Abstract

The ideas of incoherent holography were conceived after the invention of coherent-light holography and their concepts seems indirectly related to it. In this work, we adopt an approach based on statistical optics to describe the process of recording of an incoherent-object hologram as a complex spatial coherence function. A Sagnac radial shearing interferometer is used for the correlation of optical fields and a Pockels cell is used to phase shift the interfering fields with the objective to quantify and to retrieve the spatial coherence function.

©2013 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Recent advances in digital holography [Invited]

Wolfgang Osten, Ahmad Faridian, Peng Gao, Klaus Körner, Dinesh Naik, Giancarlo Pedrini, Alok Kumar Singh, Mitsuo Takeda, and Marc Wilke
Appl. Opt. 53(27) G44-G63 (2014)

Digital holography of self-luminous objects by using a Mach–Zehnder setup

Giancarlo Pedrini, Huan Li, Ahmad Faridian, and Wolfgang Osten
Opt. Lett. 37(4) 713-715 (2012)

3-D coherence holography using a modified Sagnac radial shearing interferometer with geometric phase shift

Dinesh N. Naik, Takahiro Ezawa, Yoko Miyamoto, and Mitsuo Takeda
Opt. Express 17(13) 10633-10641 (2009)

More Recommended Articles

References

  • View by:
  • Article Order
  • |
  • Year
  • |
  • Author
  • |
  • Publication
  1. D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
    [Crossref] [PubMed]
  2. L. Mertz and N. O. Young, “Fresnel transformations of images,” in Proceedings of the ICO Conference on Optical instruments and Techniques, K. J. Habell, Ed. (Chapman and Hall Ltd., 1962), p. 305.
  3. A. W. Lohmann, “Wavefront reconstruction for incoherent objects,” J. Opt. Soc. Am. 55, 1555_1–1556 (1965).
  4. G. W. Stroke and R. C. Restrick, “Holography with spatially noncoherent light,” Appl. Phys. Lett. 7(9), 229 (1965).
    [Crossref]
  5. G. Cochran, “New method of making Fresnel transforms,” J. Opt. Soc. Am. 56(11), 1513–1517 (1966).
    [Crossref]
  6. P. J. Peters, “Incoherent holography with mercury light source,” Appl. Phys. Lett. 8(8), 209–210 (1966).
    [Crossref]
  7. H. R. Worthington., “Production of holograms with incoherent illumination,” J. Opt. Soc. Am. 56(10), 1397–1398 (1966).
    [Crossref]
  8. O. Bryngdahl and A. Lohmann, “Variable magnification in incoherent holography,” Appl. Opt. 9(1), 231–232 (1970).
    [Crossref] [PubMed]
  9. C. Roddier, F. Roddier, F. Martin, A. Baranne, and R. Brun, “Twin - Image Holography with Spectrally Broad Light,” J. Opt. 11(3), 149–152 (1980).
    [Crossref]
  10. G. D. Collins, “Achromatic Fourier transform holography,” Appl. Opt. 20(18), 3109–3119 (1981).
    [Crossref] [PubMed]
  11. E. Ribak, C. Roddier, F. Roddier, and J. B. Breckinridge, “Signal-to-noise limitations in white light holography,” Appl. Opt. 27(6), 1183–1186 (1988).
    [Crossref] [PubMed]
  12. C. Falldorf, E. Kolenovic, and W. Osten, “Speckle shearography using a multiband light source,” Opt. Lasers Eng. 40(5-6), 543–552 (2003).
    [Crossref]
  13. A. Kozma and N. Massey, “Bias level reduction of incoherent holograms,” Appl. Opt. 8(2), 393–397 (1969).
    [Crossref] [PubMed]
  14. S.-G. Kim, B. Lee, and E.-S. Kim, “Removal of bias and the conjugate image in incoherent on-axis triangular holography and real-time reconstruction of the complex hologram,” Appl. Opt. 36(20), 4784–4791 (1997).
    [Crossref] [PubMed]
  15. G. Pedrini, H. Li, A. Faridian, and W. Osten, “Digital holography of self-luminous objects by using a Mach-Zehnder setup,” Opt. Lett. 37(4), 713–715 (2012).
    [Crossref] [PubMed]
  16. J. Rosen and G. Brooker, “Digital spatially incoherent Fresnel holography,” Opt. Lett. 32(8), 912–914 (2007).
    [Crossref] [PubMed]
  17. R. Kelner and J. Rosen, “Spatially incoherent single channel digital Fourier holography,” Opt. Lett. 37(17), 3723–3725 (2012).
    [Crossref] [PubMed]
  18. W. H. Carter and E. Wolf, “Correlation theory of wavefields generated by fluctuating three-dimensional, primary, scalar sources: I. General theory,” Opt. Acta (Lond.) 28(2), 227–244 (1981).
    [Crossref]
  19. A. S. Marathay, “Noncoherent-object hologram: its reconstruction and optical processing,” J. Opt. Soc. Am. A 4(10), 1861–1868 (1987).
    [Crossref]
  20. D. L. Marks, R. A. Stack, D. J. Brady, D. C. Munson, and R. B. Brady, “Visible cone-beam tomography with a lensless interferometric camera,” Science 284(5423), 2164–2166 (1999).
    [Crossref] [PubMed]
  21. M. Takeda, W. Wang, Z. Duan, and Y. Miyamoto, “Coherence holography,” Opt. Express 13(23), 9629–9635 (2005).
    [Crossref] [PubMed]
  22. D. N. Naik, T. Ezawa, Y. Miyamoto, and M. Takeda, “3-D coherence holography using a modified Sagnac radial shearing interferometer with geometric phase shift,” Opt. Express 17(13), 10633–10641 (2009).
    [Crossref] [PubMed]
  23. D. N. Naik, T. Ezawa, R. K. Singh, Y. Miyamoto, and M. Takeda, “Coherence holography by achromatic 3-D field correlation of generic thermal light with an imaging Sagnac shearing interferometer,” Opt. Express 20(18), 19658–19669 (2012).
    [Crossref] [PubMed]
  24. C. W. McCutchen, “Generalized Source and the van Cittert-Zernike Theorem: A Study of the Spatial Coherence Required for Interferometry,” J. Opt. Soc. Am. 56(6), 727–732 (1966).
    [Crossref]
  25. J. Rosen and A. Yariv, “General theorem of spatial coherence: application to three-dimensional imaging,” J. Opt. Soc. Am. A 13(10), 2091–2095 (1996).
    [Crossref]
  26. M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, 1970), Chap. 10.
  27. J. W. Goodman, Statistical Optics, 1st ed. (Wiley, 1985), Chap. 5.
  28. M. V. R. K. Murty, “A compact radial shearing interferometer based on the law of refraction,” Appl. Opt. 3(7), 853–857 (1964).
    [Crossref]
  29. T. Dartigalongue and F. Hache, “Precise alignment of a longitudinal Pockels cell for time-resolved circular dichorism experiments,” J. Opt. Soc. Am. B 20(8), 1780–1787 (2003).
    [Crossref]
  30. P. Hariharan, B. F. Oreb, and T. Eiju, “Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm,” Appl. Opt. 26(13), 2504–2506 (1987).
    [Crossref] [PubMed]

