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.     

Design of a panoramic annular lens with a long focal length

A new method to improve the design of the panoramic annular lens (PAL) optical system with long focus is introduced. Cemented lenses are used in a PAL block to improve the design freedom. A multilayer diffractive optical element (MDOE) is used in relay optics to simplify the structure of the system and to increase diffractive efficiency of the design spectral range. The diffractive efficiency of MDOE in a wide spectral range is investigated theoretically. A seven piece PAL system with a total effective focal length of 10.8 mm is realized, and the diffractive efficiency of the whole design wavelength is above 99.3%. A PAL system with all spherical surfaces is described as a comparison.     

Comprehensive focusing analysis of various Fresnel zone plates

A series-form expression for the individual diffracted field of a general annular ring is derived from the Rayleigh-Sommerfeld diffraction integral. It can be used for the accurate and fast simulation of any diffractive focusing element composed of concentric transparent rings. We present a comprehensive analysis, based on the leading term and the linear superposition principle, of the focusing performances of various Fresnel zone plates. Many problems, such as the equivalent aperture function, the diffraction efficiency, the focal spot pattern, the suppression of higher orders and the appearance of "fractional orders," and the explanation for the appearance of Fraunhofer diffraction patterns, are analytically investigated in detail. Because of the great similarity between Fresnel zone plates and multilevel diffractive lenses, most of the obtained results are also applicable to multilevel diffractive lenses.     

Apodized multilevel diffractive lenses that produce desired diffraction-limited focal spots

An apodized, multilevel diffractive lens that can produce a desired diffraction-limited focal spot is proposed for many applications, such as focusing, imaging, optical storage, and optical trapping. The three key points for the design are the innovative idea of complex conjugate subzones, the use of Babinet's principle, and the equivalent-pupil (or aperture) function theory of diffractive focusing elements composed of concentric transparent rings. As a concrete example, we numerically design a mixed multilevel diffractive lens (the highest phase level is 8) to produce a diffraction-limited Gaussian focal spot. Some related problems, such as the validity range and the combination with high-numerical-aperture refractive lenses, are also discussed.     

Harmonic diffractive lenses

The harmonic diffractive lens is a diffractive imaging lens for which the optical path-length transition between adjacent facets is an integer multiple m of the design wavelength λ(o). The total lens thickness in air is mλ(o)/(n - 1), which is m times thicker than the so-called modulo 2π diffractive lens. Lenses constructed in this way have hybrid properties of both refractive and diffractive lenses. Such a lens will have a diffraction-limited, common focus for a number of discrete wavelengths across the visible spectrum. A 34.75-diopter, 6-mm-diameter lens is diamond turned in aluminum and replicated in optical materials. The sag of the lens is 23 μm. Modulation transfer function measurements in both monochromatic and white light verify the performance of the lens. The lens approaches the diffraction limit for 10 discrete wavelengths across the visible spectrum.     

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.     

Diffractive-refractive correction units for plastic compact zoom lenses

A method of designing a plastic zoom lens with a diffractive-refractive hybrid corrector, comprising one diffractive lens and one refractive lens, is described. The efficiency of this method is demonstrated by designing a compact zoom lens for a mobile phone. This zoom design, incorporating lenses made only of two commercial optical plastics (polymethylmethacrylate and polycarbonate), provides high optical performance.     

New Design of High NA Photolithographic Lens Using Diffractive Optical Element

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Fabrication of large-aperture lightweight diffractive lenses for use in space

We describe the advantages of using diffractive (Fresnel) lenses on thin membranes over conventional optics for, among others, future space telescope projects. Fabrication methods are presented for lenses on two types of freestanding membrane up to 50 cm in size. The first is a Fresnel lens etched into a thin (380-mum) glass sheet, and the second is an ~50-mum-thick polymer membrane containing a Fresnel lens made by replication process from a specially made fused-silica master. We show optical performance analysis of all the lenses that are fabricated, including a diffraction-limited Airy spot from a 20-m- focal-length membrane lens in a diffractive telescope system.     

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.     

Diffractive-refractive hybrid corrector for achro- and apochromatic corrections of optical systems

The possibility is shown of achro- and apochromatic correction of an optical system with any residual chromatism by completing the system with a diffractive-refractive hybrid corrector comprising one diffractive lens and one or two refractive lenses.     

Diffractive-refractive behavior of kinoform lenses

The connection between the diffractive behavior and the refractive behavior of kinoform lenses is investigated. The image-forming capabilities of the diffractive element are found to be expressed as an interference pattern that is due to a set of associated refractive lenses corresponding to each zone of the kinoform. The coefficient modulating the contribution of each refracting zone is determined. The term linking the point-spread function of a refractive lens and a diffractive lens is also obtained. Spectral and spatial aspects are compared as the diffractive element approaches the refractive limit.     

