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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 15 — Jul. 29, 2013
  • pp: 17586–17591
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Displaying a high-resolution digital hologram on a low-resolution spatial light modulator with the same resolution obtained from the hologram

P.W.M. Tsang, T.-C. Poon, and C. Zhou  »View Author Affiliations


Optics Express, Vol. 21, Issue 15, pp. 17586-17591 (2013)
http://dx.doi.org/10.1364/OE.21.017586


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Abstract

In this paper, a fast method for displaying a digital, real and off-axis Fresnel hologram on a lower resolution device is reported. Preserving the original resolution of the hologram upon display is one of the important attributes of the proposed method. Our method can be divided into 3 stages. First, a digital hologram representing a given three dimensional (3D) object is down-sampled based on a fix, jitter down-sampling lattice. Second, the down-sampled hologram is interpolated, through pixel duplication, into a low resolution hologram that can be displayed with a low-resolution spatial light modulator (SLM). Third, the SLM is overlaid with a grating which is generated based on the same jitter down-sampling lattice that samples the hologram. The integration of the grating and the low-resolution hologram results in, to a good approximation, the resolution of the original hologram. As such, our proposed method enables digital holograms to be displayed with lower resolution SLMs, paving the way for the development of low-cost holographic video display.

© 2013 OSA

1. Introduction

2. Proposed method

Our proposed method can be divided into 3 stages as shown in Fig. 1
Fig. 1 Proposed method for generating the low-resolution hologram and the high resolution grating.
. The input is an amplitude, off-axis digital Fresnel hologram H(x,y) that is generated as follows. Given a 3-D object scene comprising of P object points, a complex hologram HC(x,y) is first derived with the Fresnel diffraction equation shown in Eq. (1).
HC(x,y)=j=0P1ajexp(i2πλ(xxj)2δ2+(yyj)2δ2+zj2),
(1)
where λ is the wavelength of the optical beam, and (x,y) being the horizontal and vertical coordinates of the hologram plane. The terms aj, (xj,yj), and zj denote the intensity, the horizontal and vertical co-ordinates on the vertical plane, and its axial distance from the hologram, of the jth object point, respectively. The hologram pixel is assumed a square shape with side length δ. Subsequently, the complex hologram is converted into a real, off-axis hologram H(x,y) by multiplying with an off-axis plane reference wave R(y)=exp(i2πyδsinθ/λ), and taking the real part of the product as
H(x,y)=Real[HC(x,y)R(y)].
(2)
In the optical experiments that follow, the off-set angle θ is taken to be 1.2o

3. Experimental results

Our proposed method is evaluated with an off-axis digital hologram H(x,y) comprising of 2048×2048 pixels, representing the planar image “Lenna eyes” shown in Fig. 4(a)
Fig. 4 (a) Source image “Lenna eyes”. (b) Numerical reconstruction of original hologram representing the image in Fig. 4(a). (c) Numerical reconstruction of the original hologram after down-sampling by 2 times with a uniform sampling lattice. (d) Numerical reconstruction of the original hologram after down-sampling by 2 times with the RGJD lattice. (e) Numerical reconstruction of the original hologram after down-sampling by 3 times with the RGJD lattice.
. The image is parallel to, and at an axial distance of 0.6m from the hologram. The latter has a pixel size of 7um×7um, and is generated with λ=650um. The reference plane wave R(y) is inclined at an angle of 1.2o along the vertical direction. The numerical reconstructed image at the focal plane is shown in Fig. 4(b). Next, we simulate the outcome when the hologram is displayed with a device of coarser resolution, having a pixel size of 14μm×14μm. This is accomplished by down-sampling the hologram with a factor of 2 along both the horizontal and vertical directions, so that effective pixel separation is 14μm×14μm. The numerical reconstructed image of the decimated hologram is shown in Fig. 4(c). Due to the reduction of the hologram resolution, the quality of the reconstructed image is very poor, and the Peak Signal to Noise Ratio (PSNR) as compare with the reconstructed image in Fig. 4(b) is only 11.2dB. To evaluate our proposed method, we apply RGJD (i.e., Eq. (3)) to down-sample the hologram H(x,y) with a factor of 2. The RGJD lattice G(x,y) is taken as the high resolution binary grating. Subsequently, the down-sampled hologram, denoted by HJ(x,y), is interpolated to a lower resolution hologram M(x,y) with pixel duplication. With a factor of k=2, the effective pixel size of M(x,y) is 14μm×14μm. As explained previously, HJ(x,y) can be realized by overlaying the binary grating G(x,y) onto the low resolution hologramM(x,y). Hence, evaluating HJ(x,y) will be equivalent to the evaluation of the integration of G(x,y) and M(x,y). The numerical reconstructed image of HJ(x,y) is shown in Fig. 4(d). We observe that apart from some noise contamination and blurring, the reconstructed image is similar to that derived from the original hologram, and having a PSNR of 23.85dB. Referring to Eq. (4), it can be inferred that further increasing the sampling factor is not preferred as the signal strength will be decreased substantially. However, for the sake of interest, we evaluate the result for k=3, increasing the effective pixel size to 21μm×21μm. The numerical reconstructed image is shown in Fig. 4(e). Although the quality of the image is still acceptable, the noise contamination becomes more prominent, and the PSNR drops by almost 3dB to 20.89dB.

