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Title: 3D x-ray imaging of continuous objects beyond the depth of focus limit

Abstract

X-ray ptychography is quickly becoming the standard method for sub-30 nm imaging of thick extended samples. Being a diffraction-based technique, it involves solving an inverse problem to reconstruct the sample structure from a set of measured diffraction patterns. This problem is traditionally solved to recover a 2D representation of a sample, or in some cases a series of 2D slices of the sample; one can then do standard tomography from a set of such images as the specimen is rotated. Here we present a parallelized, optimization-based algorithm to solve the ptychographic phase retrieval problem directly in 3D. Our approach is able to deal with samples that do not fit entirely within the depth of focus of the imaging system. Such samples pose additional challenges to phase retrieval algorithms because of internal diffraction effects within the sample. In conclusion, we demonstrate our approach on a computational sample modeled with 17 million complex variables.

Authors:
ORCiD logo; ORCiD logo; ORCiD logo; ORCiD logo; ORCiD logo
Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org.:
National Science Foundation (NSF); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
OSTI Identifier:
1467943
Alternate Identifier(s):
OSTI ID: 1491749
Grant/Contract Number:  
AC02-06CH11357
Resource Type:
Published Article
Journal Name:
Optica
Additional Journal Information:
Journal Name: Optica Journal Volume: 5 Journal Issue: 9; Journal ID: ISSN 2334-2536
Publisher:
Optical Society of America
Country of Publication:
United States
Language:
English
Subject:
47 OTHER INSTRUMENTATION; Computational imaging; Three-dimensional microscopy; X-ray imaging

Citation Formats

Gilles, M. A., Nashed, Y. S. G., Du, M., Jacobsen, C., and Wild, S. M. 3D x-ray imaging of continuous objects beyond the depth of focus limit. United States: N. p., 2018. Web. doi:10.1364/OPTICA.5.001078.
Gilles, M. A., Nashed, Y. S. G., Du, M., Jacobsen, C., & Wild, S. M. 3D x-ray imaging of continuous objects beyond the depth of focus limit. United States. doi:10.1364/OPTICA.5.001078.
Gilles, M. A., Nashed, Y. S. G., Du, M., Jacobsen, C., and Wild, S. M. Fri . "3D x-ray imaging of continuous objects beyond the depth of focus limit". United States. doi:10.1364/OPTICA.5.001078.
@article{osti_1467943,
title = {3D x-ray imaging of continuous objects beyond the depth of focus limit},
author = {Gilles, M. A. and Nashed, Y. S. G. and Du, M. and Jacobsen, C. and Wild, S. M.},
abstractNote = {X-ray ptychography is quickly becoming the standard method for sub-30 nm imaging of thick extended samples. Being a diffraction-based technique, it involves solving an inverse problem to reconstruct the sample structure from a set of measured diffraction patterns. This problem is traditionally solved to recover a 2D representation of a sample, or in some cases a series of 2D slices of the sample; one can then do standard tomography from a set of such images as the specimen is rotated. Here we present a parallelized, optimization-based algorithm to solve the ptychographic phase retrieval problem directly in 3D. Our approach is able to deal with samples that do not fit entirely within the depth of focus of the imaging system. Such samples pose additional challenges to phase retrieval algorithms because of internal diffraction effects within the sample. In conclusion, we demonstrate our approach on a computational sample modeled with 17 million complex variables.},
doi = {10.1364/OPTICA.5.001078},
journal = {Optica},
number = 9,
volume = 5,
place = {United States},
year = {2018},
month = {8}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1364/OPTICA.5.001078

Citation Metrics:
Cited by: 5 works
Citation information provided by
Web of Science

Figures / Tables:

Fig. 1 Fig. 1: Depth of focus as a function of x-ray photon energy for a variety of transverse resolution δr values. Also shown is the exp[−1] penetration depth µ-1 for amorphous ice (for frozen hydrated biological specimens) and silicon (for microelectronics specimens) as proxies for the thickness range of x-ray imagingmore » as a function of photon energy. As the transverse resolution δr in x-ray microscopy is improved to finer values, the DOF decreases with the square of the resolution improvement (Eq. 1), leading to a decrease in the size of a specimen that can be imaged within the projection approximation required by standard tomography.« less

