The finite-thickness model applied to designs of closed-boundary cylindrical microlenses with small f-numbers

Instead of the existing zero-thickness model (ZTM), the finite-thickness model (FTM) is employed to designs of closed-boundary cylindrical microlenses (CBCMs) with small f-numbers based on the wave-front interference principle. To demonstrate the superiority of the FTM to the ZTM in the design of CBCMs, focal performance of all the designed microlenses is investigated by the rigorous boundary element method (BEM). For CBCMs with small f-numbers, numerical results by the BEM reveal that the designed CBCMs by using the FTM possess better focal performance than the designed CBCMs by using the ZTM, such as a more exact real focal position, a smaller focal spot size, and a higher diffraction efficiency.     

Focusing performance of the closed-boundary cylindrical microlenses analyzed by the boundary element method

In this paper, we investigate the focusing performance of closed-boundary cylindrical microlenses (CBCMs) based on rigorous electromagnetic theory and the boundary element method. The CBCMs with different incident angles, different quantization-level numbers, different microlens diameters, different f-numbers, and different polarizations of incidence are studied. Several focusing performance measures, such as the focal spot size, the diffraction efficiency, the real focal position, and the normalized transmitted power, are presented. It provides very useful information in designing the CBCMs in micro-optical systems.     

Analysis of closed-boundary cylindrical microlenses with long focal depth designed by the general focal length function

In this paper, the general focal length function is used to design two-dimensional closed-boundary cylindrical microlenses (CBCMs) with long focal depth. The focusing characteristics of the designed microlenses is investigated by rigorous electromagnetic theory and the boundary element method. A number of focusing performance measures of the designed microlenses, such as the real focal depth, the focal depth range, the focal spot size, and the diffraction efficiency, are presented in detailed. As comparison, the focusing performance of the conventional lenses with the same parameters are investigated simultaneously. Our analysis indicates that the general focal length function is valid in designing CBCMs with larger extended focal depth. Comparing with the open-boundary cylindrical microlenses (OBCMs) designed using the same focal length function, we also find that the designed CBCMs with low f-number exhibit superiority of long focal depth.     

Three-dimensional particle image velocimetry: a low-cost 35 mm angular stereoscopic system for liquid flows

A low-cost 35 mm PIV stereoscopic system for liquid flows is presented which has an imaging component cost under US$9000. The system uses an angular configuration, rotating mirror image shifting and in-situ calibration techniques. Image processing algorithms based on cross correlation and bicubic interpolation are also used to calculate the 3D data from the PIV images. Results from an error analysis have shown the system to have in plane errors ranging from 4.15 to 5.95% and out of plane errors of 7.01% providing an f-number of f2 is fixed for all imaging. Subsequent application of the system to a flow field generated by a free falling sphere in wheat syrup have produced results which when compared to previous flow visualisation give good qualitative agreement. Suggested improvements to the PIV system costing US$1300 would allow operation at f-numbers down to f by modifying the cameras for the Scheimpflug condition and using a corrective liquid prism.     

Design of a hybrid diffractive/refractive achromatized telecentric f·θ lens

The design of a hybrid diffractive/refractive achromatized telecentric f·θ lens with a field of view (FOV) 50° and an effective focal length of 750 mm is presented. The optical stop is placed at the front focal plane so that it is a telecentric system. The design is based on a traditional refractive counterpart, and the designed system consists of a hybrid diffractive/refractive lens and four refractive lenses. The designed f·θ lens shows a considerable reduction in weight with a simplified structure, and exhibits superior performance compared to the refractive system. It is emphasized that the designed f·θ lens can be applied to modern color scanning systems that operate in the visible wavelength range with high performance. It can also be applied to high-energy scanning systems. When applying the designed hybrid diffractive/refractive f·θ lens to the high-energy scanning system, a big laser operating in one longitudinal mode can be replaced by a small multi-mode laser, and the scanning system can be simplified greatly with the accuracy improved.     

Measurements of f-numbers for α- and γ-bands of TiO

A pressure-driven shock tube has been used to measure electronic f-numbers for bands (three each) belonging to the α- and γ-band systems of titanium oxide. Observations were made at wavelengths of 6734 Å, 7147 Å, and 7689 Å in the γ-bands, and at 4969 Å, 5183 Å, and 5460 Å in the γ-bands. Observed variations in the f-numbers for a given electronic band system may perhaps be attributed to the interaction between vibrational and electronic motion.     

Parametric model of the BAW resonator phase-noise

Excepted for the very short terms the frequency stability of ultra-stable oscillators is mainly limited by the resonator noise. In this work we proposed a parametric model of the bulk acoustic wave (BAW) resonator phase noise based on an equivalent circuit. This model explains phase noise generated by a BAW crystal from a point of view of parametric fluctuations and proves the f⁻¹ dependences of the crystal noise. The model performance is verified with simulation. Simulation results are compared to experimental data and discussed. Comparison of three existing models is made.     

