Abstract

Limited depth of focus is among the main problems of todays see-through head-mounted displays. In this paper we propose and evaluate a new solution to this problem: the use of the coherent multiple imaging technique in a retinal projection display by incorporating an appropriate phase-only mask. The evaluation is based on a schematic eye model and on the partial coherence simulation tool SPLAT which allows us to calculate the projected retinal images of a text target. Objective image quality criteria demonstrate that this approach is promising provided that partially coherent illumination light is used. In this case, psychometric measurements reveal that the depth of focus for reading text can be extended by a factor of up to 3.2. For fully coherent and incoherent illumination, however, the retinal images suffer from structural and contrast degradation effects, respectively.

© 2004 Optical Society of America

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References

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1 (1)

M. Bass, ed., Handbook of Optics, vol. 1 (McGraw-Hill, Inc., New York, 1995)

Appl. Opt. (1)

Behaviour Research Methods & Instrumenta (1)

H. Lieberman and A. Pentland, ???Microcomputer-based estimation of psychophysical thresholds: the best PEST,??? Behaviour Research Methods & Instrumentation 14(1), 21???25 (1982)
[CrossRef]

Displays (1)

G. Edgar, J. Pope, and I. Craig, ???Visual accommodation problems with head-up and helmet-mounted displays?,??? Displays 15(2), 68???75 (1994)
[CrossRef]

Helmet- and Head-Mounted Displays 1995 (1)

R. Johnston and S. Willey, ???Development of a Commercial Retinal Scanning Display,??? in Proc. of Helmet- and Head-Mounted Displays and Symbology Design, 2???13 (W. Stephens and L.A. Haworth (Eds.), 1995).

Human Factors (1)

L. Marran and C. Schor, ???Multiaccomodative Stimuli in VR systems: Problems & Solutions,??? Human Factors 39(3), 382???388 (1997)
[CrossRef]

IEEE Computer Graphics and Applications (1)

R. Azuma, Y. Baillot, R. Behringer, S. Feiner, S. Julier, and B. MacIntyre, ???Recent Advances in Augmented Reality,??? IEEE Computer Graphics and Applications 21(6), 34???47 (2001) and references therein
[CrossRef]

IEEE Trans. on image processing (1)

Z.Wang, A. Bovik, H. Sheikh, and E. Simoncelli, ???Image Quality Assessment: From Error Visibility to Structural Similarity,??? IEEE Trans. on image processing 13(4), 600???612 (2004)
[CrossRef]

J. Opt Soc. (1)

R.J. Becherer and G.B. Parrent, ???Nonlinearity in optical imaging systems,??? J. Opt Soc. 57(12), 1479???1486 (1967)
[CrossRef]

J. Opt. Soc. Am. A (3)

Ophthal. Physiol. Opt. (1)

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. (1)

T. Tomono, ???Spectacle-type Wearable Display,??? Opt. Commun. 180, 205???210 (2000)
[CrossRef]

Opt. Eng. (1)

M. von Waldkirch, P. Lukowicz, and G. Tr¨oster, ???Effect of light coherence on depth of focus in head-mounted retinal projection displays,??? Opt. Eng. 43(7), 1552???1560 (2004)
[CrossRef]

Opt. Express (1)

Perception & Psychophysics (1)

C. Kaernbach, ???Adaptive threshold estimation with unforced-choice tasks,??? Perception & Psychophysics 63(8), 1377???1388 (2001)
[CrossRef]

Pervasive Computing 2004 (1)

M. von Waldkirch, P. Lukowicz, and G. Tröster, ???Spectacle-based display design for accommodation-free viewing,??? in Proc. of 2nd International Conference on Pervasive Computing (Pervasive 2004), LNCS vol. 3001, 106???123 (Springer-Verlag, 2004)

Proc. of the Royal Society of London (1)

H. Hopkins, ???On the diffraction theory of Optical Images,??? Proc. of the Royal Society of London. Series A, Mathematical and Physical Sciences 217(1130), 408???432 (1953)

Proc. of the Royal Society of London. (1)

H. Hopkins, ???The concept of partial coherence in optics,??? Proc. of the Royal Society of London. Series A, Mathematical and Physical Sciences 208(1093), 263???277 (1951)

Proc. SPIE (2)

K. Toh and A. Neureuther, ???Identifying and Monitoring Effects of Lens Aberrations in Projection Printing,??? in Optical Microlithography VI, H.L. Stover, ed., Proc. SPIE 772, 202???209 (1987)

J. Kollin and M. Tidwell, ???Optical Engineering Challenges of the Virtual Retinal Display,??? in Novel Optical Systems Design and Optimization, J.M. Sasian, ed., Proc. SPIE 2537, 48???60 (1995)

SID 1998 (1)

T. Sugihara and T. Miyasato, ???A Lightweight 3-D HMD with Accommodative Compensation,??? in Proc. 29th Soc. Information Display (SID98), vol. XXIX, 927???930 (San Jose, CA, 1998

Vision Res. (1)

G. Westheimer, ???The maxwellian view,??? Vision Res. 6, 669???682 (1966)
[CrossRef] [PubMed]

Other (5)

S. Inoué and K.R. Spring, ???Microscope image formation - Principles of Köhler illumination??? in Video Microscopy: the Fundamentals (Plenum Press, New York, 1997).
[CrossRef]

G. de Wit, ???A Retinal Scanning Display for Virtual Reality,??? Ph.D. thesis, TU Delft (1997).

OSLO is a registered trademark of Lambda Research Corp.

