This guest editorial introduces the Special Section on Ultraprecision Optics Fabrication and Characterization.

Due to the complexity of measurement systems for asphere and freeform surfaces, well-known artifacts are required to characterize the accuracy of the results of their form measurements. We present advancements in manufacturing and characterization of metrological multispherical freeform artifacts. The strong cooperation between the manufacturing and measurement units of Physikalisch–Technische Bundesanstalt (PTB) allows the form of the artifacts to be manufactured very accurately and the root-mean-square deviation from the desired design form to be improved by a factor of >20 compared to former results (e.g., from a value >500  nm to about 20 nm). Furthermore, a nickel/phosphorous coating is added to the copper surface, resulting in greater hardness and allowing the coated surface to be used as a reference for low-force tactile measurement systems. Four Gaussian peak fiducial marker structures are added to the design to improve the evaluation of comparison measurements. In addition to characterizing the radii in the spherical segments using PTB’s radius measurement bench, we also characterize the sphericity of the spherical segments using a Fizeau interferometer. We show form measurement results for a full-field measuring tilted-wave interferometer and compare the form measurement results in the spherical segments with measurement results obtained with the Fizeau interferometer.

Dark-field illumination is a simple yet elegant imaging technique that can be used to detect the presence of particles on a specular surface. However, the sensitivity of dark-field illumination to initial conditions affects its repeatability. This is problematic in cases where automation is desired. We present an improvement to the current method of using a modulation field that relies on phase calculations rather than intensity. As a result, we obtain a computational method that is insensitive to noise and provides clearly defined particle information, allowing a global threshold to be set for autonomous measurement purposes. After introducing the theory behind our method, we present experimental results for various scenarios and compare them to those obtained using the dark-field approach.

Loose abrasive grinding was performed on a wide range of optical workpiece materials [single crystals of Al₂O₃ (sapphire), SiC, Y₃Al₅O₁₂ (YAG), CaF₂, and LiB₃O₅ (LBO); a SiO₂-Al₂O₃-P₂O₅-Li₂O glass-ceramic (Zerodur); and glasses of SiO₂  :  TiO₂ (ULE), SiO₂ (fused silica), and P₂O₅-Al₂O₃-K₂O-BaO (phosphate)]. Using the magneto rheological finishing (MRF) taper wedge technique (where a wedge was polished on each of the ground workpieces and the resulting samples were appropriately chemically etched), the subsurface mechanical damage (SSD) characteristics were measured. The SSD depth for most of the workpiece materials was found to scale as E1^1/2  /  H₁, where E₁ is the elastic modulus and H₁ is the hardness of the workpiece. This material scaling is the same as that for the growth of lateral cracks, suggesting that lateral cracks are a dominant source for SSD rather than radial/median cracks, as previously proposed. Utilizing the SSD depth data from both this study and others, semiempirical relationships have been formulated, which allows for estimating the SSD depth as a function of workpiece material and important grinding parameters (such as abrasive size and applied pressure).

A procedure to improve the quality of the extracted phase by a passband filter within the spatial frequency domain is proposed, using the double-digital fringe projection method for obtaining the contour of the surface of different objects. This method requires the digital projection of two fringe patterns to the same object to generate an interference pattern containing moiré fringes, which are related to the shape of the measured object. The proposed method pretends to remove remnant frequencies of the projected fringes keeping only the moiré pattern.

Modern subaperture technologies mostly use the five-axis machine to follow the normal of state-of-the-art surfaces, such as aspheric, off-axis surfaces. The dual-tilt-axis tool has been widely used in optical manufacture to change the orientation of the tool. The initial tilt positions of the tool play an important role in the symmetry of tool influence function (TIF). The tilt angle errors may cause a skew TIF. We discussed the self-developed machine and its TIF models with different motion modes. Next, the effect of tilt angle errors, include spinning axis tilt error and revolution axis tilt error, was analyzed based on our self-developed polishing machine. Symmetric TIF will distort and form a skew TIF due to the angle error. There was a linear relationship between the eccentric ratio of the skew TIF and the angle error. In the experimental study, an initial adjustment was performed by utilizing a dial gauge, and then the TIF result showed that there were still some angle errors. We presented an image thresholding calibration method based on skew TIF to solve the tilt angle errors. After the new calibration, the following compared experiment got a fine symmetric, and Gauss-like TIF, and proved the validity of the proposed model and calibration method.

The application of microlaser assisted machining of precision optical components made of optical grade single-crystal Si is reviewed. An optical raytracing model is developed and used for predicting the laser interaction with the workpiece. Optical characterization of the system is shown to be in good agreement with that predicted by the model. Using the information from the simulation and experimental validation, the laser-assisted diamond turning of single-crystal Si samples is shown to have exhibited little to no brittle fracture on the surface and the potential of extending the diamond tooling life by 150%.

In addition to achieving a desired freeform profile, ensuring a superb micro-roughness finish is a key factor for successful freeform optics manufacturing. We present a pseudorandom orbiting stroke-based postprocessing technique that maintains freeform optic forms, while improving small-scale surface quality. The full-aperture tool can avoid subaperture effects, and the small stroke pseudorandom tool path guarantees the match of freeform profiles while preventing the directionality of the final surface profiles. Three independent experimental studies are designed, conducted, and presented for a wide range of optics, including magnetorheological finishing-polished BK7 glass, single-point diamond turned (SPDT) poly(methyl methacrylate), and SPDT Al6061 optics. The comparison of direct measured maps on the initial and final smoothed optics verifies the form maintenance capability of the freeform optics postprocessing technology. Surface roughness measurement highlights improvements in local surface roughness and periodic toolmark errors left by the previous polishing method.

Light scattering-based characterization techniques are fast, sensitive, and robust, which can be exploited for roughness measurements or homogeneity and defect assessment. However, only compact scattering instruments enable even large freeform surfaces to be inspected close to fabrication or even within fabrication processes. The combination of a light scattering sensor with an industrial robot, as well as its application for full surface evaluation of aspheriscal and freeform surfaces, is addressed. In addition to the technical considerations regarding the sensor, the robotic handling system, or the sample curvature, examples of application to different optical components fabricated at the Fraunhofer Institute for Applied Optics and Precision Engineering using state-of-the-art techniques are presented. The results include the discussion of anisotropic surface structures induced by diamond turning or polishing as well as the analysis of the influence of a protection layer.

