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A novel, simple, and inexpensive flexible surface-enhanced Raman-scattering (SERS) platform based on common laboratory filter paper modified with T i 3 C 2 T x flakes was reported. T i 3 C 2 T x synthesized from a T i 3 A l C 2 phase with a mixture of HCl and LiF and T i 3 C 2 T x nanosheets were characterized by the TEM, XRD, UV–Vis spectrum, and Raman spectrum. Paper-based substrate has been proven to sample on rough and irregular surfaces. Thus, T i 3 C 2 T x was further manufactured as paper substrate by the immersion method to transfer nanosheets to filter paper. SERS activity of prepared substrate was demonstrated using R6G by the same filter paper modified with and without T i 3 C 2 T x , and various concentrations of R6G were tested to prove the sensitivity of the substrates. Further detection of CV and MG certified the universality of paper substrate based on T i 3 C 2 T x nanosheets for detection of organic pollutants. The uniformity and stability were proved by CV and R6G molecules. This SERS platform combines the advantages of 2D material and flexible paper scaffolds, resulting in a highly sensitive, cost-efficient, and easy-to-manufacture large-scale flexible substrate and is expected to be used in practice.

To assess the aging of oil-paper insulation, an accelerated aging experiment is executed. Raman spectroscopy, a nondestructive detection method with access to component identification and fault diagnosis, is used to analyze the aging of oil-paper insulation. Raman feature of oil-paper insulation aging with a close relationship with the degree of polymerization is obtained based on the concept of quadratic mutual information. By analyzing the relationship between the extracted feature and the degree of polymerization of samples at different aging degrees, the feasibility of reflecting the aging degree of oil-paper insulation is determined. By load analysis, the chemical correlation between the extracted feature and oil-paper insulation aging is clarified. For eight test samples, the prediction error of degree of polymerization based on Raman features is less than 50. These results show that the features extracted in this paper are helpful to realizing the Raman spectrum diagnosis of oil-paper insulation aging.

The objective of this work was to establish the relationship between the calculated subsurface scattered-photon distribution and the mathematical quantity known as point-spread function (PSF). Photon distribution of subsurface scattered light was calculated using the Monte Carlo method developed for describing reflectance and opacity of paper and of images printed on paper. The obtained normalized photon distribution made it possible to separate optical and mechanical components of dot gain for the paper-ink system. In the presented method of obtaining the reflectance profile of a screen element, the PSF convolves with a modelled reflectance profile of that element. It was found that the PSF can be better approximated by means of the Lorentzian function when compared to the Gaussian profile that was used in the past research on this topic.

In practical measurement, we often need to measure the shape of objects with patterns or letters. As far as we know, no paper has ever reported the shape measurement for objects with patterns or letters by Fourier fringe projection profilometry (FPP). In this paper, we propose a method based on the variational decomposition T V − H i l b e r t − L 2 model and multi-scale Retinex (MSR) to measure the shape of objects with patterns and letters by Fourier FPP. In this method, we first use the T V − H i l b e r t − L 2 model to obtain the fringe part, then perform MSR enhancement on the fringe part, and finally decompose the enhanced fringe part with T V − H i l b e r t − L 2 again. We evaluate the performance of this method via application to one computer-simulated noisy fringe projection pattern and two experimental fringe projection patterns with different types of patterns or letters, and comparison with the Fourier transform method, the variational image decomposition T V − H i l b e r t − L 2 model. Furthermore, we apply the proposed method to the dynamic three-dimensional shape measurement of hand posture with pattern. The experimental results show that our method can effectively measure the dynamic shape of objects with patterns or letters from a single-frame fringe projection pattern.

In this paper, the wavelet transform algorithm is used to reduce the noise of ultraviolet (UV) light received signals. An improved calculation method of the wavelet thresholds and a new threshold function are proposed. The new threshold function avoids the discontinuity of the traditional hard threshold function. It can also avoid the constant deviation caused by the traditional soft threshold function. The improved threshold calculation method takes into account the effect of the wavelet decomposition level, and the simulation results show the effectiveness of the proposed method. Compared with other methods, the method proposed in this paper can obtain a better denoising effect.

Traditional micro-Raman spectroscopy technology has the disadvantages of a weak signal and low signal-to-noise ratio. To fix these issues, a cost-effective and rigorous design method is proposed in this paper, whereby a confocal micro-Raman spectroscopy system is designed and built, and a low-cost reflector and high-pass filter are introduced into the Raman signal-receiving module. The Raman light incident is fully perpendicular to the coupling lens by adjusting the reflection angle of the mirror, making the focus of the coupling lens highly conjugate with the focus of the microscope objective, to enhance the intensity of the Raman signal and improve the signal-to-noise ratio. In order to better apply this technology to the detection and study of microplastics in offshore sediments, a reflective illumination light path is used to avoid the visual interference caused by the capillary structure and opacity of the glass cellulose filter membrane. The detection and analysis of the microplastics on the glass cellulose filter membrane have been carried out by the confocal micro-Raman system designed, which is low cost and capable of obtaining good detection results and meeting the requirements of microplastics detection. The system designed in this paper is expected to be applied to the research and development of Raman detection equipment for microplastics in marine sediments, which is beneficial to promote the development of marine microplastic monitoring technology in the world.

