Multilayer Diffractive Optical Elements Research Articles

Tailoring Wavelength-Selective Diffraction Efficiency Using Triple-Layer Double-Relief Blazed Gratings Incorporating Materials with Intersecting Dispersion Curves

Diffractive optical elements (DOEs) fundamentally provide the possibility to simultaneously utilize multiple orders for different imaging functions within a system. However, to take advantage of this property, it is necessary to tailor the assignment of specific wavelengths or wavelength ranges with high diffraction efficiency to specific diffraction orders. To achieve this wavelength-selective assignment to different orders, simple diffractive profile shapes are not suitable; instead, multilayer DOEs are required. In this study, we conducted theoretical, scalar investigations on the diffraction efficiency of triple-layer double-relief DOEs for the purpose of tailored wavelength selectivity. Specific materials such as nanocomposites, layer materials, and high-refractive-index liquids with strong dispersion were included, in addition to inorganic glasses, to enable wide design freedom for wavelength selectivity across multiple orders. To simultaneously account for both positive and negative orders, specific material combinations featuring intersecting or touching dispersion curves were utilized. For various material combinations, we calculated significantly different efficiency profiles for multiple orders by varying the relief depths. Further, we discuss the possibility of fine-tuning the efficiency profiles by using high-index liquids as an intermediate layer between two solid profiles, whose dispersion properties can be varied continuously or at least in small steps.

Thickness optimization algorithm to improve multilayer diffractive optical elements performance.

The diffractive zone thicknesses of conventional diffractive optical elements (DOEs) are generally obtained using the thin element approximation (TEA). However, the TEA yields inaccurate results in the case of thick multilayer DOEs (MLDOEs). The extended scalar theory (EST) is an alternative thickness optimization method that depends on the diffractive order and the optimization wavelength. We developed an algorithm to research suitable EST input parameters. It combines ray-tracing and Fourier optics to provide a performance estimate for each EST parameter pair. The resulting "best" MLDOE designs for three different material combinations are analyzed using rigorous finite-difference time-domain. Compared to the TEA, the proposed algorithm can provide performing zone thicknesses.

Optical design of athermalized infrared dual-band annular folded lens with multilayer imaging diffractive optical elements

In order to realize the miniaturization of the infrared dual-band imaging system, a common optical path annular folded lens (AFL) with multilayer imaging diffractive optical element (MIDOE) is designed in this paper. The design principle of the AFL is studied, and the relationship between the obscuration ratio and the field of view is given. For the wide temperature range, the theoretical model of the optimal substrate materials selection for the MIDOE is established to achieve the high diffraction efficiency. According to theory analysis, the infrared dual-band AFL with IRG26-ZNS MIDOE is designed in the mid-wave infrared (MWIR) 3∼5 μm and long-wave infrared (LWIR) 8∼12 μm. The focal length is 50 mm, the equivalent F number is 1, and the full field of view is 14 ° The modulation transfer function (MTF) curves of each field of view are close to the diffraction limit when the spatial frequency is 20lps/mm, and the MTF values are greater than 0.61 and 0.28 in MWIR and LWIR, respectively. When the ambient temperature ranges from -40 °C to 80 °C, the high image quality is achieved in dual-band. In addition, the tolerance analysis is performed to verify machinability of the system. The research in this paper has important significance for the realization of a new generation of the low-cost, integrated dual-band imaging system.

Multilayer diffractive optical element material selection method based on transmission, total internal reflection, and thickness

The polychromatic integral diffraction efficiency (PIDE) metric is generally used to select the most suitable materials for multilayer diffractive optical elements (MLDOEs). However, this method is based on the thin element approximation, which yields inaccurate results in the case of thick diffractive elements such as MLDOEs. We propose a new material selection approach, to the best of our knowledge, based on three metrics: transmission, total internal reflection, and the optical component's total thickness. This approach, called "geometric optics material selection method" (GO-MSM), is tested in mid-wave and long-wave infrared bands. Finite-difference time-domain is used to study the optical performance (Strehl ratio) of the "optimal" MLDOE combinations obtained with the PIDE metric and the GO-MSM. Only the proposed method can provide MLDOE designs that perform. This study also shows that an MLDOE gap filled with a low index material (air) strongly degrades the image quality.

Computational Imaging in Dual-Band Infrared Hybrid Optical System with Wide Temperature Range.

