Abstract

Illuminance nonuniformity caused by natural vignetting can seriously affect the display quality of large-field-of-view (FOV) waveguide displays. In this paper, an optimization method based on the differential evolution algorithm is proposed for in-coupling grating design to improve coupling efficiency and compensate for natural vignetting. The in-coupling grating parameters are optimized to achieve efficiency distributions in which efficiency increases continuously with incidence angle, realizing uniform illuminance over a large FOV of 45°. The angular uniformity reaches 0.89. Additionally, average diffraction efficiency reaches 89.13% for transverse-electric polarization at 532 nm and 76% in the wavelength region between 450 and 700 nm.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2017 (1)

T. H. Harding and C. E. Rash, “Daylight luminance requirements for full-color, see-through, helmet-mounted display systems,” Opt. Eng. 56(5), 051404 (2017).
[Crossref]

2015 (1)

2014 (3)

2013 (3)

2012 (2)

2011 (4)

J. Rolland and K. Thompson, “See-through head worn displays for mobile augmented reality,” Commun. China Comp. Fed. 7, 28–37 (2011).

J. Carmigniani, B. Furht, M. Anisetti, P. Ceravolo, E. Damiani, and M. Ivkovic, “Augmented reality technologies, systems and applications,” Multimedia Tools Appl. 51(1), 341–377 (2011).
[Crossref]

R. Mallipeddi, P. N. Suganthan, Q.-K. Pan, and M. F. Tasgetiren, “Differential evolution algorithm with ensemble of parameters and mutation strategies,” Appl. Soft Comput. 11(2), 1679–1696 (2011).
[Crossref]

P. Rocca, G. Oliveri, and A. Massa, “Differential evolution as applied to electromagnetics,” IEEE Antennas Propag. Mag. 53(1), 38–49 (2011).
[Crossref]

2009 (3)

D. Cheng, Y. Wang, H. Hua, and M. M. Talha, “Design of an optical see-through head-mounted display with a low f-number and large field of view using a freeform prism,” Appl. Opt. 48(14), 2655–2668 (2009).
[Crossref] [PubMed]

H. Mukawa, K. Akutsu, I. Matsumura, S. Nakano, T. Yoshida, M. Kuwahara, and K. Aiki, “A full-color eyewear display using planar waveguides with reflection volume holograms,” J. Soc. Inf. Disp. 17(3), 185–193 (2009).
[Crossref]

A. Cameron, “The application of holographic optical waveguide technology to the Q-Sight family of helmet-mounted displays,” Proc. SPIE 7362, 73260H (2009).
[Crossref]

2008 (2)

2007 (2)

2006 (2)

2004 (1)

I. Gurwich, V. Weiss, L. Eisen, M. Meyklyar, and A. A. Friesem, “Design and experiments of planar optical light guides for virtual image displays,” Proc. SPIE 5182, 212–221 (2004).
[Crossref]

2002 (2)

M. M. Bayer, “Retinal scanning display: a novel HMD approach for army aviation,” Proc. SPIE 4711, 202–213 (2002).
[Crossref]

R. Shechter, Y. Amitai, and A. A. Friesem, “Compact beam expander with linear gratings,” Appl. Opt. 41(7), 1236–1240 (2002).
[Crossref] [PubMed]

2000 (1)

1999 (1)

S. Yamazaki, K. Inoguchi, Y. Saito, H. Morishima, and N. Taniguchi, “Thin wide-field-of-view HMD with free-form-surface prism and applications,” Proc. SPIE 3639, 453–462 (1999).
[Crossref]

1997 (1)

1995 (4)

1990 (1)

S. T. Yang, R. L. Hsieh, Y.-H. Lee, R. F. W. Pease, and G. Owen, “Effect of central obscuration on image formation in projection lithography,” Proc. SPIE 1264, 477–485 (1990).
[Crossref]

1986 (1)

1983 (1)

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220(4598), 671–680 (1983).
[Crossref] [PubMed]

1977 (1)

T. Tamir and S. T. Peng, “Analysis and design of grating couplers,” Appl. Phys., A Mater. Sci. Process. 14, 235–254 (1977).

1972 (1)

R. W. Gerchberg, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).

1969 (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48(9), 2909–2947 (1969).
[Crossref]

1948 (1)

I. C. Gardner and F. E. Washer, “Lenses of extremely wide angle for airplane mapping,” J. Opt. Soc. Am. A 38(5), 421–431 (1948).
[Crossref]

1947 (1)

I. C. Gardner, “Validity of the cosine-fourth-power law of illumination,” J. Res. Natl. Bur. Stand. 39(3), 213–219 (1947).
[Crossref]

Aiki, K.

