Abstract

Speckles on images in holographic projection displays (HPDs) were efficiently suppressed by the temporal sum of two diffractive images generated from diffractive optical elements (DOEs). Using a modified iterative Fourier transform algorithm, we obtained pairs of phase-only DOEs that generated the diffractive images with high negative correlation coefficients of 0.827 and 0.490 in the one-dimensional and the two-dimensional simulations, respectively. The suppression ratios of the speckles in the two simulations were 0.301 and 0.457, which were 61% and 35% lower, respectively, than the sum of the two uncorrelated images. We have successfully demonstrated that the sum of two negatively correlated images from DOEs can effectively reduce the image speckles and improve the image quality in HPD systems.

© 2011 Optical Society of America

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References

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2011 (3)

E. Buckley, “Holographic laser projection,” J. Display Technology 7, 135–140 (2011).
[CrossRef]

W.-F. Hsu, Y.-W. Chen, and Y.-H. Su, “Implementation of phase-shift patterns using a holographic projection system with phase-only diffractive optical elements,” Appl. Opt. 50, 3646–3652 (2011).
[CrossRef] [PubMed]

W.-F. Hsu and I.-L. Chu, “Speckle suppression by integrated sum of fully developed negatively correlated patterns in coherent imaging,” Prog. Electromagn. Res. B 34, 1–13 (2011).

2010 (1)

2009 (2)

2008 (1)

1999 (1)

1996 (1)

H. Aagedal, M. Schmid, T. Beth, S. Teiwes, and F. Wyrowski, “Theory of speckles in diffractive optics and its application to beam shaping,” J. Mod. Opt. 43, 1409–1421 (1996).
[CrossRef]

1990 (1)

1989 (1)

1977 (2)

1976 (1)

Aagedal, H.

H. Aagedal, M. Schmid, T. Beth, S. Teiwes, and F. Wyrowski, “Theory of speckles in diffractive optics and its application to beam shaping,” J. Mod. Opt. 43, 1409–1421 (1996).
[CrossRef]

Asakura, T.

Bay, C.

Bergmann, R. B.

Beth, T.

H. Aagedal, M. Schmid, T. Beth, S. Teiwes, and F. Wyrowski, “Theory of speckles in diffractive optics and its application to beam shaping,” J. Mod. Opt. 43, 1409–1421 (1996).
[CrossRef]

Bryngdahl, O.

Buckley, E.

E. Buckley, “Holographic laser projection,” J. Display Technology 7, 135–140 (2011).
[CrossRef]

Chang, Y.-S.

Y.-S. Chang, H. Y. Lin, and W.-F. Hsu, “Speckle suppression by 2D spatial light modulator in laser projection system,” in Proceedings SID Symposium 2011 (Society for Information Display, 2011), paper 32.2, pp. 428–431.
[CrossRef]

Chen, Y.-W.

Chu, I.-L.

W.-F. Hsu and I.-L. Chu, “Speckle suppression by integrated sum of fully developed negatively correlated patterns in coherent imaging,” Prog. Electromagn. Res. B 34, 1–13 (2011).

Dankwart, C.

Falldorf, C.

Freeman, J.

Gläbe, R.

Glückstad, J.

Golan, L.

Goodman, J. W.

J. W. Goodman, “Some fundamental properties of speckle,” J. Opt. Soc. Am. 66, 1145–1150 (1976).
[CrossRef]

J. W. Goodman, Statistical Optics (Wiley, 1985), p. 17.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed.(Roberts, 2005), Chap. 5.

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts, 2007).

Hsu, W.-F.

W.-F. Hsu and I.-L. Chu, “Speckle suppression by integrated sum of fully developed negatively correlated patterns in coherent imaging,” Prog. Electromagn. Res. B 34, 1–13 (2011).

W.-F. Hsu, Y.-W. Chen, and Y.-H. Su, “Implementation of phase-shift patterns using a holographic projection system with phase-only diffractive optical elements,” Appl. Opt. 50, 3646–3652 (2011).
[CrossRef] [PubMed]

W.-F. Hsu and C.-F. Yeh, “A novel laser projection system by use of the beam-shaping method to reduce the speckle phenomenon,” in Proceedings IDMC/3DSA/Asia Display 2009 (CD) (Society for Information Display, Taipei Chapter, 2009), paper Wed-P3-08.

Y.-S. Chang, H. Y. Lin, and W.-F. Hsu, “Speckle suppression by 2D spatial light modulator in laser projection system,” in Proceedings SID Symposium 2011 (Society for Information Display, 2011), paper 32.2, pp. 428–431.
[CrossRef]

Hubner, N.

Kopylow, C. V.

Kreyszig, E.

E. Kreyszig, Advanced Engineering Mathematics, 9th ed.(Wiley, 2006), p. 1089.

Lin, H. Y.

Y.-S. Chang, H. Y. Lin, and W.-F. Hsu, “Speckle suppression by 2D spatial light modulator in laser projection system,” in Proceedings SID Symposium 2011 (Society for Information Display, 2011), paper 32.2, pp. 428–431.
[CrossRef]

Lünemann, B.

Ohtsubo, J.

Palima, D.

Schmid, M.

H. Aagedal, M. Schmid, T. Beth, S. Teiwes, and F. Wyrowski, “Theory of speckles in diffractive optics and its application to beam shaping,” J. Mod. Opt. 43, 1409–1421 (1996).
[CrossRef]

Shoham, S.

