Abstract

In this work we present the design and fabrication of a dual-layer blazed grating (DBG) to replace a single-layer blazed grating for chromostereoscopy. Based on the physiological and physical background, we first analyze the relationship between the performance of a grating pair and color-stereo effect. The DBG is composed of two materials of different indices and fabricated upon a polyethylene terephthalate film by two steps of a roll-to-roll microreplication process. With this dual-layer design, the fabrication tolerance in the blazed facets of the grating is three times looser and more achievable as compared with that of a grating composed of single material.

© 2012 Optical Society of America

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    [CrossRef]
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  4. C. Ucke, “3-D vision with chromadepth™ glasses,” in Hands-On Experiments in Physics Education, ICPE/GIREP Conference (1998).
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    [CrossRef]
  7. T. Mäkelä, T. Haatainen, P. Majander, and J. Ahopelto, “Continuous roll-to-roll nanoimprinting of inherently conducting polyaniline,” Microelectron. Eng. 84, 877–879 (2007).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  16. L. Chun-Wei, L. Chi-Hung, and L. Shih-Chieh, “Sub-wavelength gratings fabricated on a light bar by roll-to-roll UV embossing process,” Opt. Express 19, 11299–11311 (2011).
    [CrossRef]

2011 (2)

S. Mokkapati, F. J. Beck, and K. R. Catchpole, “Analytical approach for design of blazed dielectric gratings for light trapping in solar cells,” J. Phys. D 44, 055103 (2011).
[CrossRef]

L. Chun-Wei, L. Chi-Hung, and L. Shih-Chieh, “Sub-wavelength gratings fabricated on a light bar by roll-to-roll UV embossing process,” Opt. Express 19, 11299–11311 (2011).
[CrossRef]

2010 (1)

W. Mphepö, Y.-P. Huang, P. Rudquist, and H.-P. D. Shieh, “An autosteresoscopic 3D display system based on prism patterned projection screen,” J. Disp. Technol. 6, 94–97 (2010).
[CrossRef]

2009 (1)

2007 (1)

T. Mäkelä, T. Haatainen, P. Majander, and J. Ahopelto, “Continuous roll-to-roll nanoimprinting of inherently conducting polyaniline,” Microelectron. Eng. 84, 877–879 (2007).
[CrossRef]

2005 (1)

M. T. Gale, C. H. Gimkiewicz, S. Obi, M. Schnieper, J. Söchtig, H. Thiele, and S. Westenhöfer, “Replication technology for optical microsystems,” Opt. Lasers Eng. 43, 373–386(2005).
[CrossRef]

2000 (1)

S. W. Fan, “Vector theory analysis and numerical calculation for any shape profile dielectric gratings,” Opt. Precis. Eng. 8, 5–10 (2000).

1998 (1)

M. Heckele, W. Bacher, and K. D. Muller, “Hot embossing—the molding technique for plastic microstructures,” Microsyst. Technol. 4, 122–124 (1998).
[CrossRef]

1995 (2)

Ahopelto, J.

T. Mäkelä, T. Haatainen, P. Majander, and J. Ahopelto, “Continuous roll-to-roll nanoimprinting of inherently conducting polyaniline,” Microelectron. Eng. 84, 877–879 (2007).
[CrossRef]

Bacher, W.

M. Heckele, W. Bacher, and K. D. Muller, “Hot embossing—the molding technique for plastic microstructures,” Microsyst. Technol. 4, 122–124 (1998).
[CrossRef]

Beck, F. J.

S. Mokkapati, F. J. Beck, and K. R. Catchpole, “Analytical approach for design of blazed dielectric gratings for light trapping in solar cells,” J. Phys. D 44, 055103 (2011).
[CrossRef]

Catchpole, K. R.

S. Mokkapati, F. J. Beck, and K. R. Catchpole, “Analytical approach for design of blazed dielectric gratings for light trapping in solar cells,” J. Phys. D 44, 055103 (2011).
[CrossRef]

Chi-Hung, L.

Chun-Wei, L.

Einthoven, W.

