Abstract

We propose a method for compressing a digital color Fresnel hologram based on vector quantization (VQ). The complex color hologram is first separated into three complex holograms, each representing one of the primary colors. Subsequently, each hologram is converted into what we call a real Fresnel hologram and compressed with VQ based on a universal codebook. Experimental evaluation reveals that our scheme is capable of attaining a compression ratio of over 1600 times and still preserving acceptable visual quality on the reconstructed images. Moreover, the decoding process is free from computation and highly resistant to noise contamination on the compressed data.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. T.-C.Poon, ed., Digital Holography and Three-Dimensional Display: Principles and Applications (Springer, 2006).
    [CrossRef]
  2. T.-C. Poon, “Three-dimensional television using optical scanning holography,” J. Info. Disp. 3, 12–16 (2002).
    [CrossRef]
  3. T.-C. Poon, “On the fundamentals of optical scanning holography,” Am. J. Phys. 76, 738–745 (2008).
    [CrossRef]
  4. K. Sasaki, E. Tanji, and H. Yoshikawa, “Data compression for holographic 3D image,” J. Inst. Tele. Eng. Japan 48, 1238–1244 (1994).
  5. G. A. Mills and I. Yamaguchi, “Effects of quantization in phase-shifting digital holography,” Appl. Opt. 44, 1216–1225(2005).
    [CrossRef] [PubMed]
  6. E. Darakis and J. J. Soraghan, “Use of Fresnelets for phase-shifting digital hologram compression,” IEEE Trans. Image Proc. 15, 3804–3811 (2006).
    [CrossRef]
  7. T. J. Naughton, Y. Frauel, B. Javidi, and E. Tajahuerce, “Compression of digital holograms for three-dimensional object reconstruction and recognition,” Appl. Opt. 41, 4124–4132(2002).
    [CrossRef] [PubMed]
  8. A. E. Shortt, T. J. Naughton, and B. Javidi, “A companding approach for nonuniform quantization of digital holograms of three-dimensional objects,” Opt. Express 14, 5129–5134 (2006).
    [CrossRef] [PubMed]
  9. A. E. Shortt, T. J. Naughton, and B. Javidi, “Histogram approaches for lossy compression of digital holograms of three-dimensional objects,” IEEE Trans. Image Proc. 16, 1548–1556 (2007).
    [CrossRef]
  10. A. E. Shortt, T. J. Naughton, and B. Javidi, “Vector quantisation compression of digital holograms of three-dimensional objects,” Proc. SPIE 5827, 265–273 (2005).
    [CrossRef]
  11. P. W. Tsang, W. K. Cheung, and T.-C. Poon, “Low bit-rate compression of computer-generated Fresnel holograms based on vector quantization,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2011), paper DTuD1.
  12. R. M. Gray, “Vector quantization,” IEEE ASSP Mag. 1(2), 4–29 (1984).
    [CrossRef]
  13. Y. Linde, A. Buzo, and R. M. Gray, “An algorithm for vector quantizer design,” IEEE Trans. Commun. 28, 84–95(1980).
    [CrossRef]

2008 (1)

T.-C. Poon, “On the fundamentals of optical scanning holography,” Am. J. Phys. 76, 738–745 (2008).
[CrossRef]

2007 (1)

A. E. Shortt, T. J. Naughton, and B. Javidi, “Histogram approaches for lossy compression of digital holograms of three-dimensional objects,” IEEE Trans. Image Proc. 16, 1548–1556 (2007).
[CrossRef]

2006 (2)

E. Darakis and J. J. Soraghan, “Use of Fresnelets for phase-shifting digital hologram compression,” IEEE Trans. Image Proc. 15, 3804–3811 (2006).
[CrossRef]

A. E. Shortt, T. J. Naughton, and B. Javidi, “A companding approach for nonuniform quantization of digital holograms of three-dimensional objects,” Opt. Express 14, 5129–5134 (2006).
[CrossRef] [PubMed]

2005 (2)

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

A. E. Shortt, T. J. Naughton, and B. Javidi, “Vector quantisation compression of digital holograms of three-dimensional objects,” Proc. SPIE 5827, 265–273 (2005).
[CrossRef]

2002 (2)

1994 (1)

K. Sasaki, E. Tanji, and H. Yoshikawa, “Data compression for holographic 3D image,” J. Inst. Tele. Eng. Japan 48, 1238–1244 (1994).