高维微分-差分模型的Virasoro对称子代数，多线性变量分离解和局域激发模式

寻找高维可积模型是非线性科学中的重要课题.利用无穷维Virasoro对称子代数［σ(f₁),σ(f₂)］=σ(f′₁f₂-f′₂f₁)和向量场的延拓结构理论，能够得到各种高维模型.选取一些特殊的实现，可以给出具有无穷维Virasoro对称子代数意义下的高维微分可积模型.把该方法推广到微分-差分模型上，构造出具有弱多线性变量分离可解性的(3+1)维类Toda晶格.另外，该模型的一个约化方程为具有多线性变量分离可解性的(2+1)维特殊Toda晶格.连续运用对称约化方法可以得到此特殊Toda晶格的一个(1+1)维约化方程具有多线性变量分离可解性.因为得到的精确解里含有低维任意函数，从而可以构造出丰富地局域激发模式，如dromion解，lump解，环孤子解，呼吸子解，瞬子解，混沌斑图和分形斑图等等. 关键词： Virasoro代数 微分-差分模型 变量分离 局域激发模式     

On the Connections between the Non-linearity of Equations of Motion in Quantum Theory,Asymptotic Behavior and Renormalization

It is shown that the ordinary perturbation expressions used in quantum mechanics lead to the wrong asymptotic behavior of the Heisenberg observables as function of time. This difficulty is traced to the non-linearity of the Heisenberg equations of motion and is studied in the context of a one-dimensional non-linear oscillator problem. It is found that the correct asymptotic behavior can be obtained by a process of renormalization analogous to renormalization theory in quantum field theory. It turns out that the renormalized parameters analogous to mass and wave-function renormalization are not c-numbers but are instead q-numbers. It is suggested that the renormalization parameters of quantum field theory are also q-numbers.     

Design of Sandwich Transducer Based on the Equivalent Length Algorithm

The sandwich transducer structure is comprised of three components along its main axis: the back metal cap, piezoelectric ceramic stack and the horn. The purpose of this work is to present a simplified method, referred as the equivalent length algorithm, to design the actuator parameters including each segment length and the resonance frequency f_s. The actuator length L and the propagation wavelength λ along its main axis satisfy the standing wave theory. So, define an equivalent length coefficient for each part of the actuator, and then the sandwich structure is regarded as a single material cylindrical rod with equivalent length L′. According to the standing wave theory, the equivalent length L′ of the actuator can be determined with the given resonance frequency f_s, or vice versa. The phase length of each part of the actuator in the standing wave is optimized freely in the design procedure. The actual length of each part of the actuator is determined by the equivalent length coefficient. Finally, the resonance frequencies of three given actuators are calculated with this method. They are compared with those obtained through Ansys simulation and those measured by an impedance analyzer. The results show agreement.     

Application of epidemic models to phase transitions

The Susceptible-Infected-Recovered (SIR) and Susceptible-Exposed-Infected-Recovered (SEIR) models describe the spread of epidemics in a society. In the typical case, the ratio of the susceptible individuals fall from a value S ₀ close to 1 to a final value S_f , while the ratio of recovered individuals rise from 0 to R_f?=?1???S_f . The sharp passage from the level zero to the level R_f allows also the modeling of phase transitions by the number of “recovered” individuals R(t) of the SIR or SEIR model. In this article, we model the sol–gel transition for polyacrylamide–sodium alginate (SA) composite with different concentrations of SA as SIR and SEIR dynamical systems by solving the corresponding differential equations numerically and we show that the phase transitions of “classical” and “percolation” types are represented, respectively, by the SEIR and SIR models.     

Correction of imaging errors in spatially resolved laser scattering experiments in flames

Imaging errors in spatially resolved measurements using laser scattering techniques in flames are discussed. An experimental method based on Fourier deconvolution to correct the measurements for the imaging errors is presented. The method is especially important when large gradients are recorded with lowf-number lenses in order to obtain a sufficient signal-to-noise ratio. The technique is demonstrated experimentally on OH profiles measured by laser-induced fluorescence in an atmospheric acetylen-oxygen flame.     

Weak electric and magnetic form factors for semileptonic baryon decays in a relativistic quark model

Weak electric and magnetic form factors for semileptonic baryon decays are calculated in a relativistic quark model based on the Dirac equation with the independent-quark confining potential of the formV _q(r)=1/2(1+γ ⁰)(a ² r+V ₀). The values obtained for (g ₂/g ₁) are not very much different from the nonrelativistic results of Donoghue and Holstein. The values of (g ₁/f ₁) extracted from our model calculations of (f ₂/f ₁) in the Cabibbo limit compare well with the experimental values. The values of (f ₂/f ₁) for various semileptonic transitions are also estimated incorporating phenomenologically the effect of nonzerog ₂ in the ratio (g ₁/f ₁). It is found that the SU(3)-symmetry breaking does not generate significant departures in (f ₂/f ₁) values from the corresponding Cabibbo predictions.     

