Characterization of the phase modulation property of a free-space electro-optic modulator by interframe intensity correlation matrix

Characterization of a phase modulator or phase shifter has always been an integral part of phase-modulating or phase-adjusting applications. We propose a simplified approach to characterize a phase modulator by investigating the performance of phase shifts from grabbed interferograms using the phase extraction method. After reviewing some phase analysis techniques, the interframe intensity correlation (IIC) matrix method is introduced to the investigation. The proposed strategy is illustrated by the measurement of a free-space electro-optic modulator (EOM). Placing the modulator in one arm of a Michelson interferometer, the global phase shifts are estimated by the IIC method from the phase-stepped interferograms. Experimental results demonstrate the tested EOM has a phase modulation response of at least 2π rad with a π/20 rad modulation precision for λ=1064 nm. In addition, our method is applicable to various types of phase modulator or phase shifter calibration, e.g., electro-optic phase modulator, spatial light modulator, or piezoelectric transducer (PZT).     

Theoretical simulation of a polarization modulator based on mechanical rotation of a polarizing element

The properties of three alternative designs for a polarization modulator of potential use for the measurement of vibrational circular dichroism (VCD) are evaluated and compared by use of Mueller calculus. The analysis shows that the combination of a fixed polarizer plus either a photoelastic modulator or a rotating quarter-wave plate possesses nearly the same capability for generation of time-varying, circularly polarized light. However, a modulator composed of a rotating polarizer plus a fixed birefringent plate entails considerable theoretical and experimental difficulties for use in the measurement of VCD spectra. While VCD spectra obtained with the rotating devices can be calibrated in the same manner as spectra obtained with a photoelastic modulator, Mueller analysis shows that the form of the resultant calibration signal will have a different shape. The relevant expressions for VCD and linear dichroism as well as the calibration signals are presented, and consequences for practical realization of these experiments are discussed.     

Improved method for isochromatic demodulation by RGB calibration

The red-blue-green (RGB) calibration technique consists in constructing an a priori calibration table of the isochromatic retardation versus the triplet of RGB values obtained with a RGB CCD camera. In this way a lookup table (LUT) is built in which the entry is the corresponding RGB triplet and the output is the given retardation. This calibration (a radiometric quantity) depends on the geometric and chromatic parameters of the setup. Once the calibration is performed, the isochromatic retardation at a given point of the sample is computed as the one that minimizes the Euclidean distance between the measured RGB triplet and the triplets stored in the LUT. We present an enhanced RGB calibration algorithm for isochromatic fringe pattern demodulation. We have improved the standard demodulation algorithm used in RGB calibration by changing the Euclidean cost function to a regularized one in which the fidelity term corresponds to the Euclidean distance between RGB triplets; the regularizing term forces piecewise continuity for the isochromatic retardation. Additionally we have implemented a selective search in the RGB calibration LUT. We have tested the algorithm with simulated as well as real photoelastic data with good results.     

Retardation correction for photoelastic modulator-based multichannel reflectance difference spectroscopy

The wavelength dependence of the retardation induced by a photoelastic modulator (PEM) is a central issue in multichannel modulator-based spectroscopic ellipsometry and reflectance difference spectroscopy (RDS), where the optical signal is detected simultaneously at different wavelengths. Here we present a refined analysis of the modulator crystal's retardation and its effect on the signal quality. Two retardation correction schemes that take into account the actual wavelength dependence of the stress-optic coefficient are introduced. It is demonstrated experimentally that both methods provide a better correction than the procedure currently used in multichannel RDS. We define quality factors to evaluate the actual performance of the multichannel detection system as compared with a wavelength adaptive single-channel experiment. These quality factors thus provide a useful guideline for choosing the appropriate PEM retardation or reference wavelength in a multichannel experiment.     