For an accurate modeling of natural rainbows, it is necessary to take into account the flattened shape of falling raindrops. Larger drops do also oscillate, and their axes exhibit tilt angles with respect to the vertical. In this paper, I will discuss two rare rainbow phenomena that are influenced by these effects: bright spots belonging to various rainbow orders, but appearing at remarkable angular distances from their traditional locations, as well as triple-split primary rainbows. While the former have not been observed in nature so far, the latter have been documented in a few photographs. This paper presents simulations based on natural drop size distributions using both a geometric optical model, as well as numerically calculated Möbius shifts applied to Debye series data.

Detection accuracy is an important performance indicator of ground-based telescopes and is affected mainly by pointing error, geometric distortion of the optical system, and parameter errors caused by machining error and installation error. To improve detection accuracy, a modified algorithm based on a simulated annealing algorithm is proposed in this paper; this algorithm is able to correct pointing, derive a geometric distortion solution, and re-estimate some parameters of telescopes simultaneously. The efficiency of the proposed method is verified by using the observation data of the telescope, whose aperture is 600 mm under two distortion models (the physical model and polynomial fitting model). The results show that the method presented in this paper can effectively solve the problem of nonconvergence of the distortion solution with a pointing error. The final angle error under the polynomial fitting model is 1.07″, and the pixel error is 0.06 pixels; the errors under the physical model are 1.08″ and 0.07 pixels. The correction effect under the two distortion models is basically the same, but the averaged operation speed based on the physical model is 19.45% faster.

In recent years, Raman spectroscopy techniques have been successfully applied to the area of deep-sea exploration. However, there are still some problems impeding the further application of Raman systems. For example, the large size of an underwater Raman system makes it difficult to deploy on the underwater vehicle. Meanwhile, the sensitivity is often a disadvantage, requiring improvement for detecting more trace components. To solve these problems, a new compact deep-sea in situ Raman spectroscopy system is presented in this paper. The whole system weighs 60 kg and is housed in an L800 mm×ϕ258 mm pressure vessel with an optical window on the front end cap. The main components include a 532 nm Nd:YAG laser, an optics module, a high-throughput spectrograph with 0∼4900 cm−1 spectral range and 8 cm−1 spectral resolution, a TEC-cooled 2000 pixel×256 pixel CCD detector, a PC104 embedded computer, and an electronics module. To evaluate the performance of the newly developed Raman system, systematic experiments have been carried out with solutions in laboratory, and the results have shown that the system limit of detection of SO42− is 0.4 mmol/L. The Raman system has been successfully deployed on a remote-operated vehicle on the Kexue research vessel in June 2015. The typical in situ detection results are presented in this paper, and it is shown that the Raman system is capable of detecting the Raman signal of SO42− and fluorescence of chlorophyll a (chl-a) and chromophoric dissolved organic matter (CDOM) in seawater. With 500 spectra accumulations and some data processing, the Raman signal of HCO3− is obtained. This is the first report of direct measurement of HCO3− by Raman system in in situ experiments. After further optimization, it is hoped to apply the Raman system in seafloor observation networks for long-time carbon cycling research.

Speckle shearing interferometry (shearography) is a full-field strain measurement technique that can be used in vibration analysis. In our case, we apply a method that combines the time-averaging and phase-shifting techniques. It produces binary phase patterns, where the phase changes are related to the zeroes of a Bessel J0 function, typical of time-averaging. However, the contrast and resolution are better compared to traditional time-averaging. In a previous paper, we have shown that this is particularly useful in vibration testing performed under industrial conditions, because fringe patterns are noisier than in quiet laboratory environments. This paper goes a step further in proposing a processing method for estimating the vibration amplitude, for helping non-experts to identify vibration modes. Since shearography measures the spatial derivative of displacement, spatial integration is required. Prior to that, different processes like denoising, binarization, automated nodal line detection, and amplitude assignment are applied. We analyze the performance of the method on synthetic and experimental data, in the function of noise level and fringes density. Results on data acquired in an industrial environment illustrate the good performances of the proposed method.

In the first part of the paper, a CAOS line camera is introduced for spectral imaging of one dimensional (1-D) or line targets. The proposed spectral camera uses both a diffraction grating as well as a cylindrical lens optics system to provide line imaging along the line pixels direction of the image axis and Fourier transforming operations in the orthogonal direction to provide line pixels optical spectrum analysis. The imager incorporates the Digital Micro-mirror Device (DMD)-based Coded Access Optical Sensor (CAOS) structure. The design includes a line-by-line scan option to enable two dimensional (2-D) spectral imaging. For the first time, demonstrated is line style spectral imaging using a 2850 K color temperature white light target illumination source along with visible band color bandpass filters and a moving mechanical pinhole to simulate a line target with individual pixels along 1-D that have unique spectral content. A ~412 nm to ~732 nm input target spectrum is measured using a 38 by 52 CAOS pixels spatial sampling grid providing a test image line of 38 pixels with each pixel providing a designed spectral resolution of ~6.2 nm. The spectral image is generated using the robust Code Division Multiple Access (CDMA) mode of the camera. The second part of the paper demonstrates for the first time the High Dynamic Range (HDR) operation of the Frequency Division Multiple Access (FDMA)-Time Division Multiple Access (TDMA) mode of the CAOS camera. The FDMA-TDMA mode also feature HDR recovery like the Frequency Modulation (FM)-TDMA mode, although at a much faster imaging rate and a higher Signal-to-Noise Ratio (SNR) as more than one CAOS pixel is extracted at a time., Comment: 10 pages

