Far-field diffraction pattern for corner reflectors with complex reflection coefficients
Far field diffraction pattern of corner reflector for normally incident monochromatic light, considering polarization characteristics
Alley, C. O.↗
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The far field diffraction pattern for corner reflectors with complex reflection coefficients
The far field diffraction pattern of a geometrically perfect corner reflector is examined analytically for normally incident monochromatic light. The states of polarization and the complex amplitudes of the emerging light are expressed through transformation matrices in terms of those of the original incident light for each sextant of the face in a single coordinate system. The analytic expression of the total diffraction pattern is obtained for a circular face. This expression consists of three component functions in addition to the basic Airy function. The coefficient of each function is expressed in terms of complex coefficients of reflectance of the reflecting surface. Some numerical results for different reflecting surfaces, including total internal reflection, are presented. The iso-intensity contours of the diffraction pattern evaluated from the analytical expressions for an uncoated solid corner reflector are also presented along with the photographs of the pattern.
Chang, R. F.↗
Investigation Of Far-Field Diffraction
Report describes experimental investigation of far-field diffracton by normally illuminated circular apertures with diameters of several wavelengths of incident light. Purpose of investigation to determine whether Keller's "geometrical" theory of diffraction valid for diffraction phenomena of this kind.
Wang, Yaujen↗
Single-frame far-field diffractive imaging with randomized illumination
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 are achieved. To realize these benefits, a resolution limit associated with the numerical aperture of the probe-forming optics is imposed. RPI therefore offers an attractive modality for quantitative X-ray phase imaging when temporal resolution and reliability are critical but spatial resolution in the tens of nanometers is sufficient. We discuss the method, introduce a reconstruction algorithm, and present two proof-of-concept experiments: one using visible light, and one using soft X-rays.
77 NANOSCIENCE AND NANOTECHNOLOGY↗
Single-frame far-field diffractive imaging with randomized illumination
Contains a transmission ptychography dataset collected from a chrome on glass Siemens star under optical illumination. The probe is generated by a randomized zone plate under illumination from a spatially filtered green laser. A single diffraction pattern was removed from the dataset and reported in a separate cxi file. In addition, a single exposure collected after manually defocusing the probe is reported. The ptychography dataset is used for calibration of the probe function, and the remaining diffraction patterns can be reconstructed via randomized probe imaging.
Ptychography, Randomized Probe Imaging↗
Single-frame far-field diffractive imaging with randomized illumination
Contains two transmission ptychography datasets, one collected from a Siemens star, and the second from an Fe/Gd multilayer. Both samples are under illumination from the same randomized zone plate. Each dataset has a single diffraction pattern removed, and these patterns are reported in a separate cxi file. Either ptychography dataset can be used for calibration of the probe function, and the remaining diffraction patterns can be reconstructed via randomized probe imaging.
BESSY II↗
Identify the Limits of Geometric Optics Ray Tracing by Numerically Solving the Vector Kirchhoff Integral
The properties of a pencil of light as defined approximately in the geometric optics ray tracing method are investigated. The vector Kirchhoff integral is utilized to accurately compute the electromagnetic near field in and around the pencil of light with various beam base sizes, shapes, propagation directions and medium refractive indices. If a pencil of light has geometric mean cross section size of the order p times the wavelength, it can propagate independently to a distance p2 times the wavelength, where most of the beam energy diffuses out of the beam region. This is consistent with a statement that van de Hulst made in a classical text on light scattering. The electromagnetic near fields in the pencil of light are not uniform, have complicated patterns within short distances from the beam base, and the fields tend to converge to Fraunhofer diffraction fields far away from the base.
Far field diffraction↗
Test results from LAGEOS-2 optical characterization using pulsed lasers
The Laser Geodynamic Satellite-2 (LAGEOS-2) has undergone extensive optical testing at NASA Goddard Space Flight Center during 1989. The techniques included measuring the far field diffraction pattern using cw and pulsed lasers. In the pulsed measurement technique, response of the satellite was studied by measuring the far-field diffraction pattern (FFDP) as a function of pulsewidth, wavelength, polarization, position in the FFDP, detector/processing techniques, and satellite orientation. The purpose of the pulsed laser testing was two-fold: (1) to characterize the satellite optical response with the detector and signal processing electronics currently used in most SLR stations using the portable laser ranging standard, and (2) to characterize the satellite response for various conditions using the highest bandwidth optical detector (streak camera) available for the next generation of satellite laser ranging (SLR) technology. The portable ranging standard employed multiple measurement devices and an optical calibration scheme to eliminate range-dependent and amplitude-dependent systematics. These precautions were taken to eliminate/minimize instrumental errors and provide maximum accuracy. For LAGEOS orbit (6000 Km), ground stations are located 34 to 38 Mu radians off the axis of the return signal from the satellite; therefore, an optical mask was used to restrict the field of view (FOV) of detection to this annular region of the FFDP. The two measurement techniques were implemented using an aperture sharing scheme and complemented each other by providing mutual verification.
