the integration time for Gaussian additive and Poisson shot noise within a common theoretical framework. In addition, we investigate the consequence of misjudging the noise statistics, and it is found that the degree of optimization only decays slightly if the noise statistics are misjudged. This characteristic indicates that it is not essential to know the statistics of the noise in advance.

A method of eliminating echelle mosaicking errors using a single-interferometer system combined with a mirror-echelle structure and double-angle incident light is proposed. Coplanar and in-plane mosaicking errors are, respectively, removed using interference fringes at zero order and diffraction order, and double-angle incidence light is exploited to erase the longitudinal offset. Two mirror-echelle structures, both with aluminum reserved for a mirror on the echelle plane to receive the double-angle incident light, are designed. The relationship between mosaicking error and the optical path difference is established. The evolution of the interference fringe pattern of mosaicking process is simulated, and a mosaicking experiment is then conducted following the simulation.

We propose a projection-based decoupling algorithm for a woofer–tweeter (W–T) adaptive optics system. This algorithm uses the response matrix of woofer deformable mirrors (DM) to construct a slope-based orthogonal basis, which can be used to distribute different spatial frequency aberrations to the dual DMs. At the same time, to restrain the cross coupling between the dual DMs, the command vector of the tweeter will be projected onto the slope-based orthogonal basis, and then the portion of the tweeter’s command vector, which may generate opposite shape with the woofer can be calculated and eliminated accurately. Numerical simulation for this algorithm demonstrates that it can make the woofer and tweeter correct different spatial frequency aberrations simultaneously, and have more practical value compared with the traditional decoupling algorithm. Experimental results for this algorithm are consistent with the simulation results and proved that the cross coupling between the dual DMs can be restrained well for both static and dynamic aberrations.

A thorough investigation into the efficiency and performance of off-axis, freeform illumination systems has been conducted, and a method for arriving at the optimal tilt is established for both reflective and refractive designs. The optimal tilt for refractive designs is determined by minimizing the total light lost due to Fresnel reflections across the lens, while the optimal tilt for reflective designs ensures the source is not obstructing the reflected ray bundle. For uncoated lenses, utilizing the proposed tilt can improve efficiency by more than 150%.

Polarization sensitivity is an important factor that affects the interrogation of ultrasmall arrayed waveguide grating (AWG) for fiber Bragg grating (FBG) sensor. An ultrasmall 1  ×  8 silicon-on-insulator (SoI) AWG with a core size of less than 530  μm  ×  480  μm is proposed in this study. This ultrasmall SoI AWG exhibits good transmission spectra and high polarization sensitivity. The increased channel numbers and tight structure increase the polarization sensitivity of AWG. Temperature interrogation experiments show that the FBG sensor interrogation is drastically affected when the effect of polarization sensitivity on the ultrasmall AWG is sufficiently large.

An efficient soliton mode-locking femtosecond Yb3  +    :  Y2SiO5 (Yb:YSO) laser at 1059 nm assisted with semiconductor saturable absorber mirror has been successfully realized and demonstrated. Nearly Fourier transform-limited pulse duration as short as 236 fs has been achieved with a pulse repetition frequency of 79.6 MHz and an average output power of 903 mW, corresponding to maximum pulse energy of 11.34 nJ and pulse peak power of 48 kW, respectively. The dependence of pulse duration on the intracavity pulse energy in soliton mode-locking regime has been further investigated and discussed, which is fitted by the soliton mode-locking theory and indicates the nonlinear refractive index n2 of the Yb:YSO crystal to be around 2.1 to 4.8  ×  10  −  16  cm2  /  W.

Optical properties of tapered optical fiber deposited with PbS are investigated, which is deposited based on atomic layer deposition technique with Pb(tmhd)2 and H2S as Pb and S precursors. After deposition, morphology of PbS thin film is characterized by a scanning electron microscope, and the composition is confirmed by X-ray photoelectron spectroscopy and energy dispersive spectrum. Raman spectrum shows a typical peak at 204  cm  −  1, which is assigned to the influence of the PbS structure, and it further reveals that PbS is deposited on the surface of the tapered optical fiber successfully. With a 980-nm pump laser diode, tapered optical fiber deposited with PbS applied to fiber amplifier exhibits a wide band optical gain at 1550 nm with the largest gain of 5.6 dB.

