Abstract

We propose a design of a retinal-scanning-based near-eye display for augmented reality. Our solution is highlighted by a laser scanning projector, a diffractive optical element, and a moist eye with gradient refractive indices. The working principles related to each component are comprehensively studied. Its key performance is summarized as follows. The field of view is 122°, angular resolution is 8.09′, diffraction efficiency is 57.6%, transmittance is 80.6%, uniformity is 0.91, luminance is 323 cd/m2, modulation transfer functions are above 0.99999 at 3.71 cycle/degree, contrast ratio is 4878, and distortion is less than 24%.

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

1. Introduction

For a very long time, near-eye display (NED), also known as head-mounted display, remained as a marginal technology in the display community [1]. Until recently, in the wake of augmented and virtual realities [2], it theatrically morphs into a superstar sought after by a crowd of researchers, engineers, investors, bloggers etc. Technically, NED is a type of wearable projection display [3]. Pursuant to the criterion that whether the retina is the image plane, NED can be divided into two categories, i.e. indirect projection and direct or retinal projection. For the former, the image is first projected onto a virtual image plane, and then received by the retina. To do so, the optical path needs to be folded via either a combiner [4–11] or waveguide [12–22]. As far as the field of view (FOV) is concerned, both combiner and waveguide based NEDs have limited FOVs, usually below 50° [2]. Another restriction is the paradox that FOV is inversely proportional to the exit pupil [2]. There must be a trade-off between the FOV and exit pupil. Direct or retinal projection based NED, on the other hand, refers to the case when the image is directly projected to the retina, for which the image plane coincides with the retina. Virtual retinal display (VRD) [23–25], developed by Human Interface Technology Lab of University of Washington, is a pioneering retinal projection based NED, known for its concept of retinal scanning. iOptik [26,27], a proprietary technology of Innovega, is characterized by a contact lens embedded with a zone plate. Pinlight display [28], co-developed by University of North Carolina at Chapel Hill and Nvidia, mimics a pinhole camera by an array of point light sources in front of eye. Intel―through acquisitions of Composyt Light Labs and Lemoptix―built a smart glasses prototype dubbed Vaunt with holographic optical elements (HOEs) [29]. Though the above retinal projection based NEDs are able to achieve extremely large FOVs, each has its own pros and cons. The optical setup of VRD is bulky and sophisticated, making it unwearable. iOptik has been struggling for many years in persuading the consumers to wear the contact lens. Pinlight display is vulnerable to the change of eye state, including the diopter of eye, pupil size, and rotation of eyeball. Lasting for only 4 odd years, Vaunt was aborted in part due to manufacturability of HOEs. Inspired from the said issues, we would like to present a lensless retinal scanning display (RSD), which is compact in design and immune to the change in the pupil size and diopter of eye. In what follows, its structure, working principles, and overall performance are to be elaborated.

2. Principles

2.1 Proposed structure

The proposed RSD can be decomposed into three major components, i.e. a laser scanning projector, a diffractive optical element (DOE), and an eye, as shown in Fig. 1, where dp is the distance between projector and glass, ddoe the distance between projector and DOE, dlens the distance between DOE and lens center, W the horizontal dimension of DOE, x the distance starting from the left edge of DOE, θi the angle of incident light, and θm the angle of diffracted light. Inside the temple is housed the laser scanning projector for saving the room. On the inner surface of a flat glass substrate is fabricated the DOE, which is able to converge the light coming out of the projector towards the center of lens of eye. Analogous to the Maxwellian view [30], such configuration ensures that the image formed on the retina will remain intact no matter how the eye accommodates its diopter to the distance of object. Moreover, as long as the beam size of the laser is way smaller than the pupil―minimally 2 mm across [31]―the brightness of image could be maintained regardless of the variation of pupil size. For the sake of symmetry, the DOE and eye are center-aligned.

 

Fig. 1 Proposed structure of our RSD, which can be decomposed into three major components, i.e. a laser scanning projector, a DOE, and an eye. dp is the distance between projector and glass, ddoe the horizontal distance between projector and DOE, dlens the distance between DOE and lens center, W the dimension of DOE, x the distance starting from the left edge of DOE, θi the angle of incident light, and θm the angle of diffracted light.

