Abstract

this paper discusses on the influence of decorrelation noise induced by quantization and shot-noise when recording digital holograms at very high frame rate. A criterion based on the coherence factor of the hologram phase difference is proposed. The main parameters of interest are the ratio between the reference and the object waves and the sensor dynamics, depending on the photo-electron capacity of pixels. The study is based on a full numerical simulation of the holographic process, which provides useful rules. This leads to define the optimal conditions for recording at very-high frame rate with minimization of the decorrelation noise. Experimental results obtained with frame rate at 50kHz confirm the proposed approach.

© 2015 Optical Society of America

Full Article  |  PDF Article
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References

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2015 (1)

2014 (1)

V. Denis, A. Pelat, F. Gautier, and B. Elie, “Modal overlap factor of a beam with an Acoustic Black Hole termination,” J. Sound Vibrat. 333(12), 2475–2488 (2014).
[Crossref]

2013 (2)

2012 (2)

M. Leclercq and P. Picart, “Digital Fresnel holography beyond the Shannon limits,” Opt. Express 20(16), 18303–18312 (2012).
[Crossref] [PubMed]

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. 52(9), 1275–1286 (2012).
[Crossref]

2011 (2)

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

D. P. Kelly, J. J. Healy, B. M. Hennelly, and J. T. Sheridan, “Quantifying the 2.5D imaging performance of digital holographic systems,” JEOS 6, 11034 (2011).
[Crossref]

2010 (2)

F. Verpillat, F. Joud, M. Atlan, and M. Gross, “Digital holography at shot noise level,” J. Disp. Technol. 6(10), 455–464 (2010).
[Crossref]

J. Mundt and T. Kreis, “Digital holographic recording and reconstruction of large scale objects for metrology and display,” Opt. Eng. 49(12), 125801 (2010).
[Crossref]

2009 (2)

N. Demoli, H. Halaq, K. Sariri, M. Torzynski, and D. Vukicevic, “Undersampled digital holography,” Opt. Express 17(18), 15842–15852 (2009).
[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]

2008 (3)

2007 (3)

2005 (2)

2004 (1)

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

2002 (2)

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

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

2001 (2)

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, 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]

1999 (1)

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 (1)

1996 (2)

M. Lehmann, “Phase-shifting speckle interferometry with unresolved speckles: a theoretical investigation,” Opt. Commun. 128(4-6), 325–340 (1996).
[Crossref]

U. Schnars, T. M. Kreis, and W. Jüptner, “Digital recording and numerical reconstruction of holograms: reduction of the spatial frequency spectrum,” Opt. Eng. 35(4), 977–982 (1996).
[Crossref]

1995 (1)

M. Lehmann, “Optimization of wave-field intensities in phase-shifting speckle interferometry,” Opt. Commun. 118(3-4), 199–206 (1995).
[Crossref]

Absil, E.

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.

Atlan, M.

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.

Denis, V.

V. Denis, A. Pelat, F. Gautier, and B. Elie, “Modal overlap factor of a beam with an Acoustic Black Hole termination,” J. Sound Vibrat. 333(12), 2475–2488 (2014).
[Crossref]

Elie, B.

V. Denis, A. Pelat, F. Gautier, and B. Elie, “Modal overlap factor of a beam with an Acoustic Black Hole termination,” J. Sound Vibrat. 333(12), 2475–2488 (2014).
[Crossref]

Faure, C.

Federico, A.

Fu, Y.

Gautier, F.

J. Poittevin, P. Picart, C. Faure, F. Gautier, and C. Pézerat, “Multi-point vibrometer based on high-speed digital in-line holography,” Appl. Opt. 54(11), 3185–3196 (2015).
[Crossref] [PubMed]

V. Denis, A. Pelat, F. Gautier, and B. Elie, “Modal overlap factor of a beam with an Acoustic Black Hole termination,” J. Sound Vibrat. 333(12), 2475–2488 (2014).
[Crossref]

Gross, M.

