S. Marchesini, H. N. Chapman, S. P. Hau-Riege, R. A. London, A. Szoke, H. He, M. R. Howells, H. Padmore, R. Rosen, J. C. H. Spence, U. Weierstall
The inversion of a diffraction pattern offers aberration-free diffraction-limited 3D images without the resolution and depth-of-field limitations of lens-based tomographic systems, the only limitation being radiation damage. We review our experimental results, discuss the fundamental limits of this technique and future plans.
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We demonstrate a novel imaging approach and associated reconstruction algorithm for far-field coherent diffractive imaging, based on the measurement of a pair of laterally sheared diffraction patterns. The differential phase profile retrieved from such a measurement leads to improved reconstruction accuracy, increased robustness against noise, and faster convergence compared to traditional coherent diffractive imaging methods. We measure laterally sheared diffraction patterns using Fourier-transform spectroscopy with two phase-locked pulse pairs from a high harmonic source. Using this approach…
Diffractive screens are high-resolution elements with capability for generating holographic-like images from a sequence of planes where TV frames are seen oblique to it. If we project a sequence of contour lines of an object it could be seen in continuous horizontal parallax to a size of 1m3.
Compound eyes found in insects provide intriguing sources of biological inspiration for miniaturized imaging systems. Inspired by such insect eye structures, we demonstrate an ultrathin arrayed camera enabled by a flat multilevel diffractive microlens array for super-resolution visible imaging. We experimentally demonstrated that the microlens array can achieve large fill factor (hexagonal close packing with pitch=120um), thickness of 2.6um, and diffraction-limited (strehl ratio = 0.88) achromatic performance in the visible band (450nm to 650nm). We also demonstrate super-resolution imaging wi…
The complete characterization of spatial coherence is difficult because the mutual coherence function is a complex-valued function of four independent variables. This difficulty limits the ability of controlling and optimizing spatial coherence in a broad range of key applications. Here we propose a method for measuring the complete mutual coherence function, which does not require any prior knowledge and can be scaled to measure arbitrary coherence properties for any wavelength. Our method can also be used to retrieve objects illuminated by partially coherent beam with unknown coherence prope…
We demonstrate imaging over the visible band using a single planar diffractive lens. This is enabled via multi-level diffractive optics that is designed to focus over a broad wavelength range, which we refer to as an achromatic diffractive lens (ADL). We designed, fabricated and characterized two ADLs with numerical apertures of 0.05 and 0.18. Diffraction-limited focusing is demonstrated for the NA=0.05 lens with measured focusing efficiency of over 40% across the entire visible spectrum (450nm to 750nm). We characterized the lenses with a monochromatic and a color CMOS sensor, and demonstrate…
Fibonacci or bifocal terahertz (THz) imaging is demonstrated experimentally employing silicon diffractive zone plate (SDZP) in a continuous wave mode. Images simultaneously recorded in two different planes are exhibited at 0.6 THz frequency with the spatial resolution of wavelength. Multi-focus imaging operation of the Fibonacci lens is compared with a performance of the conventional silicon phase zone plate. Spatial profiles and focal depth features are discussed varying the frequency from 0.3 THz to 0.6 THz. Good agreement between experimental results and simulation data is revealed.