This work is a continuation of previously published work on the application of fiber-based tools in precision polishing of optical components. Previous publications mainly focused on understanding how fiber-based tools remove material and the potential of such tools in reducing existing midspatial frequency errors on planar samples. In this work, an exemplary tool consisting of nylon 6/6 fibers is used in a five-axis computerized numerically controlled machine tool to evaluate the tool’s ability to polish nonplanar BK7 components. The five-axis system has an inline slurry feed system which is found to produce higher material removal rates than the nonrecirculatory slurry bath configuration used in earlier polishing tests. Polishing results obtained on planar and spherical surfaces in the five-axis system show close agreement with that predicted via convolution. A finite element model of the fiber’s interaction with a concave surface shows that the calculated local pressure distribution reflects that observed experimentally, thus further supporting the predictable behavior of fiber-based tools.

An optical setup for the nonorthogonal two-axis Lloyd’s mirror interferometer, which is composed of a nonorthogonal type of mirror-substrate assembly and a newly designed beam expansion assembly, is proposed to fabricate highly precise two-dimensional (2-D) diffraction scale gratings having uniform pattern structures over a wide area. The beam expansion assembly is designed in such a way that a thin collimated laser beam is at first generated by a small collimating lens to carry out a precise polarization modulation control of subdivided wavefronts in the beam, followed by the generation of a collimated laser beam with the expansion of the thin collimated laser beam by using a beam expander. Since a pair of high-precision half-wavelength plates made of crystalline quartz can be employed in the newly designed optical setup, a much better polarization modulation control can be expected, compared to the conventional optical setup in which low-precision large-size half-wavelength plates made of polycarbonate should have been employed. To verify the effectiveness of the proposed optical setup, theoretical calculations and some basic experiments are carried out by using a prototype optical setup to demonstrate the feasibility of the proposed optical setup for fabrication of highly precise 2-D scale gratings.

Ultraprecise mirror devices show considerable potential with view to applications in the visible and the ultraviolet spectral ranges. Aluminum alloys gather good mechanical and excellent optical properties and thus they emerge as important mirror construction materials. However, ultraprecision machining and polishing of optical aluminum surfaces are challenging, which originates from the high chemical reactivity and the heterogeneous matrix structure. Recently, several ion beam-based techniques have been developed to qualify aluminum mirrors for short-wavelength applications. We give an overview of the state-of-the-art ion beam-processing techniques for figure error correction and planarization, either by direct aluminum machining or with the aid of polymer or inorganic, amorphous surface films.

Metal mirrors are used for spaceborne optical systems, such as telescopes and spectrometers. In addition to the optical performance, the mechanical needs and the mass restrictions are important aspects during the design and manufacturing process. Using the additive manufacturing process, optimized internal lightweight structures are realized to reduce the weight of the system while keeping the mechanical stability. A mass reduction of ≈60.5  %   is achieved. Using the aluminum silicon alloy AlSi40, the thermal mismatch of the mirror base body to a necessary electroless nickel-polishing layer is minimized. Based on an exemplary mirror design, the optimization of the interior lightweight structure is described, followed by the manufacturing process from additive manufacturing to diamond turning, plating, and polishing. Finally, the results of surface metrology and light scattering measurements are presented. A final form deviation below 80 nm p  .    −  v  .   and a roughness of ∼1  nm rms could be demonstrated.

Reflection losses due to refractive index mismatch limit the obtainable diffraction efficiencies for transmission gratings in the highly dispersive regime, i.e., with period to wavelength ratios smaller than 0.7. The design and fabrication of such gratings with high-diffraction efficiencies (≥94  %  , Littrow configuration) will be discussed with an emphasis on process strategies to control the profiles in the reactive ion beam etching step. Experimental results from the manufacturing of monolithic fused silica pulse compression gratings with 3000  L  /  mm optimized for a center wavelength of 519 nm will be presented. The influence of different etching parameters such as etch gas mixture, ion incidence angle, and acceleration voltage of the ion source on profile depth, side-wall angle, duty cycle, and ultimately diffraction efficiencies will be discussed.

The lobster-eye optical system is widely used in the wide field of view (FOV) soft x-ray imaging device. The payload soft x-ray imager (SXI) onboard the solar wind magnetosphere ionosphere link explorer satellite will apply this technology to achieve panoramic imaging of the dayside magnetosphere. In order to optimize the imaging performance of SXI, we focus on geometric parameters optimization of a lobster-eye lens. The results show an appropriate microchannel ratio of length to width of lobster-eye optics with radius of curvature of 600 mm could be 30:1 (microchannel width of 40  μm and length of 1.2 mm). For a monochromatic parallel light source with energy of 1 keV, this combination of parameters can theoretically provide relatively large total effective area of about 15.52  cm² and focusing efficiency of about 0.2887 along with spatial angular resolution of about 6 arc min at the center of FOV. Combined with the actual lobster-eye optics, the aberrations from deformation of the microchannel, the deviation of radius of curvature and planar detector are analyzed. For SXI with planar CCD detector, an optimum focal length could be 304.2 mm to ensure better resolution in full FOV.

To obtain sharp images of space targets, high-accuracy restoration of degraded images corrected by an adaptive optics (AO) system is necessary. Existing algorithms are mainly based on the physical constraints of both image and point-spread function (PSF), which are usually continuously estimated in an alternately iterative manner and take a long time to restore blurred images. We propose an end-to-end blind restoration method for ground-based space target images based on conditional generative adversarial network without estimating PSF. The whole network consists of two parts, generator network and discriminator network, which are used for learning the atmospheric degradation process and achieving the purpose of generating restored images. To train the network, a simulated AO image dataset containing 4800 sharp–blur image pairs is constructed by 80 three-dimensional models of space targets combined with degradation of atmospheric turbulence. Experimental results demonstrate that the proposed method not only enhances the restoration accuracy but also improves the restoration efficiency of single-frame object images.

