Abstract

This paper presents a detailed analysis of the influence of the pixel dimension in digitally-recorded holograms. The investigation is based on both theoretical and experimental viewpoints for recordings beyond the Shannon limits. After discussing the pixel paradox, the sinc amplitude modulation is experimentally demonstration. The experimental analysis is well correlated to the theoretical basics; in addition, the filling factor of the sensor can be estimated. The analysis of the phase changes of the object show that they can be obtained with a very good contrast and that they are only limited by the decorrelation noise, as when the Shannon conditions are fulfilled.

© 2012 OSA

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  25. I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett.22(16), 1268–1270 (1997).
    [CrossRef] [PubMed]
  26. P. Picart, R. Mercier, M. Lamare, and J.-M. Breteau, “A simple method for measuring the random variation of an interferometer,” Meas. Sci. Technol.12(8), 1311–1317 (2001).
    [CrossRef]
  27. D. Middleton, Introduction to Statistical Communication Theory (McGraw Hill, 1960).
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  29. H. A. Aebischer and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun.162(4-6), 205–210 (1999).
    [CrossRef]

2012

M. Karray, P. Slangen, and P. Picart, “Comparison between digital Fresnel holography and digital image-plane holography: the role of the imaging aperture,” Exp. Mech. (2012), doi:.
[CrossRef]

2011

2009

2008

D. P. Kelly, B. M. Hennelly, C. McElhinney, and T. J. Naughton, “A practical guide to digital holography and generalized sampling,” Proc. SPIE7072, 707215 (2008).
[CrossRef]

P. Picart and J. Leval, “General theoretical formulation of image formation in digital Fresnel holography,” J. Opt. Soc. Am. A25(7), 1744–1761 (2008).
[CrossRef] [PubMed]

2005

2004

M. Liebling, T. Blu, and M. Unser, “Complex-wave retrieval from a single off-axis hologram,” J. Opt. Soc. Am. A21(3), 367–377 (2004).
[CrossRef] [PubMed]

A. Stern and B. Javidi, “Analysis of practical sampling and reconstruction from Fresnel fields,” Opt. Eng.43(1), 239–250 (2004).
[CrossRef]

2003

C. S. Guo, L. Zhang, Z. Y. Rong, and H. T. Wang, “Effect of the fill factor of CCD pixels on digital holograms: comment on the paper,” Opt. Eng.42(9), 2768–2772 (2003).
[CrossRef]

Y. Zhang, G. Pedrini, W. Osten, and H. J. Tiziani, “Image reconstruction for in-line holography with the Yang-Gu algorithm,” Appl. Opt.42(32), 6452–6457 (2003).
[CrossRef] [PubMed]

2002

Th. Kreis, “Frequency analysis of digital holography,” Opt. Eng.41(4), 771–778 (2002).
[CrossRef]

Th. Kreis, “Frequency analysis of digital holography with reconstruction by convolution,” Opt. Eng.41(8), 1829–1839 (2002).
[CrossRef]

2001

P. Picart, R. Mercier, M. Lamare, and J.-M. Breteau, “A simple method for measuring the random variation of an interferometer,” Meas. Sci. Technol.12(8), 1311–1317 (2001).
[CrossRef]

I. Yamaguchi, J. Kato, S. Ohta, and J. Mizuno, “Image formation in phase-shifting digital holography and applications to microscopy,” Appl. Opt.40(34), 6177–6186 (2001).
[CrossRef] [PubMed]

1999

C. Wagner, S. Seebacher, W. Osten, and W. Jüptner, “Digital recording and numerical reconstruction of lensless Fourier holograms in optical metrology,” Appl. Opt.38(22), 4812–4820 (1999).
[CrossRef] [PubMed]

H. A. Aebischer and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun.162(4-6), 205–210 (1999).
[CrossRef]

1997

I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett.22(16), 1268–1270 (1997).
[CrossRef] [PubMed]

Th. Kreis, M. Adams, and W. Jüptner, “Methods of digital holography: a comparison,” Proc. SPIE3098, 224–233 (1997).
[CrossRef]

1994

1993

1972

M. A. Kronrod, N. S. Merzlyakov, and L. P. Yaroslavskii, “Reconstruction of a hologram with a computer,” Sov. Phys. Tech. Phys.17, 333–334 (1972).

1967

J. W. Goodman and R. W. Laurence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett.11(3), 77–79 (1967).
[CrossRef]

Adams, M.

Th. Kreis, M. Adams, and W. Jüptner, “Methods of digital holography: a comparison,” Proc. SPIE3098, 224–233 (1997).
[CrossRef]

Aebischer, H. A.

H. A. Aebischer and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun.162(4-6), 205–210 (1999).
[CrossRef]

Asundi, A.

Blu, T.

Breteau, J.-M.