Single-Axis Ptychographic Coherent Diffractive Imaging for Spectroscopic and Wavefront Retrieval
单轴投影衍射成像技术通过单轴扫描提高通量，实现光谱和波前的同步成像，用于高效多模式实时成像。
Delivering sub-micrometer particles to an intense x-ray focus is a crucial aspect of single-particle diffractive-imaging experiments at x-ray free-electron lasers. Enabling direct visualization of sub-micrometer aerosol particle streams without interfering with the operation of the particle injector can greatly improve the overall efficiency of single-particle imaging experiments by reducing the amount of time and sample consumed during measurements. We have developed in-situ non-destructive imaging diagnostics to aid real-time particle injector optimization and x-ray/particle-beam alignment, …
Recently, there has been an explosion of interest in metalenses for imaging. The interest is primarily based on their sub-wavelength thicknesses. Diffractive lenses have been used as thin lenses since the late 19th century. Here, we show that multi-level diffractive lenses (MDLs), when designed properly can exceed the performance of metalenses. Furthermore, MDLs can be designed and fabricated with larger constituent features, making them accessible to low-cost, large area volume manufacturing, which is generally challenging for metalenses. The support substrate will dominate overall thickness …
Pixel size in cameras and other refractive imaging devices is typically limited by the free-space diffraction. However, a vast majority of semiconductor-based detectors are based on materials with substantially high refractive index. We demonstrate that diffractive optics can be used to take advantage of this high refractive index to reduce effective pixel size of the sensors below free-space diffraction limit. At the same time, diffractive systems encode both amplitude and phase information about the incoming beam into multiple pixels, offering the platform for noise-tolerant imaging with dyn…
It is generally thought that correcting chromatic aberrations in imaging requires multiple surfaces. Here, we show that by allowing the phase in the image plane of a flat lens to be a free parameter, it is possible to correct chromatic aberrations over an almost unlimited bandwidth with a single diffractive surface. Specifically, we designed, fabricated and characterized a flat multi-level diffractive lens (MDL) that images at the wavelengths from 450nm to 850nm. We experimentally characterized the focusing efficiency, modulation-transfer function, wavefront aberrations, vignetting, distortion…
We present the experimental reconstruction of sub-wavelength features from the far-field intensity of sparse optical objects: sparsity-based sub-wavelength imaging combined with phase-retrieval. As examples, we demonstrate the recovery of random and ordered arrangements of 100 nm features with the resolution of 30 nm, with an illuminating wavelength of 532 nm. Our algorithmic technique relies on minimizing the number of degrees of freedom; it works in real-time, requires no scanning, and can be implemented in all existing microscopes - optical and non-optical.
Characterizing buried layers and interfaces is critical for a host of applications in nanoscience and nano-manufacturing. Here we demonstrate non-invasive, non-destructive imaging of buried interfaces using a tabletop, extreme ultraviolet (EUV), coherent diffractive imaging (CDI) nanoscope. Copper nanostructures inlaid in SiO2 are coated with 100 nm of aluminum, which is opaque to visible light and thick enough that neither optical microscopy nor atomic force microscopy can image the buried interfaces. Short wavelength (29 nm) high harmonic light can penetrate the aluminum layer, yielding high…
Generalized reciprocal diffractive imaging for stand-alone, reference-free, fast-measurable quantitative phase microscopy
本文通过在光瞳平面引入空间滤波，将互反衍射成像（RDI）从漫射物体扩展到生物样品，实现独立、无参考、单次快速测量的定量相位显微术。
Single- and multi-layer micro-scale diffractive lens fabrication for fiber imaging probes with versatile depth-of-field
该研究提出将封装的平面衍射透镜键合到光纤端面的新方法，可制备单层及多层微尺度衍射透镜，实现灵活景深的光纤成像探针，有望支撑超薄先进成像与传感应用。
Single-particle incoherent diffractive imaging and amplified spontaneous emission in copper nanocubes
本研究通过单粒子非相干衍射成像技术，实现了高分辨率的铜纳米立方体成像，并揭示了高通量纳米成像的基本限制。
The critical properties of functional materials and nanoscale devices often originate from the coexistence of different thermodynamic phases and / or oxidization states, but sample makeup is seldom completely known a priori. Coherent diffractive imaging (CDI) provides the spatial resolution needed to observe nanoscale coexistence while returning the full amplitude and phase information of an object, but to date lacks the spectral information necessary for composition identification. Here we demonstrate CDI spectroscopy (CDIS), acquiring images of the prototypical quantum material vanadium oxid…
We designed and fabricated a flat multi-level diffractive lens (MDL) that is achromatic in the SWIR band (875nm to 1675nm). The MDL had a focal length of 25mm, aperture diameter of 8.93mm and thickness of only 2.6um. By pairing the MDL with a SWIR image sensor, we also characterized its imaging performance in terms of the point-spread functions, modulation-transfer functions, and still and video imaging.