H. Mukawa, K. Akutsu, I. Matsumura, S. Nakano, T. Yoshida, M. Kuwahara, and K. Aiki, “A full-color eyewear display using planar waveguides with reflection volume holograms,” J. Soc. Inf. Disp. 17(3), 185–193 (2009).
[Crossref]

Akutsu, K.

H. Mukawa, K. Akutsu, I. Matsumura, S. Nakano, T. Yoshida, M. Kuwahara, and K. Aiki, “A full-color eyewear display using planar waveguides with reflection volume holograms,” J. Soc. Inf. Disp. 17(3), 185–193 (2009).
[Crossref]

Amitai, Y.

R. Shechter, Y. Amitai, and A. A. Friesem, “Compact beam expander with linear gratings,” Appl. Opt. 41(7), 1236–1240 (2002).
[Crossref] [PubMed]

Y. Amitai, S. Reinhorn, and A. A. Friesem, “Visor-display design based on planar holographic optics,” Appl. Opt. 34(8), 1352–1356 (1995).
[Crossref] [PubMed]

Y. Amitai, “A Two-Dimensional Aperture Expander for Ultra-Compact, High-Performance Head-Worn Displays,” in SID Symposium Digest of Technical Papers (2005), pp. 360–363.

Y. Amitai, “Extremely Compact High-Performance HMDs Based on Substrate-Guided Optical Element,” SID Symposium Digest of Technical Papers (2004), pp. 310–313.

Anisetti, M.

J. Carmigniani, B. Furht, M. Anisetti, P. Ceravolo, E. Damiani, and M. Ivkovic, “Augmented reality technologies, systems and applications,” Multimedia Tools Appl. 51(1), 341–377 (2011).
[Crossref]

Bauer, A.

Bayer, M. M.

M. M. Bayer, “Retinal scanning display: a novel HMD approach for army aviation,” Proc. SPIE 4711, 202–213 (2002).
[Crossref]

Cameron, A.

A. Cameron, “The application of holographic optical waveguide technology to the Q-Sight family of helmet-mounted displays,” Proc. SPIE 7362, 73260H (2009).
[Crossref]

Carmigniani, J.

J. Carmigniani, B. Furht, M. Anisetti, P. Ceravolo, E. Damiani, and M. Ivkovic, “Augmented reality technologies, systems and applications,” Multimedia Tools Appl. 51(1), 341–377 (2011).
[Crossref]

Ceravolo, P.

J. Carmigniani, B. Furht, M. Anisetti, P. Ceravolo, E. Damiani, and M. Ivkovic, “Augmented reality technologies, systems and applications,” Multimedia Tools Appl. 51(1), 341–377 (2011).
[Crossref]

Cheng, D.

Cummings, W. J.

B. C. Kress and W. J. Cummings, “Towards the Ultimate Mixed Reality Experience: HoloLens Display Architecture Choices,” in SID Symposium Digest of Technical Papers (2017), pp. 127–131.

Damiani, E.

J. Carmigniani, B. Furht, M. Anisetti, P. Ceravolo, E. Damiani, and M. Ivkovic, “Augmented reality technologies, systems and applications,” Multimedia Tools Appl. 51(1), 341–377 (2011).
[Crossref]

Ding, Y.

Eisen, L.

L. Eisen, M. Meyklyar, M. Golub, A. A. Friesem, I. Gurwich, and V. Weiss, “Planar configuration for image projection,” Appl. Opt. 45(17), 4005–4011 (2006).
[Crossref] [PubMed]

I. Gurwich, V. Weiss, L. Eisen, M. Meyklyar, and A. A. Friesem, “Design and experiments of planar optical light guides for virtual image displays,” Proc. SPIE 5182, 212–221 (2004).
[Crossref]

Friesem, A. A.

Frommer, A.

A. Frommer, “11-3: Invited Paper: Lumus Optical Technology for AR,” in SID Symposium Digest of Technical Papers (2017), pp. 134–135.

Furht, B.

J. Carmigniani, B. Furht, M. Anisetti, P. Ceravolo, E. Damiani, and M. Ivkovic, “Augmented reality technologies, systems and applications,” Multimedia Tools Appl. 51(1), 341–377 (2011).
[Crossref]

Gao, C.

Gardner, I. C.

