Abstract

We present herein an original approach for the watermarking of holograms in gray tone images for use in microscopic halftone image archiving. Our concept is based on the principle of complementary holography presented in a previous contribution. The efficiency of the concept is evaluated theoretically and experimentally. We demonstrate the interest of elliptical diffraction patterns as an alternative to the usual rectangular diffraction patterns and confirm the subsidiary role of the hologram amplitude in the hologram recovery process.

© 2013 OSA

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References

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  1. J. E. LaBarca, “Preservation of photographic images for future generations: new opportunities for prints and photo books,” International Symposium on Technologies for Digital Fulfillment, Las Vegas, Nevada, 17–22 (2012).
  2. J. Palm, “The digital black hole,” article published in the framework of the TAPE project (2006). Retrieved december 2012 from http://www.tape-online.net/docs/Palm_Black_Hole.pdf
  3. C. Martinez, O. Lemonnier, F. Laulagnet, A. Fargeix, and M. F. Armand, “Micro and nano structuring for long term data preservation,” French Symposium on Emerging Technologies for micro-nanofabrication, We-L5 (2010). Retrieved december 2012 from http://jnte10.trans-gdr.lpn.cnrs.fr/FILES/JNTE10_AdvancedProgram_Final.pdf
  4. S. Perkins, “Dear Future Earthlings, A message in a bottle won’t be enough to communicate with distant generations,” Sci. News182(12), 26–28 (2012).
  5. M. S. Fu and O. C. Au, “Data hiding watermarking for halftone images,” IEEE Trans. Image Process.11(4), 477–484 (2002).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  7. C. Martinez, O. Lemonnier, F. Laulagnet, A. Fargeix, F. Tissot, and M. F. Armand, “Complementary computer generated holography for aesthetic watermarking,” Opt. Express20(5), 5547–5556 (2012).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  9. C. Martinez, A. Fargeix, O. Lemonnier, B. Martin, M. Armand, and R. Templier, “Blu-Ray mastering process applied to the manufacturing of computer generated holograms,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2009), paper DWD5. http://www.opticsinfobase.org/abstract.cfm?uri=DH-2009-DWD5
    [CrossRef]
  10. D. L. Lau and G. R. Arce, Modern Digital Halftoning, Second Edition (CRC Press, 2008).
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    [CrossRef] [PubMed]
  12. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt.21(15), 2758–2769 (1982).
    [CrossRef] [PubMed]
  13. H. Farhoosh, M. R. Feldman, S. H. Lee, C. C. Guest, Y. Fainman, and R. Eschbach, “Comparison of binary encoding schemes for electron-beam fabrication of computer generated holograms,” Appl. Opt.26(20), 4361–4372 (1987).
    [CrossRef] [PubMed]
  14. H. Beker and W. J. Dallas, “Improving binary computer holograms,” Opt. Commun.15(1), 50–53 (1975).
    [CrossRef]

2012 (2)

S. Perkins, “Dear Future Earthlings, A message in a bottle won’t be enough to communicate with distant generations,” Sci. News182(12), 26–28 (2012).

C. Martinez, O. Lemonnier, F. Laulagnet, A. Fargeix, F. Tissot, and M. F. Armand, “Complementary computer generated holography for aesthetic watermarking,” Opt. Express20(5), 5547–5556 (2012).
[CrossRef] [PubMed]

2011 (1)

2002 (1)

M. S. Fu and O. C. Au, “Data hiding watermarking for halftone images,” IEEE Trans. Image Process.11(4), 477–484 (2002).
[CrossRef] [PubMed]

2001 (1)

1987 (1)

1982 (1)

1975 (1)

H. Beker and W. J. Dallas, “Improving binary computer holograms,” Opt. Commun.15(1), 50–53 (1975).
[CrossRef]

1967 (1)

Armand, M. F.

Au, O. C.

M. S. Fu and O. C. Au, “Data hiding watermarking for halftone images,” IEEE Trans. Image Process.11(4), 477–484 (2002).
[CrossRef] [PubMed]

Beker, H.