1984 (1)

R. M. Gray, “Vector quantization,” IEEE ASSP Mag. 1(2), 4–29 (1984).
[CrossRef]

1980 (1)

Y. Linde, A. Buzo, and R. M. Gray, “An algorithm for vector quantizer design,” IEEE Trans. Commun. 28, 84–95(1980).
[CrossRef]

Buzo, A.

Y. Linde, A. Buzo, and R. M. Gray, “An algorithm for vector quantizer design,” IEEE Trans. Commun. 28, 84–95(1980).
[CrossRef]

Cheung, W. K.

P. W. Tsang, W. K. Cheung, and T.-C. Poon, “Low bit-rate compression of computer-generated Fresnel holograms based on vector quantization,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2011), paper DTuD1.

Darakis, E.

E. Darakis and J. J. Soraghan, “Use of Fresnelets for phase-shifting digital hologram compression,” IEEE Trans. Image Proc. 15, 3804–3811 (2006).
[CrossRef]

Frauel, Y.

Gray, R. M.

R. M. Gray, “Vector quantization,” IEEE ASSP Mag. 1(2), 4–29 (1984).
[CrossRef]

Y. Linde, A. Buzo, and R. M. Gray, “An algorithm for vector quantizer design,” IEEE Trans. Commun. 28, 84–95(1980).
[CrossRef]

Javidi, B.

A. E. Shortt, T. J. Naughton, and B. Javidi, “Histogram approaches for lossy compression of digital holograms of three-dimensional objects,” IEEE Trans. Image Proc. 16, 1548–1556 (2007).
[CrossRef]

A. E. Shortt, T. J. Naughton, and B. Javidi, “A companding approach for nonuniform quantization of digital holograms of three-dimensional objects,” Opt. Express 14, 5129–5134 (2006).
[CrossRef] [PubMed]

A. E. Shortt, T. J. Naughton, and B. Javidi, “Vector quantisation compression of digital holograms of three-dimensional objects,” Proc. SPIE 5827, 265–273 (2005).
[CrossRef]

T. J. Naughton, Y. Frauel, B. Javidi, and E. Tajahuerce, “Compression of digital holograms for three-dimensional object reconstruction and recognition,” Appl. Opt. 41, 4124–4132(2002).
[CrossRef] [PubMed]

Linde, Y.

Y. Linde, A. Buzo, and R. M. Gray, “An algorithm for vector quantizer design,” IEEE Trans. Commun. 28, 84–95(1980).
[CrossRef]

Mills, G. A.

Naughton, T. J.

A. E. Shortt, T. J. Naughton, and B. Javidi, “Histogram approaches for lossy compression of digital holograms of three-dimensional objects,” IEEE Trans. Image Proc. 16, 1548–1556 (2007).
[CrossRef]

A. E. Shortt, T. J. Naughton, and B. Javidi, “A companding approach for nonuniform quantization of digital holograms of three-dimensional objects,” Opt. Express 14, 5129–5134 (2006).
[CrossRef] [PubMed]

A. E. Shortt, T. J. Naughton, and B. Javidi, “Vector quantisation compression of digital holograms of three-dimensional objects,” Proc. SPIE 5827, 265–273 (2005).
[CrossRef]

T. J. Naughton, Y. Frauel, B. Javidi, and E. Tajahuerce, “Compression of digital holograms for three-dimensional object reconstruction and recognition,” Appl. Opt. 41, 4124–4132(2002).
[CrossRef] [PubMed]

Poon, T.-C.

T.-C. Poon, “On the fundamentals of optical scanning holography,” Am. J. Phys. 76, 738–745 (2008).
[CrossRef]

T.-C. Poon, “Three-dimensional television using optical scanning holography,” J. Info. Disp. 3, 12–16 (2002).
[CrossRef]

P. W. Tsang, W. K. Cheung, and T.-C. Poon, “Low bit-rate compression of computer-generated Fresnel holograms based on vector quantization,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2011), paper DTuD1.