A Brillouin optical time-domain analysis (BOTDA) technique for enhancing the probe power to +5  dBm is proposed and demonstrated, which is based on a conventional dual sideband probe setup, but the probe waves are modulated by a frequency shift keying signal. The pump distortion is compensated in the time domain with this technique. By employing a 105-km sensing fiber, this technique is experimentally validated with 2-m spatial resolution. Furthermore, another experiment is designed to show the good tolerance for the sensing fibers combined with large Brillouin frequency shift (BFS) difference, as is demonstrated in a 50-km-long sensing fiber consisting of two segments with large BFS difference (200 MHz).

A high-performance Brillouin optical time-domain analysis (BOTDA) is achieved using the Brillouin gain bandwidth reduction technique combined with high injected probe power. In the probe branch, dual-tone probe wave with fixed frequency separation is used for enhancing the probe power to +5  dBm. In the pump branch, a differential π-phase-shift long-pulse width pair is used to narrow the Brillouin gain spectrum. On the basis of high probe power and 2.5-m spatial resolution, the Brillouin gain spectrum can be narrowed to a level of 17 MHz, whereas the Brillouin gain spectrum of conventional single-pulse BOTDA sensor is 51 MHz. As a result, 50-km sensing range with 2.5-m spatial resolution and 1.1-MHz Brillouin frequency shift (BFS) accuracy has been achieved. Meanwhile, the narrowed Brillouin gain spectrum can give rise to sharp rising/falling edge in the BFS profile when the hot spots are introduced, which increases the detection robustness of the small temperature/strain change in the BOTDA system.

A tunable high-order single-sideband signal generator with optical carrier suppression (SSB-OCS generator) is proposed, which is based on frequency multiplication operation using dual-parallel Mach–Zehnder modulator (DPMZM) and Mach–Zehnder interferometer (MZI). By changing all the modulators at maximum or minimum transmission point simultaneously, the amplitude of input radio frequency (RF) signals and the phase difference between input RF signals, two high-order even or odd signals with opposite amplitude of one sideband, are generated by upper DPMZM and lower DPMZM, respectively. Then, two optical signals are coupled to reserve one sideband, and the coupled SSB-OCS signal is injected into an MZI to suppress high-order intermodulation components. The simulated results show that the first-, second-, and third-order SSB-OCS signals can be achieved, and the suppression ratio is over 30 dB, which agrees well with the theoretical prediction. This scheme is featured by the capability to generate tunable high-order SSB-OCS signal with high suppression ratio, and the operation is simple and flexible. Finally, an experiment was carried out to demonstrate the feasibility of the proposed scheme, and a first- and second-order SSB-OCS signal were obtained, respectively, and the suppression ratio is over 24 dB.

We would like to continue the discussion of specific features of light leakage in the negative curvature hollow core fibers (NCHCFs). In our previous work, it was shown that consideration of the transverse Poynting vector component of air core modes in the vicinity of core–cladding boundary wall and its streamlines is of great importance for understanding light localization mechanism in NCHCFs. Using a simple model of a capillary with the azimuthally periodic distribution of the refractive index in the capillary wall, we demonstrate that the transverse Poynting vector component behavior is similar to that of NCHCFs. We also consider the impact of a supporting tube on light leakage in NCHCFs.

