Abstract

Lack of accurate focus cues in conventional stereoscopic displays has potentially significant effects on depth perception accuracy and visual fatigue. Recently several multi-focal plane display prototypes have been demonstrated with the promise of improving the accuracy of focus cue rendering in stereoscopic displays. In this paper, we present a systematic method to address two fundamental issues in designing a multi-focal plane display: (1) the appropriate dioptric spacing between adjacent focal planes; and (2) the depth-weighted fusing function to render a continuous three-dimensional (3-D) volume using a sparse number of focal planes placed in the space. By taking account of both ocular factors of the human visual system (HVS) and display factors of a multi-focal plane system, we determine that an appropriate spacing between two adjacent focal planes should be ~0.6 diopter (D) while a smaller spacing may be necessary for further improving retinal image quality. We further develop a set of nonlinear depth-weighted fusing function with the promise of balancing perceptual continuity of a 3-D scene and retinal image quality. Our method was based on quantitative evaluation of the modulation transfer functions (MTF) of depth-fused images formed on retina.

© 2010 OSA

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2010 (1)

S. Liu, H. Hua, and D. W. 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 (3)

2008 (1)

D. M. Hoffman, A. R. Girshick, K. Akeley, and M. S. Banks, “Vergence-accommodation conflicts hinder visual performance and cause visual fatigue,” J. Vis. 8(3), 1–30 (2008).
[CrossRef] [PubMed]

2007 (1)

2006 (1)

B. T. Schowengerdt and E. J. Seibel, “True 3-D scanned voxel dis-plays using single or multiple light sources,” J. Soc. Inf. Disp. 14(2), 135–143 (2006).
[CrossRef]

2005 (1)

S. J. Watt, K. Akeley, M. O. Ernst, and M. S. Banks, “Focus cues affect perceived depth,” J. Vis. 5(10), 834–862 (2005).
[CrossRef]

2004 (3)

K. Akeley, S. J. Watt, A. R. Girshick, and M. S. Banks, “A stereo display prototype with multiple focal distances,” ACM Trans. Graph. 23(3), 804–813 (2004).
[CrossRef]

S. Suyama, S. Ohtsuka, H. Takada, K. Uehira, and S. Sakai, “Apparent 3-D image perceived from luminance-modulated two 2-D images displayed at different depths,” Vision Res. 44(8), 785–793 (2004).
[CrossRef] [PubMed]

H. Cheng, J. K. Barnett, A. S. Vilupuru, J. D. Marsack, S. Kasthurirangan, R. A. Applegate, and A. Roorda, “A population study on changes in wave aberrations with accommodation,” J. Vis. 4(4), 272–280 (2004).
[CrossRef] [PubMed]

2003 (1)

2002 (1)

G. E. Favalora, J. Napoli, D. M. Hall, R. K. Dorval, M. G. Giovinco, M. J. Richmond, and W. S. Chun, “100 million-voxel volumetric display,” Proc. SPIE 4712, 300–312 (2002).
[CrossRef]

2000 (2)

S. Suyama, M. Date, and H. Takada, “Three-dimensional display system with dual frequency liquid crystal varifocal lens,” Jpn. J. Appl. Phys. 39(Part 1, No. 2A), 480–484 (2000).
[CrossRef]

J. P. Rolland, M. W. Krueger, and A. Goon, “Multifocal planes head-mounted displays,” Appl. Opt. 39(19), 3209–3215 (2000).
[CrossRef]

1995 (3)

J. P. Wann, S. Rushton, and M. Mon-Williams, “Natural problems for stereoscopic depth perception in virtual environments,” Vision Res. 35(19), 2731–2736 (1995).
[CrossRef] [PubMed]

D. A. Atchison, M. J. Collins, C. F. Wildsoet, J. Christensen, and M. D. Waterworth, “Measurement of monochromatic ocular aberrations of human eyes as a function of accommodation by the Howland aberroscope technique,” Vision Res. 35(3), 313–323 (1995).
[CrossRef] [PubMed]

