Abstract

We present a design of a contact lens display, which features an array of collimated light-emitting diodes and a contact lens, for the augmented reality. By building the infrastructure directly on top of the eye, eye is allowed to move or rotate freely without the need of exit pupil expansion nor eye tracking. The resolution of light-emitting diodes is foveated to match with the density of cones on the retina. In this manner, the total number of pixels as well as the latency of image processing can be significantly reduced. Based on the simulation, the device performance is quantitatively analyzed. For the real image, modulation transfer functions is 0.669757 at 30 cycle/degree, contrast ratio is 5, and distortion is 10%. For the virtual image, the field of view is 82°, best angular resolution is 0.38′, modulation transfer function is above 0.999999 at 30 cycle/degree, contrast ratio is 4988, and distortion is 6%.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (5)

J. Xiao, J. Liu, J. Han, and Y. Wang, “Design of achromatic surface microstructure for near-eye display with diffractive waveguide,” Opt. Commun. 452, 411–416 (2019).
[Crossref]

C. S. A. Musgrave and F. Fang, “Contact lens materials: a materials science perspective,” Materials 12(2), 261 (2019).
[Crossref]

J. Kim, Y. Jeong, M. Stengel, K. Aksit, R. Albert, B. Boudaoud, T. Greer, J. Kim, W. Lopes, Z. Majercik, P. Shirley, J. Spjut, M. McGuire, and D. Luebke, “Foveated AR: dynamically-foveated augmented reality display,” ACM Trans. Graph. 38(4), 99 (2019).
[Crossref]

L. Mi, C. P. Chen, Y. Lu, W. Zhang, J. Chen, and N. Maitlo, “Design of lensless retinal scanning display with diffractive optical element,” Opt. Express 27(15), 20493–20507 (2019).
[Crossref]

T. Takamatsu, Y. Chen, T. Yoshimasu, M. Nishizawa, and T. Miyake, “Highly efficient, flexible wireless-powered circuit printed on a moist, soft contact lens,” Adv. Mater. Technol. 4(5), 1800671 (2019).
[Crossref]

2018 (4)

Y. Wu, C. P. Chen, L. Mi, W. Zhang, J. Zhao, Y. Lu, W. Guo, B. Yu, Y. Li, and N. Maitlo, “Design of retinal-projection-based near-eye display with contact lens,” Opt. Express 26(9), 11553–11567 (2018).
[Crossref]

Z. Shi, W. T. Chen, and F. Capasso, “Wide field-of-view waveguide displays enabled by polarization-dependent metagratings,” Proc. SPIE 10676, 1067615 (2018).
[Crossref]

G.-Y. Lee, J.-Y. Hong, S. Hwang, S. Moon, H. Kang, S. Jeon, H. Kim, J.-H. Jeong, and B. Lee, “Metasurface eyepiece for augmented reality,” Nat. Commun. 9(1), 4562 (2018).
[Crossref]

G. Tan, Y.-H. Lee, T. Zhan, J. Yang, S. Liu, D. Zhao, and S.-T. Wu, “Foveated imaging for near-eye displays,” Opt. Express 26(19), 25076–25085 (2018).
[Crossref]

2017 (6)

2016 (4)

2015 (1)

2014 (1)

A. Maimone, D. Lanman, K. Rathinavel, K. Keller, D. Luebke, and H. Fuchs, “Pinlight displays: wide field of view augmented reality eyeglasses using defocused point light sources,” ACM Trans. Graph. 33(4), 1–11 (2014).
[Crossref]

2013 (1)

J. De Smet, A. Avci, P. Joshi, D. Schaubroeck, D. Cuypers, and H. De Smet, “Progress toward a liquid crystal contact lens display,” J. Soc. Inf. Disp. 21(9), 399–406 (2013).
[Crossref]

2012 (2)

A. B. Watson and J. I. Yellott, “A unified formula for light-adapted pupil size,” J. Vision 12(10), 12 (2012).
[Crossref]

R. Sprague, A. Zhang, L. Hendricks, T. O’Brien, J. Ford, E. Tremblay, and T. Rutherford, “Novel HMD concepts from the DARPA SCENICC program,” Proc. SPIE 8383, 838302 (2012).
[Crossref]

2010 (2)

S. Liu, H. Hua, and D. Cheng, “A novel prototype for an optical see-through head-mounted display with addressable focus cues,” IEEE Trans. Visual. Comput. Graphics 16(3), 381–393 (2010).
[Crossref]