An adaptive Kalman filter (AKF) scheme for joint polarization and phase recovery is proposed and experimentally demonstrated. In this scheme, the noise covariance is estimated adaptively along with the recursive of KF. The simulation results show that the tuning parameter Q can adaptively converge to an optimal value in wide ranges of optical signal-to-noise ratio (OSNR), polarization rotation frequency, and laser linewidth. As a result, the proposed AKF has less OSNR sensitivity penalty, better polarization tracking capability, and laser linewidth tolerance compared with extended Kalman filter (EKF) with fixed Q value. Finally, in the experiment of 16 quadrature amplitude modulation system, AKF also shows a better polarization tracking capability than the EKF.

The article is mainly to solve the security problems existing in ethernet passive optical network. The most obvious thing is that when optical network unit (ONU) is registered, to prevent attackers from eavesdropping and camouflage, we need mutual authentication between the optical line terminal and ONU to ensure the legality of both sides. To solve this problem, this paper designs a bidirectional authentication scheme based on number theory research unit signature algorithm (NTRUSign), using NTRUSign algorithm for authentication, can avoid impersonation attacks but could not prevent the middle eavesdropping attacks, so the data encryption algorithm AES using the traditional transmission of encrypted. Elliptic curve Diffie–Hellman algorithm is used to carry out key exchange, as the key to the subsequent data transmission, and can be completed in the ONU registration process without the need of third-party participation. The analysis results show that this method improves the reliability of identity authentication and data transmission security.

The discrete-modulated continuous-variable quantum key distribution (DM-CV-QKD) could break the distance limitation of Gaussian-modulated CV-QKD. In practice, the high-performance error correction code plays an important role in DM-CV-QKD and affects the secure transmission distance. However, DM-CV-QKD usually works under low signal-to-noise ratio (SNR) and the design of high-performance error correction code under this condition is difficult, so that it would impose a limitation on further improvement of the secure distance. We propose a DM-CV-QKD with the machine-learning-based detector to further improve the secure distance. The numerical result shows that the proposed scheme could validly improve the system performance. Viewed from another perspective, the proposed scheme could be employed to overcome various impairments induced by the channel and thereby lower the demand of error correction codes on the SNR threshold of the quantum channel without compromising the system performance. The proposed scheme opens the door to applying machine leaning to directly process the raw secret key and improve the performance for CV-QKD systems.

An underwater wireless red-light laser transmission system using 10-Gbps 16-quadrature amplitude modulation–orthogonal frequency-division multiplexing (OFDM) modulation based on a high-speed multimode 680-nm vertical-cavity surface-emitting laser (VCSEL) was proposed and demonstrated. This study is the first attempt to adopt red light for transmitting a 10-Gbps wireless signal 6-m underwater. With the adoption of the appropriate OFDM base bandwidth and modulation parameters after studying the frequency characteristics of the high speed multimode 680-nm VCSEL and contrast experiment of modulation parameters, a good bit error rate performance and clear constellation maps are achieved.

As for the issue of the rapid wavelength interrogation of optical fiber wavelength-encoded sensor, a demodulation method combining spectrum-to-time domain information mapping and photonics time stretch technology is proposed. Using group velocity dispersion effect of dispersive elements, the spectrum of optical pulse will be mapped to a temporal waveform whose intensity mimics the spectrum. The temporal waveform is further stretched in timescale so that it is slow enough to be captured by electronic analog-to-digital converter. The performance of the proposed demodulation method is experimentally demonstrated to demodulate a wavelength-encoded sensor.

We demonstrated a 1.21-W 532-nm picoseconds (ps) green laser via second-harmonic generation (SHG) using type-I phase-matched K3B6O10Cl (KBOC) as a nonlinear optical crystal. The ps green laser was successfully generated from two types of 1064-nm ps lasers with one being operated at 10 kHz and the other at 10 Hz. Using a 7.38-W pumping power at 10 kHz as the pump, the SHG output power at 532 nm was 1.21 W with a pulse width of 34.4 ps. For the 10-Hz ps laser with pumping energy of 4.95 mJ per pulse, the output at 532 nm was 1.78 mJ per pulse, which corresponds to an optical conversion efficiency of 36.0%. The experimental results show that the KBOC crystal is a promising nonlinear optical crystal for generating ps green laser.