Typically, search research papers assume that target acquisition is described by an exponential distribution. We investigate when this assumption is valid. It is obvious that two people are more effective than one person at finding a target, but how can that be quantified? The network imaging sensor (NIS) and time-dependent search parameter (TDSP) models quantify how much more effective multiple observers are at finding a target than a single individual for a wide variety of scenarios. We reference and summarize evidence supporting the NIS and TDSP models and demonstrate how NIS model results can be expressed in terms of a reduced hyperexponential distribution for scenarios where observer and target are stationary. Target acquisition probabilities are determined by analysis and confirmed by computer simulations and perception experiments. Search by multiple stationary observers looking for a stationary target is described by the hyperexponential distribution. Stationary scenarios with multiple observers are more accurately modeled by hyperexponential rather than exponential distributions. Hyperexponential distributions are an example of phase-type distributions used in queuing and in the performance evaluation of computer networks and systems. The observation that search, queuing, and computer networks share phase-type distributions facilitates cross fertilization between these fields.

Poisson image deconvolution and denoising have received much attention in recent years. A key challenge of this problem is that the most effective prior might never exist. The purpose of our study is to investigate the characteristics of generalized l_p  /  l_q norm on the derivatives of nature images and to present an efficient method to promote hyper-Laplacian prior for the deconvolution of blurry and Poisson noisy images. We first analyze the mathematical characteristics of generalized l_p  /  l_q norm based on the Berkeley segmentation data set and implement deconvolution using generalized l_p  /  l_q norm for derivatives in high-frequency domain so as to enforce the preservation of strong edges. Then hyper-Laplacian prior is promoted for actual Poisson image deconvolution, which uses the estimated gradient information to penalize the small derivatives (often noise) and preserve large derivatives associated to image borders. Our preliminary experiments show that the proposed method can achieve higher image quality than state-of-the-art methods in terms of peak signal-to-noise ratio and noise sensitivity.

Just-noticeable difference (JND) is defined as the smallest intensity change in an image that can be noticed by the human vision system (HVS). Any perceptible distortion level must be greater than the JND. Based on this observation, a local binary pattern (LBP) is developed for image quality assessment. First, the JND map of the image is computed. The spatial and relative intensity relationships among pixels in a local neighborhood are employed to generate the proposed LBP based on the JND map. Then, image contrast is used as a weighting factor for the LBP histogram generation to characterize the structural and contrast information of the image. Finally, the contrast and structure changes due to image distortion are measured by calculating the similarity between contrast-weighted histograms of the reference and distorted images. Support vector regression is employed to pool the similarity to predict the quality. Experimental results on benchmark databases demonstrate that the proposed LBP can effectively and accurately measure image quality, which is consistent with the HVS. The proposed method achieves high consistency with subjective perception using 18 reference values and performs better than other state-of-the-art reduced reference image quality assessment methods.

We investigate an optical system for the absolute distance measurement of objects with rough surfaces, using the principle of asynchronous optical sampling (ASOPS). A telescope system collects the scattered laser light that returns from the rough surface and directs it into a collimator with high precision. The contrastive absolute distance measurement experiments are carried out using a plane mirror and objects with rough surfaces. The residual error is kept within 10  μm within a 2-ms sampling time for the rough surfaces. Our results indicate that this ASOPS method is a promising candidate for metrological applications in some industrial sites.

Our structured illumination microscopy (SIM) is based on a spatial light modulator (SLM) instead of an illumination mask, which does not need to be attached to a linear stage. This SIM can easily design the period of the one-dimensional grid related to the optical sectioning strength and can rapidly acquire three-dimensional data. The optimization of SIM with an SLM is proposed. Previous studies primarily varied magnification with a high numerical aperture objective to optimize the axial response. It is feasible to obtain the maximum optical sectioning strength by designing a grid pattern that has an appropriately high spatial frequency and to uniformly cover the entire frequency spectrum of the sample by rotating a grid pattern. We have successfully optimized SIM with such a grid and covered the frequency spectrum by rotating a grid pattern in multiple orientations.

A parallel measurement approach is presented to analyze multiple linear polarization (LP) modes using the spatial light modulator (SLM). The hologram loading onto SLM is generated by conjugate symmetric extension Fourier computer-generated holography. The mode array containing different LP modes is encoded into the hologram, which records the array amplitude and phase information. Demodulated by the SLM, the modal content and their relative powers of tested light are obtained by measuring the intensity and position of the demodulated light spot in the diffracted field. The experimental system is established and LP modes of single and few-mode step-index fibers are measured. Our method has some advantages, including simple optical setup and applicability of the higher-order modes detection. It is promising for the mode analysis of high-power fiber lasers and optical communication.

Phase extraction from a single closed interferogram with a quadratic phase plays an important role in optical interferometry. Based on the energy of the interference images of this type is concentrated in a very narrow range around a point in the fractional Fourier transform (FRFT) domain under matched angle, the FRFT technique is a useful parameter estimator for the fringe pattern, but it has not been used to retrieve the desired phase from the fringe pattern. Thus, the parameter estimation approach based on FRFT is extended to the extract phase. The phase extraction can be done without using a phase unwrapping algorithm. Moreover, for ensuring both the estimation precision and speed, a coarse-to-fine searching strategy that includes a direct searching process implemented with a large step size and an iterative searching based on quasi-Newton method is presented in this paper to implement the FRFT method. The feasibility and applicability of the proposed approach are demonstrated using simulation and experimental results. The experimental results show that the proposed method is robust to noise and obstacles.

An improved touch-trigger probe method for surface parallelism measurement is proposed, which enables conventional mechanical probe-based detection techniques to evaluate the surface parallelism degree with higher accuracy. The distance detection of the sensing probe is equipped with a simple optical arrangement associated with the digital image correlation method to perform submicron accuracy measurements. The optical arrangement consists only of an inexpensive USB digital microscope. A feasibility study of the measurement method was carried out by measuring three gauge blocks with known parallelism deviations. The experimental setup for the measurement of parallelism error of gauge blocks is described in detail. The experimental results using the proposed method are in good agreement with those certified by the supplier. It has been confirmed that the final accuracy of the developed system could be able to reach the submicron level and meet the requirement of the metrology. In addition, this system is simple to manufacture, low in cost, and easy to operate.