Z. Zheng, X. Liu, H. Li, and L. Xu, “Design and fabrication of an off-axis see-through head-mounted display with an x-y polynomial surface,” Appl. Opt. 49(19), 3661–3668 (2010).
[Crossref]

2009 (2)

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]

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]

2006 (1)

T. Levola, “Diffractive optics for virtual reality displays,” J. Soc. Inf. Disp. 14(5), 467–475 (2006).
[Crossref]

2004 (1)

Y. Amitai, “Extremely compact high-performance HMDs based on substrate-guided optical element,” Dig. Tech. Pap. - Soc. Inf. Disp. Int. Symp. 35(1), 310–313 (2004).
[Crossref]

2003 (1)

S. C. McQuaide, E. J. Seibel, J. P. Kelly, B. T. Schowengerdt, and T. A. Furness, “A retinal scanning display system that produces multiple focal planes with a deformable membrane mirror,” Displays 24(2), 65–72 (2003).
[Crossref]

2000 (1)

J. P. Rolland, “Wide-angle, off-axis, see-through head-mounted display,” Opt. Eng. 39(7), 1760–1767 (2000).
[Crossref]

1996 (1)

P. Kortum and W. Geisler, “Implementation of a foveated image coding system for image bandwidth reduction,” Proc. SPIE 2657, 350–360 (1996).
[Crossref]

1990 (1)

C. A. Curcio, K. R. Sloan, R. E. Kalina, and A. E. Hendrickson, “Human photoreceptor topography,” J. Comp. Neurol. 292(4), 497–523 (1990).
[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]

Aksit, K.

J. Kim, Y. Jeong, M. Stengel, K. Aksit, R. Albert, B. Boudaoud, T. Greer, J. Kim, W. Lopes, Z. Majercik, P. Shirley, J. Spjut, M. McGuire, and D. Luebke, “Foveated AR: dynamically-foveated augmented reality display,” ACM Trans. Graph. 38(4), 99 (2019).
[Crossref]

D. Dunn, C. Tippets, K. Torell, P. Kellnhofer, K. Aksit, P. Didyk, K. Myszkowski, D. Luebke, and H. Fuchs, “Wide field of view varifocal near-eye display using see-through deformable membrane mirrors,” IEEE Trans. Visual. Comput. Graphics 23(4), 1322–1331 (2017).
[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]

Albert, R.

J. Kim, Y. Jeong, M. Stengel, K. Aksit, R. Albert, B. Boudaoud, T. Greer, J. Kim, W. Lopes, Z. Majercik, P. Shirley, J. Spjut, M. McGuire, and D. Luebke, “Foveated AR: dynamically-foveated augmented reality display,” ACM Trans. Graph. 38(4), 99 (2019).
[Crossref]

Amitai, Y.

Y. Amitai, “Extremely compact high-performance HMDs based on substrate-guided optical element,” Dig. Tech. Pap. - Soc. Inf. Disp. Int. Symp. 35(1), 310–313 (2004).
[Crossref]

Avci, A.

J. De Smet, A. Avci, P. Joshi, D. Schaubroeck, D. Cuypers, and H. De Smet, “Progress toward a liquid crystal contact lens display,” J. Soc. Inf. Disp. 21(9), 399–406 (2013).
[Crossref]

Bass, M.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, and E. V. Stryland, Handbook of Optics 3rd Edition Volume III: Vision and Vision Optics (McGraw-Hill Education, 2009).

Boudaoud, B.

J. Kim, Y. Jeong, M. Stengel, K. Aksit, R. Albert, B. Boudaoud, T. Greer, J. Kim, W. Lopes, Z. Majercik, P. Shirley, J. Spjut, M. McGuire, and D. Luebke, “Foveated AR: dynamically-foveated augmented reality display,” ACM Trans. Graph. 38(4), 99 (2019).
[Crossref]

Bourquin, S.

T. North, M. Wagner, S. Bourquin, and L. Kilcher, “Compact and high-brightness helmet-mounted head-up display system by retinal laser projection,” J. Disp. Technol. 12(9), 982–985 (2016).
[Crossref]

Capasso, F.

Z. Shi, W. T. Chen, and F. Capasso, “Wide field-of-view waveguide displays enabled by polarization-dependent metagratings,” Proc. SPIE 10676, 1067615 (2018).
[Crossref]

Chen, C. P.

Chen, H.-S.

