Temporal autocorrelation function for a diffusing-wave spectroscopy experiment with a point source and backscattering detection

The autocorrelation function of the backscattered intensity in a diffusing-wave spectroscopy experiment that uses a point source is calculated by use of the diffusive-wave model. We show that in this approximation the calculated autocorrelation function decays faster than if the plane-source approximation were used. The design of a probe that implements this geometry is presented together with preliminary results that show the utility of the probe as a sizing tool in concentrated dispersions.     

Diffractive optical elements designed for highly precise far-field generation in the presence of artifacts typical for pixelated spatial light modulators

Diffractive optical elements (DOEs) realized by spatial light modulators (SLMs) often have features that distinguish them from most conventional, static DOEs: strong coupling between phase and amplitude modulation, a modulation versus steering parameter characteristic that may not be precisely known (and may vary with, e.g., temperature), and deadspace effects and interpixel cross talk. For an optimal function of the DOE, e.g. as a multiple-beam splitter, the DOE design must account for these artifacts. We present an iterative design method in which the optimal setting of each SLM pixel is carefully chosen by considering the SLM artifacts and the design targets. For instance, the deadspace-interpixel effects are modeled by dividing the pixel to be optimized, and its nearest neighbors, into a number of subareas, each with its unique response and far-field contribution. Besides the customary intensity control, the design targets can also include phase control of the optical field in one or more of the beams in the beam splitter. We show how this can be used to cancel a strong unwanted zeroth-order beam, which results from using a slightly incorrect modulation characteristic for the SLM, by purposely sending a beam in the same direction but with the opposite phase. All the designs have been implemented on the 256 x 256 central pixels of a reflective liquid crystal on silicon SLM with a selected input polarization state and a direction of transmission axis of the output polarizer such that for the available different pixel settings a phase modulation of ~2pi rad could be obtained, accompanied by an intensity modulation depth as high as >95%.     

Diffraction of conic and Gaussian beams by a spiral phase plate

An analytical expression for the spatial spectrum of the conic wave diffracted by a spiral phase plate (SPP) with arbitrary integer singularity of order n is obtained. Conic wave diffraction by the SPP is equivalent to plane-wave diffraction by a helical axicon. A comparison of the conic wave and Gaussian beam diffraction on a SPP is made. It is shown that in both cases a light ring is formed, with the intensity function growing in proportion to rho(2n) at small values of radial variable rho and decreasing as n(2)rho(-4) at large rho. By use of direct e-beam writing on the resist, a 32 level SPP of the 2nd order and diameter 5 mm is manufactured. By use of this SPP, a He-Ne laser beam is transformed into a beam with phase singularity and ringlike intensity distribution. A four-order binary diffractive optical element (DOE) with its transmittance proportional to a linear superposition of four angular harmonics is also manufactured. With this DOE, simultaneous optical trapping of several polystyrene beads of diameter 5 microm is performed.     

True beam smoothing in the fractional fourier transform domain

Abstract

The design of a diffractive optical element (DOE) for true beam smoothing in the fractional Fourier transform domain is described. Based on the Fresnel integrals, the intensity distribution on the output plane is calculated accurately and the discretization error of the spherical phase factor is avoided. The ‘fine design' of the DOE for true beam smoothing is completed with the sampling interval chosen as half of the traditional sampling interval. Simulation results show that the intensity at any point on the output plane fully meets the required demands, not just those sampling points used in the optimization.     

Single-element diffractive optical system for real-time processing of synthetic aperture radar data

I present an optical system for the polar formatting of data in a spotlight-mode synthetic aperture radar. This system is implemented with only one diffractive optical element (DOE). Previously such a DOE could not be produced because the phase of the required transmission function of the DOE does not obey the continuity condition, which is a prerequisite for the conventional implementation of such optical transforms. Here I show how a DOE can be produced to perform the complete polar-formatting transform by incorporating branch-point phase singularities in the transmission function of the DOE. The computation of the transmission function is shown, and numerically computed diffraction patterns obtained from this DOE are also shown.     

Double diffractive optical element system for near-field shaping

Iterative algorithms based on Fourier transform are used for the design of diffractive optical elements (DOEs), which produce a given intensity distribution, usually at the far field. For the near field, these algorithms can also be used by changing the Fourier transform for the Fresnel transform. However, when the distance between the DOE and the observation plane is short, the results obtained with this modification are not always valid. In the present work, we develop a technique for obtaining the desired intensity distribution in the near field using two DOEs in tandem. We have designed an algorithm based on the standard Gerchberg-Saxton algorithm to determine the modulation of the two DOEs. The best results are obtained when the first DOE modulates the amplitude and the second DOE modulates the phase.     

Fan-out diffractive optical elements designed for increased fabrication tolerances to linear relief depth errors

The intensity uniformity of the spots generated by fan-out diffractive optical elements (DOEs) (or kinoforms) is often highly sensitive to any fabrication error that leads to a deviation of the surface-relief depth of the DOE from its design value. Many of the fabrication errors, such as those that are due to insufficient control of development or etch rates, increase almost linearly with the desired relief depth in every position of the DOE. We present an algorithm for designing fan-out DOEs with a significantly reduced sensitivity of the intensity uniformity to such errors. The reduced sensitivity can be obtained without reducing the efficiency of the DOE. Experimental results for fabricated DOEs show that reduced sensitivity is also obtained in practice.     