This paper presents multi-path, two-photon excitation cross-section calculations for krypton, using first-order perturbation theory. For evaluation of the two-photon-transition matrix element, this paper formulates the two-photon cross-section calculation as a matrix mechanics problem. From a finite basis of states, consisting of 4 p , 5 s , 6 s , 7 s , 5 p , 6 p , 4 d , 5 d , and 6 d orbitals, electric dipole matrix elements are constructed, and a Green’s function is expressed as a truncated, spectral expansion of solutions, satisfying the Schrödinger equation. Electric dipole matrix elements are evaluated via tabulated oscillator strengths, and where those are unavailable, quantum-defect theory is used. The relative magnitudes of two-photon cross-sections for eight krypton lines in the 190–220 nm range are compared to experimental excitation spectra with good agreement. This work provides fundamental physical understanding of the Kr atom, which adds to experimental observations of relative fluorescence intensity. This is valuable when comparing excitation schemes in different environments for krypton fluorescence experiments. We conclude that two-photon excitation at 212.556 nm is optimal for single-laser, krypton tagging velocimetry or krypton planar laser-induced fluorescence.

článek se zabývá flash-pulzní termografií - metody pro termografické testování. Je popsán experimentální výzkum metody "time power transformation" pro vyhodnocení výsledků flash-pulzní termografie. Je popsán proces měření a vyhodnocení, na příkladech jsou provedeny vyhodnocení různými metodami a je ukázáno porovnání výsledků. Na příkladech jsou prezentovány výhody metody time power transformation. The paper deals with flash-pulse thermography, which is one of the most used thermographic inspection methods. The method is based on flash excitation of an inspected object and an analysis of its thermal response recorded by an infrared camera. This paper deals with a time-power transformation method (P-function) for an evaluation of the flash-pulse thermography measurement. The method is based on a transformation of the measured thermalresponse using a power function of time. An adaptation of the method is introduced, and an experimental investigation of the method is presented. The method and the evaluation procedure are described. A flash-pulse inspection of an experimental sample is performed, and the results of the inspection obtained by the P-function method and by a fast Fourier transform evaluation are compared using a contrast-to-noise ratio ranking. Advantages of the P-function method resulting from its numerical outputs for an estimation of the depth of defects are described. An influence of noise reduction and data preprocessing is discussed

Structured illumination microscopy (SIM) has attracted much research interest due to its high accuracy, strong adaptability, and high efficiency. Existing SIM is mainly based on the phase-shift technique, Hilbert transform technique, and global Fourier transform technique. The phase-shift technique is most widely applied for its higher accuracy, and both the phase-shift technique and Hilbert transform technique suffer from lower speed because multiple images are needed to obtain modulation information for each scanning step. The global Fourier transform technique has a higher speed, but the high-frequency information of the sample will inevitably be lost because a filter window is used. As a result, the global Fourier transform technique is limited to smooth surfaces. In this paper, a fast surface profilometry using SIM is proposed. It is based on the time-domain phase-shift technique (SIM-TPT), which combines one-fringe projection and phase shift. In this proposed measurement system, vertical scanning of the object is synchronized with the switching of the phase-shifted fringe pattern. As a result, only one fringe pattern must be projected, which enables a point-to-point processing defined as the local Fourier transform method in this paper to be utilized to extract the modulation information that will preserve the high-frequency information of the image so it can be applied to both smooth and rough surfaces. Compared to conventional SIM, SIM-TPT has a higher speed because it is a simpler system and can be applied to complex structures such as high roughness surfaces and steep edges.

This paper presents a novel method to achieve absolute three-dimensional shape measurement solely using square binary patterns. This method uses six patterns: three low-frequency phase-shifted patterns and three phase-shifted high-frequency patterns. The phase obtained from the low-frequency phase temporally unwraps the phase obtained from high-frequency patterns. The projector is defocused such that the high-frequency patterns produce a high-quality phase, but the phase retrieved from low-frequency patterns has a large harmonic error that fails the two-frequency temporal phase unwrapping process. In this paper, we develop a computational framework to address the challenge. The proposed computational framework includes four major approaches to alleviate the harmonic error problem: (i) use more than one period of low-frequency patterns enabled by a geometric constraint-based phase unwrapping method; (ii) artificially apply a large Gaussian filter to low-frequency patterns before phase computation; (iii) create an error lookup table to compensate for harmonic error; and (iv) develop a boundary error correction method to alleviate problems associated with filtering. Both simulation and experimental results demonstrated the success of the proposed method.

The encoding and decoding principle of the Hadamard transform spectrometer with a 2D slit-array mask is described in this paper. Based on the Hadamard transform theory, the signal-to-noise ratio (SNR) enhancement of a 2D slit-array Hadamard transform spectrometer is deduced and verified experimentally. Affected by the optical system of the spectrometer, there are differences between the experimental results and theoretical calculations. At the end of this paper, we discuss the influence of the spectrometer's optical system on the SNR enhancement based on the spatial frequency analysis.

The phase-coding method has been widely used for 3D shape measurement, which uses sinusoidal phase-shifting patterns to recover the wrapped phase and the stair phase-coding patterns to determine the fringe order. However, due to random noises and image blurring, the fringe order is always misaligned with the wrapped phase, which will lead to fringe order errors. This paper presents an enhanced phase-coding method to address this misalignment problem by using half-period codewords, in which each codeword is aligned to the half-period of the sinusoidal patterns. Then, two complementary fringe orders with half-period dislocation can be calculated, which can effectively eliminate the fringe order errors. To extend the coding range of stair phase, this paper further develops a computational scheme based on the geometric constraint method. Simulations and experiments have been carried out, and their results confirm that the enhanced method can reliably recover the 3D shape of the measured objects.

