Abstract

The limited depth of focus (DOF) is one of the main problems of today’s head mounted displays. This paper investigates ways to overcome this drawback by using the retinal scanning technology. Based on an accommodation-dependent schematic eye model the contrast function of a retinal scanning display is evaluated as a function of eye accommodation, eye position and scanning beam width. The display’s defocusing properties and the design trade-off between resolution, depth of focus and maximum image field are analyzed and discussed. The analysis indicates that an elliptically shaped scanning beam is most favorable to provide a quasi-accommodation free viewing. This elliptical beam shape is caused by the asymmetry in the scan pattern.

© 2003 Optical Society of America

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References

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    [CrossRef]
  2. G.K. Edgar, J.C. Pope, and I.R. Craig, �??Visual accommodation problems with head-up and helmet-mounted displays ?,�?? Displays, 15, 68�??75 (1994).
    [CrossRef]
  3. M.B. Spitzer, N.M. Rensing, R. McClelland, and P. Aquilino, �??Eyeglass-based systems for wearable computing,�?? Proc. IEEE ISWC�??97, 48�??51 (1997).
  4. I. Kasai, Y. Tanijiri, T. Endo, and H. Ueda, �??A forgettable near eye display,�?? Proc. IEEE ISWC�??00, 115�??118.
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    [CrossRef]
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Am. J. Optom. Physiol. Opt.

J. Tucker and W.N. Charman, �??Depth of focus and accommodation for sinusoidal gratings as a function of luminance,�?? Am. J. Optom. Physiol. Opt. 63, 58�??70 (1986).
[CrossRef] [PubMed]

Appl. Opt.

Biomed. Technik

M. Menozzi, H. Krüger, P. Lukowicz, and G. Tröster, �??Perception of brightness with a virtual retinal display using badal projection,�?? Biomed. Technik 46, 55�??62 (2001).
[CrossRef]

Displays

G.K. Edgar, J.C. Pope, and I.R. Craig, �??Visual accommodation problems with head-up and helmet-mounted displays ?,�?? Displays, 15, 68�??75 (1994).
[CrossRef]

IEEE Computer Graphics and Applications

R.T. Azuma, Y. Baillot, R. Behringer, S.K. Feiner, S. Julier, and B. MacIntyre, �??Recent advances in augmented reality,�?? IEEE Computer Graphics and Applications 21, 34�??47 (2001) and references therein.
[CrossRef]

J. Opt. Soc. Am. A

Ophthal. Physiol. Opt.

A. Popiolek-Masajada and H. Kasprzak, �??Model of the optical system of the human eye during accommodation,�?? Ophthal. Physiol. Opt. 22, 201�??208 (2002).
[CrossRef]

Opt. Commun.

M. von Waldkirch, P. Lukowicz, and G. Tr¨oster, �??LCD-based coherent wearable projection display for quasi accommodation-free imaging,�?? Opt. Commun. 217, 133�??140 (2003).
[CrossRef]

Opt. Eng.

G. C. de Wit and R. Beek, �??Effects of a small exit pupil in a virtual reality display system,�?? Opt. Eng. 36, 2158�??2162 (1997).
[CrossRef]

Proc. IEEE ISWC???00

I. Kasai, Y. Tanijiri, T. Endo, and H. Ueda, �??A forgettable near eye display,�?? Proc. IEEE ISWC�??00, 115�??118.

Proc. IEEE ISWC???97

M.B. Spitzer, N.M. Rensing, R. McClelland, and P. Aquilino, �??Eyeglass-based systems for wearable computing,�?? Proc. IEEE ISWC�??97, 48�??51 (1997).

Proc. Soc. for Information Display

J. Kollin, �??A retinal display for virtual-environment applications,�?? Proc. Soc. for Information Display XXIV, 827�??830 (1993).

Proc. SPIE

J. Kollin and M. Tidwell, �??Optical engineering challenges of the virtual retinal display,�?? Proc. SPIE 2537, 48�??60 (1995).
[CrossRef]

M. von Waldkirch, P. Lukowicz, and G. Tr¨oster, �??Impact of light coherence on depth of focus of wearable retinal displays,�?? Proc. SPIE 5186, 5-14 (2003).
[CrossRef]

Vision Res.

S. Marcos, E. Moreno, and R. Navarro, �??The depth-of-field of the human eye from objective and subjective measurements,�?? Vision Res. 39, 2039�??2049 (1999).
[CrossRef] [PubMed]

L.N. Thibos, D.L. Still, and A. Bradley, �??Characterization of spatial aliasing and contrast sensitivity in peripheral vision,�?? Vision Res. 36, 249�??258 (1996) and references therein.
[CrossRef] [PubMed]

Other

OSLO is a registered trademark of Lambda Research Corp.

M. Bass (Ed.), Handbook of optics, vol. 1, (McGraw-Hill, Inc., 1995).

D.A. Atchison and G. Smith, Optics of the human eye. (Butterworth-Heinemann, Oxford, 2000).