P. Picart, R. Mercier, M. Lamare, and J.-M. Breteau, “A simple method for measuring the random variation of an interferometer,” Meas. Sci. Technol.12(8), 1311–1317 (2001).
[CrossRef]

Demoli, N.

Depeursinge, C.

Goodman, J. W.

J. W. Goodman and R. W. Laurence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett.11(3), 77–79 (1967).
[CrossRef]

Guo, C. S.

C. S. Guo, L. Zhang, Z. Y. Rong, and H. T. Wang, “Effect of the fill factor of CCD pixels on digital holograms: comment on the paper,” Opt. Eng.42(9), 2768–2772 (2003).
[CrossRef]

Guo, Z.

Halaq, H.

Healy, J. J.

D. P. Kelly, J. J. Healy, B. M. Hennelly, and J. T. Sheridan, “Quantifying the 2.5D imaging performance of digital holographic systems,” JEOS rapid publication6, 11034 (2011).
[CrossRef]

Hennelly, B. M.

D. P. Kelly, J. J. Healy, B. M. Hennelly, and J. T. Sheridan, “Quantifying the 2.5D imaging performance of digital holographic systems,” JEOS rapid publication6, 11034 (2011).
[CrossRef]

N. Pandey and B. M. Hennelly, “Quantization noise and its reduction in lensless Fourier digital holography,” Appl. Opt.50(7), B58–B70 (2011).
[CrossRef] [PubMed]

D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, and W. T. Rhodes, “Resolution limits in practical digital holographic systems,” Opt. Eng.48(9), 095801 (2009).
[CrossRef]

D. P. Kelly, B. M. Hennelly, C. McElhinney, and T. J. Naughton, “A practical guide to digital holography and generalized sampling,” Proc. SPIE7072, 707215 (2008).
[CrossRef]

Javidi, B.

A. Stern and B. Javidi, “Analysis of practical sampling and reconstruction from Fresnel fields,” Opt. Eng.43(1), 239–250 (2004).
[CrossRef]

Jüptner, W.

Karray, M.

M. Karray, P. Slangen, and P. Picart, “Comparison between digital Fresnel holography and digital image-plane holography: the role of the imaging aperture,” Exp. Mech. (2012), doi:.
[CrossRef]

Kato, J.

Kelly, D. P.

D. P. Kelly, J. J. Healy, B. M. Hennelly, and J. T. Sheridan, “Quantifying the 2.5D imaging performance of digital holographic systems,” JEOS rapid publication6, 11034 (2011).
[CrossRef]

D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, and W. T. Rhodes, “Resolution limits in practical digital holographic systems,” Opt. Eng.48(9), 095801 (2009).
[CrossRef]

D. P. Kelly, B. M. Hennelly, C. McElhinney, and T. J. Naughton, “A practical guide to digital holography and generalized sampling,” Proc. SPIE7072, 707215 (2008).
[CrossRef]

Kreis, Th.

Th. Kreis, “Frequency analysis of digital holography,” Opt. Eng.41(4), 771–778 (2002).
[CrossRef]

Th. Kreis, “Frequency analysis of digital holography with reconstruction by convolution,” Opt. Eng.41(8), 1829–1839 (2002).
[CrossRef]

Th. Kreis, M. Adams, and W. Jüptner, “Methods of digital holography: a comparison,” Proc. SPIE3098, 224–233 (1997).
[CrossRef]

Kronrod, M. A.

M. A. Kronrod, N. S. Merzlyakov, and L. P. Yaroslavskii, “Reconstruction of a hologram with a computer,” Sov. Phys. Tech. Phys.17, 333–334 (1972).

Kühn, J.

Lamare, M.

P. Picart, R. Mercier, M. Lamare, and J.-M. Breteau, “A simple method for measuring the random variation of an interferometer,” Meas. Sci. Technol.12(8), 1311–1317 (2001).
[CrossRef]

Laurence, R. W.

J. W. Goodman and R. W. Laurence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett.11(3), 77–79 (1967).
[CrossRef]

Leval, J.

Liebling, M.

McElhinney, C.

D. P. Kelly, B. M. Hennelly, C. McElhinney, and T. J. Naughton, “A practical guide to digital holography and generalized sampling,” Proc. SPIE7072, 707215 (2008).
[CrossRef]

Mercier, R.

P. Picart, R. Mercier, M. Lamare, and J.-M. Breteau, “A simple method for measuring the random variation of an interferometer,” Meas. Sci. Technol.12(8), 1311–1317 (2001).
[CrossRef]

Merzlyakov, N. S.

M. A. Kronrod, N. S. Merzlyakov, and L. P. Yaroslavskii, “Reconstruction of a hologram with a computer,” Sov. Phys. Tech. Phys.17, 333–334 (1972).

Miao, J.

Mizuno, J.

Naughton, T. J.