Laser coarse-fine coupling scanning method by steering double prisms

Recent developments in optical communication systems have presented an emerging need for scanning and tracking dynamic targets with high accuracy. Unfortunately, conventional scanners have difficulty supplying either sufficient vision information or high scanning resolution because of the fixed optical parameters and optomechanical structure. This paper introduces a novel cascaded double-prism scanner that combines the two scanning modes of rotating and titling motions into a nested device. The analysis results show that both the vertical field angle range and the horizontal field range of the coarse scanning are no less than ±10°, with the scanning accuracy superior to 50 μrad, while the vertical field angle range and the horizontal field range of the fine scanning are, respectively, no less than 2500 μrad and 1200 μrad, with the scanning accuracy superior to 1 μrad. The scanning method not only meets the requirements of collaboratively steering the beam deviation in a large range with high accuracy but also can obtain a variety of scanning modes and trajectories, which has important engineering significance for the solution of steering a fine beam to track and position a dynamical target.     

Bessel function output from an optical correlator with a phase-only encoded inverse filter

We report on a technique for producing a Bessel function correlation output for an arbitrary input pattern. The central dark spot at the center of the Bessel function correlator output is narrower than the width of the normal correlation spot and can be extremely useful for locating the center of the correlation signal. The Bessel function is produced by convolution of the extremely sharp correlation produced by an inverse filter with the Bessel function and is encoded with a single phase-only liquid-crystal spatial light modulator. To encode amplitude information on the filter, we spatially modulate the phase encoded on the filter. Amplitude modulation is obtained by modulation of the diffraction efficiency of the phase grating. Experimental results are presented.     

Intensity and phase measurements of nondiffracting beams generated with a magneto-optic spatial light modulator

Nondiffracting beams are of interest for optical metrology applications because the size of the beam does not change as the beam propagates. However, accuracy can be increased if the diameter of the beam is smaller. One technique for accomplishing this is to use the dark axial intensity profile associated with a higher-order nondiffracting Bessel function beam. We generate these higher-order Bessel function beams with a programmable spatial light modulator. We study the intensity patterns and the phase dependence of these nondiffracting beams. In addition, we examine interference effects caused by recording these patterns onto a binary spatial light modulator.     

Simultaneous measurement of retardance and fast axis angle of a quarter-wave plate using one photoelastic modulator

A method for simultaneous measurement of the retardance and the fast axis angle of quarter-wave plate using one photoelastic modulator is presented. A laser beam passes through a polarizer, a photoelastic modulator, the quarter-wave plate to be measured, and an analyzer to be detected. Before and after the quarter-wave plate is rotated 45° at any initial fast axis direction, two detection signals are obtained to resolve simultaneously the retardance and the fast axis angle. In experiments, a quarter-wave plate was measured with fast axis angles from -89° to 90°. The average and the standard deviation of the retardances at different fast axis directions are respectively 89.50° and 0.17°. The maximum measurement deviation of the fast axis angle is 0.5°. The usefulness of the method is verified.     

Excitation of surface-plasmon polaritons by use of a zeroth-order Bessel beam

We report an experimental result that shows the excitation of surface plasmon polaritons by use of a zeroth-order Bessel beam. From the viewpoint of energy efficiency, the zeroth order Bessel beam is ideal for the local excitation of surface plasmon polaritons on a metal film. We introduce an optical setup using an axicon element in order to carry out the excitation.     

Complete Isochromatic Fringe-order Analysis in Digital Photoelasticity by Fourier Transform and Load Stepping

Abstract:  In this paper, a new fully automated photoelastic technique based on both the Fourier transform and the envelope of the fringe centres, is presented. Using two images of the isochromatics acquired with different loads and a simple calculation routine, the method allows the user the complete determination of the isochromatic fringe retardation on any arbitrary line chosen over the model domain, without the need for supplementary external information or calibration. Various experiments have corroborated the accuracy of the method, estimated theoretically to about 0.07 fringe orders. As a result of its simplicity and sufficient accuracy, the method can be used in the industrial field also by a non-expert user.     

