Abstract

Focus cues are incorrect in conventional stereoscopic displays. This causes a dissociation of vergence and accommodation, which leads to visual fatigue and perceptual distortions. Multi-plane displays can minimize these problems by creating nearly correct focus cues. But to create the appearance of continuous depth in a multi-plane display, one needs to use depth-weighted blending: i.e., distribute light intensity between adjacent planes. Akeley et al. [ACM Trans. Graph. 23, 804 (2004)] and Liu and Hua [Opt. Express 18, 11562 (2009)] described rather different rules for depth-weighted blending. We examined the effectiveness of those and other rules using a model of a typical human eye and biologically plausible metrics for image quality. We find that the linear blending rule proposed by Akeley and colleagues [ACM Trans. Graph. 23, 804 (2004)] is the best solution for natural stimuli.

© 2011 OSA

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    [CrossRef] [PubMed]

2011

T. Shibata, J. Kim, D. M. Hoffman, and M. S. Banks, “The zone of comfort: predicting visual discomfort with stereo displays,” J. Vis. 11(8), 1–29 (2011).
[CrossRef] [PubMed]

2010

K. J. MacKenzie, D. M. Hoffman, and S. J. Watt, “Accommodation to multiple-focal-plane displays: Implications for improving stereoscopic displays and for accommodation control,” J. Vis. 10(8), 1–20 (2010).
[CrossRef] [PubMed]

S. Liu and H. Hua, “A systematic method for designing depth-fused multi-focal plane three-dimensional displays,” Opt. Express 18(11), 11562–11573 (2010), http://www.opticsinfobase.org/abstract.cfm?URI=oe-18-11-11562 .
[CrossRef] [PubMed]

2009

2008

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), 33, 1–30 (2008).
[CrossRef] [PubMed]

S. Ravikumar, L. N. Thibos, and A. Bradley, “Calculation of retinal image quality for polychromatic light,” J. Opt. Soc. Am. A 25(10), 2395–2407 (2008).
[CrossRef] [PubMed]

2007

M. A. Georgeson, K. A. May, T. C. A. Freeman, and G. S. Hesse, “From filters to features: scale-space analysis of edge and blur coding in human vision,” J. Vis. 7(13), 7, 1–21 (2007).
[CrossRef] [PubMed]

2006

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

2005

T. Shibata, T. Kawai, K. Ohta, M. Otsuki, N. Miyake, Y. Yoshihara, and T. Iwasaki, “Stereoscopic 3-D display with optical correction for the reduction of the discrepancy between accommodation and convergence,” J. Soc. Inf. Disp. 13(8), 665–671 (2005).
[CrossRef]

M. Emoto, T. Niida, and F. Okano, “Repeated vergence adaptation causes the decline of visual functions in watching stereoscopic television,” J. Disp. Technol. 1(2), 328–340 (2005).
[CrossRef]

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] [PubMed]

2004

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]

A. Sullivan, “Depth cube solid-state 3D volumetric display,” Proc. SPIE 5291, 279–284 (2004).
[CrossRef]

L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, “Accuracy and precision of objective refraction from wavefront aberrations,” J. Vis. 4(4), 329–351 (2004).
[CrossRef] [PubMed]

2003

2002

2000

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).

D. R. Williams, G. Y. Yoon, J. Porter, A. Guirao, H. Hofer, and I. Cox, “Visual benefit of correcting higher order aberrations of the eye visual benefit of correcting higher order aberrations of the eye,” J. Refract. Surg. 16(5), S554–S559 (2000).
[PubMed]

1997

D. J. Field and N. Brady, “Visual sensitivity, blur and the sources of variability in the amplitude spectra of natural scenes,” Vision Res. 37(23), 3367–3383 (1997).
[CrossRef] [PubMed]

1996

J. P. Frisby, D. Buckley, and P. A. Duke, “Evidence for good recovery of lengths of real objects seen with natural stereo viewing,” Perception 25(2), 129–154 (1996).
[CrossRef] [PubMed]

1995

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]

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

1994

S. Mathews and P. B. Kruger, “Spatiotemporal transfer function of human accommodation,” Vision Res. 34(15), 1965–1980 (1994).
[CrossRef] [PubMed]

1987

M. S. Banks, W. S. Geisler, and P. J. Bennett, “The physical limits of grating visibility,” Vision Res. 27(11), 1915–1924 (1987).
[CrossRef] [PubMed]