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 6, 11034 (2011).
[Crossref]

Hennelly, B.

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 6, 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. SPIE 7072, 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]

Joud, F.

F. Verpillat, F. Joud, M. Atlan, and M. Gross, “Digital holography at shot noise level,” J. Disp. Technol. 6(10), 455–464 (2010).
[Crossref]

Jüptner, W.

U. Schnars, T. M. Kreis, and W. Jüptner, “Digital recording and numerical reconstruction of holograms: reduction of the spatial frequency spectrum,” Opt. Eng. 35(4), 977–982 (1996).
[Crossref]

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. 52(9), 1275–1286 (2012).
[Crossref]

Kato, J.

Kaufmann, G. H.

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 6, 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. SPIE 7072, 707215 (2008).
[Crossref]

Kreis, T.

J. Mundt and T. Kreis, “Digital holographic recording and reconstruction of large scale objects for metrology and display,” Opt. Eng. 49(12), 125801 (2010).
[Crossref]

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

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

Kreis, T. M.

U. Schnars, T. M. Kreis, and W. Jüptner, “Digital recording and numerical reconstruction of holograms: reduction of the spatial frequency spectrum,” Opt. Eng. 35(4), 977–982 (1996).
[Crossref]

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]

Leclercq, M.

Lehmann, M.

M. Lehmann, “Decorrelation-induced phase errors in phase-shifting speckle interferometry,” Appl. Opt. 36(16), 3657–3667 (1997).
[Crossref] [PubMed]

M. Lehmann, “Phase-shifting speckle interferometry with unresolved speckles: a theoretical investigation,” Opt. Commun. 128(4-6), 325–340 (1996).
[Crossref]

M. Lehmann, “Optimization of wave-field intensities in phase-shifting speckle interferometry,” Opt. Commun. 118(3-4), 199–206 (1995).
[Crossref]

Lesaffre, M.

Leval, J.

McElhinney, C.

D. P. Kelly, B. M. Hennelly, C. McElhinney, and T. J. Naughton, “A practical guide to digital holography and generalized sampling,” Proc. SPIE 7072, 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]

Miao, J.

Mills, G. A.

Mizuno, J.

Mundt, J.

J. Mundt and T. Kreis, “Digital holographic recording and reconstruction of large scale objects for metrology and display,” Opt. Eng. 49(12), 125801 (2010).
[Crossref]

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. SPIE 7072, 707215 (2008).
[Crossref]

Ohta, S.

Osten, W.

Pandey, N.

N. Pandey and B. 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]

Pedrini, G.

Pelat, A.

V. Denis, A. Pelat, F. Gautier, and B. Elie, “Modal overlap factor of a beam with an Acoustic Black Hole termination,” J. Sound Vibrat. 333(12), 2475–2488 (2014).
[Crossref]

Peng, X.

Pézerat, C.

Picart, P.

J. Poittevin, P. Picart, C. Faure, F. Gautier, and C. Pézerat, “Multi-point vibrometer based on high-speed digital in-line holography,” Appl. Opt. 54(11), 3185–3196 (2015).
[Crossref] [PubMed]

M. Leclercq and P. Picart, “Digital Fresnel holography beyond the Shannon limits,” Opt. Express 20(16), 18303–18312 (2012).
[Crossref] [PubMed]

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. 52(9), 1275–1286 (2012).
[Crossref]

P. Picart and J. Leval, “General theoretical formulation of image formation in digital Fresnel holography,” J. Opt. Soc. Am. A 25(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]

Poittevin, J.

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]

Rivenson, Y.

Sariri, K.

Schnars, U.

U. Schnars, T. M. Kreis, and W. Jüptner, “Digital recording and numerical reconstruction of holograms: reduction of the spatial frequency spectrum,” Opt. Eng. 35(4), 977–982 (1996).
[Crossref]

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 6, 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. 52(9), 1275–1286 (2012).
[Crossref]

Stern, A.