Super-Resolution Coherent Diffractive Imaging via Titled-Incidence Multi-Rotation-Angle Fusion Ptychography
针对相干衍射成像（CDI）受阿贝衍射极限限制的问题，提出倾斜入射多旋转角度融合叠层成像技术，结合tmf-PIE算法整合多角度数据，实现2倍分辨率增强并减轻伪影，为超分辨率成像提供新方案。
Fabrication of large area (sub 1 cm cross-section) micro-optical components in a short period of time (approximately 10 min) and with lesser number of processing steps is highly desirable and cost-effective. In the recent years, femtosecond laser fabrication technology has revolutionized the field of manufacturing by offering the above capabilities. In this study, a fundamental diffractive optical element, binary axicon i.e axicon with two phase or amplitude levels, has been designed in three configurations namely conventional axicon, photon sieve axicon (PSA) and sparse PSA and directly mille…
Fast Simulation of Wide-Angle Coherent Diffractive Imaging
本文提出了一种用于宽角相干衍射成像的快速模拟方法，通过多切片傅里叶变换提升计算效率和精度。
Coherent diffractive imaging (CDI) provides new opportunities for high resolution X-ray imaging with simultaneous amplitude and phase contrast. Extensions to CDI broaden the scope of the technique for use in a wide variety of experimental geometries and physical systems. Here, we experimentally demonstrate a new extension to CDI that encodes additional information through the use of a series of randomly coded masks. The information gained from the few additional diffraction measurements removes the need for typical object-domain constraints; the algorithm uses prior information about the masks…
One-shot full-field surface profilometry using digital diffractive-confocal imaging correlation microscope based on digital micromirror device is developed for one-shot microscopic 3D surface measurement. Optical configuration applies confocal microscope setup and was building on DMD to generate specific pinhole array arrangement for minimizing cross talk effect. An innovative method was invented to create normalized cross correlation depth response curve from diffraction patterns of the pinhole. Using this approach, the sub-micrometer scale depth can be detected with high accuracy and precisi…
Multi-spectral imagers reveal information unperceivable to humans and conventional cameras. Here, we demonstrate a compact single-shot multi-spectral video-imaging camera by placing a micro-structured diffractive filter in close proximity to the image sensor. The diffractive filter converts spectral information to a spatial code on the sensor pixels. Following a calibration step, this code can be inverted via regularization-based linear algebra, to compute the multi-spectral image. We experimentally demonstrated spectral resolution of 9.6nm within the visible band (430nm to 718nm). We further …
Coherent diffractive imaging is a technique that recovers the sample image by numerically inverting its diffraction pattern. We propose a generalization of this method for the inversion of multi-wavelength data. Using this approach, we show that separate reconstructions for each wavelength can be recovered from a single polychromatic diffraction pattern. Limitations on the number of wavelengths is provided by adapting the constraint ratio to the polychromatic situation. The method's performance is demonstrated as a function of the source spectrum, the degree of complexity within the exit wave …
Coherent diffractive imaging (CDI) is widely used to characterize structured samples from measurements of diffracting intensity patterns. We introduce a numerical framework to quantify the precision that can be achieved when estimating any given set of parameters characterizing the sample from measured data. The approach, based on the calculation of the Fisher information matrix, provides a clear benchmark to assess the performance of CDI methods. Moreover, by optimizing the Fisher information metric using deep learning optimization libraries, we demonstrate how to identify the optimal illumin…