W. Einthoven, “Stereoscopie durch Farbendifferenz,” in Albrecht von Graefe’s Archiv fur Ophthalmologie31, 211–238 (1885).

Fan, S. W.

S. W. Fan, “Vector theory analysis and numerical calculation for any shape profile dielectric gratings,” Opt. Precis. Eng. 8, 5–10 (2000).

Gale, M. T.

M. T. Gale, C. H. Gimkiewicz, S. Obi, M. Schnieper, J. Söchtig, H. Thiele, and S. Westenhöfer, “Replication technology for optical microsystems,” Opt. Lasers Eng. 43, 373–386(2005).
[CrossRef]

Gimkiewicz, C. H.

M. T. Gale, C. H. Gimkiewicz, S. Obi, M. Schnieper, J. Söchtig, H. Thiele, and S. Westenhöfer, “Replication technology for optical microsystems,” Opt. Lasers Eng. 43, 373–386(2005).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 2005).

Grann, E. B.

Haatainen, T.

T. Mäkelä, T. Haatainen, P. Majander, and J. Ahopelto, “Continuous roll-to-roll nanoimprinting of inherently conducting polyaniline,” Microelectron. Eng. 84, 877–879 (2007).
[CrossRef]

Heckele, M.

M. Heckele, W. Bacher, and K. D. Muller, “Hot embossing—the molding technique for plastic microstructures,” Microsyst. Technol. 4, 122–124 (1998).
[CrossRef]

Huang, Y.-P.

W. Mphepö, Y.-P. Huang, P. Rudquist, and H.-P. D. Shieh, “An autosteresoscopic 3D display system based on prism patterned projection screen,” J. Disp. Technol. 6, 94–97 (2010).
[CrossRef]

Kathman, A. D.

D. C. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics: Design, Fabrication, and Test (SPIE, 2003).

Majander, P.

T. Mäkelä, T. Haatainen, P. Majander, and J. Ahopelto, “Continuous roll-to-roll nanoimprinting of inherently conducting polyaniline,” Microelectron. Eng. 84, 877–879 (2007).
[CrossRef]

Mäkelä, T.

T. Mäkelä, T. Haatainen, P. Majander, and J. Ahopelto, “Continuous roll-to-roll nanoimprinting of inherently conducting polyaniline,” Microelectron. Eng. 84, 877–879 (2007).
[CrossRef]

Moharam, M. G.

Mokkapati, S.

S. Mokkapati, F. J. Beck, and K. R. Catchpole, “Analytical approach for design of blazed dielectric gratings for light trapping in solar cells,” J. Phys. D 44, 055103 (2011).
[CrossRef]

Mphepö, W.

W. Mphepö, Y.-P. Huang, P. Rudquist, and H.-P. D. Shieh, “An autosteresoscopic 3D display system based on prism patterned projection screen,” J. Disp. Technol. 6, 94–97 (2010).
[CrossRef]

Muller, K. D.

M. Heckele, W. Bacher, and K. D. Muller, “Hot embossing—the molding technique for plastic microstructures,” Microsyst. Technol. 4, 122–124 (1998).
[CrossRef]

O’Shea, D. C.

D. C. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics: Design, Fabrication, and Test (SPIE, 2003).

Obi, S.

M. T. Gale, C. H. Gimkiewicz, S. Obi, M. Schnieper, J. Söchtig, H. Thiele, and S. Westenhöfer, “Replication technology for optical microsystems,” Opt. Lasers Eng. 43, 373–386(2005).
[CrossRef]

Pommet, D. A.

Prather, D. W.

D. C. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics: Design, Fabrication, and Test (SPIE, 2003).

Rudquist, P.

W. Mphepö, Y.-P. Huang, P. Rudquist, and H.-P. D. Shieh, “An autosteresoscopic 3D display system based on prism patterned projection screen,” J. Disp. Technol. 6, 94–97 (2010).
[CrossRef]

Schnieper, M.

