Sapphire-GaN-based planar integrated free-space optical system

We report on the design and fabrication of a planar integrated free-space optical system working on the basis of binary phase diffractive optical elements (DOEs) realized in GaN on a sapphire substrate. Group III-nitride/sapphire substrates enable the parallel monolithic integration of passive microoptical elements like lenses and gratings as demonstrated here and optoelectronic devices like light emitters and photodetectors on a single wafer. We present an approach for the simultaneous optimization of the efficiency of transmissive and reflective diffractive optical elements processed in a single lithographic etching step.     

遗传算法用于衍射光学元件的优化设计

提出了一种基于遗传算法的衍射光学元件优化设计方法;在衍射光学元件设计中遗传算法运行参数对遗传算法性能有一定的影响:采用较大的群体规模,遗传算法越容易获得最优解;交叉算子越大,遗传算法全局搜索能力越强;选择算子对遗传算法的影响不是太大;如果要进一步提高解的精度,可选取较大的终止代数。数值计算结果表明,用遗传算法优化设计的衍射光学元件,其误差小于 5.2%,衍射效率达到 91.2%。遗传算法很适合衍射光学元件的优化设计。     

Speckle suppression in holographic projection displays using temporal integration of speckle images from diffractive optical elements

Speckles on images in holographic projection displays (HPDs) were efficiently suppressed by the temporal sum of two diffractive images generated from diffractive optical elements (DOEs). Using a modified iterative Fourier transform algorithm, we obtained pairs of phase-only DOEs that generated the diffractive images with high negative correlation coefficients of -0.827 and -0.490 in the one-dimensional and the two-dimensional simulations, respectively. The suppression ratios of the speckles in the two simulations were 0.301 and 0.457, which were 61% and 35% lower, respectively, than the sum of the two uncorrelated images. We have successfully demonstrated that the sum of two negatively correlated images from DOEs can effectively reduce the image speckles and improve the image quality in HPD systems.     

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.     

Design of a diffractive optical element for pattern formation in a bilingual virtual keyboard

Pattern formation is one of the many applications of diffractive optical elements (DOEs) for display. Since DOEs have lightweight and slim nature compared to other optical devices, using them as image projection device in virtual keyboards is suggested. In this paper, we present an approach to designing elements that produce distinct intensity patterns, in the far field, for two wavelengths. These two patterns are images of bilingual virtual keyboard. To achieve this with DOEs is not simple, as they are inherently wavelength specific. Our technique is based on phase periodic characteristic of wavefront using iterative algorithm to design the phase profiles.     

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.     

Phase-shifting shadow moiré based on iterative self-tuning algorithm

We proposed a general algorithm for phase-shifting shadow moiré by an iterative self-tuning algorithm. In our proposed system, the grating is translated in equal distance to introduce phase shifts across the field of view. The proposed algorithm produces accurate phase information with five interferograms and can calibrate the precise phase step during the process of the height demodulation. Compared with the traditional method, the proposed algorithm is insensitive to the height dependent effects, which is the main systematic source of error in phase-shift shadow moiré when reconstructing surfaces from fringe patterns. Numerical simulations and optical experiments show that the proposed method can eliminate the nonuniform phase-shift error and possesses a superior performance to existing typical phase-shifting algorithms.     

Design and analysis of a diffractive optical filter for use in an optoelectronic error-diffusion neural network

The design, fabrication, experimental characterization, and system-performance analysis of a diffractive optical implementation of an error-diffusion filter for use in digital image halftoning is reported. A diffractive optical filter was fabricated as an eight-level phase element that diffuses the quantization error nonuniformly in both the weighting and the spatial dimensions, according to a prescribed algorithm. Ten identical diffractive elements were fabricated on ten different wafers and subsequently characterized experimentally. A detailed error analysis including both fabrication and instrumentation errors was carried out to quantify the performance of the fabrication process as well as the expected system performance of the filters. Halftone system performance was evaluated by use of the experimental filter's performance and both quantitative and qualitative performance metrics. The results of this analysis demonstrate that multiple identical copies of a diffractive optical filter can be produced with sufficient accuracy that no loss in the halftoning system performance results.     

New Design of High NA Photolithographic Lens Using Diffractive Optical Element

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Effects of the spatial frequency composition of the target pattern and the number of quantization levels in diffractive beam shaper design

A mathematical model is derived, and numerical simulation is analyzed for laser beam shaping by using multilevel phase-only diffractive optical elements (DOEs). We used the simulated annealing algorithm to design the beam shapers. The result has an essential effect on the diffractive pattern quality caused by the spatial frequency composition of target patterns for the same incident gaussian beam size and target pattern area. The root mean square error between the diffractive and target patterns is smaller for the target patterns with lower spatial frequencies. Moreover, the effect of spatial frequency composition can be relaxed for the cases of larger incident gaussian beam size. In addition, finer quality control of a diffraction pattern can be obtained by increasing the number of quantization levels at the DOEs.     

Energy control by linking individual patterns to self-repeating diffractive optical elements

In general, as diffractive optical elements formed by use of self-repeating patterns possess beneficial characteristics such as scratch resistance, low design effort, ease of fabrication, and natural formation of large panels, an efficient design methodology that was developed with a modified preserving-the-best strategy of genetic algorithms is presented. Both genetic algorithms and simulated annealing are examined by the Markov-chain stochastic process to create the insight needed to use these two heuristic algorithms efficiently. It was found that adding the preserving-the-best strategy to traditional genetic algorithms guarantees the possibility of locating the global optimum. Combining this sufficient and necessary condition for locating a global optimum for genetic algorithms with the built-in chromosome crossover searching mechanism and its neighborhood identification makes this newly developed genetic algorithm an effective method for designing diffractive optical elements. In our study, a prototype was fabricated based on our case study with the modified genetic algorithm. The performance of this prototype was measured and analyzed. Experimental results are shown to agree well with theoretical predictions.     