The special dispersion and temperature characteristics of diffractive optical element (DOE) make them widely used in optical systems that require both athermalization and achromatic aberrations designs. The multi-layer DOE (MLDOE) can improve the diffraction efficiency of the overall broad waveband, but its diffraction efficiency decreases with changes in ambient temperature. When the ambient temperature changes, the micro-structure heights of MLDOE and the refractive index of the substrate materials change, ultimately affecting its diffraction efficiency, and, further, the optical transform function (OTF). In this paper, the influence of ambient temperature on the diffraction efficiency of MLDOE in a dual-infrared waveband is proposed and discussed, the diffraction efficiency of MLDOE caused by ambient temperature is derived, and a computational imaging method that combines optical design and image restoration is proposed. Finally, a dual-infrared waveband infrared optical system with athermalization and achromatic aberrations corrected based on computational imaging method is designed. Results show that this method can effectively reduce the diffraction efficiency of MLDOE by ambient temperature and improve the imaging quality of hybrid optical systems.

Hybrid ray-tracing/Fourier optics method to analyze multilayer diffractive optical elements.

The performance (paraxial phase delay) of conventional diffractive optical elements is generally analyzed using the analytical scalar theory of diffraction, based on thin-element approximation (TEA). However, the high thickness of multilayer diffractive optical elements (MLDOEs) means that TEA yields inaccurate results. To address this, we tested a method based on ray-tracing simulations in mid-wave and long-wave infrared wave bands and for multiple f-numbers, together with the effect of MLDOE phase delay on a collimated on-axis beam with an angular spectrum method. Thus, we accurately generate optical figures of merit (point spread function along the optical axis, Strehl ratio at the "best" focal plane, and chromatic focal shift) and, by using a finite-difference time-domain method as a reference solution, demonstrate it as a valuable tool to describe and quantify the longitudinal chromatic aberration of MLDOEs.

Substrate material selection model for dual-band multilayer diffractive optical elements with wide angle of incidence

Large angle of incidence and multi-band are the goals pursued by modern multilayer diffractive optical element (MLDOE). The polychromatic integral diffraction efficiency (PIDE) is sensitive to the incident angle and refractive index of the substrate material. Therefore, we propose a new solution for selecting a set of optimal substrate materials of MLDOE to obtain the maximum PIDE in a large angle incidence. A mathematical model is established and the substrate material selection method based on comprehensive PIDE difference comparison (SMS-CPDC) for dual-band MLDOE is proposed. The three-layer DOEs in visible-NIR dual-band and the double-layer DOEs in MWIR-LWIR dual-band are designed and discussed as the examples. In visible-NIR dual-band and MWIR-LWIR dual-band, the optimal substrate material combinations are N-PK52A-PC-P-SF69 and ZNSE-ZNS, respectively. When the comprehensive PIDE decreases to 90%, the available incident angle range is ± 51.6° for N-PK52A-PC-P-SF69 MLDOE and that is ± 10.9° for ZNSE-ZNS MLDOE; When the comprehensive PIDE decreases to 85%, the available incident angle range is ± 54.2° for N-PK52A-PC-P-SF69 MLDOE and that is ± 12.1° for ZNSE-ZNS MLDOE. The results are of great significance for the application of MLDOEs in hybrid system with a large range of incident angle and multi operating band.

Optimal design of multilayer diffractive optical element in wide angle of incidence

We propose a method for designing the multilayer diffractive optical elements (MLDOEs) to improve the polychromatic integral diffraction efficiency (PIDE) in wide angle of incidence. By comparing and analyzing the characteristic angle weighted PIDE (CAW-PIDE) in the whole angles of incidence, the optimal microstructure height combination of the MLDOE can be obtained. The optimization process and simulation examples for the single-band and multi-band MLDOE are given. Compared to the conventional method, the PIDE is obviously improved in wide angle of incidence by our method. This optimization method can be applied to different working wavebands, and the image quality of the hybrid optical system with the MLDOE can be improved in wide angle of incidence.

Modeling infrared behavior of multilayer diffractive optical elements using Fourier optics.

In this paper, we propose to explore the infrared (IR) behavior of multilayer diffractive optical elements (MLDOEs). IR MLDOEs are designed for the development of space instruments dedicated to Earth observation. The phase effect of the MLDOE on a paraxial plane wave is studied using exact kinoform shapes for each layer. The modeling of the optical path difference uses thin element approximation. Until now, MLDOEs have been designed and simulated on ray-tracing software with binary diffractive layers. In this study, after passing through the MLDOE, the field is propagated using a method that utilizes the angular spectrum of plane waves. The Strehl ratio is used to determine the "best focus" plane, where it is shown that the focalization efficiency is above 95% for the working order in the mid- and long-wave IR bands. This result, along with the very low energy content of the other orders, proves the strong imaging potential of MLDOEs for dual-band applications. It is also demonstrated that the MLDOE has the same chromatic behavior as standard DOEs, making it a very useful component for IR achromatization.