1985

1980

D. A. Owens, “A comparison of accommodative responsiveness and contrast sensitivity for sinusoidal gratings,” Vision Res. 20(2), 159–167 (1980).
[CrossRef] [PubMed]

1978

W. N. Charman and J. Tucker, “Accommodation as a function of object form,” Am. J. Optom. Physiol. Opt. 55(2), 84–92 (1978).
[PubMed]

1973

V. V. Krishnan, S. Phillips, and L. Stark, “Frequency analysis of accommodation, accommodative vergence and disparity vergence,” Vision Res. 13(8), 1545–1554 (1973).
[CrossRef] [PubMed]

1972

E. M. Granger and K. N. Cupery, “Optical merit function (SQF), which correlates with subjective image judgments,” Photogr. Sci. Eng. 16, 221–230 (1972).

1965

D. G. Green and F. W. Campbell, “Effect of focus on the visual response to a sinusoidally modulated spatial stimulus,” J. Opt. Soc. Am. A 55(9), 1154–1157 (1965).
[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), 33, 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] [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]

Applegate, R. A.

L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, “Accuracy and precision of objective refraction from wavefront aberrations,” J. Vis. 4(4), 329–351 (2004).
[CrossRef] [PubMed]

Banks, M. S.

T. Shibata, J. Kim, D. M. Hoffman, and M. S. Banks, “The zone of comfort: predicting visual discomfort with stereo displays,” J. Vis. 11(8), 1–29 (2011).
[CrossRef] [PubMed]

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), 33, 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] [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]

M. S. Banks, W. S. Geisler, and P. J. Bennett, “The physical limits of grating visibility,” Vision Res. 27(11), 1915–1924 (1987).
[CrossRef] [PubMed]

Bennett, P. J.

M. S. Banks, W. S. Geisler, and P. J. Bennett, “The physical limits of grating visibility,” Vision Res. 27(11), 1915–1924 (1987).
[CrossRef] [PubMed]

Bradley, A.

Brady, N.

D. J. Field and N. Brady, “Visual sensitivity, blur and the sources of variability in the amplitude spectra of natural scenes,” Vision Res. 37(23), 3367–3383 (1997).
[CrossRef] [PubMed]

Buckley, D.

J. P. Frisby, D. Buckley, and P. A. Duke, “Evidence for good recovery of lengths of real objects seen with natural stereo viewing,” Perception 25(2), 129–154 (1996).
[CrossRef] [PubMed]

Campbell, F. W.

D. G. Green and F. W. Campbell, “Effect of focus on the visual response to a sinusoidally modulated spatial stimulus,” J. Opt. Soc. Am. A 55(9), 1154–1157 (1965).
[CrossRef]

Charman, W. N.

W. N. Charman and J. Tucker, “Accommodation as a function of object form,” Am. J. Optom. Physiol. Opt. 55(2), 84–92 (1978).
[PubMed]

Chen, Y. L.

Cheng, X.

Cox, I.

D. R. Williams, G. Y. Yoon, J. Porter, A. Guirao, H. Hofer, and I. Cox, “Visual benefit of correcting higher order aberrations of the eye visual benefit of correcting higher order aberrations of the eye,” J. Refract. Surg. 16(5), S554–S559 (2000).
[PubMed]

Cupery, K. N.

E. M. Granger and K. N. Cupery, “Optical merit function (SQF), which correlates with subjective image judgments,” Photogr. Sci. Eng. 16, 221–230 (1972).

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).

Dorval, R. K.

G. E. Favalora, J. Napoli, D. M. Hall, R. K. Dorval, M. G. Giovinco, M. J. Richmond, and et al.., “100 million-voxel volumetric display,” Proc. SPIE 712, 300–312 (2002).
[CrossRef]

Duke, P. A.

J. P. Frisby, D. Buckley, and P. A. Duke, “Evidence for good recovery of lengths of real objects seen with natural stereo viewing,” Perception 25(2), 129–154 (1996).
[CrossRef] [PubMed]

Emoto, M.

M. Emoto, T. Niida, and F. Okano, “Repeated vergence adaptation causes the decline of visual functions in watching stereoscopic television,” J. Disp. Technol. 1(2), 328–340 (2005).
[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] [PubMed]

Favalora, G. E.

