Diffractive optics applied to eyepiece design

Eyepieces often limit the overall optical performance of visual instruments and, because of the wide field-of-view and high-performance requirements, they present a well-known difficult design problem. Improvement of existing eyepieces is limited with the use of conventional design variables. We have designed and fabricated a hybrid diffractive-refractive wide-field (>60°) eyepiece that offers significant improvements over existing conventional eyepieces. The hybrid eyepiece consists of only three common-crown refractive elements and weighs 70% less than an Erfle-type eyepiece, while having enhanced optical performance such as a 50% decrease in pupil spherical aberration and a 25% reduction in distortion. Experimental modulation transfer function results are in excellent agreement with the theoretical performance.     

Diffractive optical elements with modulated zone sizes

Abstract

The standard design for phase-only diffractive optical elements comprises a transformation of the continuous phase function into a surface relief by means of wrapping the phase into regular intervals of M2π. This results in a structure with diffractive zones aligned in a horizontal plane. We present an alternative design concept with modulated zone sizes leading to non-periodic boundary positions and non-aligned surface structures. The diffractive properties are compared to those of conventional diffractive optical elements. It can be shown that they are fully equivalent for the design wavelength, but exhibit a different spectral behaviour for deviating wavelengths. These properties are exploited for the improvement of the optical performance of blazed gratings and diffractive lenses under conditions of deviating wavelengths. Special emphasis is put on the optimization of the ratio between diffractive efficiencies of the design order and other orders for blazed gratings and focusing diffractive lenses, as well as the suppression of interference effects within Gaussian beams collimated with diffractive lenses.     

Spectral properties of multiorder diffractive lenses

Diffractive lenses have been traditionally designed with the first diffracted order. The spectral characteristics of diffractive lenses operating in higher diffracted orders differ significantly from the first-order case. Multiorder diffractive lenses offer a new degree of freedom in the design of broadband and multispectral optical systems that include diffractive optical elements. It is shown that blazing the surface-relief diffractive lens for higher diffraction orders enables the design of achromatic and apochromatic singlets. The wavelength-dependent optical transfer function and the associated Strehl ratio are derived for multiorder diffractive lenses. Experiments that illustrate lens performance in two spectral bands are described, and the results show excellent agreement with the theoretical predictions.     

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.     

Single-point diamond turning and replication of visible and near-infrared diffractive optical elements

High-fidelity diffractive surfaces have been generated with single-point diamond-turning techniques. A key to the success of this technique is the ability to shape the diamond tool tip to provide the optimum phase-relief profile, given manufacturing constraints. Replication technology is used to transfer the phase-relief surface into a thin epoxy or photopolymer layer on a glass substrate. Diffraction efficiency results for a wide range of zone widths are presented to provide the reader with a baseline of expected performance for replicated visible and near-infrared diffractive optical elements. In addition, a new method for analyzing diffractive surface structures is presented. The ray-trace algorithm quickly provides accurate results of predicted diffraction efficiency for arbitrary zone profiles, which is extremely valuable in predicting manufacturing errors.     

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。     

Planar-optic-disk pickup with diffractive micro-optics

An integrated optical-disk pickup with a diffractive planar micro-optic system is proposed. In this device, the beam follows a zigzag optical path inside a glass substrate that is used as a light guide. To fabricate off-axis diffractive optical elements, we have recently developed an electron-beam writing system with a curve-pattern generator. It is demonstrated that a transmission off-axis objective microlens, a reflection twin-focusing beam splitter, and reflection layers were integrated on a glass substrate, and such a diffractive planar micro-optic system exhibited an excellent focusing performance and operated forfocus-error signal detection, as designed.     

Design of two-dimensional polarization-selective diffractive optical elements with form-birefringent microstructures

We describe a design methodology for synthesizing polarization-sensitive diffractive optical elements based on two-dimensional form-birefringent microstructures. Our technique yields a single binary element capable of producing independent phase transformations for horizontally and vertically polarized illumination. We designed two elements for operation at 10.6 microm and fabricated them in silicon. Qualitative experimental results agree with design predictions.     

Planar-integrated talbot array illuminators

We demonstrate the planar integration of Talbot array illuminators designed to generate one-dimensional spot arrays. The array illuminator basically consists of a phase grating and a cylindrical diffractive lens integrated as a single diffractive optical element onto a transparent glass substrate. We discuss various design aspects, and we focus on problems typical for planar-integrated free-space optics like the tilted optical axis of the system. Experimental results and measurements, which were obtained from planar-integrated setups fabricated as surface-relief structures on a transparent glass substrate by use of standard photolithography, are included.     