Varghese, Thomas K.↗
Prelaunch optical characterization of the Laser Geodynamic Satellite (LAGEOS 2)
The optical range correction (the distance between the apparent retroreflective skin of the satellite and the center of mass) of the LAGEOS 2 was determined using computer analysis of theoretical and experimentally measured far field diffraction patterns, and with short pulse lasers using both streak camera-based range receivers and more conventional PMT-based range receivers. The three measurement techniques yielded range correction values from 248 to 253 millimeters dependent on laser wavelength, pulsewidth, and polarization, location of the receiver in the far field diffraction pattern and detection technique (peak, half maximum, centroid, or constant fraction). The Lidar cross section of LAGEOS 2 was measured at 4 to 10 million square meters, comparable to the LAGEOS 1.
Minott, Peter O.↗
A comprehensive simulation model of the performance of photochromic films in absorbance-modulation-optical-lithography
Optical lithography is the most prevalent method of fabricating micro-and nano-scale structures in the semiconductor industry due to the fact that patterning using photons is fast, accurate and provides high throughput. However, the resolution of this technique is inherently limited by the physical phenomenon of diffraction. Absorbance-Modulation-Optical Lithography (AMOL), a recently developed technique has been successfully demonstrated to be able to circumvent this diffraction limit. AMOL employs a dual-wavelength exposure system in conjunction with spectrally selective reversible photo-transitions in thin films of photochromic molecules to achieve patterning of features with sizes beyond the far-field diffraction limit. We have developed a finite-element-method based full-electromagnetic-wave solution model that simulates the photo-chemical processes that occur within the thin film of the photochromic molecules under illumination by the exposure and confining wavelengths in AMOL. This model allows us to understand how the material characteristics influence the confinement to sub-diffraction dimensions, of the transmitted point spread function (PSF) of the exposure wavelength inside the recording medium. The model reported here provides the most comprehensive analysis of the AMOL process to-date, and the results show that the most important factors that govern the process, are the polarization of the two beams, the ratio of the intensities of the two wavelengths, the relative absorption coefficients and the concentration of the photochromic species, the thickness of the photochromic layer and the quantum yields of the photoreactions at the two wavelengths. The aim of this work is to elucidate the requirements of AMOL in successfully circumventing the far-field diffraction limit.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Combined near- and far-field high-energy diffraction microscopy dataset for Ti-7Al tensile specimen elastically loaded in situ
High-energy diffraction microscopy (HEDM) constitutes a suite of combined X-ray characterization methods, which hold the unique advantage of illuminating the microstructure and micromechanical state of a material during concurrent in situ mechanical deformation. The data generated from HEDM experiments provides a heretofore unrealized opportunity to validate meso-scale modeling techniques, such as crystal plasticity finite element modeling (CPFEM), by explicitly testing the accuracy of these models at the length scales where the models predict their response. Combining HEDM methods with in situ loading under known and controlled boundary conditions represents a significant challenge, inspiring the recent development of a new high-precision rotation and axial motion system for simultaneously rotating and axially loading a sample. In this paper, we describe the initial HEDM dataset collected using this hardware on an alpha-titanium alloy (Ti-7Al) under in situ tensile deformation at the Advanced Photon Source, Argonne National Laboratory. We present both near-field HEDM data that maps out the grain morphology and intragranular crystallographic orientations and far-field HEDM data that provides the grain centroid, grain average crystallographic orientation, and grain average elastic strain tensor for each grain. Finally, we provide a finite element mesh that can be utilized to simulate deformation in the volume of this Ti-7Al specimen.
36 MATERIALS SCIENCE↗
Semi-transparent central stop in high-resolution X-ray ptychography using Kirkpatrick–Baez focusing
A semi-transparent central stop has been used for ptychographic coherent diffractive imaging to increase the effective dynamic range in the recording of the far-field diffraction patterns. In this way, the high flux density provided by nano-focusing Kirkpatrick–Baez mirrors can be fully exploited for high resolution and quantitative phase reconstructions. A ptychographic coherent X-ray diffractive imaging (PCDI) experiment has been carried out using 7.9 keV X-rays and Kirkpatrick–Baez focusing mirrors. By introducing a semi-transparent central stop in front of the detector the dynamic range on the detector is increased by about four orders of magnitude. The feasibility of this experimental scheme is demonstrated for PCDI applications with a resolution below 10 nm. The results are compared with reference data and an increase of resolution by a factor of two is obtained, while the deviation of the reconstructed phase map from the reference is below 1%.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Randomized probe imaging through deep k-learning
Randomized probe imaging (RPI) is a single-frame diffractive imaging method that uses highly randomized light to reconstruct the spatial features of a scattering object. The reconstruction process, known as phase retrieval, aims to recover a unique solution for the object without measuring the far-field phase information. Typically, reconstruction is done via time-consuming iterative algorithms. In this work, we propose a fast and efficient deep learning based method to reconstruct phase objects from RPI data. The method, which we call deep k-learning, applies the physical propagation operator to generate an approximation of the object as an input to the neural network. This way, the network no longer needs to parametrize the far-field diffraction physics, dramatically improving the results. Deep k-learning is shown to be computationally efficient and robust to Poisson noise. The advantages provided by our method may enable the analysis of far larger datasets in photon starved conditions, with important applications to the study of dynamic phenomena in physical science and biological engineering.
