Holographic phase retrieval and reference design

Barmherzig, David A.; Sun, Ju; Li, Po-Nan; Lane, T. J.; Candès, Emmanuel J.

doi:10.1088/1361-6420/ab23d1

Title: Holographic phase retrieval and reference design

Journal Article · 20 August 2019 · Inverse Problems

DOI: https://doi.org/10.1088/1361-6420/ab23d1 · OSTI ID:1562461

^[1]; Sun, Ju ^[1]; Li, Po-Nan ^[1]; Lane, T. J. ^[2]; Candès, Emmanuel J. ^[1]

Stanford Univ., CA (United States)
SLAC National Accelerator Lab., Menlo Park, CA (United States)

Here, a general mathematical framework and recovery algorithm is introduced for the holographic phase retrieval problem. In this problem, which arises in holographic coherent diffraction imaging, a 'reference' portion of the signal to be recovered via phase retrieval is a priori known from experimental design. A generic formula is additionally derived for the expected recovery error when the measurement data is corrupted by Poisson shot noise. This facilitates an optimization perspective towards reference design and analysis. We employ this optimization perspective towards quantifying the performance of various reference choices.

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Research Organization:: SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC02-76SF00515

OSTI ID:: 1562461

Journal Information:: Inverse Problems, Journal Name: Inverse Problems Journal Issue: 9 Vol. 35; ISSN 0266-5611

Publisher:: IOPscienceCopyright Statement

Country of Publication:: United States

Language:: English

References (60)