2012 (3)

2009 (1)

2007 (1)

2005 (1)

2003 (2)

T. Dartigalongue and F. Hache, “Precise alignment of a longitudinal Pockels cell for time-resolved circular dichorism experiments,” J. Opt. Soc. Am. B 20(8), 1780–1787 (2003).
[Crossref]

C. Falldorf, E. Kolenovic, and W. Osten, “Speckle shearography using a multiband light source,” Opt. Lasers Eng. 40(5-6), 543–552 (2003).
[Crossref]

1999 (1)

D. L. Marks, R. A. Stack, D. J. Brady, D. C. Munson, and R. B. Brady, “Visible cone-beam tomography with a lensless interferometric camera,” Science 284(5423), 2164–2166 (1999).
[Crossref] [PubMed]

1997 (1)

1996 (1)

1988 (1)

1987 (2)

1981 (2)

W. H. Carter and E. Wolf, “Correlation theory of wavefields generated by fluctuating three-dimensional, primary, scalar sources: I. General theory,” Opt. Acta (Lond.) 28(2), 227–244 (1981).
[Crossref]

G. D. Collins, “Achromatic Fourier transform holography,” Appl. Opt. 20(18), 3109–3119 (1981).
[Crossref] [PubMed]

1980 (1)

C. Roddier, F. Roddier, F. Martin, A. Baranne, and R. Brun, “Twin - Image Holography with Spectrally Broad Light,” J. Opt. 11(3), 149–152 (1980).
[Crossref]

1970 (1)

1969 (1)

1966 (4)

1965 (1)

G. W. Stroke and R. C. Restrick, “Holography with spatially noncoherent light,” Appl. Phys. Lett. 7(9), 229 (1965).
[Crossref]

1964 (1)

1948 (1)

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[Crossref] [PubMed]

Baranne, A.