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2.2 Eye model

Unlike our previous eye models [32–34], in which the eye is dry―in the absence of tear―and lens of eye has a constant refractive index, the current model factors into not only the tear but also a gradient lens [35] studied by Goncharov et. al. Figure 2 is a cross-sectional view of our schematic moist eye, consisting of tear, cornea (anterior and posterior), aqueous chamber filled with aqueous humor, iris with an opening known as pupil, lens (anterior and posterior), vitreous chamber filled with vitreous humor, and retina. Approximately, two-thirds of the eye’s optical power is derived from the cornea―including the tear―and one-third from the lens [36]. While the thickness of tear is negligibly thin―ranging from 6 to 20 μm―the irregularities of tear can cause significant visual aberrations and distortions [37].

 

Fig. 2 Cross-sectional view of our schematic moist eye, consisting of tear, cornea (anterior and posterior), aqueous chamber filled with aqueous humor, iris with an opening known as pupil, lens (anterior and posterior), vitreous chamber filled with vitreous humor, and retina.

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To model the gradient lens, an assistive virtual plane is inserted to separate the lens into the anterior and posterior halves, as shown in Fig. 3. The center of lens is―coinciding with the nodal point [38]―designated as the origin of y-z coordinate. Invoking the Goncharov’s gradient lens model [35], refractive indices na for the anterior lens and np for the posterior lens could be computed with

na(z,y)=n00+c10y2+c20y4+c01(z+zm)+c02(z+zm)2+c03(z+zm)3+c04(z+zm)4
and
np(z,y)=nmax+c10y2+c20y4+c01,2z+c02,2z2+c03,2z3+c04,2z4
respectively, where z is the distance measured from the vertex of anterior lens along the z-axis, y the distance measured from the lens center along the y-axis, zm the distance between the vertex of anterior lens and the virtual plane, n00 the starting refractive index of anterior lens, nmax the maximum refractive index, and c10, c20, c01, c02, c03, c04, c01,2, c02,2, c03,2, and c04,2 the coefficients of each term. With the parameters disclosed in [35], which are itemized in Table 1, refractive indices of lens are calculated along the horizontal and vertical directions, respectively, as shown in Fig. 4. It can be seen that the refractive index maximizes at the lens center, from which it starts to decrease towards the outermost surface.

 

Fig. 3 Cross-sectional view of lens of eye with an assistive virtual plane. The center of virtual plane is designated as the center of lens. z is the distance measured from the vertex of anterior lens along the z-axis, and y the distance measured from the lens center along the y-axis.

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Tables Icon

Table 1. Parameters of gradient lens

 

Fig. 4 Refractive indices of lens calculated along the (a) horizontal and (b) vertical directions, respectively. It can be seen that the refractive index maximizes at the center, from which it starts to decrease towards the outermost surface.

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2.3 Laser scanning projector

Figure 5 is a schematic drawing of the laser scanning projector, inside which are mounted a laser diode, a circular polarizer, a mirror, and a scanning mirror controlled by a biaxial micro-electromechanical system (MEMS) [39]. Laser is transformed to circular polarization after passing through the circular polarizer. Since the laser scanning projector is lensless, the image projected onto the retina will be always in focus―in other words, its depth of focus is infinite―even when the eye is defocused. In this regard, the laser scanning projector is essentially a pinhole camera [40]. This is a big advantage over the lens-based projector, whose image plane is at a certain distance and depth of focus is finite [3]. The depth cue of the projected image, on that other hand, shall be coupled with the distance of real object, depending on the accommodation of eye [32]. A major downside of laser scanning projector, among others, is about its low resolution―e.g. the best resolution of Microvision’s laser scanning projector is merely 848 × 480 [41]―restricted by the scanning rate of MEMS. Due to the limited choices of laser scanning projector available in the market, a set of parameters customized to our design are given in Table 2, where the resolution is 640 × 640, scanning angle (horizontal) is 17°, beam diameter at the waist D0 is 0.4 mm, luminous flux Φ is 2 lm, and contrast ratio (CR) is 5000. Being treated as a Gaussian TEM00 beam, beam diameter D of the laser enlarges as it propagates at a distance L from the waist, which is described as [42]

D=D01+(4M2λLπD02)2
where M2 is the beam quality and λ is the wavelength of laser. The beam divergence θdiv is therefore

 

Fig. 5 Schematic drawing of the laser scanning projector, inside which are mounted a laser diode, a mirror, and a scanning mirror controlled by a biaxial MEMS.