The operational reliability directly affects the practical application of optical current transformers (OCTs) in smart substations. As the key component of the OCT, the reliability of the optical current sensor (OCS) largely determines the reliability level of the OCT. This paper proposes a reliability assessment method of the OCS based on accelerated aging tests. The failure modes and failure mechanisms of the OCS are analyzed, and the concept of OCS insertion loss variation is proposed. An allowable range of insertion loss variation is selected as the failure criterion of the OCS. From the viewpoint of the OCS measurement error generated by the quantization error of the analog-to-digital converter, the allowable range of insertion loss variation is obtained. By selecting a high temperature as the accelerated thermal stress, we design the accelerated aging test scheme of the OCS and analyze the sample test data to obtain the activation energy of the OCS insertion loss failure. Based on this activation energy, the median time to failure and instantaneous failure rate curve of the OCS at normal temperature are obtained. The results indicate that the designed OCS has an expected service life of 50 years and a low instantaneous failure rate at normal temperature. This paper provides basic critical reliability analysis data for the system reliability assessment of OCTs.

The structure parameter of the anisotropic atmospheric turbulence is expressed in terms of atmospheric, oceanic anisotropic factors in x and y directions, and the oceanic turbulence parameters, which are the wavelength, the link length, the ratio of temperature to salinity contributions to the refractive index spectrum, the rate of dissipation of mean-squared temperature, and the rate of dissipation of kinetic energy per unit mass of fluid. For the purpose of expressing the structure parameter of the anisotropic atmospheric turbulence in terms of atmospheric, oceanic anisotropic factors and the oceanic turbulence parameters, the spherical wave scintillation indices that are found in weak anisotropic atmospheric turbulence and in weak oceanic turbulence are equated to each other. We aim to utilize the structure parameter expressed in this paper in the evaluations of various physical entities such as the average intensity, scintillation index, and beam spread in anisotropic oceanic turbulence by exploiting the existing solutions for the same physical entities in anisotropic atmospheric turbulence. Use of this structure parameter will help us to obtain the anisotropic oceanic turbulence results easily because such results will be found by just inserting the structure parameter expressed in this paper to the already reported corresponding results of anisotropic atmospheric turbulence. (C) 2019 Optical Society of America

Single-angle infrared (IR) reflectance spectroscopy is a proven and effective method for determining the complex optical constants n and k of condensed matter. The modern method uses a Fourier transform IR spectrometer to record the quantitative reflectance R(ν) spectra followed by application of the Kramers–Kronig transform (KKT) to obtain the complex optical constants. In order to carry out the KKT, it is essential to measure the reflectance spectra to as high and low a frequency (wavenumber) as possible. Traditionally, the reflectance spectra of solid specimens consist of large (typically>10 mm diameter) polished single-crystal faces free of defects or voids. The requirement of a large polished face, however, is not a realistic expectation for many synthetic, geologic, or rare specimens where the size is usually small and the morphology can vary. In this paper we discuss several improvements and considerations to both the hardware and far-IR measurement protocols that lead to more accurate R(ν) values and thus to more accurate n/k values, especially for small (millimeter-sized) specimens where the R(ν) spectrum is concatenated from multiple independent R(ν) spectra from overlapping hardware/spectral domains. Specifically, the improved hardware and analyses introduced here include the following: (1) providing a set of far-IR calibration standards; (2) custom-designing and manufacturing low reflectivity, stray-light reducing sample masks for small specimens; (3) minimizing stray light interaction between the sample mask, the interferometer Jacquinot stop, and the detector; (4) optimizing the methods to “splice” together the spectra from independent domains; (5) discussing what methods one can use to obtain or calculate the important R(0 cm−1) value; (6) using a quartic relationship to extrapolate from the measured R data to R(0); and (7) accounting for the limiting effects of diffraction for the spot size at the sample mask and detector for millimeter-sized specimens, especially at the very long wavelengths. These seven considerations are all highly interconnected and are discussed in turn, as well as their strong interdependencies. This paper presents a holistic approach for determining reliable n/k values of millimeter-sized samples using single-angle reflectance in the mid- and far-IR.

Space object detection is of great importance in the highly dependent yet competitive and congested space domain. The detection algorithms employed play a crucial role in fulfilling the detection component in the space situational awareness mission to detect, track, characterize, and catalog unknown space objects. Many current space detection algorithms use a matched filter or a spatial correlator on long-exposure data to make a detection decision at a single pixel point of a spatial image based on the assumption that the data follow a Gaussian distribution. Long-exposure imaging is critical to detection performance in these algorithms; however, for imaging under daylight conditions, it becomes necessary to create a long-exposure image as the sum of many short-exposure images. This paper explores the potential for increasing detection capabilities for small and dim space objects in a stack of short-exposure images dominated by a bright background. The algorithm proposed in this paper improves the traditional stack and average method of forming a long-exposure image by selectively removing short-exposure frames of data that do not positively contribute to the overall signal-to-noise ratio of the averaged image. The performance of the algorithm is compared to a traditional matched filter detector using data generated in MATLAB as well as laboratory-collected data. The results are illustrated on a receiver operating characteristic curve to highlight the increased probability of detection associated with the proposed algorithm.