Scaling of diffractive and refractive lenses for optical computing and interconnections

We discuss both numerically and analytically how the space-bandwidth product and the information density of lenses scale as functions of their diameter and f-number over many orders of magnitude. This information may be useful for the design of optical computing and interconnection systems. For diffractive lenses, cost is defined as the number of resolution elements the lithographic production system must have; the relationship of this quantity to the space-bandwidth product and information density is also given.     

复谱频域OCT系统高分辨率图像重建

为了提高复杂多层样品层析图像的分辨率,构建了复谱频域光学相干层析成像(CSOCT)系统.由于其在低亮度和高速成像方面相对于时域OCT具有更高的灵敏度,因此在光学相干层析成像系统中具有重要的作用.本文对测试样品二层盖波片进行成像实验,基于光学相干层析基本理论,采用五帧相移算法,最终获得测试样品的复谱频域OCT图像.实验结果表明,该系统可以消除谱频域OCT图像中的寄生项和镜像,改善和提高层析图像的分辨率.     

Diffractive phase elements for beam shaping: a new design method

A design method based on the Yang-Gu algorithm [Appl. Opt. 33, 209 (1994)] is proposed for computing the phase distributions of an optical system composed of diffractive phase elements that achieve beam shaping with a high transfer efficiency in energy. Simulation computations are detailed for rotationally symmetric beam shaping in which a laser beam with a radially symmetric Gaussian intensity distribution is converted into a uniform beam with a circular region of support. To present a comparison of the efficiency and the performance of the designed diffractive phase elements by use of the geometrical transformation technique, the Gerchberg-Saxton algorithm and the Yang-Gu algorithm for beam shaping, we carry out in detail simulation calculations for a specific one-dimensional beam-shaping example.     

波前分割无掩模激光干涉光刻的实现方法

激光干涉光刻不受传统光学光刻系统光源和数值孔径的限制,其极限尺寸CD达到曝光波长 的1/4,研究了波前分割双光束、三光束方法及四光束无掩模激光干涉光刻方法,提出了可用于五光束和多种多光束和多次曝光的梯形棱镜波前分割干涉光刻方法。用自行建立的梯形棱镜波前分割系统进行了多光束干涉曝光实验,得到孔尺寸约220nm的阵列图形。     

Design of fan-out kinoforms in the entire scalar diffraction regime with an optimal-rotation-angle method

An algorithm for the design of diffractive optical phase elements (kinoforms) that give rise to fan-out (i.e., spot) patterns was developed and tested. The algorithm is based on the Helmholtz-Kirchhoff rigorous scalar diffraction integral for the evaluation of the electric field behind the kinoform. The optimization of the kinoform phase modulation is performed with an efficient optimal-rotation-angle method. The algorithm permits any spatial configuration of the locations of the desired spots. For example, the spots (all or some) can be located at large angles to the optical axis (nonparaxial case) or they can be located in the near near field of the kinoform, i.e., where the Fresnel approximation is no longer valid. Two examples of fabricated kinoforms designed with this algorithm are presented.     

Subwavelength surface-relief gratings for stellar coronagraphy

We present a new design of a phase mask coronagraph implemented with subwavelength diffractive optical elements consisting of optimized surface-relief gratings. Phase mask coronagraphy is a recent technique that seeks to accommodate both high dynamic and high angular resolution imaging of faint sources around bright astrophysical objects such as exoplanets orbiting their host stars. The original design we propose is a new, integrated, and flexible solution to the pi phase-shift chromaticity of the phase mask coronagraphs. It will allow broadband observations, i.e., shorter integration times and object characterizations, by means of spectroscopic analysis. The feasibility of the component manufacturing is also considered through a tolerance study.     

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 optimization of diffractive phase elements simultaneously implementing several optical functions

The design of diffractive optical elements that incorporate several optical functions in a single element is discussed. The technique used involves iterative optimization. Aprevious paper is continued, in which initial results with few sampling points were reported. Here new results that involve a large number of sampling points are reported. Because the algorithm is computationally intensive with a large number of data points, the parallel implementation of the algorithm on a MASPAR machine is described. MASPAR is a single-instruction multiple-data machine with 16,384 processors. The computer simulations discussed involve simultaneous wavelength demultiplexing, focusing, and the filtering out of a particular wavelength component. It is shown that satisfactory designs of diffractive optical elements can be achieved by the assignment of only a small number of sampling points on the output plane that adequately specify what is required at each wavelength.     

Wavelength-multiplexing system for single-mode image transmission

The expanding use of optical communication by means of optical fibers and the situation of drastically increasing amounts of data to be transmitted urge the exploration of novel systems permitting the transmission of large amounts of spatial information by fiber with smaller spatial resolution. An optical encoding and decoding system is suggested for transmitting one- or two-dimensional images by means of a single-mode fiber. The superresolving system is based on wavelength multiplexing of the input spatial information, which is achieved with diffractive optical elements. Preliminary experimental results demonstrate the capabilities of the suggested method for the one- and two-dimensional cases.