J. E. Greivenkamp, J. Schwiegerling, J. M. Miller, and M. D. Mellinger, “Visual acuity modeling using optical raytracing of schematic eyes,” Am. J. Ophthalmol. 120(2), 227–240 (1995).
[PubMed]

1994 (1)

J. F. Heanue, M. C. Bashaw, and L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265(5173), 749–752 (1994).
[CrossRef] [PubMed]

1993 (2)

M. Mon-Williams, J. P. Warm, and S. Rushton, “Binocular vision in a virtual world: visual deficits following the wearing of a head-mounted display,” Ophthalmic Physiol. Opt. 13(4), 387–391 (1993).
[CrossRef] [PubMed]

R. A. Applegate and V. Lakshminarayanan, “Parametric representation of Stiles-Crawford functions: normal variation of peak location and directionality,” J. Opt. Soc. Am. A 10(7), 1611–1623 (1993).
[CrossRef] [PubMed]

1987 (1)

P. A. Ward, “The effect of stimulus contrast on the accommodation response,” Opththal. Physiol. Opt. 7(1), 9–15 (1987).
[CrossRef]

1959 (1)

1957 (1)

F. W. Campbell, “The depth of field of the human eye,” J. Mod. Opt. 4(4), 157–164 (1957).

1933 (1)

W. S. Stiles and B. H. Crawford, “The luminous efficiency of rays entering the eye pupil at different points,” Proc. R. Soc. Lond., B 112(778), 428–450 (1933).
[CrossRef]

Akeley, K.

D. M. Hoffman, A. R. Girshick, K. Akeley, and M. S. Banks, “Vergence-accommodation conflicts hinder visual performance and cause visual fatigue,” J. Vis. 8(3), 1–30 (2008).
[CrossRef] [PubMed]

S. J. Watt, K. Akeley, M. O. Ernst, and M. S. Banks, “Focus cues affect perceived depth,” J. Vis. 5(10), 834–862 (2005).
[CrossRef]

K. Akeley, S. J. Watt, A. R. Girshick, and M. S. Banks, “A stereo display prototype with multiple focal distances,” ACM Trans. Graph. 23(3), 804–813 (2004).
[CrossRef]

Applegate, R. A.

H. Cheng, J. K. Barnett, A. S. Vilupuru, J. D. Marsack, S. Kasthurirangan, R. A. Applegate, and A. Roorda, “A population study on changes in wave aberrations with accommodation,” J. Vis. 4(4), 272–280 (2004).
[CrossRef] [PubMed]

R. A. Applegate and V. Lakshminarayanan, “Parametric representation of Stiles-Crawford functions: normal variation of peak location and directionality,” J. Opt. Soc. Am. A 10(7), 1611–1623 (1993).
[CrossRef] [PubMed]

Atchison, D. A.

D. A. Atchison, M. J. Collins, C. F. Wildsoet, J. Christensen, and M. D. Waterworth, “Measurement of monochromatic ocular aberrations of human eyes as a function of accommodation by the Howland aberroscope technique,” Vision Res. 35(3), 313–323 (1995).
[CrossRef] [PubMed]

Banks, M. S.

G. D. Love, D. M. Hoffman, P. J. W. Hands, J. Gao, A. K. Kirby, and M. S. Banks, “High-speed switchable lens enables the development of a volumetric stereoscopic display,” Opt. Express 17(18), 15716–15725 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-18-15716 .
[CrossRef] [PubMed]

D. M. Hoffman, A. R. Girshick, K. Akeley, and M. S. Banks, “Vergence-accommodation conflicts hinder visual performance and cause visual fatigue,” J. Vis. 8(3), 1–30 (2008).
[CrossRef] [PubMed]

S. J. Watt, K. Akeley, M. O. Ernst, and M. S. Banks, “Focus cues affect perceived depth,” J. Vis. 5(10), 834–862 (2005).
[CrossRef]

K. Akeley, S. J. Watt, A. R. Girshick, and M. S. Banks, “A stereo display prototype with multiple focal distances,” ACM Trans. Graph. 23(3), 804–813 (2004).
[CrossRef]

Barnett, J. K.