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Works referenced in this record:

Phase retrieval with transverse translation diversity: a nonlinear optimization approach
journal, January 2008

  • Guizar-Sicairos, Manuel; Fienup, James R.
  • Optics Express, Vol. 16, Issue 10
  • DOI: 10.1364/OE.16.007264

Parallel ptychographic reconstruction
journal, January 2014

  • Nashed, Youssef S. G.; Vine, David J.; Peterka, Tom
  • Optics Express, Vol. 22, Issue 26
  • DOI: 10.1364/OE.22.032082

Phase recovery and lensless imaging by iterative methods in optical, X-ray and electron diffraction
journal, May 2002

  • Spence, J. C. H.; Weierstall, U.; Howells, M.
  • Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Vol. 360, Issue 1794
  • DOI: 10.1098/rsta.2001.0972

Multi-slice ptychographic tomography
journal, February 2018


Precession x-ray ptychography with multislice approach
journal, June 2015


Ptychographic microscope for three-dimensional imaging
journal, January 2014

  • Godden, T. M.; Suman, R.; Humphry, M. J.
  • Optics Express, Vol. 22, Issue 10
  • DOI: 10.1364/OE.22.012513

Signal-to-noise and radiation exposure considerations in conventional and diffraction x-ray microscopy
journal, January 2009

  • Huang, Xiaojing; Miao, Huijie; Steinbrener, Jan
  • Optics Express, Vol. 17, Issue 16
  • DOI: 10.1364/OE.17.013541

Inertial Proximal Alternating Linearized Minimization (iPALM) for Nonconvex and Nonsmooth Problems
journal, January 2016

  • Pock, Thomas; Sabach, Shoham
  • SIAM Journal on Imaging Sciences, Vol. 9, Issue 4
  • DOI: 10.1137/16M1064064

XDesign : an open-source software package for designing X-ray imaging phantoms and experiments
journal, February 2017


X-ray ptychographic and fluorescence microscopy of frozen-hydrated cells using continuous scanning
journal, March 2017


Breaking the 10 nm barrier in hard-X-ray focusing
journal, November 2009

  • Mimura, Hidekazu; Handa, Soichiro; Kimura, Takashi
  • Nature Physics, Vol. 6, Issue 2
  • DOI: 10.1038/nphys1457

Distributed Automatic Differentiation for Ptychography
journal, January 2017


Takagi-Taupin description of x-ray dynamical diffraction from diffractive optics with large numerical aperture
journal, September 2007


Direct coupling of tomography and ptychography
journal, January 2017


Fly-scan ptychography
journal, March 2015

  • Huang, Xiaojing; Lauer, Kenneth; Clark, Jesse N.
  • Scientific Reports, Vol. 5, Issue 1
  • DOI: 10.1038/srep09074

Zone plates with high efficiency in high orders of diffraction described by dynamical theory
journal, October 1997

  • Schneider, G.
  • Applied Physics Letters, Vol. 71, Issue 16
  • DOI: 10.1063/1.120069

High-Resolution Scanning X-ray Diffraction Microscopy
journal, July 2008


Learning Tomography Assessed Using Mie Theory
journal, March 2018


X-ray ptychographic computed tomography at 16 nm isotropic 3D resolution
journal, January 2014

  • Holler, M.; Diaz, A.; Guizar-Sicairos, M.
  • Scientific Reports, Vol. 4, Issue 1
  • DOI: 10.1038/srep03857

On-the-fly scans for X-ray ptychography
journal, December 2014

  • Pelz, Philipp M.; Guizar-Sicairos, Manuel; Thibault, Pierre
  • Applied Physics Letters, Vol. 105, Issue 25
  • DOI: 10.1063/1.4904943

Dose requirements for resolving a given feature in an object by coherent x-ray diffraction imaging
journal, March 2010


Dynamic Imaging Using Ptychography
journal, March 2014


Chemical composition mapping with nanometre resolution by soft X-ray microscopy
journal, September 2014


Nanoscale X-ray imaging
journal, December 2010


Proximal Heterogeneous Block Implicit-Explicit Method and Application to Blind Ptychographic Diffraction Imaging
journal, January 2015