We propose an efficient carrier-reuse scheme for intensity modulation and direct detection (IM/DD) passive optical networks (PONs) with Rayleigh backscattering (RB) noise circumvention. In our proposed system, the number of light sources is halved since no extra light sources are required for the upstream (US) transmission, and the RB noise is eliminated without using any high cost ultra-narrow filter or coherent detection. The proposed scheme efficiently utilizes orthogonal frequency division multiplexing-based carrierless amplitude and phase modulation in the downstream, where signal multiplexing and demultiplexing are performed by digital filtering. Meanwhile, the high spectrum efficiency optical single-side band (SSB) Nyquist pulse-shaped pulse amplitude modulation-4 signal is generated by utilizing dual-drive Mach–Zehnder modulator in the US. In addition, the effect of phase-to-intensity conversion of the laser phase noise on bidirectional SSB systems over 25-km standard single-mode fiber on bit error rate performance is evaluated. Results successfully verify the feasibility of our proposed efficient carrier-reuse scheme for IM/DD PONs.

The laser self-mixing interference (SMI) with two-external-cavity feedback used with a semiconductor laser is proposed and validated in the time and frequency domain. Simulation and experimental results show that mixed SMI signal is the sum of two independent SMI signals under weak feedback. This structure can measure two vibrations simultaneously using only a single detector and a single laser.

Recently, indoor positioning system (IPS) based on visible light communication (VLC) has gradually become a hot research topic. However, many existing indoor localization schemes based on VLC only provide solutions of positioning on a two-dimensional plane. Some IPSs-based VLC that focus on three-dimensional (3-D) positioning usually contain various sensors or use complex algorithms. A high-precision indoor 3-D localization scheme based on VLC using modified fruit fly optimization algorithm (MFOA) is proposed. Since it is difficult to directly calculate the coordinate of PD receiver in 3-D positioning problem, we transform the 3-D positioning problem into a global optimization problem and design the corresponding fitness function according to the Lambertian radiation pattern, which can achieve a higher accuracy and reduce system complexity. By changing the structure of fly group in the traditional fruit fly optimization algorithm and designing an adaptive search scope, the MFOA is obtained to solve the positioning problem, which leads to a nice positioning effect. With a good convergence performance, our simulation shows an average error of 0.76 cm within 20 iterations in an indoor space of 4  m  ×  4  m  ×  6  m, and most 3-D positioning errors are <1.85  cm, which shows a good positioning performance. Therefore, our indoor localization scheme has a potential value in the actual practice of indoor localization.

We propose and experimentally demonstrate a high capacity optical monitoring scheme using a self-seeding Fabry–Pérot laser diode (FP-LD) with direct modulation in a passive optical network (PON). A simple, stable, and low-cost monitoring source with side mode suppression ratio of 47 dB that consists of a FP-LD, a polarization controller, and a fiber Bragg grating is presented. The detecting signals can be encoded in two-dimension, i.e., pulse widths and wavelengths, which is very suitable for high capacity PON monitoring. The final recognition process is very simple because only the rectangular pulse width needs to be identified, especially compared with the complicated network recognition algorithm.

A beam-smoothing method that combines induced spatial incoherence (ISI) and continuous phase plate (CPP) is presented. A method designing special CPPs for ISI is proposed. Then, spatiotemporal character of focal spots with different ISI parameters and different phase plates was numerically analyzed. Using special phase plate consisting of small CPPs designed separately, with 10-nm bandwidth 527-nm light, focal spot nonuniformity at spatial wavelength 10 to 50  μm could be reduced to 2% in 130 ps and was further reduced to 0.5% in 2.3 ns. A two-lens aperture system is added to lower the nonuniformity of the near-field in the light path. Using ISI + CPP, the shape of the focal spot could be controlled perfectly, and the characteristic that the ISI + CPP focal spot changes randomly with time is beneficial to the control of laser and plasma interactions.