Diffractive optical elements for intra-cavity beam-shaping of laser modes

Abstract

Diffractive optical elements (DOE) are applied as intra-cavity mode selection devices for customizing the fundamental mode of laser resonators for high power laser systems. Using a phase-conjugating mode selecting element (MSE) in a laser oscillator, we are able to produce a good approximation to a super-Gaussian mode with a near flat intensity profile. This offers higher energy extraction from any following laser amplifiers compared to an unmodified Gaussian TEM₀₀ mode. Two different designs for operation in a 1 m cavity length Nd:YAG master oscillator are presented. Both designs are surface relief phase elements fabricated in fused silica using photolithography with reactive-ion etching to produce 16 level elements for use in transmission. One element is designed to replace the cavity end mirror, while the other stands off an arbitrary distance from the end mirror. A novel iterated design for these transmissive elements is introduced. Numerical results and experimental measurements are presented and discussed.     

Modeling of a short-term stability measuring system of quartz crystal resonators

A new numerical model of a short-term stability measuring system of quartz crystal resonators is presented. It is based on the phase bridge method using a pair of resonators driven by a low-noise source. The output signal, obtained with a phase detector, is proportional to the phase difference introduced by the resonators. The numerical transfer function of each bridge path is given by the model. The output spectral density of the phase fluctuations is computed from these transfer functions and the numerical approximation of the low-noise source. The model was applied to third overtone, SC-cut, 10 MHz BVA quartz crystal resonators. It enables the rejection of the source noise versus the resonant frequency of quartz crystal resonators to be quantified.     

Cause of failure and optimization of a V-belt pulley considering fatigue life uncertainty in automotive applications

High accuracy of dimensions and strength in design requirements are required to produce reliable automotive components with consistent strength distribution. For example, a V-belt pulley is widely used to transmit power between rotational mechanical elements. However, due to defects from the manufacturing process and heterogeneity of materials, different kinds of failure damage may occur in pulleys of identical shape and material. Common applications in the automotive industry include crankshafts, water pumps, air-conditioner compressors and power steering pumps. Although the shape and the usage of pulleys are very simple, evaluating the pulley design is difficult because the loading conditions and installation environment are complicated. This paper focuses on the clutch pulley in the A/C compressor system of automotives and cause of failure was investigated. The applied stress distribution of the pulley under high-tension and torque was obtained by using finite element analysis (FEA) and based on theses results, the life of the pulley with variation in fatigue strength was estimated with a durability analysis simulator. The results for failure probabilities of 50% and 1% were compared with the fatigue life. Incidentally, the purpose of this study was to optimize the fatigue life of vehicle components from the stochastic point of view. The fatigue life was obtained by an approximation function, and the optimum design was verified by fatigue tests considering durability and validity. The design optimization of a V-belt pulley was performed using an approximation function, which improved the fatigue life. A new shape optimization procedure was presented to improve the fatigue life of the pulley in automotive applications and the shape control concept was introduced to reduce the shape design variables. Design of experiment (DOE) was employed to evaluate the design sensitivity of fatigue life with respect to shape design variables.     

Effect of thermal conditions on the stability of a crystallization process from a melt

The stability of a crystallization process from a melt is considered in the approximation of the one-dimensional thermal problem in relation to random displacements of the liquid and solid phase interface as a function of the crystallization conditions.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 30, No. 3, pp. 532–539, March, 1976.     

Analytical solution to the optical transfer function of a scattering medium with large particles

A new analytical expression for the optical transfer function of multiple-scattering media such as clouds, mists, and dust aerosols is given in terms of their microphysical characteristics. The geometrical optics approximation is used to find local optical parameters of a scattering medium, including the simple approximation of the phase function, which is the key to the solution of the problem considered here. The optical transfer function is taken within a small-angle approximation of the radiative transfer theory. A comparison with Monte Carlo data shows a fairly satisfactory accuracy of our analytic formulas.     

Stochastic models of stable frequency and time sources and theirrelationship

Different stochastic models of a stable frequency and time sources showing white phase noise, white frequency noise, and random walk of frequency noise are considered. A continuous time model of phase fluctuations is associated with the power law model of relative frequency fluctuations. The ARIMA (0,2,2) and the Kalman models of the sampled phase derivations are derived from the continuous model. Equations relating the characteristic parameters of these three representations of the source behavior are given. The Allan variance of relative frequency fluctuations is expressed as a function of the characteristic parameters. The approximation inherent to the simplified Kalman model is discussed, and the limit of validity of this model is stated     

Improved accuracy of frequency-domain photon migration close to light source using delta–P1 approximation of the adjustable parameter f

The δ–P1 approximation can improve the accuracy of the diffusion equation in the near field. Usually, the method to determine the fractional forward-scattering peak f in the δ–P1 approximation is to compare the first two moments of the Henyey–Greenstein phase function and those of the δ–Eddington phase function. The error relative to Monte Carlo estimation still exists within a mean free path using the value f above. To overcome this defect, we put forward a new method to determine the parameter f for improving the accuracy of frequency-domain photon migration in the δ–P1 approximation if the detector is close to a light source. Results demonstrate that the adjustable f δ–P1 approximation can accurately predict photon fluence rate at distances less than half the transport mean free paths from the source.     

