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

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References

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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)

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. (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)

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)     

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Figures (4)

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

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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.

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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.

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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.

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Equations (6)

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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 ^

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