C. Roddier, F. Roddier, F. Martin, A. Baranne, and R. Brun, “Twin - Image Holography with Spectrally Broad Light,” J. Opt. 11(3), 149–152 (1980).
[Crossref]

Brady, D. J.

D. L. Marks, R. A. Stack, D. J. Brady, D. C. Munson, and R. B. Brady, “Visible cone-beam tomography with a lensless interferometric camera,” Science 284(5423), 2164–2166 (1999).
[Crossref] [PubMed]

Brady, R. B.

D. L. Marks, R. A. Stack, D. J. Brady, D. C. Munson, and R. B. Brady, “Visible cone-beam tomography with a lensless interferometric camera,” Science 284(5423), 2164–2166 (1999).
[Crossref] [PubMed]

Breckinridge, J. B.

Brooker, G.

Brun, R.

C. Roddier, F. Roddier, F. Martin, A. Baranne, and R. Brun, “Twin - Image Holography with Spectrally Broad Light,” J. Opt. 11(3), 149–152 (1980).
[Crossref]

Bryngdahl, O.

Carter, W. H.

W. H. Carter and E. Wolf, “Correlation theory of wavefields generated by fluctuating three-dimensional, primary, scalar sources: I. General theory,” Opt. Acta (Lond.) 28(2), 227–244 (1981).
[Crossref]

Cochran, G.

Collins, G. D.

Dartigalongue, T.

Duan, Z.

Eiju, T.

Ezawa, T.

Falldorf, C.

C. Falldorf, E. Kolenovic, and W. Osten, “Speckle shearography using a multiband light source,” Opt. Lasers Eng. 40(5-6), 543–552 (2003).
[Crossref]

Faridian, A.

Gabor, D.

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[Crossref] [PubMed]

Hache, F.

Hariharan, P.

Kelner, R.

Kim, E.-S.

Kim, S.-G.

Kolenovic, E.

C. Falldorf, E. Kolenovic, and W. Osten, “Speckle shearography using a multiband light source,” Opt. Lasers Eng. 40(5-6), 543–552 (2003).
[Crossref]

Kozma, A.

Lee, B.

Li, H.

Lohmann, A.

Marathay, A. S.

Marks, D. L.

D. L. Marks, R. A. Stack, D. J. Brady, D. C. Munson, and R. B. Brady, “Visible cone-beam tomography with a lensless interferometric camera,” Science 284(5423), 2164–2166 (1999).
[Crossref] [PubMed]

Martin, F.

C. Roddier, F. Roddier, F. Martin, A. Baranne, and R. Brun, “Twin - Image Holography with Spectrally Broad Light,” J. Opt. 11(3), 149–152 (1980).
[Crossref]

Massey, N.

McCutchen, C. W.

Miyamoto, Y.

Munson, D. C.

D. L. Marks, R. A. Stack, D. J. Brady, D. C. Munson, and R. B. Brady, “Visible cone-beam tomography with a lensless interferometric camera,” Science 284(5423), 2164–2166 (1999).
[Crossref] [PubMed]

Murty, M. V. R. K.

Naik, D. N.

Oreb, B. F.

Osten, W.

G. Pedrini, H. Li, A. Faridian, and W. Osten, “Digital holography of self-luminous objects by using a Mach-Zehnder setup,” Opt. Lett. 37(4), 713–715 (2012).
[Crossref] [PubMed]

C. Falldorf, E. Kolenovic, and W. Osten, “Speckle shearography using a multiband light source,” Opt. Lasers Eng. 40(5-6), 543–552 (2003).
[Crossref]

Pedrini, G.

Peters, P. J.

P. J. Peters, “Incoherent holography with mercury light source,” Appl. Phys. Lett. 8(8), 209–210 (1966).
[Crossref]

Restrick, R. C.