Conventional deformable mirrors (DM) cannot meet the requirement of aberration controlling for advanced lithography tools. This paper illustrates an approach using the property that deformation of a thin plate is similar to optical modes to realize a high fidelity multimode deformable mirror whose deformation has characteristics of optical aberration modes. The way to arrange actuators is also examined. In this paper, a 36-actuator deformable mirror is taken as an example to generate low-order Zernike modes. The result shows that this DM generates the fourth fringe Zernike mode (Z4) defocus, and primary aberration Z5-Z8 with an error less than 0.5%, generates the fifth-order aberration Z10-Z14, and generates the seventh-order aberration Z17-Z20 with an error less than 1.1%. The high fidelity replication of the Zernike mode indicates that the DM satisfies the demand of controlling aberrations corresponding to the first 20 Zernike modes in an advanced lithography tool.

Polarized radiation fields in a turbid medium are influenced by single-scattering properties of scatterers. It is common that media contain two or more types of scatterers, which makes it essential to properly mix single-scattering properties of different types of scatterers in the vector radiative transfer theory. The vector radiative transfer solvers can be divided into two basic categories: the stochastic and deterministic methods. The stochastic method is basically the Monte Carlo method, which can handle scatterers with different scattering properties explicitly. This mixture scheme is called the external mixture scheme in this paper. The deterministic methods, however, can only deal with a single set of scattering properties in the smallest discretized spatial volume. The single-scattering properties of different types of scatterers have to be averaged before they are input to deterministic solvers. This second scheme is called the internal mixture scheme. The equivalence of these two different mixture schemes of scattering properties has not been demonstrated so far. In this paper, polarized radiation fields for several scattering media are solved using the Monte Carlo and successive order of scattering (SOS) methods and scattering media contain two types of scatterers: Rayleigh scatterers (molecules) and Mie scatterers (aerosols). The Monte Carlo and SOS methods employ external and internal mixture schemes of scatterers, respectively. It is found that the percentage differences between radiances solved by these two methods with different mixture schemes are of the order of 0.1%. The differences of Q/I, U/I, and V/I are of the order of 10−5 ~ 10−4, where I, Q, U, and V are the Stokes parameters. Therefore, the equivalence between these two mixture schemes is confirmed to the accuracy level of the radiative transfer numerical benchmarks. This result provides important guidelines for many radiative transfer applications that involve the mixture of different scattering and absorptive particles.

The single-pattern Fourier transform profilometry (FTP) and double-pattern modified FTP methods have great value in high-speed three-dimensional shape measurement, yet it is difficult to retrieve absolute phase pixel by pixel. This paper presents a method that can recover absolute phase pixel by pixel for the modified FTP method. The proposed method uses two images with different frequencies, and the recovered low-frequency phase is used to temporally unwrap the high-frequency phase pixel by pixel. This paper also presents the computational framework to reduce noise impact for robust phase unwrapping. Experiments demonstrate the success of the proposed absolute phase recovery method using only two fringe patterns.

A Lie algebraic method for propagation of the Wigner quasi-distribution function under quadratic Hamiltonian was presented by Zoubi and Ben-Aryeh. We show that the same method can be used in order to propagate a rather general class of quasi distribution functions, which we call "Gaussian class". This class contains as special cases the well-known Wigner, Husimi, Glauber and Kirkwood-Rihaczek quasi-distribution functions. We present some examples of the calculation of the time-evolution of those functions., Comment: This paper was published in Applied Optics and is made available as an electronic reprint with the permission of OSA. The paper can be found at http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-53-8-1648 Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law

In a recent paper [J. Opt. Soc. Am. A 29, 2038 (2012)], we proposed a generalized high spatial resolution zonal wavefront reconstruction method for lateral shearing interferometry. The test wavefront can be reconstructed with high spatial resolution by using linear interpolation on a subgrid for initial values estimation. In the current paper, we utilize the difference between the Zernike polynomial fitting method and linear interpolation in determining the subgrid initial values. The validity of the proposed method is investigated through comparison with the previous high spatial resolution zonal method. Simulation results show that the proposed method is more accurate and more stable to shear ratios compared with the previous method. A comprehensive comparison of the properties of the proposed method, the previous high spatial resolution zonal method, and the modal method is performed.

This paper reports a ZnSe-material phase mask that is applied to athermalization of a conventional infrared imaging system. Its principle, design, manufacture, measurement, and performance validation are successively discussed. This paper concludes that a ZnSe-material phase mask has a permissible manufacturing error 2.14 times as large as a Ge-material phase mask. By constructing and solving an optimization problem, the ZnSe-material phase mask is optimally designed. The optimal phase mask is manufactured and measured with a form manufacturing error of 1.370 μm and a surface roughness value of 9.926 nm. Experiments prove that the wavefront coding athermalized longwave infrared (LWIR) imaging system works well over the temperature range from -40°C to +60°C.

The continuous linear canonical transform (LCT) can describe a wide variety of paraxial (quadratic phase) first-order optical systems. Digital algorithms to numerically calculate the LCT are therefore important in modeling the field propagations and are also of interest for many digital signal-processing applications. The continuous LCT is additive (and unitary), but discretization can destroy additivity. In this paper, the general constraint sufficient to ensure the discrete LCTs are additive is derived. Often, we wish to decompose the transform into a series of more computationally efficient steps. Having previously discussed the unitarity of such algorithms, in this paper we consider how our additivity constraint applies to the direct method (DM) and spectral method (SM) algorithms. Examples are presented showing how to correct nonadditive calculations and to appropriately choose parameters.