Über spontane Stromschwankungen in verschiedenen Elektrizitätsleitern Schottky, W. Annalen der Physik, Vol. 362, Issue 23 https://doi.org/10.1002/andp.19183622304	journal	January 1918
Phase retrieval with masks using convex optimization Jaganathan, Kishore; Eldar, Yonina; Hassibi, Babak 2015 IEEE International Symposium on Information Theory (ISIT) https://doi.org/10.1109/isit.2015.7282737	conference	June 2015
Influence of detector noise in holographic imaging with limited photon flux Wahyutama, I. S.; Tadesse, G. K.; Tünnermann, A. Optics Express, Vol. 24, Issue 19 https://doi.org/10.1364/oe.24.022013	journal	January 2016
Phase Retrieval via Wirtinger Flow: Theory and Algorithms Candes, Emmanuel; Li, Xiaodong; Soltanolkotabi, Mahdi arXiv https://doi.org/10.48550/arxiv.1407.1065	text	January 2014
Coherent X-Ray Diffraction Imaging and Characterization of Strain in Silicon-on-Insulator Nanostructures Xiong, Gang; Moutanabbir, Oussama; Reiche, Manfred Advanced Materials, Vol. 26, Issue 46 https://doi.org/10.1002/adma.201304511	journal	June 2014
Über spontane Stromschwankungen in verschiedenen Elektrizitätsleitern Schottky, W. Annalen der Physik, Vol. 362, Issue 23 https://doi.org/10.1002/andp.19183622304	journal	January 1918
X-ray holography of lensless Fourier-transform type Kikuta, S.; Aoki, S.; Kosaki, S. Optics Communications, Vol. 5, Issue 2 https://doi.org/10.1016/0030-4018(72)90005-3	journal	May 1972
Phase retrieval from coded diffraction patterns Candès, Emmanuel J.; Li, Xiaodong; Soltanolkotabi, Mahdi Applied and Computational Harmonic Analysis, Vol. 39, Issue 2 https://doi.org/10.1016/j.acha.2014.09.004	journal	September 2015
Direct retrieval of a complex wave from its diffraction pattern Martin, A. V.; Allen, L. J. Optics Communications, Vol. 281, Issue 20 https://doi.org/10.1016/j.optcom.2008.07.006	journal	October 2008
High-Dimensional Probability: An Introduction with Applications in Data Science Vershynin, Roman https://doi.org/10.1017/9781108231596	book	September 2018
Fourier Transform Holography: A Lensless Non-Destructive Imaging Technique Saliba, M.; Latychevskaia, T.; Longchamp, J. Microscopy and Microanalysis, Vol. 18, Issue S2 https://doi.org/10.1017/S1431927612004679	journal	July 2012
A New Microscopic Principle Gabor, D. Nature, Vol. 161, Issue 4098 https://doi.org/10.1038/161777a0	journal	May 1948
Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens Miao, Jianwei; Charalambous, Pambos; Kirz, Janos Nature, Vol. 400, Issue 6742 https://doi.org/10.1038/22498	journal	July 1999
Lensless imaging of magnetic nanostructures by X-ray spectro-holography Eisebitt, S.; Lüning, J.; Schlotter, W. F. Nature, Vol. 432, Issue 7019 https://doi.org/10.1038/nature03139	journal	December 2004
Fractal morphology, imaging and mass spectrometry of single aerosol particles in flight Loh, N. D.; Hampton, C. Y.; Martin, A. V. Nature, Vol. 486, Issue 7404 https://doi.org/10.1038/nature11222	journal	June 2012
Massively parallel X-ray holography Marchesini, Stefano; Boutet, Sébastien; Sakdinawat, Anne E. Nature Photonics, Vol. 2, Issue 9 https://doi.org/10.1038/nphoton.2008.154	journal	August 2008
Femtosecond diffractive imaging with a soft-X-ray free-electron laser Chapman, Henry N.; Barty, Anton; Bogan, Michael J. Nature Physics, Vol. 2, Issue 12 https://doi.org/10.1038/nphys461	journal	November 2006
In situ coherent diffractive imaging Lo, Yuan Hung; Zhao, Lingrong; Gallagher-Jones, Marcus Nature Communications, Vol. 9, Issue 1 https://doi.org/10.1038/s41467-018-04259-9	journal	May 2018
Femtosecond X-ray Fourier holography imaging of free-flying nanoparticles Gorkhover, Tais; Ulmer, Anatoli; Ferguson, Ken Nature Photonics, Vol. 12, Issue 3 https://doi.org/10.1038/s41566-018-0110-y	journal	February 2018
Invited Article: A unified evaluation of iterative projection algorithms for phase retrieval Marchesini, S. Review of Scientific Instruments, Vol. 78, Issue 1 https://doi.org/10.1063/1.2403783	journal	January 2007