H. Beker and W. J. Dallas, “Improving binary computer holograms,” Opt. Commun.15(1), 50–53 (1975).
[CrossRef]

Dallas, W. J.

H. Beker and W. J. Dallas, “Improving binary computer holograms,” Opt. Commun.15(1), 50–53 (1975).
[CrossRef]

Eschbach, R.

Fainman, Y.

Fargeix, A.

Farhoosh, H.

Feldman, M. R.

Fienup, J. R.

Fu, M. S.

M. S. Fu and O. C. Au, “Data hiding watermarking for halftone images,” IEEE Trans. Image Process.11(4), 477–484 (2002).
[CrossRef] [PubMed]

Guest, C. C.

Javidi, B.

LaBarca, J. E.

J. E. LaBarca, “Preservation of photographic images for future generations: new opportunities for prints and photo books,” International Symposium on Technologies for Digital Fulfillment, Las Vegas, Nevada, 17–22 (2012).

Laulagnet, F.

Lee, S. H.

Lemonnier, O.

Lohmann, A. W.

Martinez, C.

Paris, D. P.

Perkins, S.

S. Perkins, “Dear Future Earthlings, A message in a bottle won’t be enough to communicate with distant generations,” Sci. News182(12), 26–28 (2012).

Rosen, J.

Tanaka, K.-I.

Tissot, F.

Appl. Opt. (5)

IEEE Trans. Image Process. (1)

M. S. Fu and O. C. Au, “Data hiding watermarking for halftone images,” IEEE Trans. Image Process.11(4), 477–484 (2002).
[CrossRef] [PubMed]

Opt. Commun. (1)

H. Beker and W. J. Dallas, “Improving binary computer holograms,” Opt. Commun.15(1), 50–53 (1975).
[CrossRef]

Opt. Express (1)

Sci. News (1)

S. Perkins, “Dear Future Earthlings, A message in a bottle won’t be enough to communicate with distant generations,” Sci. News182(12), 26–28 (2012).

Other (5)

J. E. LaBarca, “Preservation of photographic images for future generations: new opportunities for prints and photo books,” International Symposium on Technologies for Digital Fulfillment, Las Vegas, Nevada, 17–22 (2012).

J. Palm, “The digital black hole,” article published in the framework of the TAPE project (2006). Retrieved december 2012 from http://www.tape-online.net/docs/Palm_Black_Hole.pdf

C. Martinez, O. Lemonnier, F. Laulagnet, A. Fargeix, and M. F. Armand, “Micro and nano structuring for long term data preservation,” French Symposium on Emerging Technologies for micro-nanofabrication, We-L5 (2010). Retrieved december 2012 from http://jnte10.trans-gdr.lpn.cnrs.fr/FILES/JNTE10_AdvancedProgram_Final.pdf

C. Martinez, A. Fargeix, O. Lemonnier, B. Martin, M. Armand, and R. Templier, “Blu-Ray mastering process applied to the manufacturing of computer generated holograms,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2009), paper DWD5. http://www.opticsinfobase.org/abstract.cfm?uri=DH-2009-DWD5
[CrossRef]

D. L. Lau and G. R. Arce, Modern Digital Halftoning, Second Edition (CRC Press, 2008).

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Figures (10)

Fig. 1
Fig. 1

(a) Principle of the coding of an image by the cell oriented computer generated holography. (b) Description of the cell geometry (d) Picture of a cell oriented CGH with period 5 µm.

Fig. 2
Fig. 2

(a) Detail of the gray tone reference image Ig. (b) Result of a usual amplitude modulation halftoning. (c) Result of halftoning with complementary CGH watermarking. (d) result of halftoning with previous CGH watermarking process.

Fig. 3
Fig. 3

Evolution of the hologram diffraction pattern amplitude as a function of the gray tone associated to the half tone pattern with various elliptical factors ρ.

