Ill-posed inverse problem in diffraction optics. tolerance analysis of diffractive lenses and gratings

A method is proposed for the prediction of deviations of the phase polynomial coefficients of diffractive optical elements from their nominal values due to fabrication errors. This problem represents an ill-posed inverse problem in diffraction optics. Its solution is based on the regularization technique resulting in an approximate stable (rather than exact but unstable) solution of the inverse problem. The proposed method can become a useful tool, providing optical designers with a possibility of including these deviations into the tolerance analysis of optical devices.     

Quasi-absolute measurement of aspheres with a combined diffractive optical element as reference

We have already reported a method for the quasi-absolute test of rotationally symmetric aspheres by means of combined diffractive optical elements (combo-DOEs). The combo-DOEs carry the information for the ideal shape of an aspheric surface under test as well as a spherical wave for the measurement at the cat's eye position. An experimental demonstration of the procedure is given. Measurements with two different designs of combo-DOEs have been conducted, and their relative advantages and disadvantages are discussed.     

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.     

Optical design comparison of 60 degrees eyepieces: one with a diffractive surface and one with aspherics

An optical design comparison is made between two 60 degrees field-of-view long-eye-relief eyepieces used for viewing a flat image-intensifier P-43 phosphor screen output. One eyepiece contains both spherical glass elements and plastic aspheric elements. The other eyepiece consists of spherical glass elements and a diffractive surface. Both optical designs were optimized by use of identical system constraints for size and weight. The eyepiece containing the diffractive surface provided an improved modulation transfer function performance and has been fabricated and tested. The fabricated lens characteristics and modulation transfer function performance closely matched the design expectations.     

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.     

Photoresist characterization and linearization procedure for the gray-scale fabrication of diffractive optical elements

We present a procedure for the characterization and the linearization of the photoresist response to UV exposure for application to the gray-scale fabrication of diffractive optical elements. A simple and reliable model is presented as part of the characterization procedure. Application to the fabrication of surface-relief diffractive optical elements is presented, and theoretical predictions are shown to agree well with experiments.     

Geometric phase lens

The design of a lens that modulates the geometric phase of an optical beam by manipulating its polarization is presented. To produce such a geometric phase element with a spatially varying phase function, one needs a wave plate with varying orientation. One can use subwavelength grooves to produce form birefringence, but the variation in orientation generally leads to branch points in the groove pattern. These branch points do not affect the phase of the traversing beam directly because the grooves are subwavelength. However, they do produce errors in the groove orientation, which indirectly leads to errors in the geometric phase function that is implemented. A design procedure is provided to compute the groove pattern for such a rotationally symmetric geometric phase element; and, with the aid of a numerical simulation, the effect of the branch points in the groove pattern on its performance is investigated.     

On-axis diffractive elements with improved signal quality in the presence of fabrication errors and wavelength tolerances

The optical function of diffractive elements is usually strongly dependent on systematic fabrication errors as well as the illumination wavelength which do not only affect the diffraction efficiency but also the intensity distribution in the signal region. In the paper a design and fabrication method for on-axis diffractive elements with significantly improved signal quality in the presence of wavelength changes and fabrication tolerances is discussed. An example of an experimentally realized beam shaper is presented.     

Beam-quality optimization of partially polarized fields

For light fields propagating through rotationally symmetric first-order optical systems, the possibility of improvement of the beam-propagation factor is shown to arise when the vectorial behavior is taken into account. For partially polarized beams, we find the optimized value of the beam-quality parameter that can be attained by using this kind of system. This value is given in terms of the beam qualities associated with the transverse polarization components of the vector field. On the basis of the so-called intensity-moment formalism, the general conditions that should be fulfilled at some plane to reach such an optimized value are determined. A procedure to experimentally get the optimization conditions is also proposed.     

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.     

二元光学元件横向加工误差对衍射效率的影响

横向加工误差包括对准误差和线宽误差,加工误差对衍射效率的影响是二元光学元件研究的重要问题.本文基于标量衍射理论,提出了一种与MATLAB相结合的分层计算方法,重点分析了4阶和8阶二元光学元件横向加工误差和衍射效率的关系.结果表明,控制8阶二元光学元件对准误差,可抑制衍射效率的迅速下降,适当调整线宽能够减小对准误差造成的...     