Chen, J.

Chen, P.-J.

Chen, W. T.

Z. Shi, W. T. Chen, and F. Capasso, “Wide field-of-view waveguide displays enabled by polarization-dependent metagratings,” Proc. SPIE 10676, 1067615 (2018).
[Crossref]

Chen, Y.

T. Takamatsu, Y. Chen, T. Yoshimasu, M. Nishizawa, and T. Miyake, “Highly efficient, flexible wireless-powered circuit printed on a moist, soft contact lens,” Adv. Mater. Technol. 4(5), 1800671 (2019).
[Crossref]

Cheng, D.

S. Liu, H. Hua, and D. Cheng, “A novel prototype for an optical see-through head-mounted display with addressable focus cues,” IEEE Trans. Visual. Comput. Graphics 16(3), 381–393 (2010).
[Crossref]

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]

Crawford, G. P.

G. P. Crawford, Flexible Flat Panel Displays (Wiley, 2007).

Curcio, C. A.

C. A. Curcio, K. R. Sloan, R. E. Kalina, and A. E. Hendrickson, “Human photoreceptor topography,” J. Comp. Neurol. 292(4), 497–523 (1990).
[Crossref]

Cuypers, D.

J. De Smet, A. Avci, P. Joshi, D. Schaubroeck, D. Cuypers, and H. De Smet, “Progress toward a liquid crystal contact lens display,” J. Soc. Inf. Disp. 21(9), 399–406 (2013).
[Crossref]

De Smet, H.

J. De Smet, A. Avci, P. Joshi, D. Schaubroeck, D. Cuypers, and H. De Smet, “Progress toward a liquid crystal contact lens display,” J. Soc. Inf. Disp. 21(9), 399–406 (2013).
[Crossref]

De Smet, J.

J. De Smet, A. Avci, P. Joshi, D. Schaubroeck, D. Cuypers, and H. De Smet, “Progress toward a liquid crystal contact lens display,” J. Soc. Inf. Disp. 21(9), 399–406 (2013).
[Crossref]

DeCusatis, C.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, and E. V. Stryland, Handbook of Optics 3rd Edition Volume III: Vision and Vision Optics (McGraw-Hill Education, 2009).

Didyk, P.

D. Dunn, C. Tippets, K. Torell, P. Kellnhofer, K. Aksit, P. Didyk, K. Myszkowski, D. Luebke, and H. Fuchs, “Wide field of view varifocal near-eye display using see-through deformable membrane mirrors,” IEEE Trans. Visual. Comput. Graphics 23(4), 1322–1331 (2017).
[Crossref]

Duan, X.

Dunn, D.

D. Dunn, C. Tippets, K. Torell, P. Kellnhofer, K. Aksit, P. Didyk, K. Myszkowski, D. Luebke, and H. Fuchs, “Wide field of view varifocal near-eye display using see-through deformable membrane mirrors,” IEEE Trans. Visual. Comput. Graphics 23(4), 1322–1331 (2017).
[Crossref]

Enoch, J.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, and E. V. Stryland, Handbook of Optics 3rd Edition Volume III: Vision and Vision Optics (McGraw-Hill Education, 2009).

Fang, F.

C. S. A. Musgrave and F. Fang, “Contact lens materials: a materials science perspective,” Materials 12(2), 261 (2019).
[Crossref]

Fischer, R. E.

R. E. Fischer, B. Tadic-Galeb, and P. R. Yoder, Optical System Design 2nd Edition (McGraw-Hill Education, 2008).

Fontaine, J.

Ford, J.

R. Sprague, A. Zhang, L. Hendricks, T. O’Brien, J. Ford, E. Tremblay, and T. Rutherford, “Novel HMD concepts from the DARPA SCENICC program,” Proc. SPIE 8383, 838302 (2012).
[Crossref]

Fuchs, H.

D. Dunn, C. Tippets, K. Torell, P. Kellnhofer, K. Aksit, P. Didyk, K. Myszkowski, D. Luebke, and H. Fuchs, “Wide field of view varifocal near-eye display using see-through deformable membrane mirrors,” IEEE Trans. Visual. Comput. Graphics 23(4), 1322–1331 (2017).
[Crossref]

A. Maimone, D. Lanman, K. Rathinavel, K. Keller, D. Luebke, and H. Fuchs, “Pinlight displays: wide field of view augmented reality eyeglasses using defocused point light sources,” ACM Trans. Graph. 33(4), 1–11 (2014).
[Crossref]

Furness, T. A.