H. Cheng, J. K. Barnett, A. S. Vilupuru, J. D. Marsack, S. Kasthurirangan, R. A. Applegate, and A. Roorda, “A population study on changes in wave aberrations with accommodation,” J. Vis. 4(4), 272–280 (2004).
[CrossRef] [PubMed]

Bashaw, M. C.

J. F. Heanue, M. C. Bashaw, and L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265(5173), 749–752 (1994).
[CrossRef] [PubMed]

Campbell, F. W.

F. W. Campbell, “The depth of field of the human eye,” J. Mod. Opt. 4(4), 157–164 (1957).

Chen, Y. L.

Cheng, D. W.

S. Liu, H. Hua, and D. W. 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]

Cheng, H.

H. Cheng, J. K. Barnett, A. S. Vilupuru, J. D. Marsack, S. Kasthurirangan, R. A. Applegate, and A. Roorda, “A population study on changes in wave aberrations with accommodation,” J. Vis. 4(4), 272–280 (2004).
[CrossRef] [PubMed]

Christensen, J.

D. A. Atchison, M. J. Collins, C. F. Wildsoet, J. Christensen, and M. D. Waterworth, “Measurement of monochromatic ocular aberrations of human eyes as a function of accommodation by the Howland aberroscope technique,” Vision Res. 35(3), 313–323 (1995).
[CrossRef] [PubMed]

Chun, W. S.

G. E. Favalora, J. Napoli, D. M. Hall, R. K. Dorval, M. G. Giovinco, M. J. Richmond, and W. S. Chun, “100 million-voxel volumetric display,” Proc. SPIE 4712, 300–312 (2002).
[CrossRef]

Collins, M. J.

D. A. Atchison, M. J. Collins, C. F. Wildsoet, J. Christensen, and M. D. Waterworth, “Measurement of monochromatic ocular aberrations of human eyes as a function of accommodation by the Howland aberroscope technique,” Vision Res. 35(3), 313–323 (1995).
[CrossRef] [PubMed]

Crawford, B. H.

W. S. Stiles and B. H. Crawford, “The luminous efficiency of rays entering the eye pupil at different points,” Proc. R. Soc. Lond., B 112(778), 428–450 (1933).
[CrossRef]

Date, M.

S. Suyama, M. Date, and H. Takada, “Three-dimensional display system with dual frequency liquid crystal varifocal lens,” Jpn. J. Appl. Phys. 39(Part 1, No. 2A), 480–484 (2000).
[CrossRef]

Diverdi, S.

C. Lee, S. Diverdi, and T. Höllerer, “Depth-fused 3D imagery on an immaterial display,” IEEE Trans. Vis. Comput. Graph. 15(1), 20–33 (2009).
[CrossRef]

Dorval, R. K.

G. E. Favalora, J. Napoli, D. M. Hall, R. K. Dorval, M. G. Giovinco, M. J. Richmond, and W. S. Chun, “100 million-voxel volumetric display,” Proc. SPIE 4712, 300–312 (2002).
[CrossRef]

Ernst, M. O.

S. J. Watt, K. Akeley, M. O. Ernst, and M. S. Banks, “Focus cues affect perceived depth,” J. Vis. 5(10), 834–862 (2005).
[CrossRef]

Favalora, G. E.

G. E. Favalora, J. Napoli, D. M. Hall, R. K. Dorval, M. G. Giovinco, M. J. Richmond, and W. S. Chun, “100 million-voxel volumetric display,” Proc. SPIE 4712, 300–312 (2002).
[CrossRef]

Gao, J.

Giovinco, M. G.

G. E. Favalora, J. Napoli, D. M. Hall, R. K. Dorval, M. G. Giovinco, M. J. Richmond, and W. S. Chun, “100 million-voxel volumetric display,” Proc. SPIE 4712, 300–312 (2002).
[CrossRef]

Girshick, A. R.