We present the results of research of the angle measurement system for direction measurements. Development of the system is based on the dynamic goniometer, whose operation is defined by continuous rotation of the platform with the autocollimating null-indicator. The measurements of angles between mirrors are provided by the null-indicator and optical encoder. The results of the system calibration with the use of standard optical polygon are presented. The computer simulation of the calibration process was carried out, and requirements to optical elements alignment accuracy were estimated.

The positional accuracy of a near-infrared (NIR) dynamic navigator is remarkably affected by two factors. One is the calibration accuracy of the navigator’s two NIR cameras, and the other is the accuracy of feature point extraction. The current lack of accurate calibration devices for NIR cameras limits further application. Therefore, in this study, an NIR camera calibration device was designed by placing the NIR light source and heat dissipation system at the back of a Halcon transparent glass template. Usage of camera calibration in a specific band and the gray centroid method based on elliptic boundary to extract feature points can further improve the accuracy of vision system calibration and measurement. Repeated tests and verifications showed that the reconstruction accuracy (<0.1  pixels) of the binocular vision system calibrated by the NIR calibration device in a specific band was better than that calibrated by traditional methods.

To save the cost of the fiber grating sensing technology demodulation equipment and broaden the range of its detection application, one heterogeneous fiber grating spectrum separation (HFGPS) method based on transfer matrix and the adaptive algorithm is proposed. First, a theoretical mode of the HFGPS method is introduced. Second, simulation experiment on linearly chirped fiber Bragg grating (LCFBG) and fiber Bragg grating (FBG) is carried out to obtain the separation effect. After simulation experiment data analyses, relative errors between the separated spectrum signal and the heterogeneous original signal are no >5.29  %  , which occurs at spectrum fringe region of FBG and LCFBG, and the separation algorithm can achieve single wavelength or multiwavelength mixing heterogeneous spectrum efficient separation with high precision. Lastly, the temperature calibration experiment is carried out on FBG temperature sensor and LCFBG to further verify the effect of the HFGPS method. After the temperature experiment data analyses, the result shows that sensitivity relative error of FBG between original and heterogeneous separated is 0.4%, and the HFGPS method can achieve heterogeneous spectrum efficient separation and has small influence on the detection performance of the FBG sensor. All these experiment data confirm that the HFGPS method can achieve effective heterogeneous spectrum separation with high precision and has certain practical application value.

In three-dimensional vision measurements, single-camera mirror binocular stereo vision systems composed of a camera and mirrors have become popular, owing to their high flexibility and compactness. However, the calibration of these systems is different from traditional two-camera stereo vision systems, because there is no rigid-body transformation between the actual camera and the virtual camera. A calibration method for single-camera mirror binocular vision system is proposed, which can establish the rigid-body transformation by rotating the image based on the sole principal point. The comparative experiments showed that the proposed method yielded a higher accuracy than the traditional method.

A proposal of the design for a deflectometric profilometer that combines several advantages in one device to achieve an ultra-precise straightness measurement as a scanning deflectometer is described. The device allows measurement of the absolute flatness of large optical surfaces at the nanometer level. The proposed setup also allows the ability to measure optical flats with both sides polished. The along-scan resolution of the measured profiles could be below a millimeter.

Solar concentrators generate energy according to the amount of radiant flux that is converted into electrical energy using a solar cell. The optimal alignment of the solar cell and the aperture stop of the concentrator photovoltaic (CPV) solar system is a critical parameter for fabricating and manufacturing steps. We designed, developed, fabricated, and verified an optoelectronic system to test alignment of CPV solar system modules that is portable and robust to implement as a step in the assembly line. In addition to the components employed in systems previously, we implement an alignment module. It consists of a thin prism in four orientations in a plane normal to the optical axis of the unit under test and its control system. Its advantage is robustness against its positioning and orientation errors. Simulations and experimental results are presented.

Phase retarders normally exhibit strong wavelength dependence. However, for use with polychromatic light, achromatic retarders, which exhibit ideally nearly identical characteristics over a wide wavelength region, are in demand. Designing such a superachromatic retarder is a challenging task for an optical system designer where retardation will be almost constant within a wide range of wavelengths. The present investigation considers a system consisting of wave plates made of different materials, which focus on near-infrared wavelength range, viz. 800 to 2000 nm. Here, a flower pollination algorithm has been used for this nonlinear optimization problem. With the help of the mentioned optimization technique, the optimal values of thicknesses of wave plates are calculated for which the system act as a quarter-wave plate. The obtained result shows a significant improvement in terms of maximum deviation of retardation for the above-mentioned wavelength range. The proposed methodology holds promise for optimizing the design of optical systems.

An ultracompact, wide bandwidth, polarization beam splitter (PBS) based on a Bloch supermode coupler is proposed. In such PBS, a subwavelength grating (SWG) waveguide is sandwiched between two identical strip waveguides as a selective coupling bridge. Profiting from the tailorable characteristics of the SWG waveguide, the coupling between TM supermodes can be made negligible. On the contrary, the TE supermodes can exchange their power efficiently, resulting in short coupling length. At wavelength of 1550 nm, the extinction ratio and insertion loss of the PBS can achieve 25.5 and 0.2 dB for TE mode and 32.1 and 0.1 dB for TM mode, respectively. Furthermore, it has a 10-dB bandwidth over 200 nm and offers a width deviation tolerance of ±15  nm. The proposed PBS can find applications in the areas of polarization-sensitive interconnection and signal processing.

In magnetorheological finishing (MRF), predicting the size of a removal function plays an important role in determining the efficiency of optical material removal. The size of the removal function can be adjusted for different immersion depths of optical parts into the MRF ribbon, which enables the development of multiple MRF-processing algorithms: dwell-time calculation, path planning, or dynamic control of MRF instruments. However, few methods for such algorithms have been developed to dynamically approximate the size of removal functions with respect to various immersion depths. Thus, the ability to dynamically approximate the size of the MRF removal function is indeed of significance. A dynamic approximation method is designed after analyzing the generation mechanism of removal function and its size; establishing the equations for size, which are further numerically analyzed and simplified for common MRF configurations; and approximating the length and width of removal function dynamically. The approximation accuracy is verified through experimental tests where UBK7 optical parts are polished on a PKC1000-Q2 MRF installation. It is revealed that the approximation errors for the length and width are less than 6% and 8%, respectively.