S. C. McQuaide, E. J. Seibel, J. P. Kelly, B. T. Schowengerdt, and T. A. Furness, “A retinal scanning display system that produces multiple focal planes with a deformable membrane mirror,” Displays 24(2), 65–72 (2003).
[Crossref]

T. A. Furness and J. S. Kollin, “Virtual retinal display,” US Patent 5,467,104 (1992).

Gao, Q.

Ge, J.

Geisler, W.

P. Kortum and W. Geisler, “Implementation of a foveated image coding system for image bandwidth reduction,” Proc. SPIE 2657, 350–360 (1996).
[Crossref]

Georgiou, A.

A. Maimone, A. Georgiou, and J. S. Kollin, “Holographic near-eye displays for virtual and augmented reality,” ACM Trans. Graph. 36(4), 1–16 (2017).
[Crossref]

Gerard, P.

Greer, T.

J. Kim, Y. Jeong, M. Stengel, K. Aksit, R. Albert, B. Boudaoud, T. Greer, J. Kim, W. Lopes, Z. Majercik, P. Shirley, J. Spjut, M. McGuire, and D. Luebke, “Foveated AR: dynamically-foveated augmented reality display,” ACM Trans. Graph. 38(4), 99 (2019).
[Crossref]

Guillaumee, M.

E. Tremblay, M. Guillaumee, and C. Moser, “Method and apparatus for head worn display with multiple exit pupils,” US Patent 9,846,307 B2 (2017).

Guo, W.

Han, J.

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J. Kim, Y. Jeong, M. Stengel, K. Aksit, R. Albert, B. Boudaoud, T. Greer, J. Kim, W. Lopes, Z. Majercik, P. Shirley, J. Spjut, M. McGuire, and D. Luebke, “Foveated AR: dynamically-foveated augmented reality display,” ACM Trans. Graph. 38(4), 99 (2019).
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Li, X.

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J. Kim, Y. Jeong, M. Stengel, K. Aksit, R. Albert, B. Boudaoud, T. Greer, J. Kim, W. Lopes, Z. Majercik, P. Shirley, J. Spjut, M. McGuire, and D. Luebke, “Foveated AR: dynamically-foveated augmented reality display,” ACM Trans. Graph. 38(4), 99 (2019).
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J. Kim, Y. Jeong, M. Stengel, K. Aksit, R. Albert, B. Boudaoud, T. Greer, J. Kim, W. Lopes, Z. Majercik, P. Shirley, J. Spjut, M. McGuire, and D. Luebke, “Foveated AR: dynamically-foveated augmented reality display,” ACM Trans. Graph. 38(4), 99 (2019).
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A. Maimone, D. Lanman, K. Rathinavel, K. Keller, D. Luebke, and H. Fuchs, “Pinlight displays: wide field of view augmented reality eyeglasses using defocused point light sources,” ACM Trans. Graph. 33(4), 1–11 (2014).
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Majercik, Z.

J. Kim, Y. Jeong, M. Stengel, K. Aksit, R. Albert, B. Boudaoud, T. Greer, J. Kim, W. Lopes, Z. Majercik, P. Shirley, J. Spjut, M. McGuire, and D. Luebke, “Foveated AR: dynamically-foveated augmented reality display,” ACM Trans. Graph. 38(4), 99 (2019).
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J. Kim, Y. Jeong, M. Stengel, K. Aksit, R. Albert, B. Boudaoud, T. Greer, J. Kim, W. Lopes, Z. Majercik, P. Shirley, J. Spjut, M. McGuire, and D. Luebke, “Foveated AR: dynamically-foveated augmented reality display,” ACM Trans. Graph. 38(4), 99 (2019).
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Miyake, T.