G. E. Favalora, J. Napoli, D. M. Hall, R. K. Dorval, M. G. Giovinco, M. J. Richmond, and et al.., “100 million-voxel volumetric display,” Proc. SPIE 712, 300–312 (2002).
[CrossRef]

Field, D. J.

D. J. Field and N. Brady, “Visual sensitivity, blur and the sources of variability in the amplitude spectra of natural scenes,” Vision Res. 37(23), 3367–3383 (1997).
[CrossRef] [PubMed]

Fortuin, M.

M. Lambooij, W. IJsselsteijn, M. Fortuin, and I. Heynderickx, “Visual discomfort and visual fatigue of stereoscopic displays: a review,” J. Imaging Sci. Technol. 53(3), 030201 (2009).
[CrossRef]

Freeman, T. C. A.

M. A. Georgeson, K. A. May, T. C. A. Freeman, and G. S. Hesse, “From filters to features: scale-space analysis of edge and blur coding in human vision,” J. Vis. 7(13), 7, 1–21 (2007).
[CrossRef] [PubMed]

Frisby, J. P.

J. P. Frisby, D. Buckley, and P. A. Duke, “Evidence for good recovery of lengths of real objects seen with natural stereo viewing,” Perception 25(2), 129–154 (1996).
[CrossRef] [PubMed]

Gao, J.

Geisler, W. S.

M. S. Banks, W. S. Geisler, and P. J. Bennett, “The physical limits of grating visibility,” Vision Res. 27(11), 1915–1924 (1987).
[CrossRef] [PubMed]

Georgeson, M. A.

M. A. Georgeson, K. A. May, T. C. A. Freeman, and G. S. Hesse, “From filters to features: scale-space analysis of edge and blur coding in human vision,” J. Vis. 7(13), 7, 1–21 (2007).
[CrossRef] [PubMed]

Giovinco, M. G.

G. E. Favalora, J. Napoli, D. M. Hall, R. K. Dorval, M. G. Giovinco, M. J. Richmond, and et al.., “100 million-voxel volumetric display,” Proc. SPIE 712, 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), 33, 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]

Granger, E. M.

E. M. Granger and K. N. Cupery, “Optical merit function (SQF), which correlates with subjective image judgments,” Photogr. Sci. Eng. 16, 221–230 (1972).

Green, D. G.

D. G. Green and F. W. Campbell, “Effect of focus on the visual response to a sinusoidally modulated spatial stimulus,” J. Opt. Soc. Am. A 55(9), 1154–1157 (1965).
[CrossRef]

Greivenkamp, J. E.

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

Guirao, A.

D. R. Williams, G. Y. Yoon, J. Porter, A. Guirao, H. Hofer, and I. Cox, “Visual benefit of correcting higher order aberrations of the eye visual benefit of correcting higher order aberrations of the eye,” J. Refract. Surg. 16(5), S554–S559 (2000).
[PubMed]

Hall, D. M.

G. E. Favalora, J. Napoli, D. M. Hall, R. K. Dorval, M. G. Giovinco, M. J. Richmond, and et al.., “100 million-voxel volumetric display,” Proc. SPIE 712, 300–312 (2002).
[CrossRef]

Hands, P. J. W.

Hesse, G. S.

M. A. Georgeson, K. A. May, T. C. A. Freeman, and G. S. Hesse, “From filters to features: scale-space analysis of edge and blur coding in human vision,” J. Vis. 7(13), 7, 1–21 (2007).
[CrossRef] [PubMed]

Heynderickx, I.

M. Lambooij, W. IJsselsteijn, M. Fortuin, and I. Heynderickx, “Visual discomfort and visual fatigue of stereoscopic displays: a review,” J. Imaging Sci. Technol. 53(3), 030201 (2009).
[CrossRef]

Hofer, H.

D. R. Williams, G. Y. Yoon, J. Porter, A. Guirao, H. Hofer, and I. Cox, “Visual benefit of correcting higher order aberrations of the eye visual benefit of correcting higher order aberrations of the eye,” J. Refract. Surg. 16(5), S554–S559 (2000).
[PubMed]

Hoffman, D. M.