Established x-ray diffraction methods allow for high-resolution structure determination of crystals, crystallized protein structures or even single molecules. While these techniques rely on coherent scattering, incoherent processes like Compton scattering or fluorescence emission -- often the predominant scattering mechanisms -- are generally considered detrimental for imaging applications. Here we show that intensity correlations of incoherently scattered x-ray radiation can be used to image the full 3D structure of the scattering atoms with significantly higher resolution compared to convent…
Coherent diffractive imaging of individual free nanoparticles has opened novel routes for the in-situ analysis of their transient structural, optical, and electronic properties. So far, single-shot single-particle diffraction was assumed to be feasible only at extreme ultraviolet (XUV) and X-ray free-electron lasers, restricting this research field to large-scale facilities. Here we demonstrate single-shot imaging of isolated helium nanodroplets using XUV pulses from a femtosecond-laser driven high harmonic source. We obtain bright wide-angle scattering patterns, that allow us to uniquely iden…
A lens performs an approximately one-to-one mapping from the object to the image planes. This mapping in the image plane is maintained within a depth of field (or referred to as depth of focus, if the object is at infinity). This necessitates refocusing of the lens when the images are separated by distances larger than the depth of field. Such refocusing mechanisms can increase the cost, complexity and weight of imaging systems. Here, we show that by judicious design of a multi-level diffractive lens (MDL) it is possible to drastically enhance the depth of focus, by over 4 orders of magnitude.…
Coherent diffractive imaging has enabled the structural analysis of individual free nanoparticles in a single shot and offers the tracking of their light induced dynamics with unprecedented spatial and temporal resolution. The retrieval of structural information from scattering images in CDI experiments is so far mostly based on the assumption of classical scattering in linear response. For strong laser fields and in particular for resonant excitations, both the linear and the classical description may no longer be valid as population depletion and stimulated emission become important. Here we…
Snapshot Multispectral Imaging Using a Diffractive Optical Network
提出一种基于衍射光学网络的多光谱成像系统，通过深度学习训练在输出视场创建虚拟光谱滤波器阵列，无需光谱滤波器或图像恢复算法即可实现快照式多光谱成像。
Compressive spectral imaging enables to reconstruct the entire three-dimensional (3D) spectral cube from a few multiplexed images. Here, we develop a novel compressive spectral imaging technique using diffractive lenses. Our technique uses a coded aperture to spatially modulate the optical field from the scene and a diffractive lens such as a photon-sieve for dispersion. The coded field is passed through the diffractive lens and then measured at a few planes using a monochrome detector. The 3D spectral cube is then reconstructed from these highly compressed measurements through sparse recovery…
Non-linear X-ray Coherent Diffractive Imaging
本文提出利用非线性X射线过程的相干衍射方法，通过分离非线性成分实现高分辨率的量子材料和生物系统时空动态成像。
Point-scanning microscopy approaches are transforming super-resolution imaging. Despite achieving parallel high-speed imaging using multifocal techniques, efficient multi-color capability with high-quality illumination is currently lacking. In this paper, we present for the first time Mechanical-scan-free and multi-Color Super-resolution Microscopy (MCoSM) by spot array illumination, which enables mechanical-scan-free super-resolution imaging with adjustable resolution and field of view (FoV) based on spatial light modulators (SLMs). Through 100s-10,000s super-resolution spot illumination with…
In this work, issues in phase retrieval in the coherent diffractive imaging (CDI) technique, from discussion on parameters for setting up a CDI experiment to evaluation of the goodness of the final reconstruction, are discussed. The distribution of objects under study by CDI often cannot be cross-validated by another imaging technique. It is therefore important to make sure that the developed CDI procedure delivers an artifact-free object reconstruction. Critical issues that can lead to artifacts are presented and recipes on how to avoid them are provided.