针尖增强拉曼系统高数值孔径物镜对焦方法研究

为提高针尖增强拉曼系统对焦准确性和效率,提出通过分析CCD相机拍摄的光斑图像的像素值实现自动对焦的方法。首先快速粗调焦缩小调焦范围,然后再慢速细调焦提高调焦精度。实验表明:与Tenengrad评价函数相比,方差评价函数更适用于针尖增强拉曼光谱测量系统自动对焦,聚焦到样品表面时对焦结果的无偏估计标准差<0.25μm,具有较高的重复性和鲁棒性;快速粗调焦可提高调焦效率,避免陷入局部最优解;慢速细调焦评价函数曲线在焦点附近呈现“M”形,可通过二次拟合提高调焦精度。     

Accurate polarization measurements with a dual photoelastic modulator

Measurements of the polarization effects in multimirror experiments by using a dual photoelastic modulator are described. The effect of single and multiple mirrors in polarization measurements in two and three dimensions is discussed, and experimental results show how symmetrical placement of mirrors in three-dimensional geometry can eliminate changes in the polarization. Calibration procedures for a dual photoelastic modulator and potential error sources such as misalignment of analyzer, signal dc offset, and neglect of aperture size are presented. Mirror-surface evolution and how it can disturb the polarization measurement are also addressed.     

A domain-reduction approach to bridging-scale simulation of one-dimensional nanostructures

We present a domain-reduction approach for the simulation of one-dimensional nanocrystalline structures. In this approach, the domain of interest is partitioned into coarse and fine scale regions and the coupling between the two is implemented through a bridging-scale interfacial boundary condition. The atomistic simulation is used in the fine scale region, while the discrete Fourier transform is applied to the coarse scale region to yield a compact Green’s function formulation that represents the effects of the coarse scale domain upon the fine/coarse scale interface. This approach facilitates the simulations for the fine scale, without the requirement to simulate the entire coarse scale domain. After the illustration in a simple 1D problem and comparison with analytical solutions, the proposed method is then implemented for carbon nanotube structures. The robustness of the proposed multiscale method is demonstrated after comparison and verification of our results with benchmark results from fully atomistic simulations.     

Range-finding by triangulation with nondiffracting beams

Nondiffracting beams are useful for alignment applications because the size of the beam does not change as the beam propagates. In this research we report a technique that allows for distance measurements with nondiffracting beams. With our approach a diffractive optical element is designed that generates two off-axis, tilted, nondiffracting Bessel function beams. These beams intersect at a desired distance from the input plane, producing interference. We generate these Bessel function arrays with a programmable spatial light modulator allowing external control over the intersection distance.     

Bessel function output from an optical correlator

We introduce a new filter for an optical correlator that produces a Bessel function correlation output. The advantage of this type of output is that the width of the central dark spot at the center of the correlator output is narrower than the width of the usual correlation spot. In addition, the dark spot is insensitive to changes in illumination intensity. We present experimental results with which we write the new filter onto a programmable magneto-optic spatial light modulator.     

New design for a photoelastic modulator

Modulation of the polarization of light can be achieved by a periodical birefringence. A new photoelastic modulator is described in this paper. In comparison with previously described apparatus, the originality of our mounting consists in the production of longitudinal resonance vibrations caused by shear stresses. These are generated by thin ceramics glued to one side of the material, birefringence modulation being thus achieved. Thanks to the use of ceramics, this modulator is much easier to construct than were the previous ones. The stray birefringence is kept very low in this instrument.     

Influence of undissolved second-phase particles on dynamic recrystallization behavior of Mg-7Sn-1Al-1Zn alloy during low-and high-temperature extrusions

This study investigates the effects of fine and coarse undissolved particles in a billet of the Mg-7Sn-1Al-1Zn (TAZ711) alloy on the dynamic recrystallization (DRX) behavior during hot extrusion at low and high temperatures and the resultant microstructure and mechanical properties of the alloy.To this end,partially homogenized (PH) and fully homogenized (FH) billets are extruded at temperatures of 250 and 450 ℃.The PH billet contains fine and coarse undissolved Mg2Sn particles in the interdendritic region and along the grain boundaries,respectively.The fine particles (＜1 μm in size) retard DRX during extrusion at 250 ℃ via the Zener pinning effect,and this retardation causes a decrease in the area fraction of dynamically recrystallized (DRXed) grains of the extruded alloy.In addition,the inhomogeneous distribution of fine particles in the PH billet leads to the formation of a bimodal DRXed grain structure with excessively grown grains in particle-scarce regions.In contrast,in the FH billet,numerous nanosized Mg2Sn precipitates are formed throughout the material during extrusion at 250 ℃,which,in turn,leads to the formation of small,uniform DRXed grains by the grain-boundary pinning effect of the precipitates.When the PH billet is extruded at the high temperature of 450 ℃,the retardation effect of the fine particles on DRX is weakened by their dissolution in the α-Mg matrix and the increased extent of thermally activated grain-boundary migration.In contrast,the coarse Mg2Sn particles in the billet promote DRX during extrusion through the particle-stimulated nucleation phenomenon,which results in an increase in the area fraction of DRXed grains.At both low and high extrusion temperatures,the extruded material fabricated using the PH billet,which contains both fine and coarse undissolved particles,has a lower tensile strength than that fabricated using the FH billet,which is virtually devoid of second-phase particles.This lower strength of the former is attributed mainly to the larger grains and/or absence of nanosized M2Sn precipitates in it.     