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Tables Icon

Table 2. Parameters for laser scanning projector

θdiv=2M2λπD0

For M2 = 1.1, λ = 532 nm, L = 50 mm, and D0 = 0.4 mm, D = 0.411 mm and θdiv = 0.93 mrad or 0.05°. As a rule of thumb, for a laser with a beam divergence less than 1 mrad, its beam can be approximated as the perfectly collimated one. Upon the reflection of MEMS, both the shape and size of the said laser beam will be altered. To match the shape and size of the subsequent DOE, MEMS is square in shape and 60 µm wide, as will be discussed later. To avoid the loss of light, a beam shaper could be inserted on top of the laser diode. Plus, in case the projector and DOE are misaligned during the mounting, it is suggested to make both of them adjustable for calibration. Incidentally, speaking of the speckle effect, a random laser made from disordered materials [43] is among the most desirable solutions.

2.4 Diffractive optical element

DOE is an array of diffraction gratings, the number of which shall match with the resolution of laser scanning projector. The size of each diffraction grating shall match with that of the beam emerging from MEMS, i.e. 60 μm. For enhancing the diffraction efficiency (DE) and eliminating the undesired diffraction orders, each grating is designed to be a slanted grating [44], as depicted in Fig. 6, where p is the grating period, hg the grating depth, wg the grating width, and β the slant angle relative to the normal. In order for the image to be immune to the change in diopter of eye, all the diffracted beams are supposed to pass through the lens center. For a grating located at a distance x from the left edge of DOE, its period p, diffraction order m, wavelength λ, incident angle θi and diffraction angle θm should satisfy both the reflection grating equation [45], i.e.

p(sinθisinθm)=mλ
and the geometry (see Fig. 1) given by
tanθi=ddoe+xdp
and

 

Fig. 6 Profile of the slanted grating, where p is the grating period, hg the grating depth, wg the grating width, β the slant angle relative to the normal, θi the incident angle, and θm the diffraction angle.

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tanθm=W/2xdlens

3. Results and discussion

3.1 Simulation setting

The performance of our RSD is quantitatively analyzed with Code V (Synopsys) and COMSOL Multiphysics (COMSOL). Capable of ray tracing, Code V lends itself to analyzing the imaging properties, such as modulation transfer function (MTF), distortion, and imaging simulation. Based on the finite element method [46], COMSOL Multiphysics is a powerful tool in dealing with the diffraction grating. The design wavelength is 532 nm.

Figure 7 outlines the optical surfaces used in Code V. The object is placed at 3 m ahead of the eye. Surfaces 1 to 8 (S1 to S8) constitute the moist eye, of which, S1 is tear, S2 anterior cornea, S3 posterior cornea, S4 iris with pupil, S5 anterior lens, S6 virtual plane, S7 posterior lens, and S8 retina. To imitate the laser scanning projector as a pinhole camera, the semi-aperture of virtual plane―where the lens center is located―is set as 30 µm, i.e. radius of the laser beam.

 

Fig. 7 Optical surfaces used in Code V. The object is placed at 3 m ahead of the eye. Surfaces 1 to 8 (S1 to S8) constitute the moist eye, of which, S1 is tear, S2 anterior cornea, S3 posterior cornea, S4 iris with pupil, S5 anterior lens, S6 virtual plane, S7 posterior lens, and S8 retina.

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The original parameters of eye are adopted from [35], wherein the eye is focused to the infinity. In our model, with the tear being added and the object distance being assigned as 3 m, those parameters need to be tweaked through an optimization, which is carried out under a constraint that the length of eye be 24 mm [34]. As a result, Table 3 summarizes the optimized parameters, where AL and PL, in turn, denote the gradient refractive indices of anterior and posterior lenses. Besides, detailed parameters for aspherical surfaces and gradient lens are provided in Table 4 and Table 5, respectively.

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Table 3. Parameters of optical surfaces used in Code V

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Table 4. Detailed parameters for aspherical surfaces

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

3.2 Ray tracing diagram

Figure 8 shows the ray tracing diagram for the fields of 0°, 10°, 20°, 30°, 40°, 50°, and 61°, from which it can be seen that all rays are converged at the lens center.

 

Fig. 8 Ray tracing diagram for the fields of 0°, 10°, 20°, 30°, 40°, 50°, and 61°. It can be seen that all rays are converged at the lens center.

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3.3 Field of view

As illustrated in Fig. 9, FOV, whose vertex is situated at the center of entrance pupil, is the angle subtended by DOE. If measured diagonally, it could be determined by

FOV=2tan1(W2+H22(der+dep))
where H is the vertical dimension of DOE, der the eye relief, and dep the distance from the vertex of tear to the center of entrance pupil, which is calculated as 3.05 mm. Say W = H = 38.4 mm and der = 12 mm, FOV is 122° (diagonal).