二元光学折/衍混合消色差望远物镜设计

首先从光栅衍射理论出发导出衍射光学元件的色散公式，并进一步推导出用一种材料进行折／衍混合消色差望远物镜设计的公式。最后给出全折射型、一个混合型消色差和一个改进型消色差望远物镜的例子，并进行了比较。结果说明，混合型透镜的性能优于全折射型透镜，而改进型消色差物镜的总体性能优于原混合消色差物镜     

Toward the diffraction limit with transmissive x-ray lenses in astronomy

We develop an analytical approach to refractive, blazed diffractive, and achromatic x-ray lenses of scalable dimensions for energies from 1 to 20 keV. Based on the parabolic wave equation, their wideband imaging properties are compared and optimized for a given spectral range. Low-Z lens materials for massive cores and rugged alternatives, such as polycarbonate or Si for flat Fresnel components, are investigated with respect to their suitability for diffraction-limited high-energy astronomy. Properly designed "hybrid" combinations can serve as an approach to x-ray telescopes with an enhanced efficiency throughout the whole considered band, nearly regardless of their inherent absorption.     

Ring-toric lens for focus-error sensing in optical data storage

We discuss the design and performance of diffractive ring-toric lenses for focus-error sensing in optical data storage. A ring-toric lens images a point source of light to a ring-shaped image. Focus-error sensing is accomplished by means of monitoring the change in ring radius: The ring expands in response to a diverging wave front, and the ring contracts in response to a converging wave front. We describe the use of a segmented phi detector to generate a focus-error signal (FES). We found that the FES slope, a measure of sensitivity to disk defocus, is higher for the ring-toric lenses described in this paper than for other techniques such as the astigmatic and the obscuration methods. We measured an FES slope of 0.7 per micrometer of disk defocus (mum(-1)). The corresponding theoretical FES slope is 0.96 mum(-1).     

Efficiency analysis of diffractive lenses

Multilevel diffractive optical elements are necessary for achieving high-efficiency performance. Here the diffraction efficiency of a multilevel phase-only diffractive lens is analyzed. Approximate, as well as more accurate, approaches are presented. Both plane-wave and Gaussian illumination are discussed. It is shown that for many practical cases the diffraction efficiency can be determined by only a single parameter that takes into account the spatial bandwidth product as well as the focal length of the lens and the illumination wavelength. The analysis is based on the scalar theory and the thin-element approximation. Justification for doing this is presented. The results are valid for lenses with at least F/5.     

对衍射光学元件温度特性的研究

大多数空间光学仪器的工作环境温度变化范围都较大。对折射元件和衍射元件的温度特性进行了分析,建立了透镜焦距和衍射效率随环境温度的变化关系,并论述了利用衍射光学元件的温度特性实现光学系统消热差的原理和设计方法。     

Self-focusing hidden bar code

A new type of diffractive optical bar code produced by computer-generated holographic technology is proposed. The message in the proposed bar code is hidden in the diffracted light of the bar code element and can be read from the first diffraction order. In contrast to the conventional hidden bar code, which needs a lens to focus the diffracted light, the proposed hidden bar code has a property of self-focusing. This self-focusing ability is achieved by modulating a function of the Fresnel zone plate into the bar code format. Consequently, the read-out process for the information in this hidden bar code avoids the use of a lens. Experiments have shown the feasibility of the proposed bar code and confirmed that it can perform better than the conventional hidden bar code.     

Refractive and diffractive properties of planar micro-optical elements

The refractive and the diffractive properties of planar micro-optical elements are investigated. The transition between purely refractive and purely diffractive planar microlenses is numerically simulated for the example of differently designed phase-matched Fresnel elements. Results obtained from numerical simulations and experiments show that the refractive and diffractive types exhibit a distinctly different behavior in the presence of small fabrication errors or wavelength deviations. Based on these results, design rules for various applications, including low- and high-numerical-aperture lenses and hybrid refractive-diffractive elements, are derived. For a high-numerical-aperture (? /# = 1.0) lens the experimental characterization of the irradiance distribution in the image space is presented and shown to agree well with theoretical predictions.     

Geometrical properties of the X-ray diffraction applied to Laue lenses

An analytical study of the geometrical properties of the X-ray diffraction applied to the case of Laue lenses is reported in this paper. The results of this investigation are analytical equations that describe the point in which a photon is diffracted as a function of the crystal position and of the X-ray source angular coordinates. In addition, the contributions to the lens Point Spread Function of each crystal is described, helping in understanding the optical properties of a Laue lens. The results obtained can be inserted in simulation and image deconvolution softwares for speeding up the calculations.