Least-squares based inverse reconstruction of in-line digital holograms

Edwin Kamau, Nicholas M. Burns, Claas Falldorf, Christoph von Kopylow, John Watson, Ralf B. Bergmann

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We present a least-squares solution for the inverse problem in in-line digital holography which is based on a point source model. We demonstrate that by reformulating the reconstruction problem as an inverse problem and by integrating a contour gradient based auto-focus search algorithm into the reconstruction routine, a more fundamental solution for the inversion of a hologram can be attained. With this approach the inversion can be calculated without any prior knowledge of the object's shape/size and without imposing any constraints on the imaging system. In a proof-of-concept study we show that our method facilitates a more accurate reconstruction, as compared to conventional methods, and that it facilitates object localization with an accuracy on the order of the optical wavelength.
Original languageEnglish
Article number075716
Pages (from-to)1-10
Number of pages10
JournalJournal of Optics
Volume15
Issue number7
DOIs
Publication statusPublished - 2 Jul 2013

Fingerprint

Holograms
Inverse problems
Holography
Imaging systems
inversions
holography
Wavelength
point sources
gradients
wavelengths

Keywords

  • diffraction
  • interference
  • holography
  • inverse problems
  • auto-focus schemes

Cite this

Kamau, E., Burns, N. M., Falldorf, C., von Kopylow, C., Watson, J., & Bergmann, R. B. (2013). Least-squares based inverse reconstruction of in-line digital holograms. Journal of Optics, 15(7), 1-10. [075716]. https://doi.org/10.1088/2040-8978/15/7/075716

Least-squares based inverse reconstruction of in-line digital holograms. / Kamau, Edwin; Burns, Nicholas M.; Falldorf, Claas; von Kopylow, Christoph; Watson, John; Bergmann, Ralf B.

In: Journal of Optics, Vol. 15, No. 7, 075716, 02.07.2013, p. 1-10.

Research output: Contribution to journalArticle

Kamau, E, Burns, NM, Falldorf, C, von Kopylow, C, Watson, J & Bergmann, RB 2013, 'Least-squares based inverse reconstruction of in-line digital holograms', Journal of Optics, vol. 15, no. 7, 075716, pp. 1-10. https://doi.org/10.1088/2040-8978/15/7/075716
Kamau, Edwin ; Burns, Nicholas M. ; Falldorf, Claas ; von Kopylow, Christoph ; Watson, John ; Bergmann, Ralf B. / Least-squares based inverse reconstruction of in-line digital holograms. In: Journal of Optics. 2013 ; Vol. 15, No. 7. pp. 1-10.
@article{3403abdccf0f4497906c1beb66a9ad64,
title = "Least-squares based inverse reconstruction of in-line digital holograms",
abstract = "We present a least-squares solution for the inverse problem in in-line digital holography which is based on a point source model. We demonstrate that by reformulating the reconstruction problem as an inverse problem and by integrating a contour gradient based auto-focus search algorithm into the reconstruction routine, a more fundamental solution for the inversion of a hologram can be attained. With this approach the inversion can be calculated without any prior knowledge of the object's shape/size and without imposing any constraints on the imaging system. In a proof-of-concept study we show that our method facilitates a more accurate reconstruction, as compared to conventional methods, and that it facilitates object localization with an accuracy on the order of the optical wavelength.",
keywords = "diffraction, interference, holography, inverse problems, auto-focus schemes",
author = "Edwin Kamau and Burns, {Nicholas M.} and Claas Falldorf and {von Kopylow}, Christoph and John Watson and Bergmann, {Ralf B.}",
note = "Acknowledgments The authors would like to thank the Deutsche Forschungsgemeinschaft (DFG) for the financial support of the project HoloReForm (grant number: KO 2894/3-2) and the subproject B5 in the Collaborative Research Center SFB-747.",
year = "2013",
month = "7",
day = "2",
doi = "10.1088/2040-8978/15/7/075716",
language = "English",
volume = "15",
pages = "1--10",
journal = "Journal of Optics",
issn = "2040-8986",
publisher = "IOP Publishing Ltd.",
number = "7",

}

TY - JOUR

T1 - Least-squares based inverse reconstruction of in-line digital holograms

AU - Kamau, Edwin

AU - Burns, Nicholas M.

AU - Falldorf, Claas

AU - von Kopylow, Christoph

AU - Watson, John

AU - Bergmann, Ralf B.

N1 - Acknowledgments The authors would like to thank the Deutsche Forschungsgemeinschaft (DFG) for the financial support of the project HoloReForm (grant number: KO 2894/3-2) and the subproject B5 in the Collaborative Research Center SFB-747.

PY - 2013/7/2

Y1 - 2013/7/2

N2 - We present a least-squares solution for the inverse problem in in-line digital holography which is based on a point source model. We demonstrate that by reformulating the reconstruction problem as an inverse problem and by integrating a contour gradient based auto-focus search algorithm into the reconstruction routine, a more fundamental solution for the inversion of a hologram can be attained. With this approach the inversion can be calculated without any prior knowledge of the object's shape/size and without imposing any constraints on the imaging system. In a proof-of-concept study we show that our method facilitates a more accurate reconstruction, as compared to conventional methods, and that it facilitates object localization with an accuracy on the order of the optical wavelength.

AB - We present a least-squares solution for the inverse problem in in-line digital holography which is based on a point source model. We demonstrate that by reformulating the reconstruction problem as an inverse problem and by integrating a contour gradient based auto-focus search algorithm into the reconstruction routine, a more fundamental solution for the inversion of a hologram can be attained. With this approach the inversion can be calculated without any prior knowledge of the object's shape/size and without imposing any constraints on the imaging system. In a proof-of-concept study we show that our method facilitates a more accurate reconstruction, as compared to conventional methods, and that it facilitates object localization with an accuracy on the order of the optical wavelength.

KW - diffraction

KW - interference

KW - holography

KW - inverse problems

KW - auto-focus schemes

U2 - 10.1088/2040-8978/15/7/075716

DO - 10.1088/2040-8978/15/7/075716

M3 - Article

VL - 15

SP - 1

EP - 10

JO - Journal of Optics

JF - Journal of Optics

SN - 2040-8986

IS - 7

M1 - 075716

ER -