Diffractive light attenuators with variable transmission

Abstract

A new application of diffractive optical elements (DOEs) for continuous or multistage adjustment of optical radiation intensity is described. The diffractive attenuators are linear or circular gratings (amplitude or phase) with constant period and diffraction efficiency that varies across the grating. The zero order of diffraction is used as the output and transmitted through the grating without angular deviation. The diffractive attenuators, in distinction to conventional analogues, allow one to change the intensity of the light beam according to predetermined function and have no limitations for power of the regulated light beam. These elements can be used in optical systems as a beam splitter with adjusted splitting coefficient. The experimental results on a circular diffractive attenuator fabricated by direct laser writing on a chromium film are presented. The range of transmission variation was 20 times within a 340° angle of attenuator turn. The possibility to use a phase diffractive attenuator as a light radiation modulator for a powerful technological laser is discussed.     

Cost-effective mass fabrication of multilevel diffractive optical elements by use of a single optical exposure with a gray-scale mask on high-energy beam-sensitive glass

We present a method for reproducing diffractive optical elements in quantity. The method is compatible with VLSI microfabrication techniques and involves generating a gray-scale mask. The gray-scale mask is employed in an optical aligner to expose an analog photoresist on any environmentally durable substrate, e.g., glass, quartz, semiconductor, or metal, one exposure for each diffractive optical element. After copies of the mask on the photoresist are developed, many substrates can be processed in parallel in a chemically assisted ion-beam etcher to transfer the microstructures on the analog resists simultaneously onto the surfaces of the substrates.     

Gradient-index rod lens with a high acceptance angle for color use by Na(+) for Li(+) exchange

The relationship between the characteristics of gradient-index rod lenses obtained by ion exchange and their mother glass compositions is studied. It is observed that Li(2)O content, R(2)O (Li(2)O + Na(2)O) content, and the Li(2)O/Na(2)O ratio are important factors in attaining a high acceptance angle and a small field curvature. Thus the gradient-index lens array is fabricated by the use of a newly developed glass composition and its optical performance; the modulation transfer function, luminous intensity, and chromatic aberration are precisely evaluated. The array is found to have a sufficiently high performance to be applicable for color use.     

Achromatic fourier processor with holographic optical lenses

An optical Fourier processor that allows the use of broadband light sources and colored inputs is designed, fabricated, and tested. We develop a design technique based on phase manipulation in the Fourier plane to construct an image processor that provides a chromatically corrected image making use of the good aberrations behavior of symmetrical optical systems. Only a small number of diffractive lenses and one achromatic refractive lens are required to obtain a real image. We verify our design experimentally using holographic lenses, which are presented, owing to their versatility, as a good alternative to expensive blazed diffractive elements.     

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.     

Multichip module with planar-integrated free-space optical vector-matrix-type interconnects

Even in the semiconductor industry, free-space optical technology is nowadays seen as a prime option for solving the continually aggravating problem with VLSI chips, namely, that the interconnect technology has failed to keep pace with the increase in communication volume. To make free-space optics compatible with established lithography-based design and fabrication techniques the concept of planar integration was proposed approximately a decade ago. Here its evolution into a photonic microsystems engineering concept is described. For demonstration, a multichip module with planar-integrated freespace optical vector-matrix-type interconnects was designed and built. It contains flip-chip-bonded vertical-cavity surface emitting laser arrays and a hybrid chip with an array of multiple-quantum-well p-i-n diodes on top of a standard complementary metal-oxide semiconductor circuit as key optoelectronic hardware components. The optical system is integrated into a handy fused-silica substrate and fabricated with surface-relief diffractive phase elements. It has been optimized for the given geometrical and technological constraints and provides a good interconnection performance, as was verified in computer simulations on the basis of ray tracing and in practical experiments.     

New Design of High NA Photolithographic Lens Using Diffractive Optical Element

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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.     

Stray-light effects of diffractive beam-shaping elements in optical microsystems

The use of diffractive beam-shaping elements in hybrid or monolithic microsystems is investigated. Compact optical systems require diffractive structures with small grating periods for creating large deflection angles. Such elements are difficult to fabricate while a low stray-light level is maintained. In addition, because of the small geometrical dimensions and the short propagation lengths in an optomechanical microsystem, any stray light generated by the diffractive structure critically affects the overall optical performance. A model for the estimation of the interference effects between the designed and the unwanted diffraction orders is developed and applied to an example of a collimating diffractive optical element. On the basis of theoretical and experimental results, design rules for the application of diffractive beam-shaping elements in microsystems are derived.     

Asphere testing with a Fizeau interferometer based on a combined computer-generated hologram

Fizeau interferometers with an additional diffractive optical element are frequently used for measuring spherical and aspherical surfaces. We present a new (to our knowledge) optical test method, in which the Fizeau principle is now perfectly fulfilled by generating reference and measuring wavefront on the last optical surface, which carries a diffractive optical element. This method has been examined experimentally by testing a reference f/0.68 spherical mirror and can be applied identically for testing aspheres. Several advantages of this method are discussed and proved experimentally.