4. Conclusion

In our proposed method, we apply RGJD and interpolation to convert a real, off-axis digital Fresnel hologram into a low-resolution hologram. By overlaying the low-resolution hologram with a binary grating that is generated based on the same RGJD lattice, a good approximation of the original hologram can be realized. The process only involves negligible amount of computation and is not restricted by the size and content of the hologram. Deriving the RGJD lattice and its associated binary grating is an off-line process, and once generated, they can be applied universally to all the input holograms. Experimental evaluation reveals that with our proposed method, the reconstructed image of a hologram can be preserved favorably after its resolution has been decreased to one third of its original value. The encouraging result suggests that such technique can be readily applied to enable high-resolution holograms to be display on a relatively lower resolution device.

Acknowledgment

This work is supported by the Chinese Academy of Sciences Visiting Professorships for Senior International Scientists Program under Grant Number 2010T2G17 and the High-End Foreign Experts Recruitment Program, China, under Grant Number GDJ 20130491009.

References and links

1.

J. Weng, T. Shimobaba, N. Okada, H. Nakayama, M. Oikawa, N. Masuda, and T. Ito, “Generation of real-time large computer generated hologram using wavefront recording method,” Opt. Express 20(4), 4018–4023 (2012). [CrossRef] [PubMed]

2.

P. Tsang, W. K. Cheung, T.-C. Poon, and C. Zhou, “Holographic video at 40 frames per second for 4-million object points,” Opt. Express 19(16), 15205–15211 (2011). [CrossRef] [PubMed]

3.

M. Stanley et al., “100-megapixel computer-generated holographic images from Active Tiling: a dynamic and scalable electro-optic modulator system,” SPIE5005, 247–258 (2003).

4.

N. Collings, “Optically Addressed Spatial Light Modulators for 3d Display,” J. Nonlinear Opt. Phys. Mater. 20(4), 453–457 (2011). [CrossRef]

5.

C. Slinger, C. Cameron, and M. Stanley, “Computer-Generated Holography as a Generic Display Technology,” Computer 38(8), 46–53 (2005). [CrossRef]

6.

H-S. Lee, H. Song, S. Lee, N. Collings, and D. Chu, “High resolution spatial light modulator for wide viewing angle holographic 3D display”, Coll. Conf. 3D Res., (CC3DR), 71–72, (2012).

7.

P. W. Tsang, T.-C. Poon, C. Zhou, and K. W. Cheung, “Binary Mask Programmable Hologram,” Opt. Express 20(24), 26480–26485 (2012). [CrossRef] [PubMed]

8.

D. E. Golberg, Genetic Algorithms in Search, Optimization, and Machine Learning, Addison Wesley, (1989).

9.

R. L. Cook, “Stochastic sampling in computer graphics,” ACM Trans. Graph. 5(1), 51–72 (1986). [CrossRef]

10.

A. V. Balakrishnan, “On the problem of time jitter in sampling,” IRE Trans. Inf. Theory 8(3), 226–236 (1962). [CrossRef]

11.

M. A. Z. Dippé and E. H. Wold, “Antialiasing Through Stochastic Sampling,” SIGGRAPH 19(3), 69–78 (1985). [CrossRef]

OCIS Codes
(090.0090) Holography : Holography
(090.1760) Holography : Computer holography
(090.1995) Holography : Digital holography

ToC Category:
Holography

History
Original Manuscript: May 8, 2013
Revised Manuscript: June 18, 2013
Manuscript Accepted: July 6, 2013
Published: July 16, 2013

Citation
P.W.M. Tsang, T.-C. Poon, and C. Zhou, "Displaying a high-resolution digital hologram on a low-resolution spatial light modulator with the same resolution obtained from the hologram," Opt. Express 21, 17586-17591 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-15-17586


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References

  1. J. Weng, T. Shimobaba, N. Okada, H. Nakayama, M. Oikawa, N. Masuda, and T. Ito, “Generation of real-time large computer generated hologram using wavefront recording method,” Opt. Express20(4), 4018–4023 (2012). [CrossRef] [PubMed]
  2. P. Tsang, W. K. Cheung, T.-C. Poon, and C. Zhou, “Holographic video at 40 frames per second for 4-million object points,” Opt. Express19(16), 15205–15211 (2011). [CrossRef] [PubMed]
  3. M. Stanley et al., “100-megapixel computer-generated holographic images from Active Tiling: a dynamic and scalable electro-optic modulator system,” SPIE5005, 247–258 (2003).
  4. N. Collings, “Optically Addressed Spatial Light Modulators for 3d Display,” J. Nonlinear Opt. Phys. Mater.20(4), 453–457 (2011). [CrossRef]
  5. C. Slinger, C. Cameron, and M. Stanley, “Computer-Generated Holography as a Generic Display Technology,” Computer38(8), 46–53 (2005). [CrossRef]
  6. H-S. Lee, H. Song, S. Lee, N. Collings, and D. Chu, “High resolution spatial light modulator for wide viewing angle holographic 3D display”, Coll. Conf. 3D Res., (CC3DR), 71–72, (2012).
  7. P. W. Tsang, T.-C. Poon, C. Zhou, and K. W. Cheung, “Binary Mask Programmable Hologram,” Opt. Express20(24), 26480–26485 (2012). [CrossRef] [PubMed]
  8. D. E. Golberg, Genetic Algorithms in Search, Optimization, and Machine Learning, Addison Wesley, (1989).
  9. R. L. Cook, “Stochastic sampling in computer graphics,” ACM Trans. Graph.5(1), 51–72 (1986). [CrossRef]
  10. A. V. Balakrishnan, “On the problem of time jitter in sampling,” IRE Trans. Inf. Theory8(3), 226–236 (1962). [CrossRef]
  11. M. A. Z. Dippé and E. H. Wold, “Antialiasing Through Stochastic Sampling,” SIGGRAPH19(3), 69–78 (1985). [CrossRef]

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