 

Fig. 9 Illustration of FOV, which is the angle subtended by DOE and whose vertex is situated at the center of entrance pupil. Say W = H = 38.4 mm and der = 12 mm, FOV is 122° (diagonal).

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3.4 Angular resolution

Angular resolution (AR) in arcminute (′) is calculated by dividing FOV in degree (°) by the number of pixels N along the diagonal, which can be written as [47]

AR=60FOVN=60FOVNh2+Nv2
where Nh and Nv are the number of pixels along the horizontal and vertical directions, respectively. For FOV = 122°, Nh = 640, and Nv = 640, angular resolution 8.09′.

3.5 Diffraction efficiency and transmittance

In modeling the grating, wave optics module of COMSOL Multiphysics using the interface of electromagnetic wave, frequency domain is employed. The boundary condition is Floquet periodicity. The incident light is linearly polarized as transverse electric (TE) mode. The diffraction order m is + 1. The glass substrate of DOE is chosen as N-BK7 (Schott), whose refractive index is 1.5195 at 532 nm. Without loss of generality, 9 gratings are picked for simulation, as shown in Fig. 10. Say dp = 10 mm, ddoe = 20 mm, and dlens = 16.73 mm, according to Eqs. (5) and (6), the incident/diffraction angles θi/θm can be calculated. Based on the optimization, the optimal grating parameters, DEs, and transmittance T for normal incidence (θi = 0°) are obtained as in Table 6. The average DE and T are 57.6% and 80.6%, respectively.

 

Fig. 10 9 gratings picked for simulation, of which 1 is on the upper-left, 2 the upper-center, 3 the upper-right, 4 the middle-left, 5 the middle-center, 6 the middle-right, 7, the lower-left, 8 the lower-center, and 9 the lower-right.

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Tables Icon

Table 6. Optimized parameters of gratings

3.6 Uniformity

As DE of each grating of DOE more or less differs, a figure of merit Γ to evaluate the uniformity is introduced as [20]

Γ=1σDEavg
where DEavg is the average DE, and σ is the standard deviation formulated as
σ=1ni=1n(DEiDEavg)2
where n is the number of gratings of interest, and i the serial number. Calculated with DEs listed in Table 6, the uniformity Γ is 0.91.

3.7 Luminance

Luminance is a measure of the luminous intensity per unit area of light that is diffracted from the DOE within the entire FOV. By this definition, we could express the luminance in terms of the luminous flux Φ, average DE DEavg of DOE, solid angle Ω subtended by DOE, and area A of DOE, i.e.

L=ΦDEavgΩA
where
Ω=4cos11+(W2dlens)2+(H2dlens)2[1+(W2dlens)2][1+(H2dlens)2]
and
A=WH
When the luminous flux of projector is 2 lm, luminance is 323 cd/m2 or nit.

3.8 Spot diagram

Figure 11 plots the spot diagram for the fields of 0°, 10°, 20°, 30°, 40°, 50°, and 61°, from which it can be seen that the spot of each field is smaller than the Airy disk.

 

Fig. 11 Spot diagram for the fields of 0°, 10°, 20°, 30°, 40°, 50°, and 61°. It can be seen that the spot of each field is smaller than the Airy disk.

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3.9 MTF

As shown in Fig. 12, MTFs are calculated as a function of spatial frequency in cycle/degree for the fields of 0° and 61° when the distances between DOE and eye are offset by 0 mm, 3 mm and 6 mm from the target eye relief of 12 mm, respectively. At 3.71 cycle/degree, which corresponds to the angular resolution of 8.09′, MTFs are above 0.99999 for all fields and eye relief offsets. This agrees with the foregoing statement on the laser scanning projector in analogy to a pinhole camera. This also indicates that even if the laser beams are not perfectly converged at the center of lens, the image quality will not be much affected.

 

Fig. 12 MTFs are calculated as a function of spatial frequency in cycle/degree for the fields of 0° and 61° when the distances between DOE and eye are offset by 0 mm, 3 mm and 6 mm from the target eye relief of 12 mm, respectively. At 3.71 cycle/degree, which corresponds to the angular resolution of 8.09′, MTFs are above 0.99999 for all fields and eye relief offsets.

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3.10 Contrast ratio

CR―the ratio of maximum intensity to minimum intensity [48]―can be deduced as

CR=CR0+1+MTF(CR01)CR0+1MTF(CR01)
where CRp is the CR of laser scanning projector. For the field of 0°, CRp = 5000, MTF = 0.99999, and CR = 4878.