Sasaki, K.

K. Sasaki, E. Tanji, and H. Yoshikawa, “Data compression for holographic 3D image,” J. Inst. Tele. Eng. Japan 48, 1238–1244 (1994).

Shortt, A. E.

A. E. Shortt, T. J. Naughton, and B. Javidi, “Histogram approaches for lossy compression of digital holograms of three-dimensional objects,” IEEE Trans. Image Proc. 16, 1548–1556 (2007).
[CrossRef]

A. E. Shortt, T. J. Naughton, and B. Javidi, “A companding approach for nonuniform quantization of digital holograms of three-dimensional objects,” Opt. Express 14, 5129–5134 (2006).
[CrossRef] [PubMed]

A. E. Shortt, T. J. Naughton, and B. Javidi, “Vector quantisation compression of digital holograms of three-dimensional objects,” Proc. SPIE 5827, 265–273 (2005).
[CrossRef]

Soraghan, J. J.

E. Darakis and J. J. Soraghan, “Use of Fresnelets for phase-shifting digital hologram compression,” IEEE Trans. Image Proc. 15, 3804–3811 (2006).
[CrossRef]

Tajahuerce, E.

Tanji, E.

K. Sasaki, E. Tanji, and H. Yoshikawa, “Data compression for holographic 3D image,” J. Inst. Tele. Eng. Japan 48, 1238–1244 (1994).

Tsang, P. W.

P. W. Tsang, W. K. Cheung, and T.-C. Poon, “Low bit-rate compression of computer-generated Fresnel holograms based on vector quantization,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2011), paper DTuD1.

Yamaguchi, I.

Yoshikawa, H.

K. Sasaki, E. Tanji, and H. Yoshikawa, “Data compression for holographic 3D image,” J. Inst. Tele. Eng. Japan 48, 1238–1244 (1994).

Am. J. Phys. (1)

T.-C. Poon, “On the fundamentals of optical scanning holography,” Am. J. Phys. 76, 738–745 (2008).
[CrossRef]

Appl. Opt. (2)

IEEE ASSP Mag. (1)

R. M. Gray, “Vector quantization,” IEEE ASSP Mag. 1(2), 4–29 (1984).
[CrossRef]

IEEE Trans. Commun. (1)

Y. Linde, A. Buzo, and R. M. Gray, “An algorithm for vector quantizer design,” IEEE Trans. Commun. 28, 84–95(1980).
[CrossRef]

IEEE Trans. Image Proc. (2)

E. Darakis and J. J. Soraghan, “Use of Fresnelets for phase-shifting digital hologram compression,” IEEE Trans. Image Proc. 15, 3804–3811 (2006).
[CrossRef]

A. E. Shortt, T. J. Naughton, and B. Javidi, “Histogram approaches for lossy compression of digital holograms of three-dimensional objects,” IEEE Trans. Image Proc. 16, 1548–1556 (2007).
[CrossRef]

J. Info. Disp. (1)

T.-C. Poon, “Three-dimensional television using optical scanning holography,” J. Info. Disp. 3, 12–16 (2002).
[CrossRef]

J. Inst. Tele. Eng. Japan (1)

K. Sasaki, E. Tanji, and H. Yoshikawa, “Data compression for holographic 3D image,” J. Inst. Tele. Eng. Japan 48, 1238–1244 (1994).

Opt. Express (1)

Proc. SPIE (1)

A. E. Shortt, T. J. Naughton, and B. Javidi, “Vector quantisation compression of digital holograms of three-dimensional objects,” Proc. SPIE 5827, 265–273 (2005).
[CrossRef]

Other (2)

P. W. Tsang, W. K. Cheung, and T.-C. Poon, “Low bit-rate compression of computer-generated Fresnel holograms based on vector quantization,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2011), paper DTuD1.

T.-C.Poon, ed., Digital Holography and Three-Dimensional Display: Principles and Applications (Springer, 2006).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Partitioning of the generated digital Fresnel hologram into nonoverlapping blocks.