T. Takamatsu, Y. Chen, T. Yoshimasu, M. Nishizawa, and T. Miyake, “Highly efficient, flexible wireless-powered circuit printed on a moist, soft contact lens,” Adv. Mater. Technol. 4(5), 1800671 (2019).
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G.-Y. Lee, J.-Y. Hong, S. Hwang, S. Moon, H. Kang, S. Jeon, H. Kim, J.-H. Jeong, and B. Lee, “Metasurface eyepiece for augmented reality,” Nat. Commun. 9(1), 4562 (2018).
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T. Takamatsu, Y. Chen, T. Yoshimasu, M. Nishizawa, and T. Miyake, “Highly efficient, flexible wireless-powered circuit printed on a moist, soft contact lens,” Adv. Mater. Technol. 4(5), 1800671 (2019).
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S. C. McQuaide, E. J. Seibel, J. P. Kelly, B. T. Schowengerdt, and T. A. Furness, “A retinal scanning display system that produces multiple focal planes with a deformable membrane mirror,” Displays 24(2), 65–72 (2003).
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S. C. McQuaide, E. J. Seibel, J. P. Kelly, B. T. Schowengerdt, and T. A. Furness, “A retinal scanning display system that produces multiple focal planes with a deformable membrane mirror,” Displays 24(2), 65–72 (2003).
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J. Kim, Y. Jeong, M. Stengel, K. Aksit, R. Albert, B. Boudaoud, T. Greer, J. Kim, W. Lopes, Z. Majercik, P. Shirley, J. Spjut, M. McGuire, and D. Luebke, “Foveated AR: dynamically-foveated augmented reality display,” ACM Trans. Graph. 38(4), 99 (2019).
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Tan, G.

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T. Takamatsu, Y. Chen, T. Yoshimasu, M. Nishizawa, and T. Miyake, “Highly efficient, flexible wireless-powered circuit printed on a moist, soft contact lens,” Adv. Mater. Technol. 4(5), 1800671 (2019).
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ACM Trans. Graph. (3)

A. Maimone, A. Georgiou, and J. S. Kollin, “Holographic near-eye displays for virtual and augmented reality,” ACM Trans. Graph. 36(4), 1–16 (2017).
[Crossref]

A. Maimone, D. Lanman, K. Rathinavel, K. Keller, D. Luebke, and H. Fuchs, “Pinlight displays: wide field of view augmented reality eyeglasses using defocused point light sources,” ACM Trans. Graph. 33(4), 1–11 (2014).
[Crossref]

J. Kim, Y. Jeong, M. Stengel, K. Aksit, R. Albert, B. Boudaoud, T. Greer, J. Kim, W. Lopes, Z. Majercik, P. Shirley, J. Spjut, M. McGuire, and D. Luebke, “Foveated AR: dynamically-foveated augmented reality display,” ACM Trans. Graph. 38(4), 99 (2019).
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Figures (18)