Searching with iterated maps Elser, V.; Rankenburg, I.; Thibault, P. Proceedings of the National Academy of Sciences, Vol. 104, Issue 2 https://doi.org/10.1073/pnas.0606359104	journal	January 2007
The Question of Phase Retrieval in Optics Walther, Adriaan Optica Acta: International Journal of Optics, Vol. 10, Issue 1 https://doi.org/10.1080/713817747	journal	January 1963
Relaxed averaged alternating reflections for diffraction imaging Luke, D. Russell Inverse Problems, Vol. 21, Issue 1 https://doi.org/10.1088/0266-5611/21/1/004	journal	November 2004
Phase retrieval in x-ray imaging based on using structured illumination Liu, Y. J.; Chen, B.; Li, E. R. Physical Review A, Vol. 78, Issue 2 https://doi.org/10.1103/PhysRevA.78.023817	journal	August 2008
Coherent Diffractive Imaging Using Phase Front Modifications Johnson, I.; Jefimovs, K.; Bunk, O. Physical Review Letters, Vol. 100, Issue 15 https://doi.org/10.1103/PhysRevLett.100.155503	journal	April 2008
High-Resolution X-Ray Lensless Imaging by Differential Holographic Encoding Zhu, Diling; Guizar-Sicairos, Manuel; Wu, Benny Physical Review Letters, Vol. 105, Issue 4 https://doi.org/10.1103/PhysRevLett.105.043901	journal	July 2010
Reconstruction of the Shapes of Gold Nanocrystals Using Coherent X-Ray Diffraction Robinson, I. K.; Vartanyants, I. A.; Williams, G. J. Physical Review Letters, Vol. 87, Issue 19 https://doi.org/10.1103/PhysRevLett.87.195505	journal	October 2001
Diffractive imaging for periodic samples: retrieving one-dimensional concentration profiles across microfluidic channels Bunk, Oliver; Diaz, Ana; Pfeiffer, Franz Acta Crystallographica Section A Foundations of Crystallography, Vol. 63, Issue 4 https://doi.org/10.1107/S0108767307021903	journal	June 2007
Relaxed averaged alternating reflections for diffraction imaging Luke, R. Acta Crystallographica Section A Foundations of Crystallography, Vol. 64, Issue a1 https://doi.org/10.1107/s0108767308096529	journal	August 2008
On phase retrieval of finite-length sequences using the initial time sample Sahinoglou, H.; Cabrera, S. D. IEEE Transactions on Circuits and Systems, Vol. 38, Issue 8 https://doi.org/10.1109/31.85639	journal	January 1991
Phase Retrieval with Application to Optical Imaging: A contemporary overview Shechtman, Yoav; Eldar, Yonina C.; Cohen, Oren IEEE Signal Processing Magazine, Vol. 32, Issue 3 https://doi.org/10.1109/MSP.2014.2352673	journal	May 2015
The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform Hayes, M. IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. 30, Issue 2 https://doi.org/10.1109/TASSP.1982.1163863	journal	April 1982
Phase Retrieval via Wirtinger Flow: Theory and Algorithms Candes, Emmanuel J.; Li, Xiaodong; Soltanolkotabi, Mahdi IEEE Transactions on Information Theory, Vol. 61, Issue 4 https://doi.org/10.1109/TIT.2015.2399924	journal	April 2015
Beyond crystallography: Diffractive imaging using coherent x-ray light sources Miao, J.; Ishikawa, T.; Robinson, I. K. Science, Vol. 348, Issue 6234 https://doi.org/10.1126/science.aaa1394	journal	April 2015
Phase Retrieval via Matrix Completion Candès, Emmanuel J.; Eldar, Yonina C.; Strohmer, Thomas SIAM Journal on Imaging Sciences, Vol. 6, Issue 1 https://doi.org/10.1137/110848074	journal	January 2013
Phase Retrieval via Matrix Completion Candès, Emmanuel J.; Eldar, Yonina C.; Strohmer, Thomas SIAM Review, Vol. 57, Issue 2 https://doi.org/10.1137/151005099	journal	January 2015
On Block-Reference Coherent Diffraction Imaging Barmherzig, David A.; Sun, Ju; Lane, T. J. Computational Optical Sensing and Imaging, Imaging and Applied Optics 2018 (3D, AO, AIO, COSI, DH, IS, LACSEA, LS&C, MATH, pcAOP) https://doi.org/10.1364/COSI.2018.CTH1B.1	conference	January 2018
Reconstructed Wavefronts and Communication Theory* Leith, Emmett N.; Upatnieks, Juris Journal of the Optical Society of America, Vol. 52, Issue 10 https://doi.org/10.1364/JOSA.52.001123	journal	January 1962
Phase retrieval by iterated projections Elser, Veit Journal of the Optical Society of America A, Vol. 20, Issue 1 https://doi.org/10.1364/JOSAA.20.000040	journal	January 2003