D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, and W. T. Rhodes, “Resolution limits in practical digital holographic systems,” Opt. Eng.48(9), 095801 (2009).
[CrossRef]

D. P. Kelly, B. M. Hennelly, C. McElhinney, and T. J. Naughton, “A practical guide to digital holography and generalized sampling,” Proc. SPIE7072, 707215 (2008).
[CrossRef]

Ohta, S.

Onural, L.

Osten, W.

Pandey, N.

N. Pandey and B. M. Hennelly, “Quantization noise and its reduction in lensless Fourier digital holography,” Appl. Opt.50(7), B58–B70 (2011).
[CrossRef] [PubMed]

D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, and W. T. Rhodes, “Resolution limits in practical digital holographic systems,” Opt. Eng.48(9), 095801 (2009).
[CrossRef]

Pavillon, N.

Pedrini, G.

Peng, X.

Picart, P.

M. Karray, P. Slangen, and P. Picart, “Comparison between digital Fresnel holography and digital image-plane holography: the role of the imaging aperture,” Exp. Mech. (2012), doi:.
[CrossRef]

P. Picart, P. Tankam, and Q. Song, “Experimental and theoretical investigation of the pixel saturation effect in digital holography,” J. Opt. Soc. Am. A28(6), 1262–1275 (2011).
[CrossRef] [PubMed]

P. Picart and J. Leval, “General theoretical formulation of image formation in digital Fresnel holography,” J. Opt. Soc. Am. A25(7), 1744–1761 (2008).
[CrossRef] [PubMed]

P. Picart, R. Mercier, M. Lamare, and J.-M. Breteau, “A simple method for measuring the random variation of an interferometer,” Meas. Sci. Technol.12(8), 1311–1317 (2001).
[CrossRef]

Rhodes, W. T.

D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, and W. T. Rhodes, “Resolution limits in practical digital holographic systems,” Opt. Eng.48(9), 095801 (2009).
[CrossRef]

Rong, Z. Y.

C. S. Guo, L. Zhang, Z. Y. Rong, and H. T. Wang, “Effect of the fill factor of CCD pixels on digital holograms: comment on the paper,” Opt. Eng.42(9), 2768–2772 (2003).
[CrossRef]

Sariri, K.

Schnars, U.

Seebacher, S.

Seelamantula, C. S.

Sheridan, J. T.

D. P. Kelly, J. J. Healy, B. M. Hennelly, and J. T. Sheridan, “Quantifying the 2.5D imaging performance of digital holographic systems,” JEOS rapid publication6, 11034 (2011).
[CrossRef]

Slangen, P.

M. Karray, P. Slangen, and P. Picart, “Comparison between digital Fresnel holography and digital image-plane holography: the role of the imaging aperture,” Exp. Mech. (2012), doi:.
[CrossRef]

Song, Q.

Stern, A.

A. Stern and B. Javidi, “Analysis of practical sampling and reconstruction from Fresnel fields,” Opt. Eng.43(1), 239–250 (2004).
[CrossRef]

Tankam, P.

Tiziani, H. J.

Torzynski, M.

Unser, M.

Vukicevic, D.

Wagner, C.

Waldner, S.

H. A. Aebischer and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun.162(4-6), 205–210 (1999).
[CrossRef]

Wang, H. T.

C. S. Guo, L. Zhang, Z. Y. Rong, and H. T. Wang, “Effect of the fill factor of CCD pixels on digital holograms: comment on the paper,” Opt. Eng.42(9), 2768–2772 (2003).
[CrossRef]

Xu, L.

Yamaguchi, I.

Yaroslavskii, L. P.

M. A. Kronrod, N. S. Merzlyakov, and L. P. Yaroslavskii, “Reconstruction of a hologram with a computer,” Sov. Phys. Tech. Phys.17, 333–334 (1972).

Zhang, L.

C. S. Guo, L. Zhang, Z. Y. Rong, and H. T. Wang, “Effect of the fill factor of CCD pixels on digital holograms: comment on the paper,” Opt. Eng.42(9), 2768–2772 (2003).
[CrossRef]

Zhang, T.

Zhang, Y.

Appl. Opt.

Appl. Phys. Lett.

J. W. Goodman and R. W. Laurence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett.11(3), 77–79 (1967).
[CrossRef]

Exp. Mech.

M. Karray, P. Slangen, and P. Picart, “Comparison between digital Fresnel holography and digital image-plane holography: the role of the imaging aperture,” Exp. Mech. (2012), doi:.
[CrossRef]

J. Opt. Soc. Am. A

JEOS rapid publication

D. P. Kelly, J. J. Healy, B. M. Hennelly, and J. T. Sheridan, “Quantifying the 2.5D imaging performance of digital holographic systems,” JEOS rapid publication6, 11034 (2011).
[CrossRef]

Meas. Sci. Technol.