Fig. 2
Fig. 2

Enlarged view of an image block in H ( x , y ) .

Fig. 3
Fig. 3

a, Color image positioned at z = 0.3 m from the hologram. b, Optical reconstructed image at z = 0.3 m with a LCOS display of the generated digital Fresnel color hologram representing the source image in Fig. 3a. c, Random color image for training the codebook.

Fig. 4
Fig. 4

Optical reconstructed image of the generated digital Fresnel color holograms representing the image in Fig. 3a. Each of the holograms is compressed by 204 times (408 times with respect to the original complex hologram) b, Optical reconstructed image of the generated digital Fresnel color holograms representing the image in Fig. 3a. Each of the holograms is compressed by 460 times (920 times with respect to the original complex hologram). c, Optical reconstructed image of the generated digital Fresnel color holograms representing the image in Fig. 3b. Each of the holograms is compressed by 819 times (1638 times with respect to the original complex hologram).

Fig. 5
Fig. 5

a, Optical reconstructed image of the generated digital Fresnel color holograms representing the image in Fig. 3a. Each of the holograms is compressed with JPEG 2000 by 199 times (398 times with respect to the original complex hologram). b, Optical reconstructed image of the generated digital Fresnel color holograms representing the image in Fig. 3a. Each of the holograms is compressed with JPEG 2000 by 443 times (886 times with respect to the original complex hologram). c, Optical reconstructed of the generated digital Fresnel color holograms representing the image in Fig. 3b. Each of the holograms is compressed with JPEG 2000 by 820 times (1640 times with respect to the original complex hologram).

Fig. 6
Fig. 6

a, Image reconstruction of the holograms that have been compressed with the proposed method by 408 times, and contaminated with 6% noise on the encoded data. b, Image reconstruction of the holograms that have been compressed with the proposed method by 920 times, and contaminated with 6% noise on the encoded data. c, Image reconstruction of the holograms that have been compressed with the proposed method by 1638 times, and contaminated with 6% noise on the encoded data.

Fig. 7
Fig. 7

Optical reconstructed image with a LCOS display of an excerpt frame of the generated digital Fresnel color hologram sequence representing the globe image. Reconstructed images of other views of the hologram are shown in View 1.

Fig. 8
Fig. 8

a, Optical reconstructed image of the generated digital Fresnel color hologram representing the globe image. Each of the generated digital Fresnel holograms is compressed by 204 times (408 times with respect to the original complex hologram). Reconstructed images of other views of the compressed holograms are shown in View 2. b, Optical reconstructed image of the generated digital Fresnel color hologram representing the globe image. Each of the generated digital Fresnel holograms is compressed by 460 times (920 times with respect to the original complex hologram plane). Reconstructed images of other views of the compressed holograms are shown in View 3. c, Optical reconstructed image of the generated digital Fresnel color hologram. Each of the generated digital Fresnel holograms is compressed by 819 times (1638 times with respect to the original complex hologram plane). Reconstructed images of other views of the compressed holograms are shown in View 4.

Datasets

Datasets associated with ISP articles are stored in an online database called MIDAS. Clicking a "View" link in an OSA ISP article will launch the ISP software (if installed) and pull the relevant data from MIDAS. Visit MIDAS to browse and download the datasets directly. A package containing the PDF article and full datasets is available in MIDAS for offline viewing.

Questions or Problems? See the ISP FAQ. Already used the ISP software? Take a quick survey to tell us what you think.

Tables (2)

Tables Icon

Table 1 LBG Algorithm in Codebook Generation [13]

Tables Icon

Table 2 Settings of the Hologram Generation Process

Equations (4)

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

H ( x , y ) = j = 0 N 1 a j r j exp ( i k r j ) ,
d ( s j , c q ) = s j c q = m = 0 k 1 ( s j m c q m ) 2 ,
CR = k × Q m = k × Q log 2 N .
H i ( x , y ) = RE [ B ( y ) H i ( x , y ) ] , i = 0 , 1 , or 2 ,

Metrics