The yybar diagram for Gaussian beam optics is employed to model the behavior of an interferometer system testing very small radius parts. The model was developed to overcome the limitations and known inconsistencies of a paraxial optics representation used to evaluate a calibration method for testing cylindrical wave optics using a fiber reference test. Gaussian beam analysis inherently contains physical optics conditions, and the yybar diagram method provides both an intuitive and powerful framework to generate analytical solutions. Particularly, we show how to model an interferometric test from a Fizeau transmission sphere (TS), to a small test ball and back to the TS, and yield test ball radius limits as a function of the test wavelength and TS F  /  #. A computation of error estimates for measuring the radius of curvature of the test balls is also presented.

Rectangular pupils are employed in many optical applications such as lasers and anamorphic optics, as well as for detection and metrology systems such as some Shack−Hartmann wavefront sensors and deflectometry systems. For optical fabrication, testing, and analysis in the rectangular domain, it is important to have a well-defined set of polynomials that are orthonormal over a rectangular pupil. Since we often measure the gradient of a wavefront or surface, it is necessary to have a polynomial set that is orthogonal over a rectangular pupil in the vector domain as well. We derive curl (called C) polynomials based on two-dimensional (2-D) versions of Chebyshev polynomials of the first kind. Previous work derived a set of polynomials (called G polynomials) that are obtained from the gradients of the 2-D Chebyshev polynomials. We show how the two sets together can be used as a complete representation of any vector data in the rectangular domain. The curl polynomials themselves or the complete set of G and C polynomials has many interesting applications. Two of those applications shown are systematic error analysis and correction in deflectometry systems and mapping imaging distortion.

An irradiance distribution model for laser triangulation displacement sensors is proposed, which is more suitable for practical applications than the geometric optical model (GOM). Based on the irradiance distribution model, a convergence algorithm is developed. Compared with the design parameter optimized method based on the GOM, the convergence algorithm can be used for optimization of not only the traditional design parameters including view angle and object distance but also the waist of the source laser beam. Additionally, using this convergence algorithm, the nonlinearity can be evaluated in the design stage. To validate the convergence algorithm, two example cases are performed. The results show that the nonlinearities are reduced to 6.3098 and 5.7946  μm, respectively.

Thulium fiber lasers (TFL) are being developed as alternatives to conventional holmium:YAG lasers for lithotripsy. TFLs emit at two primary infrared (IR) wavelengths, 1908 or 1940 nm, closely matching high (70°C) and low (22°C) temperature water absorption peaks in tissue, respectively. Water, which is present in the pores of kidney stones and fluid environment of the urinary tract as well as delivered through the working channel of the ureteroscope during lithotripsy, is a primary absorber of IR laser radiation. The water absorption peak shifts from 1940 to 1920 nm with increasing water temperature during laser ablation. At high water temperatures (70°C), the absorption coefficient is 150  cm^−  1 at 1908 nm and 135  cm^−  1 at 1940 nm. The goal of this study was to determine whether this 10% difference translates into a measurable difference in kidney stone ablation rates. Two TFLs (1908 and 1940 nm) were tested at similar laser parameters of 35 mJ energy/pulse, 500-μs pulse duration, 300-Hz pulse rate, and 10.5-W average power, using 200-μm-core silica optical fibers. The handheld fiber was maintained in contact with 6- to 9-mm diameter uric acid (UA) stones, immersed in a saline bath with saline flow (n  =  10  stones  /  group). Laser irradiation time to fragment and pass all stone fragments through a 1-mm sieve was measured and then divided into initial stone mass to calculate stone ablation rates. For each laser group (1908 and 1940 nm), initial stone mass was 270  ±  60  mg versus 260  ±  50  mg, respectively (p  =  0.9). Stone ablation rates measured 0.9  ±  0.2 and 0.9  ±  0.1  mg s^−  1 (p  =  0.9). Stone ablation thresholds measured 8  ±  7 and 5  ±  13  J cm^−  2 (p  =  0.8). There was no significant difference in UA stone ablation thresholds and ablation rates between 1908- and 1940-nm wavelengths. Newer, more compact, efficient, and higher peak power TFLs operating at 1940 nm provide comparable stone ablation rates to older 1908-nm TFLs for similar laser parameters.

We report on an approach for a compact ultrafast thin-disk multipass laser amplifier making use of a highly compact geometric folding scheme. The setup is also suitable to minimize the effects caused by natural convection of hot air in front of the thin-disk on the amplified laser beam as it facilitates to orient the laser disk with its axis in the vertical direction. The efficacy of this approach is analyzed with finite-element method simulations of the heated laser crystal in ambient air with different orientations of the thin laser disk. The experiments confirm a significant improvement of the amplifier performance in terms of stability and an increase of the output power with nearly diffraction-limited beam quality (M²  ≤  1.4) by a factor of 3 with respect to the conventional orientation of the laser disk.

Recently, a 1.55-μm pulsed coherent Doppler LIDAR system using all fiber optical components was developed to achieve real-time measurements of wind fields. The system employs 100-μJ pulse energy at 10 kHz pulse repetition rate. In addition, the system consists of a fiber-based optical transceiver unit, a two-axis scanner, and a multicore digital signal processor (DSP) for real-time signal processing. With compact and mobile design, the LIDAR is easy to transport and deploy for different field campaigns. For a different application of LIDAR, the range resolution can change manually. A horizontal detection range of 10 km is achieved with the temporal and spatial resolution of 1 s and 30 m, respectively. Field experiments compared with an anemometer show that correlation coefficient of the different wind speed measurements is 0.953; the correlation coefficient for wind direction values is 0.967. Continuous wind profiles of the planetary boundary layer are presented to demonstrate the stability of the system.

We present an energy management scheme for the power-over-fiber system used in the electric power industry. The scheme dynamically adjusts output power of the system by tuning the driven current of the laser, according to the power consumption of the external load, which is deduced by the output current and voltage of the photovoltaic cell. In addition, an auxiliary power is employed to increase the output power and improve the dynamic response of the system. Experiments were made in which the static response, dynamic response, and the stability of the scheme were tested. The results show that our scheme can automatically control the output power of the system corresponding to the external load, which leads to the alleviation of the working temperature and potentially increases the reliability of the system and even prolongs the lifetime.