  • Hesse, Robert; Luke, D. Russell; Sabach, Shoham
  • SIAM Journal on Imaging Sciences, Vol. 8, Issue 1
  • DOI: 10.1137/14098168X

An annealing algorithm to correct positioning errors in ptychography
journal, September 2012


Nanoscale x-ray imaging of circuit features without wafer etching
journal, March 2017


Electron ptychographic microscopy for three-dimensional imaging
journal, July 2017


Learning approach to optical tomography
journal, January 2015

  • Kamilov, Ulugbek S.; Papadopoulos, Ioannis N.; Shoreh, Morteza H.
  • Optica, Vol. 2, Issue 6
  • DOI: 10.1364/OPTICA.2.000517

Translation position determination in ptychographic coherent diffraction imaging
journal, January 2013

  • Zhang, Fucai; Peterson, Isaac; Vila-Comamala, Joan
  • Optics Express, Vol. 21, Issue 11
  • DOI: 10.1364/OE.21.013592

The scattering of electrons by atoms and crystals. I. A new theoretical approach
journal, October 1957


Phase retrieval of arbitrary complex-valued fields through aperture-plane modulation
journal, April 2007


The xraylib library for X-ray–matter interactions. Recent developments
journal, November 2011

  • Schoonjans, Tom; Brunetti, Antonio; Golosio, Bruno
  • Spectrochimica Acta Part B: Atomic Spectroscopy, Vol. 66, Issue 11-12
  • DOI: 10.1016/j.sab.2011.09.011

High-Resolution Multislice X-Ray Ptychography of Extended Thick Objects
journal, February 2014


Satellite radar interferometry: Two-dimensional phase unwrapping
journal, July 1988

  • Goldstein, Richard M.; Zebker, Howard A.; Werner, Charles L.
  • Radio Science, Vol. 23, Issue 4
  • DOI: 10.1029/RS023i004p00713

A phase retrieval algorithm for shifting illumination
journal, November 2004

  • Rodenburg, J. M.; Faulkner, H. M. L.
  • Applied Physics Letters, Vol. 85, Issue 20
  • DOI: 10.1063/1.1823034

Reconstructing state mixtures from diffraction measurements
journal, February 2013


TomoPy: a framework for the analysis of synchrotron tomographic data
journal, August 2014

  • Gürsoy, Dogˇa; De Carlo, Francesco; Xiao, Xianghui
  • Journal of Synchrotron Radiation, Vol. 21, Issue 5
  • DOI: 10.1107/S1600577514013939

Ptychographic transmission microscopy in three dimensions using a multi-slice approach
journal, January 2012

  • Maiden, A. M.; Humphry, M. J.; Rodenburg, J. M.
  • Journal of the Optical Society of America A, Vol. 29, Issue 8
  • DOI: 10.1364/JOSAA.29.001606

An improved ptychographical phase retrieval algorithm for diffractive imaging
journal, September 2009


A novel photocatalytic microreactor bundle that does not require an electric power source
journal, January 2012

  • Katayama, Kenji; Takeda, Yuki; Kuwabara, Kenta
  • Chemical Communications, Vol. 48, Issue 59
  • DOI: 10.1039/c2cc33525e

Artifact mitigation of ptychography integrated with on-the-fly scanning probe microscopy
journal, July 2017

  • Huang, Xiaojing; Yan, Hanfei; Ge, Mingyuan
  • Applied Physics Letters, Vol. 111, Issue 2
  • DOI: 10.1063/1.4993744

Effectiveness of iterative algorithms in recovering phase in the presence of noise
journal, December 2006

  • Williams, Garth; Pfeifer, Mark; Vartanyants, Ivan
  • Acta Crystallographica Section A Foundations of Crystallography, Vol. 63, Issue 1
  • DOI: 10.1107/S0108767306047209

The Reconstruction of a Three-Dimensional Structure from Projections and its Application to Electron Microscopy
journal, June 1970

  • Crowther, R. A.; DeRosier, D. J.; Klug, A.
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 317, Issue 1530
  • DOI: 10.1098/rspa.1970.0119

Multi-slice ptychography with large numerical aperture multilayer Laue lenses
journal, January 2018