Su, Y.-H.

Taghizadeh, M. R.

Teiwes, S.

H. Aagedal, M. Schmid, T. Beth, S. Teiwes, and F. Wyrowski, “Theory of speckles in diffractive optics and its application to beam shaping,” J. Mod. Opt. 43, 1409–1421 (1996).
[CrossRef]

Waddie, A. J.

Wilkinson, T.

Wyrowski, F.

Yeh, C.-F.

W.-F. Hsu and C.-F. Yeh, “A novel laser projection system by use of the beam-shaping method to reduce the speckle phenomenon,” in Proceedings IDMC/3DSA/Asia Display 2009 (CD) (Society for Information Display, Taipei Chapter, 2009), paper Wed-P3-08.

Appl. Opt. (4)

J. Display Technology (1)

E. Buckley, “Holographic laser projection,” J. Display Technology 7, 135–140 (2011).
[CrossRef]

J. Mod. Opt. (1)

H. Aagedal, M. Schmid, T. Beth, S. Teiwes, and F. Wyrowski, “Theory of speckles in diffractive optics and its application to beam shaping,” J. Mod. Opt. 43, 1409–1421 (1996).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Opt. Express (2)

Opt. Lett. (2)

Prog. Electromagn. Res. B (1)

W.-F. Hsu and I.-L. Chu, “Speckle suppression by integrated sum of fully developed negatively correlated patterns in coherent imaging,” Prog. Electromagn. Res. B 34, 1–13 (2011).

Other (7)

J. W. Goodman, Statistical Optics (Wiley, 1985), p. 17.

E. Kreyszig, Advanced Engineering Mathematics, 9th ed.(Wiley, 2006), p. 1089.

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts, 2007).

J.Turunen and F.Wyrowski eds., Diffractive Optics for Industrial and Commercial Applications (Akademie Verlag, 1997).

W.-F. Hsu and C.-F. Yeh, “A novel laser projection system by use of the beam-shaping method to reduce the speckle phenomenon,” in Proceedings IDMC/3DSA/Asia Display 2009 (CD) (Society for Information Display, Taipei Chapter, 2009), paper Wed-P3-08.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed.(Roberts, 2005), Chap. 5.

Y.-S. Chang, H. Y. Lin, and W.-F. Hsu, “Speckle suppression by 2D spatial light modulator in laser projection system,” in Proceedings SID Symposium 2011 (Society for Information Display, 2011), paper 32.2, pp. 428–431.
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Schematic of an HPD system.

Fig. 2
Fig. 2

(a) Part of the uncorrelated images and (b) the sums of two and four images of (a). The diffractive images are produced by the DOEs using the IFTA. The speckle contrasts and the correlation coefficients are listed in Table 1.

Fig. 3
Fig. 3

(a) Target image generated by reversing the speckles in Image 1, and (b) the diffractive images produced by the DOEs using the modified IFTA. The speckle contrasts and the correlation coefficients are listed in Table 2.

Fig. 4
Fig. 4

(Simulation) (a) Target image, (b) the diffractive image of DOE1, (c) the diffractive image of DOE2 designed using the modified IFTA with the target image of reversed speckles of (b), and (d) the sum of the images (b) and (c). ρ b , c = 0.490 . The speckle contrasts of the gray regions are listed in Table 3.

Fig. 5
Fig. 5

(Experiment) (a) Target image, (b) the diffractive image of DOE1, (c) the diffractive image of DOE2 designed using the modified IFTA with the target image of reversed speckles of (b), and (d) the sum of the images (b) and (c). ρ b , c = 0.495 in the IFTA design and simulations. The speckle contrasts of the gray regions are listed in Table 4.

Fig. 6
Fig. 6

Experimental results of (a) the target image adapted from the USAF 1951 test pattern. The part, marked with a red square in (a), of the diffractive images produced by (b) DOE1, (c) DOE2, and (d) in the summed image.

Tables (4)

Tables Icon

Table 1 Suppression Results of the Diffractive Images of Four 1D DOEs in Fig. 2 a

Tables Icon

Table 2 Suppression Results of the Diffractive Images of Two 1D DOEs in Fig. 3 a

Tables Icon

Table 3 (Simulations) Speckle Contrasts and the Suppression Ratios of the Four Gray Regions in the Images of the 2D DOEs in Fig. 4 a

Tables Icon

Table 4 (Experiment) Speckle Contrasts and the Suppression Ratios of the Four Gray Regions in the Images of the 2D DOEs in Fig. 5 a

Equations (7)

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

U f ( x , y ) = exp [ j k 2 f ( 1 d f ) ( x 2 + y 2 ) ] j λ f × U SLM ( ξ , η ) · exp [ j 2 π λ f ( ξ x + η y ) ] d ξ d η ,
U f ( x , y ) = C · FT { U SLM ( ξ , η ) } | f x = x λ f , f y = y λ f ,
C S = σ S I ¯ S ,
I ¯ S = I ¯ 1 + I ¯ 2 ,
σ S = ( I S 2 I t ) 2 ¯ = σ 1 2 + σ 2 2 + 2 ρ σ 1 σ 2 ,
ρ = ( I 1 I t ) ( I 2 I t ) ¯ σ 1 σ 2 .
C S = ( C 1 + C 2 ) 2 2 ( 1 ρ ) C 1 C 2 4 ,

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