3.11 Distortion

Distortion, which measures the difference between the paraxial and actual image heights, is defined as [49]

Distortion=hahphp
where hp is the paraxial image height calculated with the first-order approximation, and ha is the actual image height. As the retina is a non-flat image surface, the chief ray shall be extended to intersect the flat paraxial image surface for calculating the image height. As can be seen in Fig. 13, the distortion is 24%, give or take.

 

Fig. 13 Distortion versus the field angle. For the fact that the eye is far from being an ideal imaging system, distortion is an inherent characteristic of all retinal projection based NEDs.

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3.12 Simulated imaging

Figure 14 shows the original image alongside the see-through retinal and projected retinal images. Compared to the original one, the projected retinal image is, while distorted, sharp and bright as a whole. In particular, the uncompromised brightness is extremely critical for the outdoors usage.

 

Fig. 14 (a) Original image (photographer: C. P. Chen, location: Duku Highway, Xinjiang, China), (b) see-through retinal image, and (c) projected retinal image. Compared to the original one, the projected retinal image is, while distorted, sharp and bright as a whole.

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4. Conclusions

A lensless RSD and its working principles have been proposed. Its structure is highlighted by a laser scanning projector, a DOE, and a moist eye. To precisely model the eye, tear and gradient lens are taken into account. Based on the simulation, FOV is 122°, angular resolution is 8.09′, average DE of DOE is 57.6%, average transmittance of DOE is 80.6%, uniformity is 0.91, luminance is 323 cd/m2, MTFs are above 0.99999 at 3.71 cycle/degree for all fields and offsets, CR is 4878, and distortion is 24%. As opposed to other retinal projection based NEDs [32–34], our RSD exhibits several unique features. First, no lens―except the lens of eye―is involved. Second, the projected retinal image is focus free. If constructed as a binocular RSD, it would be inherently free of the vergence-accommodation conflict [50]. Third, DOE is used as a combiner, making the device compact in design and suitable for see-through augmented reality. Fourth, the retinal image is immune to the change in the diopter of eye and pupil size. Instead, it will be subject to the rotation of eye, thereby fixating the eye to look straight ahead. That being said, a user can still look around by rotating his/her head if the head tracking is enabled.

Funding

National Natural Science Foundation of China (61831015); Science and Technology Commission of Shanghai Municipality (19ZR1427200, 1801H163000, 1701H169200); Shanghai Rockers Inc. (15H100000157).

Acknowledgments

Special thanks to Dr. Site Zhang (LightTrans, Germany) for his insightful comments on the manuscript.

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43. B. Redding, M. A. Choma, and H. Cao, “Speckle-free laser imaging using random laser illumination,” Nat. Photonics 6(6), 355–359 (2012). [CrossRef]   [PubMed]  

44. T. Levola and P. Laakkonen, “Replicated slanted gratings with a high refractive index material for in and outcoupling of light,” Opt. Express 15(5), 2067–2074 (2007). [CrossRef]   [PubMed]  

45. E. G. Loewen and E. Popov, Diffraction Gratings and Applications (Marcel Dekker, 1997).

46. COMSOL, “An introduction to the finite element method,” https://www.comsol.com/multiphysics/finite-element-method.

47. W. Zhang, C. P. Chen, L. Mi, Y. Lu, M. Zhu, X. Ren, R. Tang, and N. Maitlo, “A retinal-projection-based near-eye display with contact lens for mixed reality,” Proc. SPIE 11040, 1104005 (2019). [CrossRef]  

48. L. Mi, C. P. Chen, Y. Lu, W. Zhang, M. Zhu, R. Tang, X. Ren, and N. Maitlo, “A lensless retinal scanning display for augmented reality,” in SID Display Week (2019), pp. 1583–1586.

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

50. H. Hua, “Enabling focus cues in head-mounted displays,” Proc. IEEE 105(5), 805–824 (2017). [CrossRef]  

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  48. L. Mi, C. P. Chen, Y. Lu, W. Zhang, M. Zhu, R. Tang, X. Ren, and N. Maitlo, “A lensless retinal scanning display for augmented reality,” in SID Display Week (2019), pp. 1583–1586.
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    [Crossref]

2019 (1)

W. Zhang, C. P. Chen, L. Mi, Y. Lu, M. Zhu, X. Ren, R. Tang, and N. Maitlo, “A retinal-projection-based near-eye display with contact lens for mixed reality,” Proc. SPIE 11040, 1104005 (2019).
[Crossref]

2018 (3)

L. Mi, W. Zhang, C. P. Chen, Y. Zhou, Y. Li, B. Yu, and N. Maitlo, “A retinal-projection-based near-eye display for virtual reality,” Proc. SPIE 10676, 106761C (2018).