Fig. 1.
Fig. 1. Cross-section view of the proposed contact lens display. Adjacent to the cornea is a thin layer of contact lens for fixing the refractive errors. On top of the contact lens is fabricated an array of LEDs, each pixel of which is able to emit a collimated beam of light towards the center of lens of eye. For the sake of symmetry, the contact lens, LED array and eye are center-aligned.
Fig. 2.
Fig. 2. Illustration of eccentricity. The eccentricity is a rotation angle ɛ about the axis connecting the center of fovea and the center of eye.
Fig. 3.
Fig. 3. Density of cones versus the eccentricity [32]. The positive sign of eccentricity signifies the temporal side, while the negative sign the nasal side. It can be seen that cones are vastly concentrated at the fovea, whose eccentricity is up to 3.3°. Between −13.6° to −21.6° at the nasal side is a photoreceptor-free region called blind spot.
Fig. 4.
Fig. 4. Suppose two LEDs A and B on the cornea are just resolvable and coaxial with two cones A′ and B′ on the retina. Relative to the center of lens, the angle subtended by A and B is equivalent to the angle α subtended by A′ and B′.
Fig. 5.
Fig. 5. Visual acuity (decimal) versus the eccentricity. The visual acuity drops dramatically as the eccentricity rises. Within the fovea, the best visual acuity can be as high as 2.6.
Fig. 6.
Fig. 6. Geometry of contact lens. R1 is the radius of curvature of front surface, R2 the radius of curvature of back surface, Re the radius of curvature of edge, tc the thickness, d the overall diameter, and do the optical zone diameter.
Fig. 7.
Fig. 7. Schematic of a collimated LED―an LED in tandem with a collimator―being sandwiched between the substrate and contact lens. The collimator is basically an optical fiber with a high-refractive-index core in the middle surrounded by a low-refractive-index cladding.
Fig. 8.
Fig. 8. Picture a ray (yellow line) is incident to the contact lens at a field angle θ, then refracted towards the center of lens at an angle β, and finally hits the retina at an eccentricity ɛ. del is the distance from the center of lens to center of eye, dcl the distance from contact lens to center of lens, r the radius of eye, and R1 the radius of curvature of front surface of lens.
Fig. 9.
Fig. 9. Pupil size versus the luminance. Pupil diameter ranges from 2 to 8 mm. When L = 500 cd/m2, D = 2.40 mm. Incidentally, different levels of luminance will trigger different modes of vision. When L > 5 cd/m2, D < 3.96 mm and photopic vision takes effect, in which cones dominate. When 5 cd/m2 > L > 0.005 cd/m2, 3.96 mm < D < 7.35 mm and mesopic vision takes effect, in which both cones and rods are active. When L < 0.005 cd/m2, D > 7.35 mm and scotopic vision takes effect, in which only rods are active.
Fig. 10.
Fig. 10. Number of LEDs versus the field angle. Interestingly, the blind spot will leave a blank area not covered by LEDs on the contact lens.
Fig. 11.
Fig. 11. Number of pixels―at an aspect ratio of 16:9―required to yield an angular resolution of 1′ is computed with respect to the diagonal FOVs. Take a FOV of 100° as an instance. The minimal numbers of pixels for the non-foveated and foveated displays are 15.38 and 3.20 million, respectively. The latter is merely about 1/5 of the former.
Fig. 12.
Fig. 12. Optical surfaces defined in Code V, which are in turn (1) contact lens, (2) anterior cornea, (3) posterior cornea, (4) pupil, (5) anterior lens, (6) virtual plane, (7) posterior lens, and (8) retina. For the real image, the object is positioned at 3 m ahead of the eye. For the virtual image, the object coincides with the contact lens.
Fig. 13.
Fig. 13. Geometric relationship among FOV and other parameters. D is the pupil size, dpl the distance from the center of the lens to the pupil, dcl the distance from contact lens to center of lens, and R1 the radius of curvature of front surface of lens.
Fig. 14.
Fig. 14. FOV versus the pupil size. When the pupil is 2.4 mm in diameter, FOV is 82°. When the pupil dilates to 8 mm in diameter, FOV reaches up to 142°.
Fig. 15.
Fig. 15. Angular resolution versus the field angle. The best angular resolution is 0.38′ at 0°, whereas the worst is 3.11′ at −41°.
Fig. 16.
Fig. 16. MTFs calculated as a function of spatial frequency in cycle/degree. For the real image, MTF of the field of 0° is 0.669757 at 30 cycle/degree. For the virtual image, MTFs of all fields are above 0.999999 at 30 cycle/degree.
Fig. 17.
Fig. 17. Distortion versus the field angle. Distortions of real and virtual images are 10% and 6%, respectively.
Fig. 18.
Fig. 18. (a) Original image (Snell chart), (b) real image, and (c) virtual image. The foveated effect of the virtual image is not visible. The reason is that, in Code V and other simulation tools, the influence of photoreceptor cells on the image has yet to be factored into.

Tables (6)

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Table 1. Maximum angular resolution of four different regions on the retina

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Table 2. Parameters of contact lens

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Table 3. Parameters of optical surfaces used in Code V

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Table 4. Parameters for aspherical surfaces

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Table 5. Parameters for gradient refractive indices of anterior and posterior lenses

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Table 6. Parameters for calculating FOV

Equations (14)

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

V A = 1 a n g u l a r r e s o l u t i o n
α = 2 sin 1 [ sin ( 1 / ρ 2 [ r sin ( ε ) ] 2 + [ r cos ( ε ) + d e l ] 2 ) ]
P c = P g 1 d g P g
P c = ( n 1 ) ( 1 R 1 1 R 2 )
D c < 2.4 λ π n 1 2 n 2 2
θ = β + sin 1 n d c l sin β R 1 sin 1 d c l sin β R 1
β = sin 1 ( r sin ε ) 2 ( r sin ε ) 2 + ( r cos ε + d e l ) 2
D = 0.11 Y + 14.64 ( L π F O V 2 4 × 846 ) 0.41 + 2 + 0.0022 Y + 1.937
N i = π sin β sin ( α i 2 )
N = i = 1 M N i
F O V = 2 ( tan 1 D 2 d p l + sin 1 n D d c l R 1 D 2 + 4 d p l 2 sin 1 D d c l R 1 D 2 + 4 d p l 2 )
A n g u l a r r e s o l u t i o n = 21600 sin θ N i
C R = C R 0 + 1 + M T F ( C R 0 1 ) C R 0 + 1 M T F ( C R 0 1 )
Distortion = h a h p h a

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