Catastrophes in wavefront-coding spatial-domain design

Spatial-domain design for wavefront-coding systems frequently simplifies the defining oscillatory integral of the point spread function (PSF) by means of the stationary phase approximation (SPA). Although the SPA applies over much of the support of the PSF, it tends to break down at or near the regions of highest intensity. A branch of mathematics known as catastrophe theory is shown to provide tools that can ferret out important design information precisely at the points where the SPA is unphysical.     

Rigorous electromagnetic design of finite-aperture diffractive optical elements by use of an iterative optimization algorithm

We propose a rigorous electromagnetic design of two-dimensional and finite-aperture diffractive optical elements (DOEs) that employs an effective iterative optimization algorithm in conjunction with a rigorous electromagnetic computational model: the finite-difference time-domain method. The iterative optimization process, the finite-difference time-domain method, and the angular spectrum propagation method are discussed in detail. Without any approximation based on the scalar theory, the algorithm can produce rigorous design results, both numerical and graphical, with fast convergence, reasonable computational cost, and good design quality. Using our iterative algorithm, we designed a diffractive cylindrical lens and a 1-to-2-beam fanner for normal-incidence TE-mode illumination, thus showing that the optimization algorithm is valid and competent for rigorously designing diffractive optical elements. Concerning the problem of fabrication, we also evaluated the performance of the DOE when the DOE profile is discrete.     

声强传感器特性对扫描声强法确定声源声功率的影响

文中以典型的矩形测量面方波扫描路径为例 ,分析了扫描声强法测量声源声功率时双传声器互谱声强传感器的有限差分近似误差、近场效应误差、相位不匹配误差与声源频率、测量面离声源的距离以及声强传感器两传声器间的间隔之间的关系。结果表明根据声源频率合理地选取参数可以减小声强传感器所带来的误差 ,从而为保证扫描声强法测量声源声功率测量准确度提供了依据。     

Symmetry in Partially Coherent Imaging of Semi-transparent Edges

Abstract

The extended linear approximation [1] is applied to defocused imaging of semi-transparent edges. The approximated intensity distributions are given and the influence of the following parameters are studied: edge transparency and phase shift, coherence parameter and defocusing. For an opaque edge and a phase edge approximated intensity curves are compared to curves obtained by the exact calculation with the ‘bilinear transfer function’. It is shown that characteristic effects of the image intensity can be referred to the two transfer functions of the extended linear approximation and that it is possible to separate the influence of the object and the system, which is the principal advantage of the use of transfer functions.     

An innovation funnel process for set-based conceptual design via DOE exploration,DEA selection and computer simulation

This paper presents a conceptual design approach including pattern creation from designers, alternative exploration with a DOE matrix, alternative analysis via computer simulation and alternative selection by DEA analysis. Designers possessing domain knowledge create various design patterns to meet the requirements of product performance and customer expectations. Then, based on these design patterns, the alternatives, considered as decision-making units (DMUs), are extracted from various quality level combinations by following the use of the DOE matrix. The nature of the DOE matrix ensures that distinctive representatives are constructed for all design alternatives. The total alternatives (DMUs) consist of the alternatives associated with all the patterns. Computer simulation with ANSYS software is introduced to convert the quality level combination of each alternative (DMU) into simulated outputs, which are further categorised into DEA inputs and DEA outputs for DEA frontier analysis. Four DEA methods, CCR-min input, CCR-max output, BCC-min input and BCC-max output, are used for analysing typical market representatives resulting from market uncertainty. The found efficiencies are used to rank and select the explored alternatives (DMUs) for the next stage of the detailed design. A bike-frame product is chosen as an example to demonstrate the proposed approach. The results clearly show that the proposed approach enables designers to economically select appropriate design alternatives that satisfy performance expectations during the conceptual design stage.     

Schlieren systems with coherent illumination for quantitative measurements

Schlieren systems with a coherent light source were investigated by the Fourier optics technique. The imaging properties of the systems with various cutoff filters were studied. Systems with a graded piecewise linear filter and a Gaussian step function convolution (graded) filter are considered, demonstrating that the image can be approximated by the geometrical-optics theory of conventional schlieren systems. A nonlinear phase contribution was estimated, allowing for the measurement of strong phase objects. Within the framework of linear approximation the results are described by the phase derivative point-spread function, introduced in this paper as the schlieren point-spread function. In addition, modification of the Lopez cutoff filter is proposed, demonstrating its superiority over the piecewise linear and the Gaussian step convolution filters. Simulations of coherent schlieren imaging as well as phase derivative measurements were performed. Finally, the imaging properties of the schlieren systems with the different filters are compared.