Efficient optimization of diffractive optical elements based on rigorous diffraction models.

An efficient optimization strategy for the design of diffractive optical elements that is based on rigorous diffraction theory is described. The optimization algorithm combines diffraction models of different degrees of accuracy and computational complexity. A fast design algorithm for diffractive optical elements is used to yield estimates of the optimum surface profile based on paraxial diffraction theory. These estimates are subsequently evaluated with a rigorous diffraction model. This scheme allows one to minimize the need to compute diffraction effects rigorously, while providing accurate design. We discuss potential applications of this scheme as well as details of an implementation based on a modified Gerchberg-Saxton algorithm and the finite-difference time-domain method. Illustrative examples are provided in which we use the algorithm to design Fourier array illuminators.     

Iterative Fourier transform algorithm with regularization for the optimal design of diffractive optical elements

There is a trade-off between uniformity and diffraction efficiency in the design of diffractive optical elements. It is caused by the inherent ill-posedness of the design problem itself. For the optimal design, the optimum trade-off needs to be obtained. The trade-off between uniformity and diffraction efficiency in the design of diffractive optical elements is theoretically investigated based on the Tikhonov regularization theory. A novel scheme of an iterative Fourier transform algorithm with regularization to obtain the optimum trade-off is proposed.     

Optimal implementation of a microspectrometer based on a single flat diffraction grating

An analytical model has been developed and applied to explore the limits in the design of a highly miniaturized planar optical microspectrometer based on an imaging diffraction grating. This design tool has been validated as providing the smallest possible dimensions while maintaining acceptable spectral resolution. The resulting planar spectrometer is composed of two parallel glass plates, which contain all components of the device, including a reflective slit and an imaging diffraction grating. Fabrication is based on microelectromechanical system technology and starts with a single glass wafer; IC-compatible deposition and lithography are applied to realize the parts in aluminum, which makes the microspectrometer highly tolerant for component mismatch. The fabricated spectrometer was mounted directly on top of an image sensor and takes up a volume of only 50 mm(3). The measured spectral resolution of 6 nm (FWHM) in the 100 nm operating wavelength range (600-700 nm) is in agreement with a model calculation.     

光栅衍射特性的耦合波分析、计算与讨论

本文从麦克斯韦方程组及电磁场边界条件出发,推导了广泛应用于各类光栅衍射问题的矢量分析方法--严格的耦合波分析方法.针对光栅的衍射特性,编写了基于严格的耦合波分析方法的计算程序,并以TE模情形为例对光栅的衍射效率和收敛性作了数值计算.结果表明,当谐波数不断增加,即便对于厚光栅(d/λ>10)情形,光栅的衍射效率仍将收敛于某一确定值.     

An ultrasonic Gaussian transducer and its diffraction field: theory and practice

In this paper, the authors present a novel way to describe the diffraction field for a Gaussian source, which becomes a Gaussian itself. It is described by the Rayleigh surface integral based on the Huygens' theorem. The derivation does not require the parabolic approximation used by previous authors. An improved spherical button Gaussian transducer design also is presented to verify the theory. A theoretical principle of this design based on electromagnetic theory is developed. Both megahertz and kilohertz experimental results show that the sound fields generated by Gaussian transducers of this design agree very well with the theoretical predictions.     

反射型超声衍射CT迭代重建算法

本文以傅立叶衍射定理为基础,将非均匀傅立叶变换和迭代法相结合,用正则化方法处理迭代的收敛问题,建立了反射型超声衍射成像算法。数据直接在频域中的非均匀频率点上比较,避免了频域内插引入的误差。本算法也减少了采样数据量,降低了运算的复杂度。实验结果表明,在迭代次数不多情况下,重建图像可以达到较好的视觉效果。     

A Simple Diffraction Calculation of Magneto-optical Disc Systems

Abstract

A simple diffraction calculation method for magneto-optical disc systems is described. It is based on the extended scalar theory introduced in this paper. Some calculated results are shown for optical systems with different conditions. This method has a role, especially in the system design.     