D. M. Hoffman, A. R. Girshick, K. Akeley, and M. S. Banks, “Vergence-accommodation conflicts hinder visual performance and cause visual fatigue,” J. Vis. 8(3), 1–30 (2008).
[CrossRef] [PubMed]

K. Akeley, S. J. Watt, A. R. Girshick, and M. S. Banks, “A stereo display prototype with multiple focal distances,” ACM Trans. Graph. 23(3), 804–813 (2004).
[CrossRef]

Goon, A.

Greivenkamp, J. E.

J. E. Greivenkamp, J. Schwiegerling, J. M. Miller, and M. D. Mellinger, “Visual acuity modeling using optical raytracing of schematic eyes,” Am. J. Ophthalmol. 120(2), 227–240 (1995).
[PubMed]

Hall, D. M.

G. E. Favalora, J. Napoli, D. M. Hall, R. K. Dorval, M. G. Giovinco, M. J. Richmond, and W. S. Chun, “100 million-voxel volumetric display,” Proc. SPIE 4712, 300–312 (2002).
[CrossRef]

Hands, P. J. W.

Heanue, J. F.

J. F. Heanue, M. C. Bashaw, and L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265(5173), 749–752 (1994).
[CrossRef] [PubMed]

Hesselink, L.

J. F. Heanue, M. C. Bashaw, and L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265(5173), 749–752 (1994).
[CrossRef] [PubMed]

Hoffman, D. M.

Höllerer, T.

C. Lee, S. Diverdi, and T. Höllerer, “Depth-fused 3D imagery on an immaterial display,” IEEE Trans. Vis. Comput. Graph. 15(1), 20–33 (2009).
[CrossRef]

Hua, H.

Kasthurirangan, S.

H. Cheng, J. K. Barnett, A. S. Vilupuru, J. D. Marsack, S. Kasthurirangan, R. A. Applegate, and A. Roorda, “A population study on changes in wave aberrations with accommodation,” J. Vis. 4(4), 272–280 (2004).
[CrossRef] [PubMed]

Kirby, A. K.

Krueger, M. W.

Lakshminarayanan, V.

Lee, C.

C. Lee, S. Diverdi, and T. Höllerer, “Depth-fused 3D imagery on an immaterial display,” IEEE Trans. Vis. Comput. Graph. 15(1), 20–33 (2009).
[CrossRef]

Lewis, J. W. L.

Liu, S.

S. Liu, H. Hua, and D. W. 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]

S. Liu and H. Hua, “Time-multiplexed dual-focal plane head-mounted display with a liquid lens,” Opt. Lett. 34(11), 1642–1644 (2009).
[CrossRef] [PubMed]

Love, G. D.

Marsack, J. D.

H. Cheng, J. K. Barnett, A. S. Vilupuru, J. D. Marsack, S. Kasthurirangan, R. A. Applegate, and A. Roorda, “A population study on changes in wave aberrations with accommodation,” J. Vis. 4(4), 272–280 (2004).
[CrossRef] [PubMed]

Mellinger, M. D.

J. E. Greivenkamp, J. Schwiegerling, J. M. Miller, and M. D. Mellinger, “Visual acuity modeling using optical raytracing of schematic eyes,” Am. J. Ophthalmol. 120(2), 227–240 (1995).
[PubMed]

Miller, J. M.

J. E. Greivenkamp, J. Schwiegerling, J. M. Miller, and M. D. Mellinger, “Visual acuity modeling using optical raytracing of schematic eyes,” Am. J. Ophthalmol. 120(2), 227–240 (1995).
[PubMed]

Mon-Williams, M.

J. P. Wann, S. Rushton, and M. Mon-Williams, “Natural problems for stereoscopic depth perception in virtual environments,” Vision Res. 35(19), 2731–2736 (1995).
[CrossRef] [PubMed]

M. Mon-Williams, J. P. Warm, and S. Rushton, “Binocular vision in a virtual world: visual deficits following the wearing of a head-mounted display,” Ophthalmic Physiol. Opt. 13(4), 387–391 (1993).
[CrossRef] [PubMed]

Napoli, J.