Continuous motion scan ptychography: characterization for increased speed in coherent x-ray imaging
journal, January 2015

  • Deng, Junjing; Nashed, Youssef S. G.; Chen, Si
  • Optics Express, Vol. 23, Issue 5
  • DOI: 10.1364/OE.23.005438

Multislice does it all—calculating the performance of nanofocusing X-ray optics
journal, January 2017

  • Li, Kenan; Wojcik, Michael; Jacobsen, Chris
  • Optics Express, Vol. 25, Issue 3
  • DOI: 10.1364/OE.25.001831

X-Ray Interactions: Photoabsorption, Scattering, Transmission, and Reflection at E = 50-30,000 eV, Z = 1-92
journal, July 1993

  • Henke, B. L.; Gullikson, E. M.; Davis, J. C.
  • Atomic Data and Nuclear Data Tables, Vol. 54, Issue 2, p. 181-342
  • DOI: 10.1006/adnd.1993.1013

Optical Tomographic Image Reconstruction Based on Beam Propagation and Sparse Regularization
journal, March 2016

  • Kamilov, Ulugbek S.; Papadopoulos, Ioannis N.; Shoreh, Morteza H.
  • IEEE Transactions on Computational Imaging, Vol. 2, Issue 1
  • DOI: 10.1109/TCI.2016.2519261

Phase tomography from x-ray coherent diffractive imaging projections
journal, January 2011

  • Guizar-Sicairos, Manuel; Diaz, Ana; Holler, Mirko
  • Optics Express, Vol. 19, Issue 22
  • DOI: 10.1364/OE.19.021345

X-ray ptychography with extended depth of field
journal, January 2016

  • Tsai, Esther H. R.; Usov, Ivan; Diaz, Ana
  • Optics Express, Vol. 24, Issue 25
  • DOI: 10.1364/OE.24.029089

Ptychographic X-ray computed tomography at the nanoscale
journal, September 2010

  • Dierolf, Martin; Menzel, Andreas; Thibault, Pierre
  • Nature, Vol. 467, Issue 7314
  • DOI: 10.1038/nature09419

Proximal alternating linearized minimization for nonconvex and nonsmooth problems
journal, July 2013

  • Bolte, Jérôme; Sabach, Shoham; Teboulle, Marc
  • Mathematical Programming, Vol. 146, Issue 1-2
  • DOI: 10.1007/s10107-013-0701-9

Diffraction Images in Systems with an Annular Aperture
journal, February 1953


Continuous scanning mode for ptychography
journal, January 2014

  • Clark, Jesse N.; Huang, Xiaojing; Harder, Ross J.
  • Optics Letters, Vol. 39, Issue 20
  • DOI: 10.1364/OL.39.006066

Subwavelength coherent imaging of periodic samples using a 13.5 nm tabletop high-harmonic light source
journal, March 2017

  • Gardner, Dennis F.; Tanksalvala, Michael; Shanblatt, Elisabeth R.
  • Nature Photonics, Vol. 11, Issue 4
  • DOI: 10.1038/nphoton.2017.33

Coupled wave description of the diffraction by zone plates with high aspect ratios
journal, May 1992


Fourier Images: I - The Point Source
journal, May 1957


Fast Gradient-Based Algorithms for Constrained Total Variation Image Denoising and Deblurring Problems
journal, November 2009


Strategies for high-throughput focused-beam ptychography
journal, August 2017

  • Jacobsen, Chris; Deng, Junjing; Nashed, Youssef
  • Journal of Synchrotron Radiation, Vol. 24, Issue 5
  • DOI: 10.1107/S1600577517009869

The Race to X-ray Microbeam and Nanobeam Science
journal, December 2011


High-resolution diffraction microscopy using the plane-wave field of a nearly diffraction limited focused x-ray beam
journal, August 2009


High-resolution non-destructive three-dimensional imaging of integrated circuits
journal, March 2017

  • Holler, Mirko; Guizar-Sicairos, Manuel; Tsai, Esther H. R.
  • Nature, Vol. 543, Issue 7645
  • DOI: 10.1038/nature21698

    Works referencing / citing this record:

    Coupled ptychography and tomography algorithm improves reconstruction of experimental data
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    Multimodal x-ray nanotomography
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