Complex-field imaging is indispensable for numerous applications at wavelengths from X-ray to THz, with amplitude describing transmittance (or reflectivity) and phase revealing intrinsic structure of the target object. Coherent diffraction imaging (CDI) employs iterative phase retrieval algorithms to process diffraction measurements and is the predominant non-interferometric method to image complex fields. However, the working spectrum of CDI is quite narrow, because the diffraction measurements on which it relies require dense array detection with ultra-high dynamic range. Here we report a single-pixel CDI technique that works for a wide waveband. A single-pixel detector instead of an array sensor is employed in the far field for detection. It repeatedly records the DC-only component of the diffracted wavefront scattered from an object as it is illuminated by a sequence of binary modulation patterns. This decreases the measurements' dynamic range by several orders of magnitude. We employ an efficient single-pixel phase-retrieval algorithm to jointly recover the object's 2D amplitude and phase maps from the 1D intensity-only measurements. No a priori object information is needed in the recovery process. We validate the technique's quantitative phase imaging nature using both calibrated phase objects and biological samples, and demonstrate its wide working spectrum with both 488-nm visible light and 980-nm near-infrared light. Our approach paves the way for complex-field imaging in a wider waveband where 2D detector arrays are not available, with broad applications in life and material sciences.
Optical diffraction tomography is an indispensable tool for studying objects in three-dimensions due to its ability to accurately reconstruct scattering objects. Until now this technique has been limited to coherent light because spatial phase information is required to solve the inverse scattering problem. We introduce a method that extends optical diffraction tomography to imaging spatially incoherent contrast mechanisms such as fluorescent emission. Our strategy mimics the coherent scattering process with two spatially coherent illumination beams. The interferometric illumination pattern en…
The history of computing started with analog computers consisting of physical devices performing specialized functions such as predicting the trajectory of cannon balls. In modern times, this idea has been extended, for example, to ultrafast nonlinear optics serving as a surrogate analog computer to probe the behavior of complex phenomena such as rogue waves. Here we discuss a new paradigm where physical phenomena coded as an algorithm perform computational imaging tasks. Specifically, diffraction followed by coherent detection, not in its analog realization but when coded as an algorithm, bec…
We present a deep neural network to reduce coherent noise in three-dimensional quantitative phase imaging. Inspired by the cycle generative adversarial network, the denoising network was trained to learn a transform between two image domains: clean and noisy refractive index tomograms. The unique feature of this network, distinct from previous machine learning approaches employed in the optical imaging problem, is that it uses unpaired images. The learned network quantitatively demonstrated its performance and generalization capability through denoising experiments of various samples. We concl…
We propose and experimentally demonstrate a nonlinear-optics approach to pattern recognition with single-pixel imaging and deep neural network. It employs mode selective image up-conversion to project a raw image onto a set of coherent spatial modes, whereby its signature features are extracted nonlinear-optically. With 40 projection modes, the classification accuracy reaches a high value of 99.49% for the MNIST handwritten digit images, and up to 95.32% even when they are mixed with strong noise. Our experiment harnesses rich coherent processes in nonlinear optics for efficient machine learni…
Lensless imaging is a popular research field for the advantages of small size, wide field-of-view and low aberration in recent years. However, some traditional lensless imaging methods suffer from slow convergence, mechanical errors and conjugate solution interference, which limit its further application and development. In this work, we proposed a lensless imaging method based on spatial light modulator (SLM) with unknown modulation curve. In our imaging system, we use SLM to modulate the wavefront of object, and introduce the ptychographic scanning algorithm that is able to recover the compl…
It is demonstrated that an object distribution can be successfully retrieved from its diffraction pattern or hologram, even if some of the measured intensity samples are missing. The maximum allowable number of missing values depends on the linear oversampling ratio s, where the higher the value of s, the more intensity samples can be missing. For a real-valued object, the ratio of missing pixels to the total number of pixels should not exceed (1 - 2/s^2) or (1 - 1/s^2) in the acquired diffraction pattern or hologram, respectively. For example, even 5% of the measured intensity values at an ov…
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), using both X-rays and electrons, has made extremely rapid progress over the past two decades. The associated reconstruction algorithms are typically iterative, and seeded with a crude first estimate. A deterministic method for Bragg Coherent Diffraction Imaging (Pavlov et al., Sci. Rep. 7, 1132 (2017)) is used as a more refined starting point for a shrink-wrap iterative reconstruction procedure. The appropriate comparison with the autocorrelation function as a starting point is performed. Real-space and Fourier-space error metrics are used to analyse the con…
Stanford University（斯坦福大学）；SLAC National Accelerator Laboratory（SLAC国家加速器实验室）
A new reference design is introduced for holographic coherent diffraction imaging. This consists in two references - "block" and "pinhole" shaped regions - placed adjacent to the imaging specimen. An efficient recovery algorithm is provided for the resulting holographic phase retrieval problem, which is based on solving a structured, overdetermined linear system. Analysis of the expected recovery error on noisy data, which is contaminated by Poisson shot noise, shows that this simple modification synergizes the individual references and hence leads to uniformly superior performance over single…
This paper addresses three-dimensional signal distortion and image reconstruction issues in x-ray Bragg coherent diffraction imaging (BCDI) in the event of a general non-orthogonal orientation of the area detector with respect to the diffracted beam. Growing interest in novel BCDI adaptations at fourth-generation synchrotron light sources has necessitated improvisations in the experimental configuration and the subsequent data analysis. One such possibly unavoidable improvisation that is envisioned in this paper is a photon-counting area detector whose face is tilted away from the perpendicula…
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, precluding real-time imaging. 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 o…
We present a compact, diffuser-assisted, single-pixel computational camera. A rotating ground glass diffuser is adopted, in preference to a commonly used digital micro-mirror device (DMD), to encode a two-dimensional (2D) image into single-pixel signals. We retrieve images with an 8.8% sampling ratio after the calibration of the pseudo-random pattern of the diffuser under incoherent illumination. Furthermore, we demonstrate hyperspectral imaging with line array detection by adding a diffraction grating. The implementation results in a cost-effective single-pixel camera for high-dimensional ima…
As a critical component of coherent X-ray diffraction imaging (CDI), phase retrieval has been extensively applied in X-ray structural science to recover the 3D morphological information inside measured particles. Despite meeting all the oversampling requirements of Sayre and Shannon, current phase retrieval approaches still have trouble achieving a unique inversion of experimental data in the presence of noise. Here, we propose to overcome this limitation by incorporating a 3D Machine Learning (ML) model combining (optional) supervised learning with transfer learning. The trained ML model can …
Bragg Coherent Diffraction Imaging (BCDI) is a powerful strain imaging tool, often limited by beam-induced sample instability for small particles and high power densities. Here, we devise and validate an adapted diffraction volume assembly algorithm, capable of recovering three-dimensional datasets from particles undergoing uncontrolled and unknown rotations. We apply the method to gold nanoparticles which rotate under the influence of a focused coherent X-ray beam, retrieving their three-dimensional shapes and strain fields. The results show that the sample instability problem can be overcome…