I. C. Gardner and F. E. Washer, “Lenses of extremely wide angle for airplane mapping,” J. Opt. Soc. Am. A 38(5), 421–431 (1948).
[Crossref]

I. C. Gardner, “Validity of the cosine-fourth-power law of illumination,” J. Res. Natl. Bur. Stand. 39(3), 213–219 (1947).
[Crossref]

Gaylord, T.

Gaylord, T. K.

M. G. Moharam, T. K. Gaylord, E. B. Grann, and D. A. Pommet, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. 12(5), 1068–1076 (1995).
[Crossref]

M. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of metallic surface-relief gratings,” J. Opt. Soc. Am. A 3(11), 1780–1787 (1986).
[Crossref]

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220(4598), 671–680 (1983).
[Crossref] [PubMed]

Gerchberg, R. W.

R. W. Gerchberg, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).

Girardot, A.

Golub, M.

Grann, E. B.

M. Moharam, D. A. Pommet, E. B. Grann, and T. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. A 12(5), 1077–1086 (1995).
[Crossref]

M. G. Moharam, T. K. Gaylord, E. B. Grann, and D. A. Pommet, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. 12(5), 1068–1076 (1995).
[Crossref]

Green, R. O.

Grossman, M.

B. Kress, V. Raulot, and M. Grossman, “Exit pupil expander for wearable see-through displays,” Proc. SPIE 8368, 83680D (2012).
[Crossref]

Gu, P. F.

Gurwich, I.

L. Eisen, M. Meyklyar, M. Golub, A. A. Friesem, I. Gurwich, and V. Weiss, “Planar configuration for image projection,” Appl. Opt. 45(17), 4005–4011 (2006).
[Crossref] [PubMed]

I. Gurwich, V. Weiss, L. Eisen, M. Meyklyar, and A. A. Friesem, “Design and experiments of planar optical light guides for virtual image displays,” Proc. SPIE 5182, 212–221 (2004).
[Crossref]

Ha, Y.

Harding, T. H.

T. H. Harding and C. E. Rash, “Daylight luminance requirements for full-color, see-through, helmet-mounted display systems,” Opt. Eng. 56(5), 051404 (2017).
[Crossref]

He, F.

Hsieh, R. L.

S. T. Yang, R. L. Hsieh, Y.-H. Lee, R. F. W. Pease, and G. Owen, “Effect of central obscuration on image formation in projection lithography,” Proc. SPIE 1264, 477–485 (1990).
[Crossref]

Hua, H.

Huang, H.

Inoguchi, K.

S. Yamazaki, K. Inoguchi, Y. Saito, H. Morishima, and N. Taniguchi, “Thin wide-field-of-view HMD with free-form-surface prism and applications,” Proc. SPIE 3639, 453–462 (1999).
[Crossref]

Itoh, M.

Ivkovic, M.

J. Carmigniani, B. Furht, M. Anisetti, P. Ceravolo, E. Damiani, and M. Ivkovic, “Augmented reality technologies, systems and applications,” Multimedia Tools Appl. 51(1), 341–377 (2011).
[Crossref]

Jin, G.

Kang, Y.

Kim, N.

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220(4598), 671–680 (1983).
[Crossref] [PubMed]

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48(9), 2909–2947 (1969).
[Crossref]

Kress, B.

B. Kress and T. Starner, “A review of head-mounted displays (HMD) technologies and applications for consumer electronics,” Proc. SPIE 8720, 87200A (2013).
[Crossref]

B. Kress, V. Raulot, and M. Grossman, “Exit pupil expander for wearable see-through displays,” Proc. SPIE 8368, 83680D (2012).
[Crossref]

Kress, B. C.

B. C. Kress and W. J. Cummings, “Towards the Ultimate Mixed Reality Experience: HoloLens Display Architecture Choices,” in SID Symposium Digest of Technical Papers (2017), pp. 127–131.

Kuwahara, M.

H. Mukawa, K. Akutsu, I. Matsumura, S. Nakano, T. Yoshida, M. Kuwahara, and K. Aiki, “A full-color eyewear display using planar waveguides with reflection volume holograms,” J. Soc. Inf. Disp. 17(3), 185–193 (2009).
[Crossref]

Laakkonen, P.

Lee, Y.-H.

S. T. Yang, R. L. Hsieh, Y.-H. Lee, R. F. W. Pease, and G. Owen, “Effect of central obscuration on image formation in projection lithography,” Proc. SPIE 1264, 477–485 (1990).
[Crossref]

Levola, T.

Li, G.

Li, L.