Phase retrieval in crystallography and optics Millane, R. P. Journal of the Optical Society of America A, Vol. 7, Issue 3 https://doi.org/10.1364/JOSAA.7.000394	journal	January 1990
Phase retrieval using two Fourier-transform intensities Kim, Wooshik; Hayes, Monson H. Journal of the Optical Society of America A, Vol. 7, Issue 3 https://doi.org/10.1364/JOSAA.7.000441	journal	January 1990
A non-iterative reconstruction method for direct and unambiguous coherent diffractive imaging Podorov, S. G.; Pavlov, K. M.; Paganin, D. M. Optics Express, Vol. 15, Issue 16 https://doi.org/10.1364/OE.15.009954	journal	January 2007
Holography with extended reference by autocorrelation linear differential operation Guizar-Sicairos, Manuel; Fienup, James R. Optics Express, Vol. 15, Issue 26 https://doi.org/10.1364/OE.15.017592	journal	January 2007
High dynamic range coherent imaging using compressed sensing He, Kuan; Sharma, Manoj Kumar; Cossairt, Oliver Optics Express, Vol. 23, Issue 24 https://doi.org/10.1364/OE.23.030904	journal	January 2015
Influence of detector noise in holographic imaging with limited photon flux Wahyutama, I. S.; Tadesse, G. K.; Tünnermann, A. Optics Express, Vol. 24, Issue 19 https://doi.org/10.1364/OE.24.022013	journal	January 2016
Reconstruction of an object from the modulus of its Fourier transform Fienup, J. R. Optics Letters, Vol. 3, Issue 1, p. 27-29 https://doi.org/10.1364/OL.3.000027	journal	January 1978
Direct image reconstruction from a Fourier intensity pattern using HERALDO Guizar-Sicairos, Manuel; Fienup, James R. Optics Letters, Vol. 33, Issue 22 https://doi.org/10.1364/OL.33.002668	journal	January 2008
Ameobal Pathogen Mimivirus Infects Macrophages through Phagocytosis Ghigo, Eric; Kartenbeck, Jürgen; Lien, Pham PLoS Pathogens, Vol. 4, Issue 6 https://doi.org/10.1371/journal.ppat.1000087	journal	June 2008
Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers Boyd, Stephen; Parikh, Neal; Chu, Eric https://doi.org/10.1561/2200000016	book	January 2011
Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers Boyd, Stephen Now Foundations and Trends https://doi.org/10.1561/9781601984616		January 2010
Reconstruction of the Shapes of Gold Nanocrystals Using Coherent X-Ray Diffraction Pfeifer, M. A.; Pitney, J. A.; Robinson, I. K. The American Physical Society https://doi.org/10.17877/de290r-11299	text	January 2001
Femtosecond X-ray Fourier holography imaging of free-flying nanoparticles Gorkhover, Tais; Ulmer, Anatoli; Ferguson, Ken Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2018-01363	text	January 2018
Ameobal Pathogen Mimivirus Infects Macrophages through Phagocytosis Ghigo, Eric; Kartenbeck, Jürgen; Lien, Pham ETH Zurich https://doi.org/10.3929/ethz-b-000010855	text	January 2008
Phase Retrieval via Matrix Completion Candes, Emmanuel J.; Eldar, Yonina; Strohmer, Thomas arXiv https://doi.org/10.48550/arxiv.1109.0573	preprint	January 2011
Phase Retrieval from Coded Diffraction Patterns Candes, Emmanuel; Li, Xiaodong; Soltanolkotabi, Mahdi arXiv https://doi.org/10.48550/arxiv.1310.3240	preprint	January 2013
Phase Retrieval via Wirtinger Flow: Theory and Algorithms Candes, Emmanuel; Li, Xiaodong; Soltanolkotabi, Mahdi arXiv https://doi.org/10.48550/arxiv.1407.1065	text	January 2014
In situ coherent diffractive imaging Lo, Yuan Hung; Zhao, Lingrong; Gallagher-Jones, Marcus arXiv https://doi.org/10.48550/arxiv.1703.07219	text	January 2017
Phase retrieval by iterated projections Elser, Veit arXiv https://doi.org/10.48550/arxiv.math/0111080	preprint	January 2001
Relaxed Averaged Alternating Reflections for Diffraction Imaging Luke, D. Russell arXiv https://doi.org/10.48550/arxiv.math/0405208	text	January 2004
Fourier transform holography: a lensless non-destructive imaging technique Saliba, M.; Latychevskaia, T.; Longchamp, J. Cambridge University Press https://doi.org/10.5167/uzh-155371	text	January 2012

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