A stable temperature calibration method based on radial basis function neural network (RBFNN) is proposed to obtain the complex relationship between the temperature and the center wavelength of fiber Bragg grating (FBG) with high accuracy and excellent stability. We introduce the regularized and generalized RBFNN, respectively, and test the accuracy of trained models. Experimental results demonstrate that the maximum absolute error (MAE) and root-mean-squared error (RMSE) of regularized RBFNN are 1.1098°C and 0.1982°C, respectively, in fitting and 1.0206°C and 0.1997°C, respectively, in testing, and the MAE and RMSE of generalized RBFNN are 1.1099°C and 0.1982°C, respectively, in fitting and 1.0209°C and 0.1997°C, respectively, in testing. Compared with existing methods, such as polynomial fitting and back propagation neural network, RBFNN has significantly improved the accuracy and stability of FBG temperature calibration and has considerable application prospect in FBG temperature measurement.

An erbium-doped fiber ring laser operating at the C-band is experimentally demonstrated. A maximum output laser power of 0.13 dBm with a step-like spectrum and 3-dB bandwidth of more than 0.4 nm is obtained. Output power is theoretically simulated and fits well with experiment data. A slight improvement in signal-to-noise ratio is observed when the ring laser is applied in an optical fiber sensing system compared to a conventional superluminescent laser, and its compatibility with dense wavelength division multiplexing (DWDM) is verified. We believe the ring laser in this article has potential in the future use of a DWDM optical fiber sensing system.

A magnetic field sensor based on the magnetic fluid injected into all the cladding air holes of the solid core photonic crystal fiber (PCF) is proposed. The 8.5 cm length of the PCF filled with magnetic fluid relates to single mode fiber to compose a Mach–Zehnder interferometer. The sensor relies on the tunable refractive index of the magnetic fluid and the characteristics of the PCF. A series of magnetic field strength is applied to this sensing structure. From the experimental results, the sensitivity of the magnetic field sensor is obtained as 7.055  ×  10^−  4  dB  /  nT while a small change in wavelength shift is found. Due to a simple and easy fabrication technique, high sensitivity, and compactness, we are confident that the proposed sensor will find potential applications in measuring the magnetic field.

Virtualization is becoming a promising method for supporting various emerging applications, and achieving efficient embedding of virtual requests in elastic optical networks (EONs) has become a popular issue in network virtualization research. Meanwhile, multicast request mapping of EONs has become more challenging than that of conventional optical networks. Since the problem of minimizing the embedding cost and redundant transmission in multicast request embedding is NP-hard, we propose an efficient heuristic algorithm, called the virtual optical multicast-tree embedding algorithm based on the node correlation degree (VOME-NCD) to address the problem of low transmission redundancy. When embedding the virtual optical multicast request, it is based on the mapping of the correlation degree of each virtual node. Through extensive simulations, we demonstrate that VOME-NCD outperforms other embedding solutions in terms of the embedding cost, blocking probability, redundancy cost, and router hop count.

High-quality tungsten disulfide (WS₂) nanosheets are fabricated by thermal decomposition method and successfully used as a saturable absorber (SA) for passively Q-switched Nd  :  GdVO₄ laser operating at 1063 nm. The nonlinear optical measurements of the WS₂ nanosheets reveal efficient saturable absorption properties at 1  μm showing a modulation depth of 9% and a saturation intensity of 89.87  μJ  /  cm². The maximum average output power of 1.2 W is obtained with the shortest pulse width of 57.96 ns and the highest repetition rate of 1.11 MHz. The results indicate that WS₂ nanosheets could be an excellent SA for high repetition rate and high peak power laser generation.

Potassium titanyl phosphate (KTiOPO₄, KTP) possesses superior properties in several optical applications. A KTP crystal is irradiated by swift Kr^8  + ions with high energies and low fluences. The stopping and range of ions in matter code is used to simulate the energy deposition process of swift Kr^8  + ions in the irradiated crystal. The electronic and nuclear stopping power profiles of swift Kr^8  + ions irradiated on the KTP crystal are simulated, and the micro-Raman spectrum of the irradiated layer at different depths is measured by a confocal micro-Raman system. The results show that the high electronic energy loss can cause lattice damage along the ion trajectory, whereas the nuclear energy loss causes damage at the end of the ion track. The optical transmission properties of the irradiated KTP crystal are researched at visible and near-infrared bands.

A 5  ×  25-Gbaud wavelength-division-multiplexing passive optical network (WDM-PON) employing probabilistic shaping 4-level pulse amplitude modulation (PS-PAM4) with direct detection is proposed and experimentally demonstrated. Each optical carrier at the optical line terminal (OLT) carries a 25-Gbaud PS-PAM4 signal based on Maxwell–Boltzmann distribution. By employing PS-PAM4, the receiver power sensitivity (RPS) and fiber nonlinear effect tolerance of the system can be significantly improved and enhanced compared with the unshaped one, which can provide abundant system loss budget for the legacy optical distribution networks. The experimental results show that, compared with the WDM-PON employing uniform PAM4, the superior RPS of 1.44 dB and the fiber nonlinear effect tolerance improvement of 3.07 dB over 20-km standard single-mode fiber transmission are obtained for the proposed system. In addition, the system performance by introducing a blind adaptive pre-equalization based on the joint applications of constant modulus algorithm and decision-directed least-mean-square error algorithm, which can accurately compensate for the signal high-frequency loss caused by the electro-optical components, such as digital-to-analog converter, optical modulators, and electrical drivers at the OLT, is also experimentally investigated.

Optical injection is an effective way to generate a tuned microwave photonic filter (MPF). However, the tuning range of the optical injection-based MPF is limited by the nonlinear dynamics and the nonideal roll-off optical filter. To enlarge the tuning range of the MPF, a polarization modulated optical signal injection distributed feedback semiconductor laser is employed. The method is free from the nonlinear dynamics and the nonideal roll-off optical filter. The experimental result shows that the proposed MPF can be tuned from 0 to 40 GHz by directly tuning the center wavelength of the optical carrier. The tuning range can be increased if polarization modulator and photodetector with larger bandwidth are exploited. To the best of our knowledge, this is the largest frequency tuning range of optical injection-based MPF.