Liu, W.

Liu, X.

Lv, W.

Mallipeddi, R.

R. Mallipeddi, P. N. Suganthan, Q.-K. Pan, and M. F. Tasgetiren, “Differential evolution algorithm with ensemble of parameters and mutation strategies,” Appl. Soft Comput. 11(2), 1679–1696 (2011).
[Crossref]

Martins, R.

Massa, A.

P. Rocca, G. Oliveri, and A. Massa, “Differential evolution as applied to electromagnetics,” IEEE Antennas Propag. Mag. 53(1), 38–49 (2011).
[Crossref]

Matsumura, I.

H. Mukawa, K. Akutsu, I. Matsumura, S. Nakano, T. Yoshida, M. Kuwahara, and K. Aiki, “A full-color eyewear display using planar waveguides with reflection volume holograms,” J. Soc. Inf. Disp. 17(3), 185–193 (2009).
[Crossref]

Meyklyar, M.

L. Eisen, M. Meyklyar, M. Golub, A. A. Friesem, I. Gurwich, and V. Weiss, “Planar configuration for image projection,” Appl. Opt. 45(17), 4005–4011 (2006).
[Crossref] [PubMed]

I. Gurwich, V. Weiss, L. Eisen, M. Meyklyar, and A. A. Friesem, “Design and experiments of planar optical light guides for virtual image displays,” Proc. SPIE 5182, 212–221 (2004).
[Crossref]

Moharam, M.

Moharam, M. G.

M. G. Moharam, T. K. Gaylord, E. B. Grann, and D. A. Pommet, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. 12(5), 1068–1076 (1995).
[Crossref]

Morishima, H.

S. Yamazaki, K. Inoguchi, Y. Saito, H. Morishima, and N. Taniguchi, “Thin wide-field-of-view HMD with free-form-surface prism and applications,” Proc. SPIE 3639, 453–462 (1999).
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H. Mukawa, K. Akutsu, I. Matsumura, S. Nakano, T. Yoshida, M. Kuwahara, and K. Aiki, “A full-color eyewear display using planar waveguides with reflection volume holograms,” J. Soc. Inf. Disp. 17(3), 185–193 (2009).
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H. Mukawa, “A full color eyewear display using holographic planar waveguides,” in SID International Symposium Digest of Technical Papers (2008), pp. 89–92.

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H. Mukawa, K. Akutsu, I. Matsumura, S. Nakano, T. Yoshida, M. Kuwahara, and K. Aiki, “A full-color eyewear display using planar waveguides with reflection volume holograms,” J. Soc. Inf. Disp. 17(3), 185–193 (2009).
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T. Tamir and S. T. Peng, “Analysis and design of grating couplers,” Appl. Phys., A Mater. Sci. Process. 14, 235–254 (1977).

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S. Yamazaki, K. Inoguchi, Y. Saito, H. Morishima, and N. Taniguchi, “Thin wide-field-of-view HMD with free-form-surface prism and applications,” Proc. SPIE 3639, 453–462 (1999).
[Crossref]

Tasgetiren, M. F.

R. Mallipeddi, P. N. Suganthan, Q.-K. Pan, and M. F. Tasgetiren, “Differential evolution algorithm with ensemble of parameters and mutation strategies,” Appl. Soft Comput. 11(2), 1679–1696 (2011).
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Wilmington, I.

I. Wilmington and M. Valera, “Waveguide-Based Display Technology,” in SID Symposium Digest of Technical Papers (2013), pp. 278–280.

Wilson, D. W.

Wyrowski, F.

Xu, C.

Yamazaki, S.

S. Yamazaki, K. Inoguchi, Y. Saito, H. Morishima, and N. Taniguchi, “Thin wide-field-of-view HMD with free-form-surface prism and applications,” Proc. SPIE 3639, 453–462 (1999).
[Crossref]

Yang, J.

Yang, S. T.

S. T. Yang, R. L. Hsieh, Y.-H. Lee, R. F. W. Pease, and G. Owen, “Effect of central obscuration on image formation in projection lithography,” Proc. SPIE 1264, 477–485 (1990).
[Crossref]

Yatagai, T.

Yi, A. Y.

Yoshida, T.

H. Mukawa, K. Akutsu, I. Matsumura, S. Nakano, T. Yoshida, M. Kuwahara, and K. Aiki, “A full-color eyewear display using planar waveguides with reflection volume holograms,” J. Soc. Inf. Disp. 17(3), 185–193 (2009).
[Crossref]

Yoshikawa, N.