Guo, Zhen (ORCID:0000000213473451)↗
AI-enabled high-resolution scanning coherent diffraction imaging
Ptychographic imaging is a powerful means of imaging beyond the resolution limits of typical x-ray optics. Capturing recovered images from raw ptychographic data, however, requires the solution of an inverse problem, namely, phase retrieval. Phase retrieval algorithms are computationally expensive, which precludes real-time imaging. In this work, we propose PtychoNN, an approach to solve the ptychography data inversion problem based on a deep convolutional neural network. We demonstrate how the proposed method can be used to predict real-space structure and phase at each scan point solely from the corresponding far-field diffraction data. Our results demonstrate the practical application of machine learning to recover high fidelity amplitude and phase contrast images of a real sample hundreds of times faster than current ptychography reconstruction packages. Furthermore, by overcoming the constraints of iterative model-based methods, we can significantly relax sampling constraints on data acquisition while still producing an excellent image of the sample. Besides drastically accelerating acquisition and analysis, this capability has profound implications for the imaging of dose sensitive, dynamic, and extremely voluminous samples.
47 OTHER INSTRUMENTATION↗
Real-time coherent diffraction inversion using deep generative networks
Abstract Phase retrieval, or the process of recovering phase information in reciprocal space to reconstruct images from measured intensity alone, is the underlying basis to a variety of imaging applications including coherent diffraction imaging (CDI). Typical phase retrieval algorithms are iterative in nature, and hence, are time-consuming and computationally expensive, making real-time imaging a challenge. Furthermore, iterative phase retrieval algorithms struggle to converge to the correct solution especially in the presence of strong phase structures. In this work, we demonstrate the training and testing of CDI NN, a pair of deep deconvolutional networks trained to predict structure and phase in real space of a 2D object from its corresponding far-field diffraction intensities alone. Once trained, CDI NN can invert a diffraction pattern to an image within a few milliseconds of compute time on a standard desktop machine, opening the door to real-time imaging.
97 MATHEMATICS AND COMPUTING↗
Nanotechnology Infrared Optics for Astronomy Missions
We have used the "MicroStripes" code (Flomerics, Inc.) to perform full-, near- and far-field diffraction modeling of metal mesh performance on substrates. Our Miles Code software, which approximates the full calculation in a quick, gui-based window, is useful as an iterative device by adjusting the input parameters (index of refraction, thickness, etc.) to provide agreement with the full calculation. However, despite the somewhat extravagant claims by the MicroStripes manufacturer, this code is also not perfect because numerous free parameters must be set. Key among these, as identified in our earlier papers and proposal documents, is the high frequency (i.e., far IR) character of the real and imaginary parts of the index of refraction of the metal mesh, the high frequency character of the real and imaginary parts of the index of refraction of the substrate, and the character of the interface between the mesh and the substrate material, and in particular the suppression (or possible enhancement) of surface effects at the interface.
Frogel, Jay↗
A combined Kirkpatrick-Baez mirror and multilayer lens for sub-10 nm x-ray focusing
We have used a combined optical system of a high gain elliptic Kirkpatrick-Baez mirror system (KB) and a multilayer Laue lens (MLL) positioned in the focal plane of the KB for hard x-rays nano-focusing. The two-step focusing scheme is based on a high acceptance and high gain elliptical mirror with moderate focal length and a MLL with ultra-short focal length. Importantly, fabrication constraints, i.e. in mirror polishing and bending, as well as MLL deposition can be significantly relaxed, since (a) the mirror focus in the range of 200-500 nm is sufficient, and (b) the number of layers of the MLL can be correspondingly small. First demonstrations of this setup at the coherence beamline of the PETRA III storage ring yield a highly divergent far-field diffraction pattern, from which the autocorrelation function of the near-field intensity distribution was obtained. The results show that the approach is well suited to reach smallest spot sizes in the sub-10nm range at high flux.
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
Subwavelength nanopatterning of photochromic diarylethene films
The resolution of optical patterning is constrained by the far-field diffraction limit. In this letter, we describe an approach that exploits the unique photo- and electro-chemistry of diarylethene photochromic molecules to overcome this diffraction limit and achieve sub-wavelength nanopatterning.
36 MATERIALS SCIENCE↗