Design of achromatic annular folded lens with multilayer diffractive optics for the visible and near-IR wavebands.

In this paper, the annular folded lens (AFL) is applied to the realization of a miniaturized system for the visible and near-IR spectrums (0.45-1.1μm). In order to correct the chromatic aberration, a hybrid AFL is designed with the multilayer diffractive optical element (MLDOE) in which the substrate materials are precision molded glasses. We propose a new design method of the MLDOE to improve the polychromatic integral diffraction efficiency (PIDE) that makes it suitable for the optical path of the AFL. By comparing the characteristic angle weighted PIDE (CAW-PIDE), the optimal microstructure heights of the MLDOE can be obtained, and the effect of diffraction efficiency on image quality can be minimized for the entire incident angle range. The design results show that the ratio of total length to the focal length is only 0.332, and comprehensive modulation transfer function considering the diffraction efficiency is larger than 0.26 at 166 lp/mm. This study can provide a new idea for designing a broadband, miniaturized, and low-cost imaging system.

Design and analysis of a hybrid optical system containing a multilayer diffractive optical element with improved diffraction efficiency.

We present a compressive image quality evaluation for a hybrid optical system containing a multilayer diffractive optical element (MLDOE). We take effects from both incident angle and waveband into consideration to improve the diffraction efficiency of the MLDOE. With this MLDOE design, it can ensure accurate image quality evaluation for hybrid optical systems. The results show that this design enables a diffraction-efficiency-improved MLDOE, and further ensures accurate image quality of the modulation transfer function and better optical system structure of the hybrid surveillance lens. The results are of great significance for the optimal design of hybrid imaging optical systems.

Azimuthal multiplexing 3D diffractive optics

Diffractive optics have increasingly caught the attention of the scientific community. Classical diffractive optics are 2D diffractive optical elements (DOEs) and computer-generated holograms (CGHs), which modulate optical waves on a solitary transverse plane. However, potential capabilities are missed by the inherent two-dimensional nature of these devices. Previous work has demonstrated that extending the modulation from planar (2D) to volumetric (3D) enables new functionalities, such as generating space-variant functions, multiplexing in the spatial or spectral domain, or enhancing information capacity. Unfortunately, despite significant progress fueled by recent interest in metasurface diffraction, 3D diffractive optics still remains relatively unexplored. Here, we introduce the concept of azimuthal multiplexing. We propose, design, and demonstrate 3D diffractive optics showing this multiplexing effect. According to this new phenomenon, multiple pages of information are encoded and can be read out across independent channels by rotating one or more diffractive layers with respect to the others. We implement the concept with multilayer diffractive optical elements. An iterative projection optimization algorithm helps solve the inverse design problem. The experimental realization using photolithographically fabricated multilevel phase layers demonstrates the predicted performance. We discuss the limitations and potential of azimuthal multiplexing 3D diffractive optics.

Analytical and comprehensive optimization design for multilayer diffractive optical elements in infrared dual band

We present an analytical and comprehensive optimization design for multilayer diffractive optical elements (MLDOEs) in infrared dual band for angular incidence. The diffraction efficiency of MLDOEs is affected by both wavelength and incident angle. Accordingly, the proposed optimization design considers comprehensive factors for its further design and evaluation. It can realize high diffraction efficiency and optimal microstructures of MLDOEs in dual band for angular incidence. By using numerical simulations, we demonstrate the modulation transfer function (MTF) at the cutoff frequency in an infrared dual-band optical system. It was found that such a design provides more accurate results, which helps achieve both higher MTF and smaller microstructure heights.

Comprehensive polychromatic integral diffraction efficiency sensitivity to tilt error for multilayer diffractive optical elements with oblique incidence.

Oblique incidence is the general working state for multilayer diffractive optical elements (MLDOEs) in an imaging optical system. The polychromatic integral diffraction efficiency (PIDE) is very sensitive to the incident angle. Therefore, it is necessary to analyze the effect of tilt error on diffraction efficiency/PIDE with oblique incidence. The theoretical model of the relationship between the diffraction efficiency and tilt error with oblique incidence is presented, and the effect of tilt error on diffraction efficiency/PIDE is analyzed. The analysis model of comprehensive PIDE for a certain range of incident angles and the tilt error for MLDOEs is established. The simulation results showed that the comprehensive PIDE is sensitive to tilt angle with oblique incidence, and the tolerance of the tilt error angle can be determined by the comprehensive PIDE. The tilt error tolerance is furthermore investigated with decenter error based on the maximum of comprehensive PIDE. The method and results can be used to guide the tolerance formulation of tilt error for MLDOEs in hybrid optical systems.