High-efficiency production of propagation-invariant spot arrays

Tailoring of the transverse intensity profiles of propagation-invariant optical fields is considered. The design of diffractive elements capable of realizing such fields by Fourier synthesis is discussed. High-efficiency realization of finite-aperture approximations of the constructed fields is demonstrated in a system consisting of two multilevel diffractive elements. The first element is a diffractive toroidal lens, which focuses the incident field into a ring pattern. The second diffractive element, located at the focal plane of the first element, introduces the phase modulation necessary to realize the desired transverse intensity profile behind a separate collimating lens. The influence of the fabrication errors of the diffractive elements on the fidelity of the propagation-invariant spot array is simulated, and system-integration aspects based on substrate-mode planar-integrated optics are considered.     

New Design of High NA Photolithographic Lens Using Diffractive Optical Element

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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.     

On-axis beam extinction through diffraction design and analysis

To optimize the functions of the surface-relief diffractive optical elements for optical limiters and other applications, we present a systematic design and analysis with numerical illustrations of the transmission properties of different surface-relief phase gratings and Fabry-Perot elements. The spectral response and the tolerance of fabrication errors have been included. An analysis shows that the blazed grating and the echelon grating, a multilevel element as a substitute of the blazed grating, can make the on-axis transmittance very low (less than 1% with one grating) over the broad visible band with a large tolerance of fabrication errors. The results are highly significant for the design of optical-limiting devices.     

Laser direct-write gray-level mask and one-step etching for diffractive microlens fabrication

High-efficiency diffractive optical elements can be achieved by an increase in the number of phase levels. We present a technique for laser direct-write gray-level masks on high-energy-beam-sensitive glass and one-step etching on the gray-level mask plate for the production of high-efficiency diffractive optical elements. Sixteen-phase-level diffractive microlenses and microlens arrays with a focusing efficiency of approximately 94% have been realized by use of the one-step nonphotolithographic fabrication technique.     

Focusing and the optical transfer function in a rotationally symmetric optical system

Two criteria of focusing in a rotationally symmetric optical system, the focal-amplification ratio and the encircled-energy factor, are expressed by the integrals of the optical transfer function, thus providing a simple relation between these two types of characteristics. The approximation of the optical transfer function of diffractive lenses is made possible on the basis of this relation, as is an estimation of the effect of certain apodizers on the image quality.     

Space-variant interconnections based on diffractive optical elements for neural networks: architectures and cross-talk reduction

Optical architectures for fully connected and limited-fan-out space-variant weighted interconnections based on diffractive optical elements for fixed-connection multilayer neural networks are investigated and compared in terms of propagation lengths, system volumes, connection densities, and interconnection cross talk. For a small overall system volume the limited-fan-out architecture can accommodate a much larger number of input and output nodes. However, the interconnection cross talk of the limited-fan-out space-variant architecture is relatively high owing to noise from the diffractive-optical-element reconstructions. Therefore a cross-talk reduction technique based on a modified design procedure for diffractive optical elements is proposed. It rearranges the reconstruction pattern of the diffractive optical elements such that less noise lands on each detector region. This technique is verified by the simulation of one layer of an interconnection system with 128 x 128 input nodes, 128 x 128 output nodes, and weighted connections that fan out from each input node to the nearest 5 x 5 array of output nodes. In addition to a significant cross-talk reduction, this technique can reduce the propagation length and system volume.     

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。     

Implementation of phase-shift patterns using a holographic projection system with phase-only diffractive optical elements

We proposed a method to implement spatial phase-shift patterns with subdiffraction limited features through a holographic projection system. The input device of the system displayed phase-only diffractive optical elements that were calculated using the iterative Fourier-transform algorithm with the dummy-area method. By carefully designing the target patterns to the algorithm, the diffractive optical elements generated the Fourier-transformed images containing the phase-shift patterns in which the widths of dark lines were smaller than the diffraction limit. With these demonstrations, we have successfully shown that the near-field phase-shift lithographic technique can be realized through an inexpensive maskless lithographic system and can still achieve subdiffraction limited images.