M. T. Gale, C. H. Gimkiewicz, S. Obi, M. Schnieper, J. Söchtig, H. Thiele, and S. Westenhöfer, “Replication technology for optical microsystems,” Opt. Lasers Eng. 43, 373–386(2005).
[CrossRef]

Shieh, H.-P. D.

W. Mphepö, Y.-P. Huang, P. Rudquist, and H.-P. D. Shieh, “An autosteresoscopic 3D display system based on prism patterned projection screen,” J. Disp. Technol. 6, 94–97 (2010).
[CrossRef]

Shih-Chieh, L.

Sinzinger, S.

Söchtig, J.

M. T. Gale, C. H. Gimkiewicz, S. Obi, M. Schnieper, J. Söchtig, H. Thiele, and S. Westenhöfer, “Replication technology for optical microsystems,” Opt. Lasers Eng. 43, 373–386(2005).
[CrossRef]

Steenblik, R. A.

R. A. Steenblik, “Stereoscopic process and apparatus using different deviations of different colors,” U. S. Patent 5,002,364 (1991).

Suleski, T. J.

D. C. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics: Design, Fabrication, and Test (SPIE, 2003).

Swanson, G. J.

G. J. Swanson and W. B. Veldkamp, “High efficiency, multilevel diffractive optical elements,” U. S. Patent 4,895,790(1990).

Testorf, M.

Thiele, H.

M. T. Gale, C. H. Gimkiewicz, S. Obi, M. Schnieper, J. Söchtig, H. Thiele, and S. Westenhöfer, “Replication technology for optical microsystems,” Opt. Lasers Eng. 43, 373–386(2005).
[CrossRef]

Tseng, C.-C.

Ucke, C.

C. Ucke, “3-D vision with chromadepth™ glasses,” in Hands-On Experiments in Physics Education, ICPE/GIREP Conference (1998).

Veldkamp, W. B.

G. J. Swanson and W. B. Veldkamp, “High efficiency, multilevel diffractive optical elements,” U. S. Patent 4,895,790(1990).

Wang, M.-W.

Westenhöfer, S.

M. T. Gale, C. H. Gimkiewicz, S. Obi, M. Schnieper, J. Söchtig, H. Thiele, and S. Westenhöfer, “Replication technology for optical microsystems,” Opt. Lasers Eng. 43, 373–386(2005).
[CrossRef]

Appl. Opt. (1)

J. Disp. Technol. (1)

W. Mphepö, Y.-P. Huang, P. Rudquist, and H.-P. D. Shieh, “An autosteresoscopic 3D display system based on prism patterned projection screen,” J. Disp. Technol. 6, 94–97 (2010).
[CrossRef]

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

J. Phys. D (1)

S. Mokkapati, F. J. Beck, and K. R. Catchpole, “Analytical approach for design of blazed dielectric gratings for light trapping in solar cells,” J. Phys. D 44, 055103 (2011).
[CrossRef]

Microelectron. Eng. (1)

T. Mäkelä, T. Haatainen, P. Majander, and J. Ahopelto, “Continuous roll-to-roll nanoimprinting of inherently conducting polyaniline,” Microelectron. Eng. 84, 877–879 (2007).
[CrossRef]

Microsyst. Technol. (1)

M. Heckele, W. Bacher, and K. D. Muller, “Hot embossing—the molding technique for plastic microstructures,” Microsyst. Technol. 4, 122–124 (1998).
[CrossRef]

Opt. Express (2)

Opt. Lasers Eng. (1)

M. T. Gale, C. H. Gimkiewicz, S. Obi, M. Schnieper, J. Söchtig, H. Thiele, and S. Westenhöfer, “Replication technology for optical microsystems,” Opt. Lasers Eng. 43, 373–386(2005).
[CrossRef]

Opt. Precis. Eng. (1)

S. W. Fan, “Vector theory analysis and numerical calculation for any shape profile dielectric gratings,” Opt. Precis. Eng. 8, 5–10 (2000).

Other (6)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 2005).