Fig. 4
Fig. 4

Description of the phase retrieval process used to design a halftone image with complementary CGH watermarking.

Fig. 5
Fig. 5

(a) Evolution of the mean squared error between the original holographic image and the estimation of the holographic image recovery. (b) Holographic image recovered at first iteration (detail of the image given below). (c) Holographic image recovered after two iterations. (d) Holographic image recovered after 200 iterations.

Fig. 6
Fig. 6

Diffraction efficiency in the first order for uniform 2D gratings using complementary holography design as a function of the gray tone associated to the half tone/diffractive pattern for various elliptical factor ρ, dotted lines show the diffraction efficiency for rectangular pattern gratings with associated rectangular factor.

Fig. 7
Fig. 7

Experimental results of the first order diffraction efficiency for various uniform gray tone gratings for open and opaque diffraction patterns (resp. open and filled circles), theoretical diffraction efficiency is given for t1 - t2 = 0.55 (solid line) and for a +/− 10% error in the transmission value (broken lines).

Fig. 8
Fig. 8

Experimental results of the first order diffraction efficiency for 0.4 uniform gray tone gratings for various elliptical factors ρ, the solid line shows the theoretical diffraction efficiency for t1 - t2 = 0.55.

Fig. 9
Fig. 9

(a) Reference gray tone image. (b), (c) and (d) Microscopic view of the halftone image with complementary CGH watermarking with magnification range x5, x20 and x50.

Fig. 10
Fig. 10

(a) Experimentally recovered holographic image in the case of a phase retrieval process based on image Ig with 300 iterations. (b) and (c) Experimentally recovered holographic image in the case a random phase mask and hologram amplitude given by Ig or by a 0.5 uniform gray tone.

Equations (17)

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FFT( I h )= A nm e i α nm
A nm = w y nm 2 J 1 ( π.w x nm )
α nm =2π. d nm
w nm =2 I nm g π
Γ nm = π.ρ.w x nm 2 4
{ A nm h = ρ. I nm g π × J 1 ( 2 π. I nm g ρ ) if wx 1 ρ A nm h = 1 2 J 1 ( 4. I nm g ) if wx> 1 ρ
{ I nm f = I nm g if I nm g 0.5 I nm f =1 I nm g if I nm g >0.5
{ I nm t =0 if I nm g 0.5 I nm t =1 if I nm g >0.5
A nm h = I nm f 2 × J 1 ( 4 I nm f 2 )
H ˜ ( ν x , ν y )=Q n,m C nm ( x h , y h ) e 2πi( x h ν x + y h ν y ) d x h d y h
C nm ( x h , y h )= t 1 × D wx,wy ( x h ( n+ d nm ).Λ, y h m.Λ )+ t 2 ×[ R( x h n.Λ, y h m.Λ ) D wx,wy ( x h ( n+ d nm ).Λ, y h m.Λ ) ]
D wx,wy ( x,y ) =1 if 4. ( x wx.Λ ) 2 +4. ( y wy.Λ ) 2 1 =0 if 4. ( x wx.Λ ) 2 +4. ( y wy.Λ ) 2 >1
R( x,y ) =1 if | x | Λ 2 &| y | Λ 2 =0 if | x |> Λ 2 &| y |> Λ 2
I( ν x , ν y )= Q 2 . Λ 4 . { ( t 1 t 2 )× π.wx.wy 4 ×2 J 1 ( π.Λ.κ ) π.Λ.κ + t 2 × sin( π.Λ. ν x ) π.Λ. ν x × sin( π.Λ. ν y ) π.Λ. ν y } 2 With:κ= w x 2 ν x 2 +w y 2 ν y 2 .
η 0,0 = [ ( t 1 t 2 )× π.wx.wy 4 + t 2 ] 2
η 1,0 = ( t 1 t 2 ) 2 × ( wy. J 1 ( π.wx ) 2 ) 2
η 1,0 = ( t 1 t 2 ) 2 × ( wy. sin( π.wx ) π ) 2

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