Scalar modified Bessel-Gauss beams and waves

For modified Bessel-Gauss beams, the modulating function for the Gaussian, instead of a Bessel function of real argument, is a Bessel function of imaginary argument. The modified Bessel-Gauss beams and their full wave generalizations are treated with particular attention to the spreading properties on propagation for the azimuthal mode numbers m=0 and m=1. The spreading on propagation of the peak and the null in the radiation pattern obtained in the propagation direction for m=0 and m=1, respectively, is substantially less for the modified Bessel-Gauss waves than that for the corresponding Bessel-Gauss waves. The total power transported by the waves is determined and compared with that of the corresponding paraxial beam to assess the quality of the paraxial beam approximation for the wave. The powers in the Bessel-Gauss wave and the modified Bessel-Gauss wave are finite in contrast to that in the Bessel wave. With respect to both the spreading properties and the quality of the paraxial beam approximation, the modified Bessel-Gauss beam is an improvement over the Bessel-Gauss beam.     

Wet packing of blended fine and coarse aggregate

All codified methods for measuring the packing density of aggregate are carried out under dry condition. However, these dry packing methods do not account for the effect of water in the concrete mix. In a previous study, a wet packing method for measuring the packing density of fine aggregate under wet condition has been developed and it was found that the packing density of fine aggregate can be substantially higher under wet condition than dry condition. Nevertheless, many researchers still believe that for coarse aggregate, it does not matter much whether the packing density is measured under dry or wet condition. In this study, the wet packing method was extended to measure the packing density of coarse aggregate and blended fine and coarse aggregate. The results revealed that whilst the packing density of coarse aggregate is only slightly higher under wet condition than dry condition, the packing density of blended fine and coarse aggregate is highly dependent on whether the aggregate is dry or wet. Hence, when measuring the packing density of blended aggregate, the wet packing method should always be used.     

Model reduction for nonlinear multiscale parabolic problems using dynamic mode decomposition

In this article, a model reduction technique is presented to solve nonlinear multiscale parabolic problems using dynamic mode decomposition. The multiple scales and nonlinearity bring great challenges for simulating the problems. To overcome this difficulty, we develop a model reduction method for the nonlinear multiscale dynamic problems by integrating constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) with dynamic mode decomposition (DMD). CEM-GMsFEM has shown great efficiency to solve linear multiscale problems in a coarse space. However, using CEM-GMsFEM to directly solve multiscale nonlinear parabolic models involves dynamically computing the residual and the Jacobian on a fine grid. This may be very computationally expensive because the evaluation of the nonlinear term is implemented in a high-dimensional fine scale space. As a data-driven method, DMD can use observation data and give an explicit expression to accurately describe the underlying nonlinear dynamic system. To efficiently compute the multiscale nonlinear parabolic problems, we propose a CEM-DMD model reduction by combing CEM-GMsFEM and DMD. The CEM-DMD reduced model is a coarsen linear model, which avoids the nonlinear solver in the fine space. It is crucial to judiciously choose observation in DMD. Only proper observation can render an accurate DMD model. In the context of CEM-DMD, we introduce two different observations: fine scale observation and coarse scale observation. In the construction of DMD model, the coarse scale observation requires much less computation than the fine scale observation. The CEM-DMD model using the coarse scale observation gives a complete coarse model for the nonlinear multiscale dynamic systems and significantly improves the computation efficiency. To show the performance of the CEM-DMD using the different observations, we present a few numerical results for the nonlinear multiscale parabolic problems in heterogeneous porous media.