Recent theoretical work suggested upper bounds on the operating bandwidths of flat lenses. Here, we show how these bounds can be circumvented via a multi-level diffractive lens (MDL) of diameter = 100 mm, focal length = 200 mm, device thickness = 2.4μ m and operating bandwidth from ? = 400 nm to 800 nm. We further combine the MDL with a refractive lens to demonstrate a hybrid telescope. By appealing to coherence theory, we show that the upper bound on relative bandwidth is surprisingly independent of lens diameter or numerical aperture, but is only limited by the bandwidth of the image sensor.…
Attosecond science has been transforming our understanding of electron dynamics in atoms, molecules and solids. However, to date almost all of the attoscience experiments have been based on spectroscopic measurements because attosecond pulses have intrinsically very broad spectra due to the uncertainty principle and are incompatible with conventional imaging systems. Here we report an important advance towards achieving attosecond coherent diffractive imaging. Using simulated attosecond pulses, we simultaneously reconstruct the spectrum, 17 probes and 17 spectral images of extended objects fro…
Quantitative phase imaging (QPI) through random diffusers using a diffractive optical network
本文提出一种全光衍射光学网络，可将随机衍射器后隐藏物体的相位信息转换为强度变化，无需外部电源即可实现高速、低功耗的定量相位成像与重建。
Multispectral Quantitative Phase Imaging Using a Diffractive Optical Network
本研究提出一种经深度学习优化的衍射光学处理器，可单次快照实现透明样本的多光谱定量相位成像，经数值模拟验证了9/16可见波段的稳定成像性能与泛化能力，为高通量相位成像提供紧凑低功耗方案。
Multiplane Quantitative Phase Imaging Using a Wavelength-Multiplexed Diffractive Optical Processor
提出一种波长复用衍射光学处理器，通过深度学习训练的衍射层将不同轴向平面的2D相位分布转化为编码于不同波长通道的强度图案，实现单视场多平面全光定量相位成像，并经数值模拟和太赫兹实验验证。
Broadband Unidirectional Visible Imaging Using Wafer-Scale Nano-Fabrication of Multi-Layer Diffractive Optical Processors
本文提出一种基于深度学习与晶圆级纳米加工的宽带偏振不敏感单向可见光成像仪，通过两层16级纳米相位特征实现正向高保真成像与反向阻挡，支持大规模高通量制造，可广泛应用于安全、国防和电信领域。
Quantitative phase imaging (QPI) is a label-free computational imaging technique that provides optical path length information of specimens. In modern implementations, the quantitative phase image of an object is reconstructed digitally through numerical methods running in a computer, often using iterative algorithms. Here, we demonstrate a diffractive QPI network that can synthesize the quantitative phase image of an object by converting the input phase information of a scene into intensity variations at the output plane. A diffractive QPI network is a specialized all-optical processor design…
Ptychography enables coherent diffractive imaging (CDI) of extended samples by raster scanning across the illuminating XUV/X-ray beam thereby generalizing the unique advantages of CDI techniques. Table-top realizations of this method are urgently needed for many applications in sciences and industry. Previously, it was only possible to image features much larger than the illuminating wavelength with table-top ptychography although knife-edge tests suggested sub-wavelength resolution. However, most real-world imaging applications require resolving of the smallest and closely-spaced features of …
HD snapshot diffractive spectral imaging and inferencing
提出基于衍射滤波器阵列的高清快照光谱成像系统，单次拍摄即可获取空间与光谱信息，实现25通道高分辨率重建，并在生物组织分类、食品质量评估等应用中验证了准确推断能力。
Lensless cameras are a class of imaging devices that shrink the physical dimensions to the very close vicinity of the image sensor by replacing conventional compound lenses with integrated flat optics and computational algorithms. Here we report a diffractive lensless camera with spatially-coded Voronoi-Fresnel phase to achieve superior image quality. We propose a design principle of maximizing the acquired information in optics to facilitate the computational reconstruction. By introducing an easy-to-optimize Fourier domain metric, Modulation Transfer Function volume (MTFv), which is related …
Compressive single-pixel imaging via a wavelength-multiplexed spatially incoherent diffractive optical processor
本文提出结合波长复用非相干衍射光学处理器与紧凑型数字神经网络的压缩单像素成像方法，通过优化变换矩阵与神经网络实现高效成像，实验验证了其在生物医学成像等领域的应用潜力。
Super-resolution imaging using super-oscillatory diffractive neural networks
提出光学超振荡衍射神经网络(SODNN)，通过衍射层与非线性调制入射光场产生超振荡效应，在远场实现无旁瓣且长景深的0.407λ超分辨焦点及多波长多焦点阵列，突破衍射极限。
Imaging through diffusive media is a challenging problem, where the existing solutions heavily rely on digital computers to reconstruct distorted images. We provide a detailed analysis of a computer-free, all-optical imaging method for seeing through random, unknown phase diffusers using diffractive neural networks, covering different deep learning-based training strategies. By analyzing various diffractive networks designed to image through random diffusers with different correlation lengths, a trade-off between the image reconstruction fidelity and distortion reduction capability of the diff…