P. Picart, R. Mercier, M. Lamare, and J.-M. Breteau, “A simple method for measuring the random variation of an interferometer,” Meas. Sci. Technol.12(8), 1311–1317 (2001).
[CrossRef]

Opt. Commun.

H. A. Aebischer and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun.162(4-6), 205–210 (1999).
[CrossRef]

Opt. Eng.

D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, and W. T. Rhodes, “Resolution limits in practical digital holographic systems,” Opt. Eng.48(9), 095801 (2009).
[CrossRef]

C. S. Guo, L. Zhang, Z. Y. Rong, and H. T. Wang, “Effect of the fill factor of CCD pixels on digital holograms: comment on the paper,” Opt. Eng.42(9), 2768–2772 (2003).
[CrossRef]

A. Stern and B. Javidi, “Analysis of practical sampling and reconstruction from Fresnel fields,” Opt. Eng.43(1), 239–250 (2004).
[CrossRef]

Th. Kreis, “Frequency analysis of digital holography,” Opt. Eng.41(4), 771–778 (2002).
[CrossRef]

Th. Kreis, “Frequency analysis of digital holography with reconstruction by convolution,” Opt. Eng.41(8), 1829–1839 (2002).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. SPIE

Th. Kreis, M. Adams, and W. Jüptner, “Methods of digital holography: a comparison,” Proc. SPIE3098, 224–233 (1997).
[CrossRef]

D. P. Kelly, B. M. Hennelly, C. McElhinney, and T. J. Naughton, “A practical guide to digital holography and generalized sampling,” Proc. SPIE7072, 707215 (2008).
[CrossRef]

Sov. Phys. Tech. Phys.

M. A. Kronrod, N. S. Merzlyakov, and L. P. Yaroslavskii, “Reconstruction of a hologram with a computer,” Sov. Phys. Tech. Phys.17, 333–334 (1972).

Other

J. W. Goodman, Introduction to Fourier Optics (Second Edition, McGraw-Hill Editions, 1996).

D. Middleton, Introduction to Statistical Communication Theory (McGraw Hill, 1960).

W. B. Davenport and W. L. Root, Random Signals and Noise (McGraw Hill, 1958).

Supplementary Material (1)

» Media 1: MPG (1584 KB)     

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Figures (7)

Fig. 1
Fig. 1

Virtual periodicity of the reconstructed field and lateral shift of the object.

Fig. 2
Fig. 2

Shannon limits and amplitude modulation vs lateral shift of the object.

Fig. 3
Fig. 3

Optical setup for investigating the pixel influence.

Fig. 4
Fig. 4

Amplitude modulation vs lateral object shift.

Fig. 5
Fig. 5

Experimental visualization of the cyclic periodicity and sinc attenuation (Media 1)

Fig. 6
Fig. 6

Phase changes extracted from the tilt measurement, (a) raw, (b) filtered

Fig. 7
Fig. 7

Noise rms and correlation factor vs the lateral shift of the object

Equations (8)

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

H= | R | 2 + | O | 2 + R * O+R O * ,
O( x,y, d 0 )= i λ d 0 exp( 2iπ d 0 λ )exp( iπ λ d 0 ( x 2 + y 2 ) ) × A ( X,Y )exp( iπ λ d 0 ( X 2 + Y 2 ) )exp( 2iπ λ d 0 ( xX+yY ) )dXdY ,
H D ( l p x ,k p y , d 0 )= l p x Δ x /2 l p x + Δ x /2 k p y Δ y /2 k p y + Δ y /2 H( x,y, d 0 )dxdy ,
rect( x Δ x , y Δ y )={ 1if| x | Δ x /2and| y | Δ y /2 0ifnot ,
H D ( x,y, d 0 ) x=l p x ,y=k p y =H( x,y, d 0 )rect( x Δ x , y Δ y ).
A r ( X,Y, d 0 )= iexp( 2iπ d 0 /λ ) λ d 0 exp[ iπ λ d 0 ( X 2 + Y 2 ) ] × k=0 k=K1 l=0 l=L1 H D ( l p x ,k p y , d 0 ) exp[ iπ λ d 0 ( l 2 p x 2 + k 2 p y 2 ) ]exp[ 2iπ λ d 0 ( lX p x +kY p y ) ].
H D ( l p x ,k p y , d 0 ) | O( l p x ,k p y , d 0 ) | 2 + | R( l p x ,k p y ) | 2 +O( l p x ,k p y , d 0 ) R * ( l p x ,k p y )sinc( π u 0 Δ x )sinc( π v 0 Δ y ) + O * ( l p x ,k p y , d 0 )R( l p x ,k p y )sinc( π u 0 Δ x )sinc( π v 0 Δ y ).
p( ε )= 1| μ | 2π ( 1 β 2 ) 3/2 ( β sin 1 β+ πβ 2 + 1 β 2 ).

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