A. Uzan, Y. Rivenson, and A. Stern, “Speckle denoising in digital holography by nonlocal means filtering,” Appl. Opt. 52(1), A195–A200 (2013).
[Crossref] [PubMed]

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

Torzynski, M.

Uzan, A.

Verpillat, F.

F. Verpillat, F. Joud, M. Atlan, and M. Gross, “Digital holography at shot noise level,” J. Disp. Technol. 6(10), 455–464 (2010).
[Crossref]

Verrier, N.

Vukicevic, D.

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]

Xu, L.

Yamaguchi, I.

Appl. Opt. (9)

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]

G. A. Mills and I. Yamaguchi, “Effects of quantization in phase-shifting digital holography,” Appl. Opt. 44(7), 1216–1225 (2005).
[Crossref] [PubMed]

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

M. Lesaffre, N. Verrier, and M. Gross, “Noise and signal scaling factors in digital holography in weak illumination: relationship with shot noise,” Appl. Opt. 52(1), A81–A91 (2013).
[Crossref] [PubMed]

M. Gross, M. Atlan, and E. Absil, “Noise and aliases in off-axis and phase-shifting holography,” Appl. Opt. 47(11), 1757–1766 (2008).
[Crossref] [PubMed]

Y. Fu, G. Pedrini, and W. Osten, “Vibration measurement by temporal Fourier analyses of a digital hologram sequence,” Appl. Opt. 46(23), 5719–5727 (2007).
[Crossref] [PubMed]

J. Poittevin, P. Picart, C. Faure, F. Gautier, and C. Pézerat, “Multi-point vibrometer based on high-speed digital in-line holography,” Appl. Opt. 54(11), 3185–3196 (2015).
[Crossref] [PubMed]

A. Uzan, Y. Rivenson, and A. Stern, “Speckle denoising in digital holography by nonlocal means filtering,” Appl. Opt. 52(1), A195–A200 (2013).
[Crossref] [PubMed]

M. Lehmann, “Decorrelation-induced phase errors in phase-shifting speckle interferometry,” Appl. Opt. 36(16), 3657–3667 (1997).
[Crossref] [PubMed]

Exp. Mech. (1)

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. 52(9), 1275–1286 (2012).
[Crossref]

J. Disp. Technol. (1)

F. Verpillat, F. Joud, M. Atlan, and M. Gross, “Digital holography at shot noise level,” J. Disp. Technol. 6(10), 455–464 (2010).
[Crossref]

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

J. Sound Vibrat. (1)

V. Denis, A. Pelat, F. Gautier, and B. Elie, “Modal overlap factor of a beam with an Acoustic Black Hole termination,” J. Sound Vibrat. 333(12), 2475–2488 (2014).
[Crossref]

JEOS (1)

D. P. Kelly, J. J. Healy, B. M. Hennelly, and J. T. Sheridan, “Quantifying the 2.5D imaging performance of digital holographic systems,” JEOS 6, 11034 (2011).
[Crossref]

Meas. Sci. Technol. (1)

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. (3)

M. Lehmann, “Phase-shifting speckle interferometry with unresolved speckles: a theoretical investigation,” Opt. Commun. 128(4-6), 325–340 (1996).
[Crossref]

M. Lehmann, “Optimization of wave-field intensities in phase-shifting speckle interferometry,” Opt. Commun. 118(3-4), 199–206 (1995).
[Crossref]

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. (6)

U. Schnars, T. M. Kreis, and W. Jüptner, “Digital recording and numerical reconstruction of holograms: reduction of the spatial frequency spectrum,” Opt. Eng. 35(4), 977–982 (1996).
[Crossref]

J. Mundt and T. Kreis, “Digital holographic recording and reconstruction of large scale objects for metrology and display,” Opt. Eng. 49(12), 125801 (2010).
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Figures (9)