We study a polarization beam splitting phenomenon in modified annular photonic crystals. The modified structures are composed of square and triangular lattices with circular and square air holes in a dielectric background in which a dielectric rod is added to each air hole. The inner dielectric rods are not located at the center of the holes and are oriented relative to the lattice axis. At first, isofrequency contours of the structures are numerically investigated for different sizes of air holes and rods, using the plane wave expansion method. The effects of additional rods are clearly demonstrated in terms of tilted contours, which is effective in the direction of flow of light for different polarizations. Finally, the finite-difference time-domain method is utilized to depict the different traveling path of two orthogonal transverse magnetic and electric polarizations.

The theoretical approach to investigate the frequency pulling phenomenon, when the optoelectronic oscillator is injected by a weak radio frequency (RF) signal, is presented. The differential equation for the phase perturbation is derived. The analytical expressions of the phase-difference after locking and lock-range are derived here. Here, we also study the influence of the injection RF signal on the beat frequency, average frequency, and actual pull-in frequency. Also, the dependency of beat frequency and average frequency on injection frequency is studied here. All the analytical expressions clearly reveal the frequency pulling phenomenon from fast-beat state through quasi-locked state to locked state. Simulation results are also given in support of the theoretical study.

The temperature mode of development of the latent image of a holographic recording on a photothermoplastic medium when heated by unmodulated laser radiation is studied. The solution of the nonstationary heat conduction problem for multilayer structures made it possible to obtain an analytical expression for the temperature of the recording surface, depending on the thermophysical parameters of the carrier layers and on the power of the heating source. It is shown that, depending on the optical properties of the layers of the material and on the wavelength of the heating radiation, different modes of development of holograms on photothermoplastic carriers are realized.

A design method of a three-direction double-loop strain sensor for two-dimensional (2-D) strain is proposed and analyzed. The strain sensor is made up of three sensing arms and each arm is made of fiber Bragg gratings (FBG) sensor surface glued on titanium alloy substrate. The substrate has double loops to improve the sensor’s measurement range. The strain sensor is unique in that by designing three single arms of strain sensors in different direction, a 2-D strain’s maximum strain value and direction can be precisely determined. In comparison with common unidirectional strain sensor, this has great value for structural health monitoring. With finite element analysis and measurement demonstration, it is shown the measurement range of the strain sensor is increased by seven times compared with normal FBG sensor. The strain sensor’s measurement range can reach 1% (±5000  μϵ) with accuracy of 0.6%. An accurate and real-time monitoring system based on the sensor is presented, which demonstrated the sensor’s fast speed and high reliability.

We report a production technique of reducing the polarization-dependent loss (PDL) always present in arc-induced long-period fiber gratings (LPFGs). The proposed fabrication method is based upon the rotation of the optical fiber by an axial angle of 180 deg at each electric arc discharge, therefore, inducing opposite point-by-point asymmetric modulations over the entire length of the LPFG. PDL measurements of different arc-induced LPFGs fabricated by both the conventional and proposed method are presented. Finally, the obtained results show a significant decrease of the intrinsic PDL of arc-induced LPFGs with the proposed fabrication technique.

Tight focusing of laser light using a polarization converter and an adaptive lens is demonstrated. The polarization converter is used to convert the linearly polarized light into a radially polarized light. The adaptive lens is used to focus the radially polarized light on a spot. At the focused spot, a large component of the electric field is along the longitudinal direction, and the focused power density is enhanced. The size of the focused spot can be changed by changing the focal length of the lens. When the focal length of the lens becomes shorter, the focused spot becomes tighter. The mechanisms of the two devices are introduced, and the theory of tight focusing is experimentally supported. Tight focusing of radially polarized laser light with a controllable spot size has potential applications in super-resolution imaging, material processing, and microparticle trapping.

This erratum corrects a figure published in the article “Three-dimensional reflection screens fabricated by holographic wavefront printer.”

Erratum to correct a figure error in the Optical Engineering article “Features of light leakage from the negative curvaturehollow core fibers.”