Yue, W.

Zhang, D.

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Appl. Opt. (7)

Appl. Phys., A Mater. Sci. Process. (1)

T. Tamir and S. T. Peng, “Analysis and design of grating couplers,” Appl. Phys., A Mater. Sci. Process. 14, 235–254 (1977).

Appl. Soft Comput. (1)

R. Mallipeddi, P. N. Suganthan, Q.-K. Pan, and M. F. Tasgetiren, “Differential evolution algorithm with ensemble of parameters and mutation strategies,” Appl. Soft Comput. 11(2), 1679–1696 (2011).
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H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48(9), 2909–2947 (1969).
[Crossref]

Commun. China Comp. Fed. (1)

J. Rolland and K. Thompson, “See-through head worn displays for mobile augmented reality,” Commun. China Comp. Fed. 7, 28–37 (2011).

IEEE Antennas Propag. Mag. (1)

P. Rocca, G. Oliveri, and A. Massa, “Differential evolution as applied to electromagnetics,” IEEE Antennas Propag. Mag. 53(1), 38–49 (2011).
[Crossref]

J. Opt. Soc. Am. (1)

M. G. Moharam, T. K. Gaylord, E. B. Grann, and D. A. Pommet, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. 12(5), 1068–1076 (1995).
[Crossref]

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J. Opt. Soc. Korea (1)

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I. C. Gardner, “Validity of the cosine-fourth-power law of illumination,” J. Res. Natl. Bur. Stand. 39(3), 213–219 (1947).
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T. Levola, “Diffractive optics for virtual reality displays,” J. Soc. Inf. Disp. 14(5), 467–475 (2006).
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H. Mukawa, K. Akutsu, I. Matsumura, S. Nakano, T. Yoshida, M. Kuwahara, and K. Aiki, “A full-color eyewear display using planar waveguides with reflection volume holograms,” J. Soc. Inf. Disp. 17(3), 185–193 (2009).
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J. Carmigniani, B. Furht, M. Anisetti, P. Ceravolo, E. Damiani, and M. Ivkovic, “Augmented reality technologies, systems and applications,” Multimedia Tools Appl. 51(1), 341–377 (2011).
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Opt. Eng. (1)

T. H. Harding and C. E. Rash, “Daylight luminance requirements for full-color, see-through, helmet-mounted display systems,” Opt. Eng. 56(5), 051404 (2017).
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Opt. Express (7)

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Proc. SPIE (7)

I. Gurwich, V. Weiss, L. Eisen, M. Meyklyar, and A. A. Friesem, “Design and experiments of planar optical light guides for virtual image displays,” Proc. SPIE 5182, 212–221 (2004).
[Crossref]

S. T. Yang, R. L. Hsieh, Y.-H. Lee, R. F. W. Pease, and G. Owen, “Effect of central obscuration on image formation in projection lithography,” Proc. SPIE 1264, 477–485 (1990).
[Crossref]

A. Cameron, “The application of holographic optical waveguide technology to the Q-Sight family of helmet-mounted displays,” Proc. SPIE 7362, 73260H (2009).
[Crossref]

B. Kress, V. Raulot, and M. Grossman, “Exit pupil expander for wearable see-through displays,” Proc. SPIE 8368, 83680D (2012).
[Crossref]

M. M. Bayer, “Retinal scanning display: a novel HMD approach for army aviation,” Proc. SPIE 4711, 202–213 (2002).
[Crossref]

S. Yamazaki, K. Inoguchi, Y. Saito, H. Morishima, and N. Taniguchi, “Thin wide-field-of-view HMD with free-form-surface prism and applications,” Proc. SPIE 3639, 453–462 (1999).
[Crossref]

B. Kress and T. Starner, “A review of head-mounted displays (HMD) technologies and applications for consumer electronics,” Proc. SPIE 8720, 87200A (2013).
[Crossref]

Science (1)

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220(4598), 671–680 (1983).
[Crossref] [PubMed]

Other (11)

H. Mukawa, “A full color eyewear display using holographic planar waveguides,” in SID International Symposium Digest of Technical Papers (2008), pp. 89–92.

T. Tušar and B. Filipič, “Differential evolution versus genetic algorithms in multiobjective optimization,” Evolutionary Multi-Criterion Optimization, S. Obayashi, K. Deb, C. Poloni, T. Hiroyasu, and T. Murata, eds. (Springer, 2007), pp. 257–271.

M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging (Taylor & Francis, 1998).