This paper proposes a spectropolarimetric detection method based on three photoelastic modulators (3PEMs) and an acousto-optic tunable filter (AOTF). Operating the 3PEMs at slightly resonant frequencies (ωsub1/sub,ωsub2/sub,ωsub3/sub) generates a different frequency signal that modulates the polarized component of the incident light at a low-frequency (0, 2ωsub1/sub-2ωsub3/sub, ωsub2/sub-ωsub3/sub). The frequency of the low-frequency modulation component is two to three orders of magnitude lower than the resonant frequency of any of the 3PEMs so the general area array detector can realize the detection. I, Q, and U of the incident light's Stokes parameters can be obtained in only one detection by extracting the low-frequency component from the detector's signals, and then combining it with an AOTF to finally realize the spectropolarimetric imaging detection. The paper introduces the basic principle, preliminarily verifies feasibility through a corresponding numerical simulation and experiment, and makes an error analysis on the polarization detection results according to factors of difference frequency and phase delay amplitude. The theory has potential application value to spectropolarimetric technology.

Experimental data with multiple overlapping spectral lines must often be fitted to theoretical line shape models. This paper describes an efficient program for performing least-squares fits of such data to Galatry and Voigt profiles. The algorithm and program design considerations are presented in detail, and some examples are given to demonstrate its use. The procedure described in this paper may also be used for more complex line shape profiles.

This paper is a 1-D analysis of the degradation caused by image sampling and interpolative reconstruction. The analysis includes the sample-scene phase as an explicit random parameter and provides a complete characterization of this image degradation as the sum of two terms: one term accounts for the mean effect of undersampling (aliasing) and nonideal reconstruction averaged over all sample-scene phases; the other term accounts for variations about this mean. The results of this paper have application to the design and performance analysis of image scanning, sampling, and reconstruction systems.

The spatial structure of the optical field on the detector of a laser Doppler velocimeter is examined. It is shown that for sufficiently small scatterers, the optical field is a traveling wave of shape determined by the detector optics alone. The direction of travel of the optical field reflects that of the scattering particle. Thus, the direction of motion of the particle is determined by temporal correlation of photocurrents from two spatially offset detector arrays. The arrays also eliminate the Doppler pedestal as shown by Ogiwara (1979). In this paper, the theory of the new method is described; experimental implementation will be described in a complementary paper.

In this paper, it is proven that for any optical system with a circular exit pupil and wavefronts affected by any aberrations, the borders of all leaving rays are caustic surfaces and/or marginal rays. Several examples are shown for wavefronts affected by linear combinations of Zernike aberrations.

A 1.55-microm continuous-wave heterodyne Doppler lidar (HDL) with three receiver-detector units is used to validate experimentally the findings presented in the Guerit et al. companion paper [Appl. Opt. 41, 2232 (2002)] on the effectiveness of independent realizations to improve HDL performance (velocity or power estimates or both) at a low carrier-to-noise ratio (CNR). In fact, noise has a detrimental effect on the accumulation techniques, so in the Guerit et al. companion paper, the chances of getting "heavy" speckles in HDL signal from many receiver-detector units on a single- or several-shot basis are investigated theoretically and numerically with the Zrnic HDL model. The experimental results enable us to conclude there is a very good agreement (better than 95%) between the performance computed from actual HDL data and from the theoretical prediction.

The unmanned aerial vehicle (UAV) offers unique advantages of autonomous flight capability and small coefficient of risk, and is increasingly being used in harbor-border inspection to ensure security and orderly operation of harbors. In response to the influence of external factors such as electromagnetic interference in harbor-border inspection, this paper utilizes UAV and visible light communication (VLC) to build an efficient system to track maritime targets near the harbor reliably. In a VLC scenario, a geometrical equation for transmitter positioning is first proposed based on the received signal strength of the optical signal emitted by the target. On this basis, linear iterative positioning (LIP) using first-order Taylor expansion is proposed to realize online beam tracking. Furthermore, quadratic approximative iterative positioning (QAIP), a more precise approximation of the geometrical equation, is proposed based on second-order Taylor expansion. Simulation results show that the proposed algorithms can track targets effectively, and QAIP can achieve higher accuracy with no noise or high signal-to-noise ratio. In addition, compared with the geometrical solution, LIP and QAIP have faster computing speeds and fixed overheads.

Phase-shifting profilometry (PSP) is a three-dimensional (3D) measurement method of point-to-point calculation. The consistency of object position is the prerequisite to ensure the successful application of PSP in moving objects. The position information of an object can be well characterized by the modulation patterns, and hence a high-quality modulation pattern is the guarantee of pixel-matching accuracy. In this paper, a generic modulation pattern enhancement method for rigid moving objects based on the Hilbert transform is proposed. First, the Hilbert transform is employed to suppress the zero-frequency components of the fringe pattern, and a hybrid digital filter window is applied to filter out the positive fundamental frequency components for a higher signal-to-noise ratio. Then the grid-based motion statistics for fast, ultra-robust feature correspondence algorithm is used to match the high-quality modulation patterns between two adjacent frames, and the object positions in the three deformed patterns are made consistent by image clipping. Finally, the three-step PSP is used to reconstruct the 3D shape of the measured object. Experimental results demonstrate that the proposed method can substantially improve the quality of the modulation pattern, achieve high-precision pixel matching, and ultimately reduce the motion-introduced phase error.