G. E. Favalora, J. Napoli, D. M. Hall, R. K. Dorval, M. G. Giovinco, M. J. Richmond, and W. S. Chun, “100 million-voxel volumetric display,” Proc. SPIE 4712, 300–312 (2002).
[CrossRef]

Ogle, K. N.

Ohtsuka, S.

S. Suyama, S. Ohtsuka, H. Takada, K. Uehira, and S. Sakai, “Apparent 3-D image perceived from luminance-modulated two 2-D images displayed at different depths,” Vision Res. 44(8), 785–793 (2004).
[CrossRef] [PubMed]

Pansing, C. W.

Richmond, M. J.

G. E. Favalora, J. Napoli, D. M. Hall, R. K. Dorval, M. G. Giovinco, M. J. Richmond, and W. S. Chun, “100 million-voxel volumetric display,” Proc. SPIE 4712, 300–312 (2002).
[CrossRef]

Rolland, J. P.

Roorda, A.

H. Cheng, J. K. Barnett, A. S. Vilupuru, J. D. Marsack, S. Kasthurirangan, R. A. Applegate, and A. Roorda, “A population study on changes in wave aberrations with accommodation,” J. Vis. 4(4), 272–280 (2004).
[CrossRef] [PubMed]

Rushton, S.

J. P. Wann, S. Rushton, and M. Mon-Williams, “Natural problems for stereoscopic depth perception in virtual environments,” Vision Res. 35(19), 2731–2736 (1995).
[CrossRef] [PubMed]

M. Mon-Williams, J. P. Warm, and S. Rushton, “Binocular vision in a virtual world: visual deficits following the wearing of a head-mounted display,” Ophthalmic Physiol. Opt. 13(4), 387–391 (1993).
[CrossRef] [PubMed]

Sakai, S.

S. Suyama, S. Ohtsuka, H. Takada, K. Uehira, and S. Sakai, “Apparent 3-D image perceived from luminance-modulated two 2-D images displayed at different depths,” Vision Res. 44(8), 785–793 (2004).
[CrossRef] [PubMed]

Schowengerdt, B. T.

B. T. Schowengerdt and E. J. Seibel, “True 3-D scanned voxel dis-plays using single or multiple light sources,” J. Soc. Inf. Disp. 14(2), 135–143 (2006).
[CrossRef]

Schwartz, J. T.

Schwiegerling, J.

J. E. Greivenkamp, J. Schwiegerling, J. M. Miller, and M. D. Mellinger, “Visual acuity modeling using optical raytracing of schematic eyes,” Am. J. Ophthalmol. 120(2), 227–240 (1995).
[PubMed]

Seibel, E. J.

B. T. Schowengerdt and E. J. Seibel, “True 3-D scanned voxel dis-plays using single or multiple light sources,” J. Soc. Inf. Disp. 14(2), 135–143 (2006).
[CrossRef]

Stiles, W. S.

W. S. Stiles and B. H. Crawford, “The luminous efficiency of rays entering the eye pupil at different points,” Proc. R. Soc. Lond., B 112(778), 428–450 (1933).
[CrossRef]

Suyama, S.

S. Suyama, S. Ohtsuka, H. Takada, K. Uehira, and S. Sakai, “Apparent 3-D image perceived from luminance-modulated two 2-D images displayed at different depths,” Vision Res. 44(8), 785–793 (2004).
[CrossRef] [PubMed]

S. Suyama, M. Date, and H. Takada, “Three-dimensional display system with dual frequency liquid crystal varifocal lens,” Jpn. J. Appl. Phys. 39(Part 1, No. 2A), 480–484 (2000).
[CrossRef]

Takada, H.

S. Suyama, S. Ohtsuka, H. Takada, K. Uehira, and S. Sakai, “Apparent 3-D image perceived from luminance-modulated two 2-D images displayed at different depths,” Vision Res. 44(8), 785–793 (2004).
[CrossRef] [PubMed]

S. Suyama, M. Date, and H. Takada, “Three-dimensional display system with dual frequency liquid crystal varifocal lens,” Jpn. J. Appl. Phys. 39(Part 1, No. 2A), 480–484 (2000).
[CrossRef]

Tan, B.