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] [PubMed]

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] [PubMed]

2017 (7)

2016 (3)

2015 (1)

2014 (2)

X. Hu and H. Hua, “High-resolution optical see-through multi-focal-plane head-mounted display using freeform optics,” Opt. Express 22(11), 13896–13903 (2014).
[Crossref] [PubMed]

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), 89 (2014).
[Crossref]

2013 (1)

2012 (2)

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]

B. Redding, M. A. Choma, and H. Cao, “Speckle-free laser imaging using random laser illumination,” Nat. Photonics 6(6), 355–359 (2012).
[Crossref] [PubMed]

2010 (1)

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

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] [PubMed]

2007 (2)

2006 (1)

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

1992 (1)

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.

Y. Amitai, “Extremely compact high-performance HMDs based on substrate-guided optical element,” in SID Symposium Digest of Technical Papers (2004), pp. 310–313.
[Crossref]

Bailey, I. L.

Bullimore, M. A.

Cao, H.

B. Redding, M. A. Choma, and H. Cao, “Speckle-free laser imaging using random laser illumination,” Nat. Photonics 6(6), 355–359 (2012).
[Crossref] [PubMed]

Chen, C. P.

Chen, H.-S.

Chen, P.-J.

Cheng, D.

Choma, M. A.

B. Redding, M. A. Choma, and H. Cao, “Speckle-free laser imaging using random laser illumination,” Nat. Photonics 6(6), 355–359 (2012).
[Crossref] [PubMed]

Dainty, C.

Duan, X.

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.

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), 89 (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]

Gao, Q.

Ge, J.

Georgiou, A.

A. Maimone, A. Georgiou, and J. S. Kollin, “Holographic near-eye displays for virtual and augmented reality,” ACM Trans. Graph. 36(4), 85 (2017).
[Crossref]

Gérard, P.

Goncharov, A. V.

Guo, W.

Hendricks, L.

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]

Hong, J.-Y.

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] [PubMed]

Hu, X.

Hua, H.

Huang, Z.

Hwang, S.

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] [PubMed]

Jacobs, R. J.

Jeon, S.

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] [PubMed]

Jeong, J.-H.

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] [PubMed]

Jin, G.

Jin, H.

Kang, H.

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] [PubMed]

Keller, K.

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), 89 (2014).
[Crossref]

Kelly, J. P.

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]

Kim, H.

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] [PubMed]

Kollin, J. S.

A. Maimone, A. Georgiou, and J. S. Kollin, “Holographic near-eye displays for virtual and augmented reality,” ACM Trans. Graph. 36(4), 85 (2017).
[Crossref]

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.

Lanman, D.

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), 89 (2014).
[Crossref]

Lee, B.

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] [PubMed]

Lee, G.-Y.

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] [PubMed]

Levola, T.

Li, X.

Li, Y.

Lin, Y.-H.

Liu, J.

Liu, P.

Liu, S.

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

Liu, Z.

Lu, Y.

W. Zhang, C. P. Chen, L. Mi, Y. Lu, M. Zhu, X. Ren, R. Tang, and N. Maitlo, “A retinal-projection-based near-eye display with contact lens for mixed reality,” Proc. SPIE 11040, 1104005 (2019).
[Crossref]

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] [PubMed]

Luebke, D.

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), 89 (2014).
[Crossref]

Maimone, A.

A. Maimone, A. Georgiou, and J. S. Kollin, “Holographic near-eye displays for virtual and augmented reality,” ACM Trans. Graph. 36(4), 85 (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), 89 (2014).
[Crossref]

Maitlo, N.

W. Zhang, C. P. Chen, L. Mi, Y. Lu, M. Zhu, X. Ren, R. Tang, and N. Maitlo, “A retinal-projection-based near-eye display with contact lens for mixed reality,” Proc. SPIE 11040, 1104005 (2019).
[Crossref]

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] [PubMed]

L. Mi, W. Zhang, C. P. Chen, Y. Zhou, Y. Li, B. Yu, and N. Maitlo, “A retinal-projection-based near-eye display for virtual reality,” Proc. SPIE 10676, 106761C (2018).

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]

McQuaide, S. C.

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]

Mi, L.