We propose a photonic approach to generating frequency-doubled triangular waveforms using a dual-parallel Mach–Zehnder modulator (DPMZM). Most previous modulator-based schemes require additional processing of optical sidebands using filters or a dispersive element. In our work, optical processing of optical components is no longer necessary. The triangular waveforms with a repetition rate twice the frequency of the applied microwave signal can be directly generated by properly setting the bias and driven signal of the DPMZM. Since there is no additional optical processing, the proposed structure is cost effective. The repetition rate of the generated waveform is freely tunable over a wide bandwidth since there is no optical or electrical filter involved. The proposed approach is theoretically analyzed and experimentally demonstrated. Triangular waveforms with the repetition rates of 6, 8, and 10 GHz are successfully generated.

We have proposed an 8 phase-shift-keying (PSK) optical millimeter-wave (MMW) signal generation scheme with frequency quintupling enabled by an electro-optical phase modulator (PM) and a wavelength selective switch. In this scheme, the radio frequency (RF) carrier with 8PSK signal is modulated on the lightwave via the PM with simple precoding but constant Euclidean distance, and is recovered to the original 8PSK signal with the frequency-quintupling RF carrier based on the phase periodicity of an 8PSK signal. By optimizing the voltage amplitude of the 8PSK RF driving signal, the generated frequency-quintupled 8PSK MMW signal is maximized at a given laser launch power. A radio over fiber simulation link is built to demonstrate the theoretical analysis. The simulated constellations and bit-error-rate curves show that the frequency-quintupling 8PSK MMW signal has good transmission performance. The simulation results agree well with our theoretical prediction.

On the basis of the extended Huygens–Fresnel principle and the spatial power spectrum of the refractive index fluctuations of ocean water, a propagation formula for on-axis average intensity of hollow Gaussian beams (HGBs) in oceanic turbulence is analytically obtained. Furthermore, the propagation properties of an HGB in oceanic turbulence are studied numerically in detail. The numerical results indicate that the initial beams with a higher beam order, longer blue–green wavelength, and larger waist width are helpful in mitigating the influence of turbulent ocean. Meanwhile, an HGB may propagate a much longer distance in weak oceanic turbulence by decreasing the dissipation rate of mean-square temperature and the ratio of temperature and salinity, as well as increasing the dissipation rate of turbulent kinetic energy per unit mass of fluid. The simulations also verify that HGBs have more resiliency to oceanic turbulence effects than ordinary Gaussian beams. Our research is expected to provide useful guidance for understanding the propagation characteristics of structured light beams in turbulent media.

A receiver optical subassembly (ROSA) based on hybrid integrated technology is designed and fabricated. It consists of an 8-channel arrayed waveguide grating (AWG) with 2% refractive index difference, two 4-channel positive intrinsic-negative photodetector arrays, and two 4-channel transimpedance amplifier arrays. A flat-top optical spectrum was observed because the output waveguides have a multimode structure, and the average 1-dB bandwidth of AWG channels is 2.8 nm. The insertion loss of all channels is between −1.8 and −2.9  dB, and the cross talk between adjacent channel is less than −20  dB. The ROSA shows a maximum responsivity of 0.4  A  /  W and 3-dB bandwidth of more than 22 GHz for four channels, which can meet the data transmission rate of 25  Gb  /  s. In the future, we will improve the fabrication process to achieve a transmission rate of 8  ×  25  Gb  /  s.

Intersection of two or more silicon slot waveguides is inevitable in modern optical integrated circuits based on a silicon-on-insulator platform. We design a Maxwell’s fisheye lens as the crossing medium for three Si slot waveguides and numerically investigate its characteristics, such as insertion loss, cross talk, and bandwidth. For the 3  ×  3 slot waveguide crossing, the average insertion loss of 1.2 dB and cross talk levels lower than −15.1  dB are achieved in an ultrawideband wavelength range of 415 nm covering the entire O, E, S, C, L, and U bands of optical communications. The footprint of the 3  ×  3 silicon slot waveguide crossing presented in our paper is merely 2  ×  2  μm², which is considerably smaller compared to the previously designed Si slot waveguide crossings even with fewer ports. The proposed design can be expanded to support the intersection of more slot waveguides.

A polarization independent 1  ×  3 equal optical power splitter (OPS) based on the self-collimation effect in two-dimensional (2-D) photonic crystal (PC) is proposed. Two splitter structures are introduced in the self-collimation 2-D PC, both of which have an air layer and a row of defect air holes. The proposed OPS is simulated using Rsoft software combined with plane wave expansion method and two finite-difference time-domain method. The results show that the beam for transverse electric (TE) mode and transverse magnetic (TM) mode can be self-collimated and divided equally into three outputs at the operating wavelength of 1310 nm. The transmission efficiencies are 95% for TE mode and 93% for TM mode, and the corresponding additional losses are 0.223 and 0.315 dB for TE mode and TM mode, respectively. The steady times are lower than 1.4 ps. The proposed polarization independent 1  ×  3 equal OPS will have potential applications in optical fiber communication system.

We proposed and developed an integrated fluorescent oxygen gas-sensor probe module based on asymmetric 1  ×  2 optical waveguides that can transmit power from an optical source and the fluorescence signal with high efficiency simultaneously. The fluorescent oxygen gas-sensor comprises an optical source part, optical detector part, and optical sensing probe part. The optical sensing probe comprises asymmetric 1  ×  2 optical waveguides coated with an oxygen-sensitive fluorescent film on the end face of the optical waveguide. This optical probe module can transmit the optical power and fluorescence signal with high efficiency because of the same optical path for transmission of the optical source and the fluorescence signal. In addition, this structure facilitates an integrated miniature oxygen-sensor module. We optimally designed the asymmetric 1  ×  2 optical waveguides with an asymmetric structure and different two core size. Then, we fabricated the polymeric asymmetric optical waveguides using the UV imprint lithography process suitable for cost-effective mass production. The optical oxygen-sensor probe transmitted the optical source power and the fluorescence signal with 80% and 82% efficiency, respectively. An oxygen-sensitive fluorescent film was coated on the end face of the optical waveguide by using the spray coating method. The oxygen-gas detection sensor constructed using this optical probe module with 1  ×  2 asymmetric optical waveguides could measure the concentration with 0.3% resolution for a gas concentration range of 0% to 25%. This optical oxygen-sensor probe module facilitates a compact, simple, and cheap measurement system.