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

J.W. Goodman, Introduction to Fourier Optics, (McGraw-Hill, Inc., New York, 1996)

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Figures (13)

Fig. 1.
Fig. 1.

Principal setup of the retinal projection display. P1 signifies the L 1-focal plane with the aperture stop and the pupil phase mask (PM) for the multiple imaging. L 1 to L 3 represent lenses and P 2 the eye pupil plane. The straight lines show the axial illumination rays while the dotted lines indicate the LCD-imaging.

Fig. 2.
Fig. 2.

The accommodation-dependent schematic eye model as used for all simulations.

Fig. 3.
Fig. 3.

Schematic illustration of eye motion in case of fully coherent illumination. The dots within the exit pupil depict the Fourier transform pattern of the LCD image.

Fig. 4.
Fig. 4.

Image quality functions C and S in terms of eye accommodation ΔD for various values of ε and with (Δδ,δ̄)=(0.5D,3.5D). The data were calculated with σ=0.5 and a font size viewing angle αv =0.4deg.

Fig. 5.
Fig. 5.

Image quality functions C and S in terms of ΔD for various values of Δδ with (ε,δ̄)=(11D,3.5D). Again, σ=0.5 and αv =0.4deg.

Fig. 6.
Fig. 6.

Image quality functions C and S for σ=0 in terms of ΔD for various values of ε and with (Δδ,δ̄)=(0.5D,3.5D). Again, αv =0.4deg. The grey unfilled symbols show the former results for ε=11D with partially coherent illumination for comparison.

Fig. 7.
Fig. 7.

Image quality functions C and S for σ=∞ in terms of ΔD for various values of ε and with (Δδ,δ̄)=(0.5D,3.5D). Again, αv =0.4deg. The grey unfilled symbols show the former results for ε=11D with partially coherent illumination for comparison.

Fig. 8.
Fig. 8.

Phase profile ψdisp of the rotationally symmetric phase-only mask PM.

Fig. 9.
Fig. 9.

First row: retinal images for ε=0D and σ=0.5 for comparison. The other three rows show the retinal images for the three coherence levels when the designed phase-mask PM (see Fig. 8) is applied. The labels below the images indicate (σ/ΔD). Again, αv =0.4deg.

Fig. 10.
Fig. 10.

Image quality functions C and S in terms of coherence level σ and eye accommodation ΔD. The phase-mask PM used is described by (εδ,δ̄)=(11D,0.5D,3.5D). Again, αv =0.4deg.

Fig. 11.
Fig. 11.

Contrast and structural image quality averaged over the considered range of accommodation [0D,6D] in terms of σ.

Fig. 12.
Fig. 12.

(a) shows the psychometric functions of one subject for the first experiment for all three αv -values and σ=0.4. The ordinate shows the subject’s performance as proportion of answers ‘better or equal quality’. The measured performances are indicated by circles (▦) while the squares (▪) signify the derived thresholds. The threshold error bars indicate the 95%-confidence interval. The inset shows the reference image for αv =0.4deg. (b) shows the results of the first experiment based on 7 subjects (see text).

Fig. 13.
Fig. 13.

Results of the second experiment (estimation of the DOF) based on 7 subjects.

Equations (7)

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f ( x , y ) = P ( x , y ) · e i ψ ( x , y ) = P ( x , y ) · e i ( ψ disp ( x , y ) + ψ eye ( x , y ) )
ψ disp ( ρ ) = π λ δ ρ 2
ψ disp ( ρ ) = angle [ l = 0 L w l e i ϕ l e i ( π λ δ l ρ 2 ) ]
C = 2 s x s y s x 2 + s y 2 and S = s xy s x s y
ψ disp ( ρ ) = angle [ l = 0 L e i π l ( 1 L + Δδ λ ρ 2 ) ] + π λ δ 0 ρ 2
I ( u , v ) m , n , p , q C m , n , p , q a m , q a p , q * e 2 π i NA NA [ ( m p ) u + ( n q ) v ]
C m , n , p , q γ ( x , y ) f ( x + β m , y + β n ) f * ( x + β p , y + β q ) dxdy

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