Digital Fresnel holography beyond the Shannon limits

doi:10.1364/OE.20.018303

Digital Fresnel holography beyond the Shannon limits

Mathieu Leclercq and Pascal Picart »View Author Affiliations

Optics Express, Vol. 20, Issue 16, pp. 18303-18312 (2012)
http://dx.doi.org/10.1364/OE.20.018303

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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.

OCIS Codes
(090.0090) Holography : Holography
(090.1760) Holography : Computer holography
(100.3010) Image processing : Image reconstruction techniques
(120.5050) Instrumentation, measurement, and metrology : Phase measurement
(090.1995) Holography : Digital holography

ToC Category:
Holography

History
Original Manuscript: June 1, 2012
Revised Manuscript: July 5, 2012
Manuscript Accepted: July 16, 2012
Published: July 25, 2012

Citation
Mathieu Leclercq and Pascal Picart, "Digital Fresnel holography beyond the Shannon limits," Opt. Express 20, 18303-18312 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-16-18303

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References

J. W. Goodman and R. W. Laurence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett.11(3), 77–79 (1967). [CrossRef]
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).
U. Schnars and W. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt.33(2), 179–181 (1994). [CrossRef] [PubMed]
L. Onural, “Diffraction from a wavelet point of view,” Opt. Lett.18(11), 846–848 (1993). [CrossRef] [PubMed]
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]
Th. Kreis, M. Adams, and W. Jüptner, “Methods of digital holography: a comparison,” Proc. SPIE3098, 224–233 (1997). [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]
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]
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]
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]
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]
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]
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, 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. Pavillon, C. S. Seelamantula, J. Kühn, M. Unser, and C. Depeursinge, “Suppression of the zero-order term in off-axis digital holography through nonlinear filtering,” Appl. Opt.48(34), H186–H195 (2009). [CrossRef] [PubMed]
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]
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]
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]
L. Xu, X. Peng, Z. Guo, J. Miao, and A. Asundi, “Imaging analysis of digital holography,” Opt. Express13(7), 2444–2452 (2005). [CrossRef] [PubMed]
N. Demoli, H. Halaq, K. Sariri, M. Torzynski, and D. Vukicevic, “Undersampled digital holography,” Opt. Express17(18), 15842–15852 (2009). [CrossRef] [PubMed]
J. W. Goodman, Introduction to Fourier Optics (Second Edition, McGraw-Hill Editions, 1996).
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]
I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett.22(16), 1268–1270 (1997). [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]
D. Middleton, Introduction to Statistical Communication Theory (McGraw Hill, 1960).
W. B. Davenport and W. L. Root, Random Signals and Noise (McGraw Hill, 1958).
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]

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

[2] 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).

[3] U. Schnars and W. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt.33(2), 179–181 (1994). [CrossRef] [PubMed]

[4] L. Onural, “Diffraction from a wavelet point of view,” Opt. Lett.18(11), 846–848 (1993). [CrossRef] [PubMed]

[5] 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]

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

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

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

[9] 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]

[10] 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]

[11] 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]

[12] 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]

[13] 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]

[14] 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]

[15] 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]

[16] N. Pavillon, C. S. Seelamantula, J. Kühn, M. Unser, and C. Depeursinge, “Suppression of the zero-order term in off-axis digital holography through nonlinear filtering,” Appl. Opt.48(34), H186–H195 (2009). [CrossRef] [PubMed]

[17] 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]

[18] 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]

[19] 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]

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

[21] L. Xu, X. Peng, Z. Guo, J. Miao, and A. Asundi, “Imaging analysis of digital holography,” Opt. Express13(7), 2444–2452 (2005). [CrossRef] [PubMed]

[22] N. Demoli, H. Halaq, K. Sariri, M. Torzynski, and D. Vukicevic, “Undersampled digital holography,” Opt. Express17(18), 15842–15852 (2009). [CrossRef] [PubMed]

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

[24] 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]

[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).

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

[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]

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Digital Fresnel holography beyond the Shannon limits