M. I. Olsson and M. W. Martin, “Wearable display device,” U. S. Patent D680152.

Y. Amitai, “Extremely Compact High-Performance HMDs Based on Substrate-Guided Optical Element,” SID Symposium Digest of Technical Papers (2004), pp. 310–313.

A. Travis, “Wide field-of-view virtual image projector,” U. S. Patent 2013/0329301.

B. C. Kress and W. J. Cummings, “Towards the Ultimate Mixed Reality Experience: HoloLens Display Architecture Choices,” in SID Symposium Digest of Technical Papers (2017), pp. 127–131.

C. E. Rash, Helmet mounted displays: Design issues for rotary-wing aircraft (SPIE, 1999), Vol. 93.

I. Wilmington and M. Valera, “Waveguide-Based Display Technology,” in SID Symposium Digest of Technical Papers (2013), pp. 278–280.

Y. Amitai, “A Two-Dimensional Aperture Expander for Ultra-Compact, High-Performance Head-Worn Displays,” in SID Symposium Digest of Technical Papers (2005), pp. 360–363.

A. Frommer, “11-3: Invited Paper: Lumus Optical Technology for AR,” in SID Symposium Digest of Technical Papers (2017), pp. 134–135.

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Figures (13)

Fig. 1
Fig. 1 Schematic of the waveguide display configuration. SLGs: subwavelength linear gratings, WG: waveguide, V: viewer.
Fig. 2
Fig. 2 Geometry of planar waveguide with in-coupling and out-coupling surface relief gratings.
Fig. 3
Fig. 3 Structure and diffraction order distributions of the in-coupling grating.
Fig. 4
Fig. 4 Flowchart of the proposed optimization approach to in-coupling grating design.
Fig. 5
Fig. 5 (a) Relation between diffraction efficiency and FOV for a non-optimized grating and an efficiency-optimized grating. (b) Diffraction efficiency versus wavelength for a non-optimized grating and an efficiency-optimized grating.
Fig. 6
Fig. 6 (a) Relation between diffraction efficiency and FOV for different in-coupling gratings. (b) Diffraction efficiency versus wavelength for different in-coupling gratings.
Fig. 7
Fig. 7 (a) Ray-tracing simulation of the prism coupling method. (b) Ray-tracing simulation of the grating coupling method for one-dimensional exit pupil expansion (1-D EPE). (c) Ray-tracing simulation of the grating coupling method for two-dimensional exit pupil expansion (2-D EPE).
Fig. 8
Fig. 8 Angular distributions of (a) input and (b) output light in polar coordinates with the prism coupling method: input (0°, ± 10°, ± 20°).
Fig. 9
Fig. 9 Angular distributions of (a) input and (b) output light in polar coordinates with the grating coupling method: input (0°, ± 10°, ± 20°).
Fig. 10
Fig. 10 Relationship between coupling efficiency and FOV for different coupling methods.
Fig. 11
Fig. 11 Comparison of average coupling efficiency and angular uniformity of four coupling methods. NON: non-optimized grating, HEO: high-efficiency optimized grating, Prism: prism coupling, and Optimal: high-angular-uniformity and high-efficiency optimized grating.
Fig. 12
Fig. 12 Diffraction efficiency distributions for different incident angles. The solid black curve is an envelope curve that covers the entire visible spectrum.
Fig. 13
Fig. 13 Relationship between TM diffraction efficiency and FOV for two types of optimization.

Tables (2)

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Table 1 Optimized parameters and diffraction efficiencies of in-coupling grating

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Table 2 Effects of slight variations of parameters

Equations (11)

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E= E 0 cos 4 β,
k m = 2π λ n 1 (sin θ 0 cos φ 0 ,cos θ 0 ,sin θ 0 sin φ 0 ).
k i,m = 2π λ n i (sin θ i,m cos φ i,m ,cos θ i,m ,sin θ i,m sin φ i,m ),
n i sin θ i,m sin φ i,m = n 1 sin θ 0 sin φ 0 =γ,
n i sin θ i,m cos φ i,m = n 1 sin θ 0 cos φ 0 +m λ T = α 0 +m λ T .
T<min { λ 1 γ 2 α 0 , λ 1 γ 2 + α 0 }.
T< λ 1+| α 0,max | .
min obj= wi(DEdesign DEtarget ) i 2 ,
v i = X r1 +F×( X r2 X r3 ), r1r2r3i
y i ={ v i if U i CR x i otherwise ,
Γ=1 I max I min I max + I min , I=η× cos 4 θ,

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