The Directional Polarimetric Camera (DPC) is the first Chinese multi-angle polarized Earth observation satellite sensor, which was successfully launched on 9 May 2018, onboard the GaoFen-5 satellite in the Chinese High-Resolution Earth Observation Program. The DPC’s observation is one of the most important space-borne multi-spectral, multi-angular polarimetric measurements of the global Earth-atmosphere system at the present stage. Although rigorous radiometric calibration had been performed for the DPC before launch, its in-flight performance may change because of the process of launch, harsh environment of space, and aging of the sensor. Due to the absence of the onboard calibration system, vicarious calibration methods are necessary for the DPC’s in-flight performance monitoring and calibration. In this paper, we adapted the Rayleigh absolute calibration method, the sun glint inter-band calibration method, and the sun glint polarization calibration method to the DPC sensor. First, the calibration errors of these three methods caused by ancillary data uncertainties (e.g., aerosol, chlorophyll concentration, absorption gases amount, and wind speed) were analyzed in detail. The error budgets show that the aerosol parameters (optical thickness and aerosol model) are some of the critical factors affecting both the radiometric and polarimetric calibration accuracies for the Rayleigh and sun glint methods. The DPC radiometric and polarimetric in-flight calibration during its commissioning phase was then implemented. The absolute coefficients of short spectral bands (443, 490, 565, and 670 nm) were calibrated by the well-characterized Rayleigh scattering signal over the ocean. Using the 565 nm band as a reference band, the Rayleigh absolute calibration was then transferred to other bands (443, 490, 670, and 865 nm) through inter-band calibration using the specular reflection of the sun over the ocean. The polarization measurements of the DPC at polarized bands (490, 670, and 865 nm) were calibrated with the polarized reflection of the sun glint over ocean. The preliminary results show that the radiometric sensitivity of the DPC changed very little after launch at the four visible bands. The absolute calibration coefficient differences from pre-flight calibration are smaller than 0.5% at the 443 and 670 nm bands, while they are within ± 2 % at the 490 and 565 nm bands. However, a large deviation at 865 nm band of about 9% from pre-flight calibration was indicated by the sun glint inter-band calibration. The degree of linear polarization measurement of the DPC is validated with high accuracy of about 0.02 at the 865 nm band, while the deviation at 490 and 670 nm bands are relatively larger, reaching 0.04. The DPC/GaoFen-5 shows a good in-flight performance of radiometric measurement and generally reliable polarimetric measurement after launch.

The modal holographic wavefront sensor enables fast measurement of individual aberration modes without the need for time-consuming calculations. However, the measurement accuracy suffers greatly from intermodal crosstalk, caused when the wavefront contains more aberrations than the one to be measured. In this paper, we present sensor optimization to minimize this effect and show the improvement when using Karhunen–Lòeve instead of Zernike modes as the basis. Finally, we show in simulation that an open-loop adaptive optics system based on the optimized sensor can be used to correct the effect of realistic, dynamic atmospheric turbulence on a wavefront and increase its Strehl ratio significantly.

Polarimetric imaging cameras require polarimetric calibration to accurately estimate the incident Stokes vector of incoming radiation. This calibration establishes a relationship between changes in the sensor signal and incident Stokes vector. In the standard procedure, an imager is presented with a set of input Stokes vectors with two different radiance values. In the long-wavelength infrared (LWIR) and mid-wavelength infrared bands, blackbodies with different temperatures are used for each set of Stokes vectors. The radiometric offset is subtracted, and standard radiometric or nonuniformity correction procedures are performed in a separate step. This paper proposes an alternative all-in-one approach that combines radiometric calibration, nonuniformity correction, and polarimetric calibration. The standard and proposed methods are compared for a division-of-time LWIR polarimeter. The proposed calibration method achieves an RMS error of 0.34% compared with the conventional technique’s error of 0.83%, yielding a factor of 2.4 improvement in the reconstructed accuracy of a linear Stokes vector; in addition, it is less time-consuming and less prone to ambient temperature fluctuations than the typical two-point method. The method also accounts for beam wander and narcissus effects and enables simple, straightforward polarimetric measurement.

Terahertz (THz) testing, by the frequency modulated continuous wave (FMCW) system, is often hampered by the limited range resolution. Thus, in this paper, a software method is proposed to reconstruct the range profile, yielding significant improvements in range resolution and in signal parameter extraction. Specifically, the multiple signal characterization algorithm is first introduced to indicate a higher-resolution range profile qualitatively and to acquire the echoes’ initial values. Then, multiple Gaussian functions are applied to fit those echoes in the whole original range profile and to accurately extract the parameters, including the amplitude, range, and width, of each echo. Finally, with these parameters, the range profile can be more precisely and flexibly reconstructed, facilitating the following detection procedure to a great extent. Both the simulated and the real THz data, acquired by a 150–220 GHz FMCW imager, have been used to demonstrate the superiority and effectiveness of our method, qualitatively and quantitatively.

This two-part paper demonstrates the use of wave-optics simulations to model the effects of dynamic speckle. In Part II, we formulate closed-form expressions for the analytical irradiance correlation coefficient, specifically in the image plane of an optical system. These expressions are for square, circular, and Gaussian limiting apertures and four different modes of extended-object motion, including in-plane and out-of-plane translation and rotation. Using a phase-screen approach, we then simulate the equivalent scattering from an optically rough extended object, where we assume that the surface heights are uniformly distributed and delta correlated from grid point to grid point. For comparison to the analytical irradiance correlation coefficient, we also calculate the numerical irradiance correlation coefficient from the dynamic speckle after propagation from the simulated object plane to the simulated image plane. Overall, the analytical and numerical results definitely demonstrate that, relative to theory, the dynamic speckle in the simulated image plane is properly correlated from one frame to the next. Such validated wave-optics simulations provide the framework needed to model more sophisticated setups and obtain accurate results for system-level studies.

