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 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Gabor, “A new microscopic principle,” Nature161(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. A4(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,” Science284(5423), 2164–2166 (1999).
    [CrossRef] [PubMed]
  21. M. Takeda, W. Wang, Z. Duan, and Y. Miyamoto, “Coherence holography,” Opt. Express13(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. Express17(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. Express20(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. A13(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. B20(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

2009

2007

2005

2003

T. Dartigalongue and F. Hache, “Precise alignment of a longitudinal Pockels cell for time-resolved circular dichorism experiments,” J. Opt. Soc. Am. B20(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

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,” Science284(5423), 2164–2166 (1999).
[CrossRef] [PubMed]

1997

1996

1988

1987

1981

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

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

1969

1966

1965

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

1964

1948

D. Gabor, “A new microscopic principle,” Nature161(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,” Science284(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,” Science284(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,” Nature161(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,” Science284(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,” Science284(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,” Science284(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.

Appl. Phys. Lett.

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

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

J. Opt.

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.

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Nature

D. Gabor, “A new microscopic principle,” Nature161(4098), 777–778 (1948).
[CrossRef] [PubMed]

Opt. Acta (Lond.)

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

Opt. Lasers Eng.

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.

Science

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,” Science284(5423), 2164–2166 (1999).
[CrossRef] [PubMed]

Other

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.

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).

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.

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.

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.

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.

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