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Title: Near-field limitations of Fresnel-regime coherent diffraction imaging

Coherent diffraction imaging (CDI) is a rapidly developing form of imaging that offers the potential of wavelength-limited resolution without image-forming lenses. In CDI, the intensity of the diffraction pattern is measured directly by the detector, and various iterative phase retrieval algorithms are used to “invert” the diffraction pattern and reconstruct a high-resolution image of the sample. But, there are certain requirements in CDI that must be met to reconstruct the object. Although most experiments are conducted in the “far-field”—or Fraunhofer—regime where the requirements are not as stringent, some experiments must be conducted in the “near field” where Fresnel diffraction must be considered. According to the derivation of Fresnel diffraction, successful reconstructions can only be obtained when the small-angle number, a derived quantity, is much less than one. We show, however, that it is not actually necessary to fulfill the small-angle condition. The Fresnel kernel well approximates the exact kernel in regions where the phase oscillates slowly, and in regions of fast oscillations, indicated by large A n , the error between kernels should be negligible due to stationary-phase arguments. Finally we verify, by experiment, this conclusion with a helium neon laser setup and show that it should hold at x-raymore » wavelengths as well.« less
Authors:
ORCiD logo [1] ; ORCiD logo [1] ;  [1] ;  [1] ; ORCiD logo [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Report Number(s):
LA-UR-16-28161
Journal ID: ISSN 2469-9950; PRBMDO; TRN: US1702797
Grant/Contract Number:
AC52-06NA25396; 20120278ER
Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 96; Journal Issue: 5; Conference: American Physical Society 4 Corners Meeting ; 2016-10-21 - 2016-10-22 ; Las Cruces, New Mexico, United States; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Research Org:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org:
USDOE National Nuclear Security Administration (NNSA)
Country of Publication:
United States
Language:
English
Subject:
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND TECHNOLOGY; optics, Fresnel, near field imaging
OSTI Identifier:
1375870
Alternate Identifier(s):
OSTI ID: 1374066

Pound, Benjamin A., Barber, John L., Nguyen, Kimberly, Tyson, Matthew C., and Sandberg, Richard L.. Near-field limitations of Fresnel-regime coherent diffraction imaging. United States: N. p., Web. doi:10.1103/PhysRevB.96.054104.
Pound, Benjamin A., Barber, John L., Nguyen, Kimberly, Tyson, Matthew C., & Sandberg, Richard L.. Near-field limitations of Fresnel-regime coherent diffraction imaging. United States. doi:10.1103/PhysRevB.96.054104.
Pound, Benjamin A., Barber, John L., Nguyen, Kimberly, Tyson, Matthew C., and Sandberg, Richard L.. 2017. "Near-field limitations of Fresnel-regime coherent diffraction imaging". United States. doi:10.1103/PhysRevB.96.054104. https://www.osti.gov/servlets/purl/1375870.
@article{osti_1375870,
title = {Near-field limitations of Fresnel-regime coherent diffraction imaging},
author = {Pound, Benjamin A. and Barber, John L. and Nguyen, Kimberly and Tyson, Matthew C. and Sandberg, Richard L.},
abstractNote = {Coherent diffraction imaging (CDI) is a rapidly developing form of imaging that offers the potential of wavelength-limited resolution without image-forming lenses. In CDI, the intensity of the diffraction pattern is measured directly by the detector, and various iterative phase retrieval algorithms are used to “invert” the diffraction pattern and reconstruct a high-resolution image of the sample. But, there are certain requirements in CDI that must be met to reconstruct the object. Although most experiments are conducted in the “far-field”—or Fraunhofer—regime where the requirements are not as stringent, some experiments must be conducted in the “near field” where Fresnel diffraction must be considered. According to the derivation of Fresnel diffraction, successful reconstructions can only be obtained when the small-angle number, a derived quantity, is much less than one. We show, however, that it is not actually necessary to fulfill the small-angle condition. The Fresnel kernel well approximates the exact kernel in regions where the phase oscillates slowly, and in regions of fast oscillations, indicated by large A n , the error between kernels should be negligible due to stationary-phase arguments. Finally we verify, by experiment, this conclusion with a helium neon laser setup and show that it should hold at x-ray wavelengths as well.},
doi = {10.1103/PhysRevB.96.054104},
journal = {Physical Review B},
number = 5,
volume = 96,
place = {United States},
year = {2017},
month = {8}
}