This paper describes the dependence of the precision of digital holographic methods on measurement parameters. The predominantly discussed parameters are illumination intensity and its homogeneity, surface microroughness, the influence of measurement geometry, as well as object shape, since most of them can be optimized by experimental arrangement. Frequency sweeping digital holography as well as dual-wavelength digital holography in the Fourier arrangement are tested and the results are discussed. It transpires that the methods are not very sensitive to object microroughness or overall reflectivity. Instead, it is the similarity of signal and reference waves that has the highest impact on measurement. After parameter optimization, the holographic methods can be advantageously used for ground surface measurements in optical workshops.

Morphology-dependent resonances (MDRs) for a coated spherical particle are important because of their extensive applications. However, MDRs for coated spherical particles are more complicated than those for homogeneous particles. In this paper, a general expression is proposed for calculating the scattering efficiency of a specific layer of coated particle. Reformulations of internal scattering efficiency are made, which provides a new, to the best of our knowledge, method to investigate the resonance in the core and in the shell independently. MDRs in the core can be shown in four cases on the outmost scattering efficiency curve. To investigate the reason of the resonance, the relationships between MDRs in the core, outmost scattering efficiency, and partial wave are analyzed. It is numerically shown that the expressions are reliable and efficient, which provides a theoretical fundamental for studying of resonances of multilayered particles and for measurement.

In a previous paper [Appl. Opt.52, 4151 (2013)], we presented the first- and second-order derivatives of a ray for a flat boundary surface to design prisms. In this paper, that scheme is extended to determine the Jacobian and Hessian matrices of a skew ray as it is reflected/refracted at a spherical boundary surface. The validity of the proposed approach as an analysis and design tool is demonstrated using an axis-symmetrical system for illustration purpose. It is found that these two matrices can provide the search direction used by existing gradient-based schemes to minimize the merit function during the optimization stage of the optical system design process. It is also possible to make the optical system designs more automatic, if the image defects can be extracted from the Jacobian and Hessian matrices of a skew ray.

This paper demonstrates the application of a thermometry method in turbulent sooting non-premixed flames using filtered Rayleigh scattering (FRS). Fuel tailoring is used to establish a specific C 2 H 2 -based fuel mixture such that temperature can be determined accurately by a single FRS measurement over the entirety of mixture fraction space, or equivalently, for all relevant thermo-chemical states. Evaluation is performed in a hierarchy of flows to establish measurement precision and accuracy. Initial assessments in a series of heated fuel mixtures; non-sooting, near-adiabatic flat flames; and laminar non-premixed sooting flames show accuracy of the approach over a full range of expected temperatures and high single-shot measurement precision (e.g., 65 < S N R < 80 ) for temperatures between 1900 and 2200 K. Subsequently, 2D temperature measurements are evaluated in a turbulent non-premixed sooting flame. For the current fuel mixture, the local mixture-averaged Rayleigh scattering cross section is nearly constant over all composition space, and thus traditional laser Rayleigh scattering (LRS) is used as a measurement standard in the absence of soot. The results show excellent agreement between the proposed FRS thermometry approach and LRS in non-sooting regions. In the presence of soot, the proposed FRS-based approach shows no signs of interference. In addition, 2D temperature imaging shows high SNR (60–74) over all temperature conditions. Thus, we believe the proposed methodology successfully provides a high-resolution 2D temperature method under turbulent sooting flame conditions.

In this paper, we are concerned with denoising in experimentally obtained electronic speckle pattern interferometry (ESPI) speckle fringe patterns with poor quality. We extend the application of two existing oriented partial differential equation (PDE) filters, including the second-order single oriented PDE filter and the double oriented PDE filter, to two experimentally obtained ESPI speckle fringe patterns with very poor quality, and compare them with other efficient filtering methods, including the adaptive weighted filter, the improved nonlinear complex diffusion PDE, and the windowed Fourier transform method. All of the five filters have been illustrated to be efficient denoising methods through previous comparative analyses in published papers. The experimental results have demonstrated that the two oriented PDE models are applicable to low-quality ESPI speckle fringe patterns. Then for solving the main shortcoming of the two oriented PDE models, we develop the numerically fast algorithms based on Gauss-Seidel strategy for the two oriented PDE models. The proposed numerical algorithms are capable of accelerating the convergence greatly, and perform significantly better in terms of computational efficiency. Our numerically fast algorithms are extended automatically to some other PDE filtering models.

In our previous paper [Appl. Opt.51, 8490 (2012)] we considered the Zernike polynomials for a unit annular ellipse aperture. In that paper many equations were used and were solved by MATLAB language and by hand, and many times these rewritten equations had some written mistakes. In the Diaz and Mahajan comment [Appl. Opt.52, 5962 (2013)] on the work, some remarks were true and others were not. In this reply, we will discuss their comment in detail.

The paper presents a method for automated defect identification from fringe patterns. The method relies on computing the fringe signal’s Wigner–Ville distribution followed by a supervised machine learning algorithm. Our machine learning approach enables robust detection of fringe pattern defects of varied shapes and alleviates the limitations associated with thresholding-based techniques that require careful control of the threshold parameter. The potential of the proposed method is demonstrated via numerical simulations to identify different types of defect patterns at various noise levels. In addition, the practical applicability of the method is validated by experimental results.

Numerical integration of two-dimensional gradient data is an important step for many slope-measuring optical instruments. However, existing methods are limited by low accuracy or data location restrictions. The zonal integration algorithm in this paper is a generalized process that works with unordered data via Taylor series approximations of finite difference calculations. This method does not require iteration, and all significant steps rely on matrix calculations for a least-squares solution. Simultaneous integration and interpolation is achieved with high accuracy and arbitrary data locations.