W. Zhang, C. P. Chen, L. Mi, Y. Lu, M. Zhu, X. Ren, R. Tang, and N. Maitlo, “A retinal-projection-based near-eye display with contact lens for mixed reality,” Proc. SPIE 11040, 1104005 (2019).
[Crossref]

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] [PubMed]

L. Mi, W. Zhang, C. P. Chen, Y. Zhou, Y. Li, B. Yu, and N. Maitlo, “A retinal-projection-based near-eye display for virtual reality,” Proc. SPIE 10676, 106761C (2018).

C. P. Chen, L. Zhou, J. Ge, Y. Wu, L. Mi, Y. Wu, B. Yu, and Y. Li, “Design of retinal projection displays enabling vision correction,” Opt. Express 25(23), 28223–28235 (2017).
[Crossref]

Moon, S.

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] [PubMed]

Mukawa, H.

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]

Nakano, S.

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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O’Brien, T.

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).
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Pan, C.

Pang, Y.

Rathinavel, K.

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), 89 (2014).
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Redding, B.

B. Redding, M. A. Choma, and H. Cao, “Speckle-free laser imaging using random laser illumination,” Nat. Photonics 6(6), 355–359 (2012).
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Ren, X.

W. Zhang, C. P. Chen, L. Mi, Y. Lu, M. Zhu, X. Ren, R. Tang, and N. Maitlo, “A retinal-projection-based near-eye display with contact lens for mixed reality,” Proc. SPIE 11040, 1104005 (2019).
[Crossref]

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

Rutherford, T.

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]

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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).
[Crossref]

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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).
[Crossref]

Sprague, R.

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]

Talha, M. M.

Tan, G.

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W. Zhang, C. P. Chen, L. Mi, Y. Lu, M. Zhu, X. Ren, R. Tang, and N. Maitlo, “A retinal-projection-based near-eye display with contact lens for mixed reality,” Proc. SPIE 11040, 1104005 (2019).
[Crossref]

Tremblay, E.

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).
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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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Yuan, J.

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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]

Zhang, W.

W. Zhang, C. P. Chen, L. Mi, Y. Lu, M. Zhu, X. Ren, R. Tang, and N. Maitlo, “A retinal-projection-based near-eye display with contact lens for mixed reality,” Proc. SPIE 11040, 1104005 (2019).
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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).
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L. Mi, W. Zhang, C. P. Chen, Y. Zhou, Y. Li, B. Yu, and N. Maitlo, “A retinal-projection-based near-eye display for virtual reality,” Proc. SPIE 10676, 106761C (2018).

Zhang, Y.

Zhang, Z.

Zhao, J.

Zhao, T.

Zhou, L.

Zhou, Y.

L. Mi, W. Zhang, C. P. Chen, Y. Zhou, Y. Li, B. Yu, and N. Maitlo, “A retinal-projection-based near-eye display for virtual reality,” Proc. SPIE 10676, 106761C (2018).

Zhu, M.

W. Zhang, C. P. Chen, L. Mi, Y. Lu, M. Zhu, X. Ren, R. Tang, and N. Maitlo, “A retinal-projection-based near-eye display with contact lens for mixed reality,” Proc. SPIE 11040, 1104005 (2019).
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Appl. Opt. (3)

Displays (1)

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S. Liu, H. Hua, and D. Cheng, “A novel prototype for an optical see-through head-mounted display with addressable focus cues,” IEEE Trans. Vis. Comput. Graph. 16(3), 381–393 (2010).
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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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Nat. Photonics (1)

B. Redding, M. A. Choma, and H. Cao, “Speckle-free laser imaging using random laser illumination,” Nat. Photonics 6(6), 355–359 (2012).
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Figures (14)