Cumulative Diminuations with Fibonacci Approach,Golden Section and Physics

In this study, physical quantities of a nonequilibrium system in the stages of its orientation towards equilibrium has been formulated by a simple cumulative diminuation mechanism and Fibonacci recursion approximation. Fibonacci p-numbers are obtained in power law forms and generalized diminuation sections are related to diminuation percents. The consequences of the fractal structure of space and the memory effects are concretely established by a simple mechanism. Thus, the reality why nature prefers power laws rather than exponentials ones is explained. It has been introduced that, Fibonacci p-numbers are elements of a Generalized Cantor set. The fractal dimensions of the Generalized Cantor sets have been obtained by different methods. The generalized golden section which was used by M.S. El Naschie in his works on high energy physics is evaluated in this frame.     

On the optical properties of monopole, multipole magnetic lenses

In this paper the spherical and chromatic aberration coefficients for the theoretical model B(Z)=B₀(a/Z)ⁿ, which represented the multipole magnetic lenses, were calculated to express the magnitude analytically. The results are presented in a Tretner's (Optik 16 (1959) 155) form, which is particularly suited to the determination of lenses of optimum performance.     

PbS红外探测器低频噪声物理模型及缺陷表征研究

为了表征PbS薄膜光导红外探测器的材料缺陷,详细推导了1/f和产生-复合(g-r)噪声物理模型,并由实验数据验证了模型的准确性. 利用1/f噪声与表面缺陷关系,计算了不同偏压下表面陷阱密度. 得到该值随偏压升高而增加,由此得出1/f噪声与所加偏压成正比变化,与实验测试结果相一致. 在此模型基础上,研究了g-r噪声与深能级缺陷特征参量的关系,提出由低频噪声表征缺陷激活能、简并因子、俘获截面等缺陷参数的方法. 关键词： 红外探测器 1/f噪声')" href="#">1/f噪声 噪声')" href="#">g-r噪声 缺陷     

A Fixed-Tuned W-Band Waveguide SIS Mixer with 4.0-7.5 GHz IF

The design and performance of a fixed-tuned W-band SIS mixer with a wide band IF of 4.0-7.5 GHz is presented. Waveguide-to-stripline transition of the SIS mixer is designed using the lumped-gap-source port provided by HFSS^TM. Measured receiver noise temperature is less than 25 K in the frequency range of 95-120 GHz, with a minimum value of around 19 K achieved. Mixer noise temperature is determined to be about 8.5 K, which is around twice the quantum limit (i.e., 2hw/k). In spite of the high IF frequencies (f ₀ = 6 GHz), the performance of the SIS receiver is comparable or even superior to those of the best mechanically-tunable waveguide SIS receivers at low IF frequencies (f ₀ = 1.5 GHz). This result suggests that it is easy to design waveguide-to-stripline transitions without scale-model measurements.     

Effect of illumination types on focusing performance of closed-boundary cylindrical microlenses

The effect of illumination types on closed-boundary cylindrical microlenses (CBCMs) is investigated by rigorous electromagnetic theory and boundary element method. As a result, the focusing performance of CBCMs with different illumination types are different to each other, while the optics elements cannot be considered as pure phase element for small f-number.     

一种基于傅里叶变换的分析载波条纹的新方法

针对传统傅里叶变换法处理光载波干涉条纹图时会有边缘效应产生的问题,提出了一种基于傅里叶变换法的外推延拓方法,并从理论上进行了数学推导。为了验证这种方法的正确性,分别对一维数字信号和二维空间载波条纹图进行了数值模拟,进一步分析了误差产生的原因,并与传统的傅里叶变换法对比。结果表明该法可以有效抑制传统傅里叶变换法处理光载波干涉条纹图时边缘效应所造成的较大误差,在基于空间域相位调制技术的波面干涉测量中,对空间载波条纹图进行处理,可以使相位的计算精度达到3.3 mrad。     

Gravitational lensing and <Emphasis Type="Italic">f</Emphasis> (<Emphasis Type="Italic">R</Emphasis>) theories in the Palatini approach

We investigate gravitational lensing in the Palatini approach to the f (R) extended theories of gravity. Starting from an exact solution of the f (R) field equations, which corresponds to the Schwarzschild–de Sitter metric and, on the basis of recent studies on this metric, we focus on some lensing observables, in order to evaluate the effects of the nonlinearity of the gravity Lagrangian. We give estimates for some astrophysical events, and show that these effects are tiny for galactic lenses, but become interesting for extragalactic ones.