We have developed fiber-based optical thermocouples (OTCs) for fast temperature sensing in extreme environments. Our OTCs consist of a thin film of dysprosium-doped yttrium aluminum garnet (Dy:YAG)—a well-known two-color thermometry phosphor—deposited on the end of a sapphire fiber using pulsed laser deposition. Temperature sensing is achieved by comparing the relative intensities of photoluminescence arising from two closely spaced Dy^3  + excited states. Using a combination of time-gated detection and blackbody background subtraction, we are able to measure Dy:YAG’s photoluminescence up to 2033 K, which is one of the highest temperatures obtained in literature. However, we are only able to use the photoluminescence spectra for temperature sensing up to 1773 K due to poor signal-to-noise ratio for higher temperatures. These results suggest the possibility of measuring higher temperatures with time-gated detectors designed for low-light levels. After characterizing the fiber-based OTCs’ temperature response, we next demonstrate their functionality using subsecond pulsed CO₂ laser heating using both intensified charge-coupled device detection and a photodiode-based software time-gating technique. In the lab, we have utilized this technique to measure temperatures at rates up to 80 kHz. In addition, we comment on the applicability of OTCs to fast temperature sensing in turbulent flows and estimate rise times on the order of several hundred microseconds for a 1-μm OTC film.

In recent years, traditional complementary metal–oxide–semiconductor (CMOS) scaling techniques have begun to reach the technological limits of available materials. A revolution in block-to-block communication is necessary to meet the ever-growing demand for microprocessor computational power. On-chip optical communication has been designated as a promising solution to circumvent the CMOS scaling bottlenecks: second-order phenomenon, which causes significant interconnect delays, and the nonscalability of the thermal voltage, which becomes significant in submicron CMOS technology. The metal oxide semiconductor quantum well transistor, a silicon-on-insulator metal–oxide–semiconductor field-effect transistor device, with a channel thickness reduced to the single nanometer scale is examined. The nanometric gate oxide, silicon, and buried oxide heterostructure in the channel forms a quantum potential well, creating discrete sub-bands within the silicon layer. Inter-sub-band-transitions within the quantum well may allow for radiative recombination in indirect band gap materials.

We proposed and systematically analyzed the propagation properties of periodic segmented waveguides and nanowire waveguides where the segments and nanowires have been considered to be composed of multilayers of silicon and silica with subwavelength thickness. We demonstrated, through a comprehensive number of numerical simulations involving modal analysis, that the artificial uniaxial negative anisotropy introduced by the multilayered segments or nanowire can be used to engineer waveguides with independent polarization propagation characteristic over the entire band of optical communication frequencies.

A lead selenide (PbSe) NC-based phototransistor memory (PTM), wherein graphene oxide (GO) sheets covered by Au nanoparticles (NCs) act as double charge trapping layers, is studied under near-infrared (NIR) light. The memory window (ΔV_th) can be significantly enlarged by light-assisted programming and erasing processes, wherein the photogenerated carriers in a PbSe NCs channel can be trapped and detrapped by the GO/Au NCs charge-trapping layers. The PTM achieved an enhanced ΔV_th from 0.7 V in the dark to 1.8 V under the NIR light, due to the increasing number of photogenerated charges due to the NIR light. The PTM exhibited high responsivity (R), external quantum efficiency (EQE), and detectivity (D  *  ) of about 13.9  A  /  W, 2.2  ×  10³  %  , and 1.5  ×  10⁸ Jones, respectively. Due to the good photoresponsibility of the PbSe NCs, the PTM exhibited a large ΔV_th under low programming/erasing voltages under the NIR light and realized multilevel memory. The results presented on photoassisted memory may pave a way to large-area, flexible, low-temperature fabrication, and photoreactive memory devices.

A fiber Bragg grating (FBG) pressure sensor using a composite structure comprising a square diaphragm, steel trusses, and vertical beams is proposed and studied. The deflection of the square diaphragm due to the applied pressure is transferred as an axial force on the FBG mounted at the end of the vertical beams. Measurement principle and stress analysis of the pressure sensor are introduced. The experimental results indicate that the pressure sensitivity of the sensor is 622.71  pm  /  MPa across the range of 0 to 2 MPa with a good linearity recorded at 99.996%, and the hysteresis and repeatability of the pressure sensor are calculated to be 0.6639% full-scale output (FSO) and 0.2773% FSO, respectively. In addition, the relative error of the sensor after temperature compensation was found to be 1.46%, which indicates an effective elimination of the effect of the temperature on pressure measurement.

Photoelectric functional material WS₂ thin film on SiC substrate was synthesized. Both 15 and 150 nm thickness of WS₂ film were deposited on an n-doped SiC substrate (7.37  ×  10¹⁹  cm^−  3) by pulsed laser deposition method. Optical properties of the WS₂  /  SiC material were discovered. (I) a photovoltaic effect: (1) there is a cutoff wavelength λ_c (661 nm), which means the wavelength of an incident monochromatic light must be less than λ_c in order to have the photovoltaic effect; (2) the incident light must be polarized. (3) It was found that the maximum open circuit voltage output is 6.3 V in a condition of 40 mW @ 532 nm. (II) Wavelength blueshift: when a laser of 532 nm is used in the experiment to incident perpendicularly through the thin layer WS₂  /  SiC film stack, which is driven by an external electric field, it is found that the 532-nm photons are blueshifted 1.33 nm under a 30 V (DC) voltage. We also find that the blueshift of the laser wavelength is tunable with the applied voltage. Inverse Compton scattering of the photon by both electron and hole is used to explain this blueshift, the consistency of experimental results and the theoretical calculation for the wavelength blueshift was found.