A. Gullstrand, Appendix II in �??Handbuch der Physiologischen Optik�??. (Voss, Hamburg, 1909).

G.C. de Wit, A Retinal scanning display for virtual reality. (PhD thesis, TU Delft, 1997).

B.A. Wandell, Foundations of vision. (Sunderland, Massachusetts, 1995).

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Figures (10)

Fig. 1.
Fig. 1.

Schematical illustration of the VRD principle (after [11]). The left zoom shows the scanning mirror setup (with SH and SV indicating the horizontal and vertical mirror, respectively). The right zoom focuses on the region, where the laser beam enters the eye. σcor signifies the radius of the beam at the eye’s cornea. This parameter will play an important role in the subsequent simulations.

Fig. 2.
Fig. 2.

The accommodation-dependent schematic eye model as used for all simulations. The numbered labels indicate the surfaces as parameterized in Tab. 1. CR indicates the center of rotation as explained in the text.

Fig. 3.
Fig. 3.

Due to the high foveal resolution the eye moves to bring selected image parts to the fovea. The cross in the grey rectangle indicates the corresponding image part which the eye is currently gazing at.

Fig. 4.
Fig. 4.

(a) shows the through-focus CF in x and y-direction for three different spatial frequencies. The bright circles (∘) indicate the x-direction whereas the filled ones (∙) signify the y-direction. Here the scanning step δy was 15µm. (b) shows the respective CF in x-direction in terms of eye accommodation and spatial frequency. In both cases the corneal beam radius σcor has been set to 350µm.

Fig. 5.
Fig. 5.

The through-focus CF for different values of the corneal beam radius σcor . The spatial frequency f was set to the standard frequency f=6.2cyc/deg.

Fig. 6.
Fig. 6.

a) CF-isolines for f=6.2cyc/deg as a function of corneal beam radius and changes in eye accommodation. The CF-level values are indicated at the right edge. The bold line signifies the DOF at CF=0.7. b) The circles (∙) show the optimum corneal beam radius in terms of spatial frequency as explained in the text. The triangles (▾) indicate the corresponding maximum depth of focus. The dashed lines symbolize the discussed example at f=6.2cyc/deg.

Fig. 7.
Fig. 7.

Isolines of the CF for ΔD=0 and with σcor =350µm as a function of spatial frequency and eye rotation. The CF level values are indicated in the plot. The iris’ radius was set to 1.5mm.

Fig. 8.
Fig. 8.

The maximum image field as a function of corneal beam radius for a retinal scanning system without pupil tracking. The data are evaluated for f=6.2cyc/deg with a iris’ radius of 1.5mm. The maximum image field is defined as twice the rotating angle where the CF has decreased to 0.7.

Fig. 9.
Fig. 9.

CF in horizontal direction in terms of eye rotation α and changes in eye accommodation ΔD for the standard frequency f=6.2cyc/deg.

Fig. 10.
Fig. 10.

Trade-off between depth of focus (DOF) and maximum image field for three different spatial frequencies. The lines connect points of the same frequency, but with different σcor -values. In contrast the symbols indicate points with the same σcor -value at different frequencies. Unfilled symbols indicate data in x-direction, whereas filled symbols signify the y-direction. The selected frequencies correspond to the capital letter “E” of font sizes 10/14/18 pt when being viewed from 50cm.

Tables (2)

Tables Icon

Table 1. Geometry of the schematic wide-angle eye model in the unaccommodated state

Tables Icon

Table 2. Dependence of the lens parameters on changes of the eye accommodation ΔD (in diopters)

Equations (13)

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C F ( f , Δ D , σ cor ) = c ( f , Δ D , σ cor ) c
c = ( I max I min ) ( I max + I min )
c = ( I max I min ) ( I max + I min )
I ( x i , y i ) = C T 0 T g ( t ) PSF ( x i ( t ) , y i ( t ) ) d t
I ( x i , y i ) = C T k = 1 n 0 x max g ( x , k δ y ) PSF ( x i x , y i k δ y ) d x v ( x , k δ y )
g ( x , y ) = { 1 for ( 4 m 2 ) Δ x x < 4 m , m , y 0 for 4 m x < ( 4 m + 2 ) Δ x , m , y
I max x ( y i ) = I ( x i = Δ x , y i ) k g ( x , k δ y ) PSF ( Δ x x , y i k δ y ) d x
< I max x > g ( x ) PSF x ( Δ x x ) dx · 1 δ y 0 δ y k PSF y ( y i k δ y ) d y i
< I max x > m 1 1 PSF x ( Δ x ( x ˜ + 4 m ) ) d x ˜ · 1 δ y 0 δ y k PSF y ( y i k δ y ) d y i
< I min x > m 1 3 PSF x ( Δ x ( x ˜ + 4 m ) ) d x ˜ · 1 δ y 0 δ y k PSF y ( y i k δ y ) d y i
g ( x , y ) = { 1 for q δ y y δ y , x 0 for 0 y ( q 1 ) δ y , x
I max y n k = 1 q PSF y ( ( q + 1 2 2 n q + k ) δ y )
I min y n k = 1 q PSF y ( ( q 1 2 2 n q + k ) δ y )

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