G. W. Stroke and R. C. Restrick, “Holography with spatially noncoherent light,” Appl. Phys. Lett. 7(9), 229 (1965).
[Crossref]

Ribak, E.

Roddier, C.

E. Ribak, C. Roddier, F. Roddier, and J. B. Breckinridge, “Signal-to-noise limitations in white light holography,” Appl. Opt. 27(6), 1183–1186 (1988).
[Crossref] [PubMed]

C. Roddier, F. Roddier, F. Martin, A. Baranne, and R. Brun, “Twin - Image Holography with Spectrally Broad Light,” J. Opt. 11(3), 149–152 (1980).
[Crossref]

Roddier, F.

E. Ribak, C. Roddier, F. Roddier, and J. B. Breckinridge, “Signal-to-noise limitations in white light holography,” Appl. Opt. 27(6), 1183–1186 (1988).
[Crossref] [PubMed]

C. Roddier, F. Roddier, F. Martin, A. Baranne, and R. Brun, “Twin - Image Holography with Spectrally Broad Light,” J. Opt. 11(3), 149–152 (1980).
[Crossref]

Rosen, J.

Singh, R. K.

Stack, R. A.

D. L. Marks, R. A. Stack, D. J. Brady, D. C. Munson, and R. B. Brady, “Visible cone-beam tomography with a lensless interferometric camera,” Science 284(5423), 2164–2166 (1999).
[Crossref] [PubMed]

Stroke, G. W.

G. W. Stroke and R. C. Restrick, “Holography with spatially noncoherent light,” Appl. Phys. Lett. 7(9), 229 (1965).
[Crossref]

Takeda, M.

Wang, W.

Wolf, E.

W. H. Carter and E. Wolf, “Correlation theory of wavefields generated by fluctuating three-dimensional, primary, scalar sources: I. General theory,” Opt. Acta (Lond.) 28(2), 227–244 (1981).
[Crossref]

Worthington, H. R.

Yariv, A.

Appl. Opt. (7)

Appl. Phys. Lett. (2)

P. J. Peters, “Incoherent holography with mercury light source,” Appl. Phys. Lett. 8(8), 209–210 (1966).
[Crossref]

G. W. Stroke and R. C. Restrick, “Holography with spatially noncoherent light,” Appl. Phys. Lett. 7(9), 229 (1965).
[Crossref]

J. Opt. (1)

C. Roddier, F. Roddier, F. Martin, A. Baranne, and R. Brun, “Twin - Image Holography with Spectrally Broad Light,” J. Opt. 11(3), 149–152 (1980).
[Crossref]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. B (1)

Nature (1)

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[Crossref] [PubMed]

Opt. Acta (Lond.) (1)

W. H. Carter and E. Wolf, “Correlation theory of wavefields generated by fluctuating three-dimensional, primary, scalar sources: I. General theory,” Opt. Acta (Lond.) 28(2), 227–244 (1981).
[Crossref]

Opt. Express (3)

Opt. Lasers Eng. (1)

C. Falldorf, E. Kolenovic, and W. Osten, “Speckle shearography using a multiband light source,” Opt. Lasers Eng. 40(5-6), 543–552 (2003).
[Crossref]

Opt. Lett. (3)

Science (1)

D. L. Marks, R. A. Stack, D. J. Brady, D. C. Munson, and R. B. Brady, “Visible cone-beam tomography with a lensless interferometric camera,” Science 284(5423), 2164–2166 (1999).
[Crossref] [PubMed]

Other (4)

L. Mertz and N. O. Young, “Fresnel transformations of images,” in Proceedings of the ICO Conference on Optical instruments and Techniques, K. J. Habell, Ed. (Chapman and Hall Ltd., 1962), p. 305.

A. W. Lohmann, “Wavefront reconstruction for incoherent objects,” J. Opt. Soc. Am. 55, 1555_1–1556 (1965).

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, 1970), Chap. 10.

J. W. Goodman, Statistical Optics, 1st ed. (Wiley, 1985), Chap. 5.

Supplementary Material (4)

» Media 1: MP4 (552 KB)     
» Media 2: MP4 (566 KB)     
» Media 3: MP4 (583 KB)     
» Media 4: MP4 (599 KB)     

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1 Geometry for recording of information from an incoherently illuminated object.