Fig. 1
Fig. 1 (a) coherence factor |μ| extracted from the noise measurement according to the different simulation conditions (α, Rc), (b) optimal recording condition leading to |μ|>0.90 (white area); numbered red dots corresponds to selected data in Fig. 2, Fig. 3, Fig. 4, Fig. 5; dashed yellow lines in Fig. 1(a) and 1(b): plots for |O|2 = {1,10,100,1000,10000} photo electrons.
Fig. 2
Fig. 2 (a) simulated phase difference for the two instants (reference map), (b) calculated phase map at point n°2 in Fig. 1(b), Rc = 1000 and α = 5%, coherence factor |μ| = 0.501, (c) calculated phase map at point n°5 in Fig. 1(b), Rc = 300 and α = 60%, coherence factor |μ| = 0.993.
Fig. 3
Fig. 3 (a) noise map for point n°2, |μ| = 0.501, (b) noise map for point n°5, |μ| = 0.993, (c) probability densities extracted from the phase noise (red: fitting with Eq. (4), black estimated probability density from data).
Fig. 4
Fig. 4 (a), (b) and (c) point n°1 in Fig. 1(b) with Rc = 1 and α = 10%, coherence factor |μ| = 0.823, (a) probability density of the quantization gray levels of the digital hologram, (b) noisy phase difference, (c) probability density of the phase noise (extracted from simulation data and fitted with Eq. (4)), (d), (e), and (f) point n°3 in Fig. 1(b), Rc = 8500 and α = 40%, |μ| = 0.824, (d), (e), (f) same as (a), (b) and (c).
Fig. 5
Fig. 5 (a), (b) and (c) point n°4 in Fig. 1(b) with Rc = 60 and α = 20%, |μ| = 0.989, (a) probability density of the quantization gray levels of the digital hologram, (b) noisy phase difference, (c) probability density of the phase noise (extracted from simulation data and fitted with Eq. (4)), (d), (e), and (f) point n°6, Rc = 950 and α = 80%, |μ| = 0.988, (d), (e), (f) same as (a), (b) and (c).
Fig. 6
Fig. 6 (a) Experimental set-up for experimental quality assessment of quantization-induced decorrelation noise (PBS: polarizing beam splitter), (b) measurement of the optical power of the reference beam, (c) measurement of the optical power of the object beam.
Fig. 7
Fig. 7 (a) set of 100 measurements plotted in 3D space vs exposure time and parameters (Rc,α), the red dot and number if attached to one measurement, (b) the set of data plotted in the optimal zone, numbered yellow and green dots: 6 data points used in Fig. 8 and Fig. 9.
Fig. 8
Fig. 8 (a) point n°1 in Fig. 7(b), Rc = 7.81 and α = 2.7%, coherence factor μ = 0.900, with respectively from the left to the right, the probability density of the quantization gray levels of the recorded experimental hologram, the phase difference map between the two instants (mod 2π), and the probability density of the phase noise (extracted from experimental data and fitted with Eq. (4)), (b) point n°2, Rc = 125, α = 17%, μ = 0.913, (c) point n°3, Rc = 125, α = 48%, μ = 0.909.
Fig. 9
Fig. 9 same as Fig. 8, (a) point n°4, Rc = 4.2, α = 0.2%, μ = 0.564, (b) point n°5, Rc = 825, α = 13.8%, μ = 0.772, (c) point n°6, Rc = 2185, α = 23.7%, μ = 0.769.

Equations (7)

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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 ,
A r ( X,Y, d 0 )= iexp( 2iπ d 0 /λ ) λ d 0 exp[ iπ λ d 0 ( X 2 + Y 2 ) ] × k l H( 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 ) ],
p( ε )= 1 | μ | 2 2π ( 1 β 2 ) 3/2 ( β sin 1 β+ πβ 2 + 1 β 2 ).
Rc= | R | 2 | O | 2 ,
α=100 | R | 2 N pe ,
H n =H+randn× H ,

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