Fig. 1
Fig. 1 Proposed structure of our RSD, which can be decomposed into three major components, i.e. a laser scanning projector, a DOE, and an eye. dp is the distance between projector and glass, ddoe the horizontal distance between projector and DOE, dlens the distance between DOE and lens center, W the dimension of DOE, x the distance starting from the left edge of DOE, θi the angle of incident light, and θm the angle of diffracted light.
Fig. 2
Fig. 2 Cross-sectional view of our schematic moist eye, consisting of tear, cornea (anterior and posterior), aqueous chamber filled with aqueous humor, iris with an opening known as pupil, lens (anterior and posterior), vitreous chamber filled with vitreous humor, and retina.
Fig. 3
Fig. 3 Cross-sectional view of lens of eye with an assistive virtual plane. The center of virtual plane is designated as the center of lens. z is the distance measured from the vertex of anterior lens along the z-axis, and y the distance measured from the lens center along the y-axis.
Fig. 4
Fig. 4 Refractive indices of lens calculated along the (a) horizontal and (b) vertical directions, respectively. It can be seen that the refractive index maximizes at the center, from which it starts to decrease towards the outermost surface.
Fig. 5
Fig. 5 Schematic drawing of the laser scanning projector, inside which are mounted a laser diode, a mirror, and a scanning mirror controlled by a biaxial MEMS.
Fig. 6
Fig. 6 Profile of the slanted grating, where p is the grating period, hg the grating depth, wg the grating width, β the slant angle relative to the normal, θi the incident angle, and θm the diffraction angle.
Fig. 7
Fig. 7 Optical surfaces used in Code V. The object is placed at 3 m ahead of the eye. Surfaces 1 to 8 (S1 to S8) constitute the moist eye, of which, S1 is tear, S2 anterior cornea, S3 posterior cornea, S4 iris with pupil, S5 anterior lens, S6 virtual plane, S7 posterior lens, and S8 retina.
Fig. 8
Fig. 8 Ray tracing diagram for the fields of 0°, 10°, 20°, 30°, 40°, 50°, and 61°. It can be seen that all rays are converged at the lens center.
Fig. 9
Fig. 9 Illustration of FOV, which is the angle subtended by DOE and whose vertex is situated at the center of entrance pupil. Say W = H = 38.4 mm and der = 12 mm, FOV is 122° (diagonal).
Fig. 10
Fig. 10 9 gratings picked for simulation, of which 1 is on the upper-left, 2 the upper-center, 3 the upper-right, 4 the middle-left, 5 the middle-center, 6 the middle-right, 7, the lower-left, 8 the lower-center, and 9 the lower-right.
Fig. 11
Fig. 11 Spot diagram for the fields of 0°, 10°, 20°, 30°, 40°, 50°, and 61°. It can be seen that the spot of each field is smaller than the Airy disk.
Fig. 12
Fig. 12 MTFs are calculated as a function of spatial frequency in cycle/degree for the fields of 0° and 61° when the distances between DOE and eye are offset by 0 mm, 3 mm and 6 mm from the target eye relief of 12 mm, respectively. At 3.71 cycle/degree, which corresponds to the angular resolution of 8.09′, MTFs are above 0.99999 for all fields and eye relief offsets.
Fig. 13
Fig. 13 Distortion versus the field angle. For the fact that the eye is far from being an ideal imaging system, distortion is an inherent characteristic of all retinal projection based NEDs.
Fig. 14
Fig. 14 (a) Original image (photographer: C. P. Chen, location: Duku Highway, Xinjiang, China), (b) see-through retinal image, and (c) projected retinal image. Compared to the original one, the projected retinal image is, while distorted, sharp and bright as a whole.

Tables (6)

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Table 1 Parameters of gradient lens

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Table 2 Parameters for laser scanning projector

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Table 3 Parameters of optical surfaces used in Code V

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Table 4 Detailed parameters for aspherical surfaces

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Table 5 Detailed parameters for gradient refractive indices of anterior and posterior lenses

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Table 6 Optimized parameters of gratings

Equations (16)

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

n a ( z,y )= n 00 + c 10 y 2 + c 20 y 4 + c 01 ( z+ z m )+ c 02 ( z+ z m ) 2 + c 03 ( z+ z m ) 3 + c 04 ( z+ z m ) 4
n p ( z,y )= n max + c 10 y 2 + c 20 y 4 + c 01,2 z+ c 02,2 z 2 + c 03,2 z 3 + c 04,2 z 4
D= D 0 1+ ( 4 M 2 λL π D 0 2 ) 2
θ div = 2 M 2 λ π D 0
p( sin θ i sin θ m )=mλ
tan θ i = d doe +x d p
tan θ m = W/2 x d lens
FOV=2 tan 1 ( W 2 + H 2 2( d er + d ep ) )
AR= 60FOV N = 60FOV N h 2 + N v 2
Γ=1 σ D E avg
σ= 1 n i=1 n ( D E i D E avg ) 2
L= ΦD E avg ΩA
Ω=4 cos 1 1+ ( W 2 d lens ) 2 + ( H 2 d lens ) 2 [ 1+ ( W 2 d lens ) 2 ][ 1+ ( H 2 d lens ) 2 ]
A=WH
CR= C R 0 +1+MTF( C R 0 1 ) C R 0 +1MTF( C R 0 1 )
Distortion= h a h p h p

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