Download Full Size | PPT Slide | PDF

Fig. 2
Fig. 2 (a) Experimental set up for recording the hologram as complex spatial coherence function. (b) -(e) One of the interferograms recorded with objects 1, 2, 3 and 4 respectively shown in top left corner in (a). (f)-(i) corresponding fringe contrast and (j)-(m) corresponding fringe phase jointly representing the complex spatial coherence function at the back focal plane of lens L1.

Download Full Size | PPT Slide | PDF

Fig. 3
Fig. 3 Photographs showing different sections in focus (a), (b) of object 1; (c), (d) of object 2; (e), (f) of object 3 and (g) of object 4.

Download Full Size | PPT Slide | PDF

Fig. 4
Fig. 4 (a)-(d) Single-frame excerpts from video and describe a combined image of amplitude and phase of the reconstructed objects, object 1 (Media 1), object 2 (Media 2), object 3 (Media 3)and object 4 (Media 4) respectively. The corresponding media files show the amplitude and phase of the reconstructed object in x-y plane as we vary z from −5mm to + 5mm.

Download Full Size | PPT Slide | PDF

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

U ' λ ( x ^ , y ^ , z ^ =0,z' )= exp[ −i k Z ( x ^ , y ^ ;λ )z' ] iλf ∬ A λ ( x,y,z',t )exp[ −i 2π λf ( x x ^ +y y ^ ) ] dxdy
Γ ' λ ( x ^ 1 , y ^ 1 , x ^ 2 , y ^ 2 , z ^ =0,z' )=〈 U ' λ * ( x ^ 1 , y ^ 1 , z ^ =0,z' )U ' λ ( x ^ 2 , y ^ 2 , z ^ =0,z' ) 〉
 Γ ' λ ( x ^ 1 , y ^ 1 , x ^ 2 , y ^ 2 , z ^ =0,z' ) =κ ( λf ) −2 exp[ −i[ k Z ( x ^ 2 , y ^ 2 ;λ )− k Z ( x ^ 1 , y ^ 1 ;λ ) ]z' ]                                                         × ∬ η( x 1 , y 1 ,z';λ ) exp[ −i 2π λf ( x 1 ( x ^ 2 − x ^ 1 )+ y 1 ( y ^ 2 − y ^ 1 ) ) ]d x 1 d y 1
〈 A λ * ( x 1 , y 1 ,z',t ) A λ ( x 2 , y 2 ,z',t ) 〉 t =κη( x 1 , y 1 ,z';λ )δ( x 2 − x 1 , y 2 − y 1 )
Γ( x ^ 1 , y ^ 1 , x ^ 2 , y ^ 2 , z ^ =0 ) = ∬ Γ ' λ ( x ^ 1 , x ^ 2 , y ^ 1 , y ^ 2 , z ^ =0,z' )dz'dλ                                              =κ f −2 ∬ λ −2 exp[ −i[ k Z ( x ^ 2 , y ^ 2 ;λ )− k Z ( x ^ 1 , y ^ 1 ;λ ) ]z' ]                              ×{ ∬ η( x 1 , y 1 ,z';λ ) exp[ −i 2π λf ( x 1 ( x ^ 2 − x ^ 1 )+ y 1 ( y ^ 2 − y ^ 1 ) ) ]d x 1 d y 1 }dz'dλ
η ˜ ( x,y,z )= ∬ Γ( x ^ 1 , y ^ 1 , x ^ 2 , y ^ 2 , z ^ =0 ) exp[ i[ k Z ( x ^ 2 , y ^ 2 ;λ )− k Z ( x ^ 1 , y ^ 1 ;λ ) ]z ]                         ×exp[ i 2π λf ( x( x ^ 2 − x ^ 1 )+y( y ^ 2 − y ^ 1 ) ) ]d( x ^ 2 − x ^ 1 )d( y ^ 2 − y ^ 1 )                     = ( α− α −1 ) 2 ∬ Γ( α −1 x ^ , α −1 y ^ ,α x ^ ,α y ^ , z ^ =0 )                 ×exp[ i[ k Z ( α x ^ ,α y ^ ;λ )− k Z ( α −1 x ^ , α −1 y ^ ;λ ) ]z ]exp[ i 2π λf ( α− α −1 )( x 1 x ^ + y 1 y ^ ) ]d x ^ d y ^

Metrics