D. C. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics: Design, Fabrication, and Test (SPIE, 2003).

W. Einthoven, “Stereoscopie durch Farbendifferenz,” in Albrecht von Graefe’s Archiv fur Ophthalmologie31, 211–238 (1885).

R. A. Steenblik, “Stereoscopic process and apparatus using different deviations of different colors,” U. S. Patent 5,002,364 (1991).

C. Ucke, “3-D vision with chromadepth™ glasses,” in Hands-On Experiments in Physics Education, ICPE/GIREP Conference (1998).

G. J. Swanson and W. B. Veldkamp, “High efficiency, multilevel diffractive optical elements,” U. S. Patent 4,895,790(1990).

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Figures (13)

Fig. 1.
Fig. 1.

Observer’s relative positions Dr and Dg, and Db the viewing angles θr, θg and θb to the apparent colors.

Fig. 2.
Fig. 2.

Triangular profile of a standard SBG.

Fig. 3.
Fig. 3.

Transition from the diffractive blazed grating to the refractive prism is related to the wavelength and the structure size.

Fig. 4.
Fig. 4.

The intensity in the Fourier plane of a blazed grating for varying illumination wavelengths (a) 633 nm and (b) 473 nm. The intensity distribution Iprism(ν), IPeriodic(ν), and I(ν) are represented in blue, green, and red, respectively.

Fig. 5.
Fig. 5.

Distribution of the diffraction intensity at +1 diffraction order of the SBG as function of α from 1.1° to 3.3°. The intensity distribution of R (633 nm), G (532 nm), and B (473 nm) are represented in red, green, and blue, respectively.

Fig. 6.
Fig. 6.

Schematic of a DBG.

Fig. 7.
Fig. 7.

Distribution of the diffraction intensity at +1 diffraction order of the DBG as a function of α from 18.05° to 20.05° and γ (74.95°, solid curve; 75.95°, dashed-dotted curve; 76.95°, dash curve). The intensity distribution of R (633 nm), G (532 nm), and B (473 nm) are represented in red, green, and blue, respectively.

Fig. 8.
Fig. 8.

(a) Roller is processed by a diamond tool with the designed profile. (b) The UV resin is dispensed onto a 188 µm thick PET film, imprinted by the roller, and hardened by the UV source. (c) To fabricate the second layer of DBG, the other UV resin is dispensed onto the first layer, imprinted by a flat roller, and hardened by the UV source.

Fig. 9.
Fig. 9.

SEM figures of the fabricated (a) SBG and (b) DBG (before embossing the second layer). The surface is mounted at a 30° incident angle to the SEM electron beam.

Fig. 10.
Fig. 10.

The diffraction patterns of SBG under the (from left to right) red, green, and blue incident laser beams.

Fig. 11.
Fig. 11.

The diffraction patterns of DBG under the (from left to right) red, green, and blue incident laser beams.

Fig. 12.
Fig. 12.

The diffraction of color bars in a black background through a fabricated (left) SBG and a (right) DBG.

Fig. 13.
Fig. 13.

(left) A 2D color image is viewed through a pair of DBG. A slight difference (indicated by the red arrows) can be observed in the generated 3D images for the right and the left eyes.

Tables (1)

Tables Icon

Table 1. The Diffraction Efficiencies of the First Transmission Order of SBG and DBG

Equations (9)

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

θr=tan1(W/2Dr).
mλ=Λ(sinθdifsinθinc),
n×sinα=sin(α+θr).
h=Λ×α=λRnR1.
T(x)=Tprism(x)Tperiodic(x)=exp[ikαx(n1)]×rect(xΛ)Σmδ(xmd)rect(xNΛ),
I(ν)=FT{T(x)}=FT{Tprism(x)Tperiodic(x)}=Iprism(ν)·Iperiodic(ν)=sinc2{[ναn1λ]Λ}msinc2[νmΛ]NΛ=sinc2{νλRα(nR1)Q}msinc2[νmΛ]NΛ,
Q=(n1)λR(nR1)λ.
n1×sinα=n2×sin(α+θ),n2×sinθ=sinθr.
h=tanα×tanβ×Λtanα+tanβ.

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