Generation of a high depth of focus with constant transversal spot size using a phase-only pupil filter

A novel approach is proposed to obtain an extended depth of focus (DoF) in white light with constant transversal spot size within the DoF. It combines a phase-only pupil filter based on multiplexed radial zones with alternating quartic phase functions. The design is first tested via numerical simulations of the point spread function (PSF) based on the scalar diffraction theory. The results for a fourfold gain of the depth of focus are experimentally verified with a phase-only spatial light modulator liquid crystal device combined with a 3D PSF measurement system. A close conformity between the experimental and simulation results proves the effectiveness of the proposed approach.     

A fast method of calculating diffraction loss between two facing transducers

A fast method of calculating the diffraction loss between two facing circular ultrasonic transducers of unequal size is presented. This problem is directly applicable for minimization of diffraction loss in acoustic lens design. Graphs for amplitude and phase are presented that can be used to design lenses with the optimal transducer size for minimum diffraction loss. The theory is extended to include the diffraction loss determination in anisotropic materials. The results are in good agreement with previous experimental and theoretical results of the equal-transducer-size case. The effect of diffraction on pulsed excitation is also treated.     

Analysis and design of a concave diffraction grating with total-internal-reflection facets by a hybrid diffraction method

A novel hybrid diffraction method is introduced to simulate the diffraction and imaging of a planar-integrated concave grating that has total internal reflection (TIR) facets. The Kirchhoff-Huygens diffraction formula is adopted to simulate the propagation of the lightwave field in the free-propagation region, and a rigorous coupled-wave analysis is used to calculate the polarization-dependent diffraction by the grating. The hybrid diffraction method can be used to analyze accurately the imaging properties as well as the polarization-dependent diffraction characteristics of a concave grating. The dependence of several merit parameters of a concave grating with TIR facets on its basic geometric parameters is studied. Compared with one with metallic echelle facets, a concave grating with TIR facets shows a much lower polarization-dependent loss. Since more performance specifications can be considered in the design of a concave grating than with the conventional scalar method, design error can be reduced greatly with the present hybrid diffraction method.     

Diffractive optical elements as raster-image generators

The use of diffractive optical elements (DOEs) to generate complex raster images for a primarily artistic purpose is dealt with. Aspects of human vision that are relevant for the design of such elements are discussed. A design method based on an iterative Fourier transform algorithm and extended with elements from the direct-binary-search and the simulated-annealing algorithms is described. The proposed method provides a large set of parameters that can be adjusted freely to optimize it for any given design task. For demonstration a phase-only DOE was designed that generates an image of a Chinese dragon as a diffraction pattern. It was realized as a surface-relief element on a planar substrate through multilevel binary lithography and reactive-ion etching. Experimental tests confirm the usefulness of the design and the fabrication procedures to achieve excellent image quality.     

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.     

Computer-generated microcooled reflection holograms in silicon for material processing with a CO(2) laser

We report on the design, fabrication, and testing of multilevel computer-generated reflection holograms in Si for CO(2) laser material processing for laser intensities of <2 kW/cm(2). The holograms are designed with an iterative method based on scalar diffraction theory. In this case the reconstructed intensity distribution is independent of the incident high-power laser mode. For achieving high diffraction efficiencies, multilevel staircase surface topologies are fabricated by multimask and reactive ion-etching technology on the front side of a polished Si wafer. For efficient hologram cooling, a gratinglike structure of microchannels is chemically etched on the back side of the Si wafer. Absorption and deformation measurements have been carried out on both a microcooled flat mirror and a reflection hologram. The maximum deformation amounts to 200 nm and is 10 times smaller than comparable conventional uncoated Cu mirrors. A diffraction efficiency of 88% is achieved with an eight-level reflection hologram and a 30-mm-diameter CO(2) laser beam with a power of 5 kW.     