双波段多层衍射光学元件的基底材料选择方法研究及其在变焦系统中的应用

双波段多层衍射光学元件的基底材料选择方法研究及其在变焦系统中的应用

Integral diffraction efficiency model for multilayer diffractive optical elements with wide angles of incidence in case of polychromatic light.

Oblique incidence is the normal working mode for diffractive optical elements (DOEs). The diffraction efficiency is very sensitive to the angle of incidence for multilayer diffractive optical elements (MLDOEs). Therefore, the design and diffraction efficiency analysis of MLDOEs with wide angles of incidence is of universal significance and practice. We propose an integral diffraction efficiency model for MLDOEs with wide angles of incidence in case of polychromatic light and then describe this corresponding optimal design in detail. It is shown that high diffraction efficiency can be realized by the surface micro-structure heights optimization, ensuring high modulation transfer function (MTF) for MLDOEs with wide angles of incidence in hybrid optical systems. On this basis, we present the optimal design process and simulation of an MLDOE working in visible waveband with optical plastic materials combination PMMA and POLYCARB as the two-layer substrates. The result shows that with this optimal design, we can achieve the maximum diffraction efficiency and minimum micro-structure heights, which makes the MLDOE design exactly over the entire waveband and wide angles of incidence especially for zoom hybrid optical system.

Optimization and analysis of infrared multilayer diffractive optical elements with finite feature sizes.

Infrared multilayer diffractive optical elements (MLDOEs) usually own microstructure heights of a few hundred micrometers. The design and fabrication of those elements are more difficult than MLDOEs working in the visible waveband, especially for MLDOEs with high numerical aperture and finite feature sizes. Based on scalar diffraction theory and manufacturing errors, the effective area method for improving diffraction efficiency of infrared MLDOEs is developed. Closed-form analytical relations among diffraction efficiency, microstructure heights, microstructure periods, and incident angles are derived and verified in the infrared waveband. Then, optimized microstructure heights of infrared MLDOEs with different microstructure zone widths in the infrared wavelengths 3-5 μm and 8-12 μm at normal incidence can be obtained. The results indicate that the microstructure heights of infrared MLDOEs determined by the method have higher diffraction efficiency than former design methods. The method is verified by the rigorous electromagnetic method. Finally, the influence of incident angles on infrared MLDOEs is investigated. Our results show that the suggested microstructure parameters of MLDOEs both produce higher diffraction efficiencies than that of structure designed by scalar diffraction theory and may lead to more efficient hybrid diffractive-diffractive optical systems based on MLDOEs.

Tolerance analysis on decenter error of multilayer diffractive optical elements based on polychromatic integral diffraction efficiency.

The decenter error can determine the polychromatic integral diffraction efficiency (PIDE) over a broad wave band of hybrid optical systems and further the imaging quality. The mathematical model of the relationship between the decenter error and the PIDE of multilayer diffractive optical elements (MLDOEs) is presented, and the expressions are derived based on phase delay of diffractive optical elements for both normal and oblique incident situations. Finally, the sensitivity of PIDE to the decenter error for MLDOEs used in a long-infrared wave band with a material combination of ZNS-ZNSE is analyzed, and then the decenter error tolerance is proposed to ensure high PIDE over a broad wave band as well as diffraction efficiency at the designed wavelengths. The analysis methods and results could be useful for guiding the decenter error of MLDOEs in hybrid optical systems for optical engineers.

Design of dual-band infrared zoom lens with multilayer diffractive optical elements.

A mid-wave infrared (MWIR)/long-wave infrared (LWIR) dual-band zoom lens design with multilayer diffractive optical elements (MLDOEs) is presented. The mathematical relationship between the substrate material selection for dual-band MLDOE and polychromatic integral diffraction efficiency (PIDE) is deduced in the oblique incident situation, and further, a method for optimal selection of substrate material is proposed to obtain the high PIDE in an incident angle range. In the optimization process, the optimal substrate material combination is selected based on the proposed method, and the principle of lens material replacement is discussed. After optimization, the 5× hybrid dual-band infrared zoom system is obtained, which consists of seven lenses. The modulation transfer function values in all configurations are larger than 0.5 and 0.3 in MWIR and LWIR, respectively. The distortion values are less than 2% both in MWIR and LWIR for all configurations.

镀有增透膜的多层衍射光学元件的优化设计方法

镀有增透膜的多层衍射光学元件的优化设计方法