Uehira, K.

S. Suyama, S. Ohtsuka, H. Takada, K. Uehira, and S. Sakai, “Apparent 3-D image perceived from luminance-modulated two 2-D images displayed at different depths,” Vision Res. 44(8), 785–793 (2004).
[CrossRef] [PubMed]

Vilupuru, A. S.

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Figures (6)

Fig. 1
Fig. 1

Schematic model of a depth fused dual-focal plane display. Pixels on the front (A) and back (B) focal planes are located at z 1 and z 2 respectively from the eye, and the fused pixel (C) is located at z (z 2<z<z 1). All distances are defined in dioptric units.

Fig. 2
Fig. 2

(a) Modulation transfer functions of a depth-fused dual-focal plane display as a function of dioptric spacings of 0.2D (green circle markers), 0.4D (square), 0.6D (star), 0.8D (diamond), and 1.0D (triangle). (b) Modulation transfer functions as a function of accommodations with z = 1.3, 1.2, 1.1, 1.0, 0.9, 0.8, 0.7D. Medial focal plane is setup at 1D and the luminance ratio is L 1/L = 0.5. MTF of the ideal viewing condition is plotted as a light green dashed line, and defocused MTFs are plotted as red ( + 0.3D) and blue (−0.3D) dashed lines respectively in (a).

Fig. 3
Fig. 3

Simulated retinal images of a Snellen E target in a depth-fused dual-focal plane display, with z 1 = 1.3D, z 2 = 0.7D, and w 1 = 0.5. The accommodative distances are z = 1.3D in (a), (d), (g), (j); z = 1.0D in (b), (e), (h), (k); and z = 0.7D in (c), (f), (i), (l), respectively. The target spatial frequencies are v = 2cpd in (a), (b), (c); v = 5cpd in (d), (e), (f), v = 10cpd, in (g), (h), (i); and v = 30cpd in (j), (k), (l) respectively. The sizes of the above pictures are proportional to the relative sizes viewed on the retina.

Fig. 4
Fig. 4

Simulated accommodation cue versus depth filter curves (black solid line), and the nonlinearly-fitted curves (red dashed line) in a 6-focal plane DFD display, with z 1 = 3D, z 6 = 0D, and Δz = 0.6D. Blue and green dashed lines indicate the box and linear depth filters respectively.

Fig. 5
Fig. 5

(a) Depth map of a 3-D scene rendered by shaders, and retinal images of the same scene rendered by (b) box (c) linear and (d) nonlinear depth filters in a 6-focal plane DFD display.

Fig. 6
Fig. 6

Comparison of MTFs in a dual-focal plane DFD display by using linear (green circle) and nonlinear (red square) depth-weighted fusing functions respectively. Front and back focal planes are assumed at z 1 = 1.8D and z 2 = 1.2D respectively, and accommodation distance is z = 1.8D (a), 1.7D (b), 1.6D (c), 1.5D (d), 1.4D (e), 1.3D (f), and 1.2D (g), respectively.

Tables (2)

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Table 1 Parametric Dependence of Retinal Image Quality for n-Focal Plane DFD Displays

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Table 2 Parameters of Eq. (5) for a 6-Focal Plane DFD Display

Equations (5)

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L = L 1 ( z ) + L 2 ( z ) = w 1 ( z ) L + w 2 ( z ) L ,
z ^ = f ( w 1 , w 2 ) .
w i ( z ) = { g i ( z ) , z i z z i + 1 . ( 1 i < n ) 1 g i 1 ( z ) , z i 1 z z i . ( 2 i n ) .
P S F 12 ( z ) = w 1 ( z ) P S F 1 ( z , z 1 ) + w 2 ( z ) P S F 2 ( z , z 2 ) ,
g i ( z ) = L i ( z ) / L = 1 1 1 + exp ( z z ' i , i + 1 Δ z ' ) , z i z z i + 1 . ( 1 i < 6 ) ,

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