Diffraction effects of telescope secondary mirror spiders on various image-quality criteria

Diffraction from secondary mirror spiders can significantly affect the image quality of optical telescopes; however, these effects vary drastically with the chosen image-quality criterion. Rigorous analytical calculations of these diffraction effects are often unwieldy, and virtually all commercially available optical design and analysis codes that have a diffraction-analysis capability are based on numerical Fourier-transform algorithms that frequently lack an adequate sampling density to model narrow spiders. The effects of spider diffraction on the Strehl ratio (or peak intensity of the diffraction image), full width at half-maximum of the point-spread function, the fractional encircled energy, and the modulation transfer function are discussed in detail. A simple empirical equation is developed that permits accurate engineering calculations of fractional encircled energy for an arbitrary obscuration ratio and spider configuration. Performance predictions are presented parametrically in an attempt to provide insight into this sometimes subtle phenomenon.     

基于最大熵原理的复合形法及其在边坡稳定分析中的应甩

将最大熵原理应用于基本复合形法的优化计算中,旨在提高算法的寻优成功率.具体步骤为选取复形中熵最大的顶点为寻优点;在复形其余各点的加权中心点与寻优点的连线上,搜索比寻优点改善的新顶点;并替换掉寻优点构成新的复形;如此迭代直至复形中的信息被完全利用.采用基本复合形法和基于最大熵原理的复合形法对两个复杂土坡的最小安全系数进行了搜索,结果表明基于最大熵原理的复合形法的全局搜索能力有了明显改善.     

基于STEP的CAx信息管理与系统集成的研究

结合制造业实施CIMS的整体设计要求，提出了基于STEP集成技术设计新型CAx信息管理与集成系统（CAx-IMIS)的基本构架，全面分析了这一系统应具备的基本功能，以Pro/E工具软件为基础，建立、管理零件信息模型，基于SDAI生成STEP中性文件实现数据交换的基本思路，探讨了在产品全生命周期内产品数据在CAx系统间的交换与共享。     

Optimization of sawtooth surface-relief gratings: effects of substrate refractive index and polarization

The effect of the refractive index of the substrate together with the incident polarization on the optimization of sawtooth surface-relief gratings (SRGs) is investigated. The global optimum diffraction efficiencies of the -1st forward-diffracted order of sawtooth SRGs are 63.3% occurring at n2=1.47 for TE polarization and 73.8% occurring at n2=2.88 for TM polarization. Incident TE polarization has higher optimum diffraction efficiency than TM polarization for all n2<1.85. In contrast, TM polarization has higher optimum diffraction efficiency than TE polarization for all n2>1.85. A polymer (n2=1.5) optimum sawtooth SRG exhibits 62.6% efficiency for TE polarization. A silicon (n2=3.475) optimum sawtooth SRG exhibits 68.6% efficiency for TM polarization. These sawtooth SRGs are compared to right-angle-face trapezoidal SRGs. It is found that the optimum profiles of right-angle-face trapezoidal SRGs have only very slightly increased efficiencies over sawtooth SRGs (0.04% for TE and 0.55% for TM).     

Multiresolution phase retrieval in the fresnel region by use of wavelet transform

A multiresolution (multiscale) analysis based on wavelet transform is applied to the problem of optical phase retrieval from the intensity measured in the in-line geometry (lens-free). The transport-of-intensity equation and the Fresnel diffraction integral are approximated in terms of a wavelet basis. A solution to the phase retrieval problem can be efficiently found in both cases using the multiresolution concept. Due to the hierarchical nature of wavelet spaces, wavelets are well suited to multiresolution methods that contain multigrid algorithms. Appropriate wavelet bases for the best solution approximation are discussed. The proposed approach reduces the computational complexity and accelerates the convergence of the solution. It is robust and reliable, and successful on both simulated and experimental images obtained with hard x rays.     

Optimum structural design with stability constraints

This paper presents an optimization method based on optimality criterion for minimum weight of structures with stability requirements. A recurrence relation is derived and the method is explained in the context of the displacement method of finite element analysis. The incipient buckling of the structure is determined by a linear eigenvalue solution. The method is programmed for trusses and frames. Illustrative problems are given to show the applicability of the method of design of structures with a large number of design variables.