Subwavelength Imaging using a Solid-Immersion Diffractive Optical Processor
本文提出一种基于固体浸没层与深度学习联合优化衍射编码器-解码器的全光成像方法，在太赫兹频段实验实现相位和振幅物体的亚波长分辨与放大重建。
Dynamic Coherent Diffractive Imaging Using Only a Support Constraint in the Complex Plane
本文提出一种仅利用样本动态的时间增量先验，通过近场衍射电影重建时变相位物体的方法，并在空间光调制器和光聚合3D打印实验中验证了其有效性。
We introduce a single-frame diffractive imaging method called randomized probe imaging (RPI). In RPI, a sample is illuminated by a structured probe field containing speckles smaller than the sample's typical feature size. Quantitative amplitude and phase images are then reconstructed from the resulting far-field diffraction pattern. The experimental geometry of RPI is straightforward to implement, requires no near-field optics, and is applicable to extended samples. When the resulting data are analyzed with a complimentary algorithm, reliable reconstructions which are robust to missing data ar…
We consider the problem of blind ptychography, that is the joint estimation of an unknown object and an illumination function from diffraction intensity measurements. In ptychography, diffraction measurements from neighboring regions of the same object are related to each other by a pairwise relationship between overlapping frames. When the illumination is well known, the relationship among frames is given by a linear projection operator. We propose a power iteration-projection algorithm that minimizes the global pairwise discrepancy among frames. We accelerate the convergence of power method …
A hybrid imaging system is a simultaneous physical arrangement of a refractive lens and a multilevel phase mask (MPM) as a diffractive optical element (DOE). The favorable properties of the hybrid setup are improved extended-depth-of-field (EDoF) imaging and low chromatic aberrations. We built a fully differentiable image formation model in order to use neural network techniques to optimize imaging. At the first stage, the design framework relies on the model-based approach with numerical simulation and end-to-end joint optimization of both MPM and imaging algorithms. In the second stage, MPM …
Far-field characterization of small objects is severely constrained by the diffraction limit. Existing tools achieving sub-diffraction resolution often utilize point-by-point image reconstruction via scanning or labelling. Here, we present a new imaging technique capable of fast and accurate characterization of two-dimensional structures with at least wavelength/25 resolution, based on a single far-field intensity measurement. Experimentally, we realized this technique resolving the smallest-available to us 180-nm-scale features with 532-nm laser light. A comprehensive analysis of machine lear…
Pseudoscopic enlarged images are obtained by projecting diffraction-encoded images onto a diffractive screen
Theory predicts that with an ultrashort and extremely bright coherent X-ray pulse, a single diffraction pattern may be recorded from a large macromolecule, a virus, or a cell before the sample explodes and turns into a plasma. Here we report the first experimental demonstration of this principle using the FLASH soft X-ray free-electron laser. An intense 25 fs, 4 10^13 W/cm^2 pulse, containing 10^12 photons at 32 nm wavelength, produced a coherent diffraction pattern from a nano-structured non-periodic object, before destroying it at 60,000 K. A novel X-ray camera assured single photon detectio…
Piston sensing for sparse aperture systems via all-optical diffractive neural network
针对稀疏孔径成像中的实时活塞校正问题，提出基于光学衍射神经网络的活塞感知方法，通过可探测强度直接将光场复振幅转换为活塞值，无需成像采集与电学处理，仿真显示其在单色光和宽带光下均具高精度，极大提升了实时性能。
A diffractive arrangement that allows imaging of an object without any intermediate or complementary element is presented. This optical system with only two diffraction gratings forms color images with white light.
Imaging through diffusers presents a challenging problem with various digital image reconstruction solutions demonstrated to date using computers. We present a computer-free, all-optical image reconstruction method to see through random diffusers at the speed of light. Using deep learning, a set of diffractive surfaces are designed/trained to all-optically reconstruct images of objects that are covered by random phase diffusers. We experimentally demonstrated this concept using coherent THz illumination and all-optically reconstructed objects distorted by unknown, random diffusers, never used …
Role of Spatial Coherence in Diffractive Optical Neural Networks
本文研究空间相干性对衍射光学神经网络性能的影响，提出高效模拟非相干和部分相干照明的数值方法，并在MNIST数据集上验证了不同相干性下的处理能力。
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