T. Shibata, J. Kim, D. M. Hoffman, and M. S. Banks, “The zone of comfort: predicting visual discomfort with stereo displays,” J. Vis. 11(8), 1–29 (2011).
[CrossRef] [PubMed]

K. J. MacKenzie, D. M. Hoffman, and S. J. Watt, “Accommodation to multiple-focal-plane displays: Implications for improving stereoscopic displays and for accommodation control,” J. Vis. 10(8), 1–20 (2010).
[CrossRef] [PubMed]

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), 33, 1–30 (2008).
[CrossRef] [PubMed]

Hong, X.

L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, “Accuracy and precision of objective refraction from wavefront aberrations,” J. Vis. 4(4), 329–351 (2004).
[CrossRef] [PubMed]

L. N. Thibos, X. Hong, A. Bradley, and X. Cheng, “Statistical variation of aberration structure and image quality in a normal population of healthy eyes,” J. Opt. Soc. Am. A 19(12), 2329–2348 (2002).
[CrossRef] [PubMed]

Hua, H.

IJsselsteijn, W.

M. Lambooij, W. IJsselsteijn, M. Fortuin, and I. Heynderickx, “Visual discomfort and visual fatigue of stereoscopic displays: a review,” J. Imaging Sci. Technol. 53(3), 030201 (2009).
[CrossRef]

Iwasaki, T.

T. Shibata, T. Kawai, K. Ohta, M. Otsuki, N. Miyake, Y. Yoshihara, and T. Iwasaki, “Stereoscopic 3-D display with optical correction for the reduction of the discrepancy between accommodation and convergence,” J. Soc. Inf. Disp. 13(8), 665–671 (2005).
[CrossRef]

Kawai, T.

T. Shibata, T. Kawai, K. Ohta, M. Otsuki, N. Miyake, Y. Yoshihara, and T. Iwasaki, “Stereoscopic 3-D display with optical correction for the reduction of the discrepancy between accommodation and convergence,” J. Soc. Inf. Disp. 13(8), 665–671 (2005).
[CrossRef]

Kim, J.

T. Shibata, J. Kim, D. M. Hoffman, and M. S. Banks, “The zone of comfort: predicting visual discomfort with stereo displays,” J. Vis. 11(8), 1–29 (2011).
[CrossRef] [PubMed]

Kirby, A. K.

Krishnan, V. V.

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Kruger, P. B.

S. Mathews and P. B. Kruger, “Spatiotemporal transfer function of human accommodation,” Vision Res. 34(15), 1965–1980 (1994).
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Lambooij, M.

M. Lambooij, W. IJsselsteijn, M. Fortuin, and I. Heynderickx, “Visual discomfort and visual fatigue of stereoscopic displays: a review,” J. Imaging Sci. Technol. 53(3), 030201 (2009).
[CrossRef]

Lewis, J. W. L.

Liu, S.

Love, G. D.

MacKenzie, K. J.

K. J. MacKenzie, D. M. Hoffman, and S. J. Watt, “Accommodation to multiple-focal-plane displays: Implications for improving stereoscopic displays and for accommodation control,” J. Vis. 10(8), 1–20 (2010).
[CrossRef] [PubMed]

Mathews, S.

S. Mathews and P. B. Kruger, “Spatiotemporal transfer function of human accommodation,” Vision Res. 34(15), 1965–1980 (1994).
[CrossRef] [PubMed]

May, K. A.

M. A. Georgeson, K. A. May, T. C. A. Freeman, and G. S. Hesse, “From filters to features: scale-space analysis of edge and blur coding in human vision,” J. Vis. 7(13), 7, 1–21 (2007).
[CrossRef] [PubMed]

Mellinger, M. D.

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

Miller, J. M.

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

Miyake, N.

T. Shibata, T. Kawai, K. Ohta, M. Otsuki, N. Miyake, Y. Yoshihara, and T. Iwasaki, “Stereoscopic 3-D display with optical correction for the reduction of the discrepancy between accommodation and convergence,” J. Soc. Inf. Disp. 13(8), 665–671 (2005).
[CrossRef]

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).
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Napoli, J.

G. E. Favalora, J. Napoli, D. M. Hall, R. K. Dorval, M. G. Giovinco, M. J. Richmond, and et al.., “100 million-voxel volumetric display,” Proc. SPIE 712, 300–312 (2002).
[CrossRef]

Niida, T.

M. Emoto, T. Niida, and F. Okano, “Repeated vergence adaptation causes the decline of visual functions in watching stereoscopic television,” J. Disp. Technol. 1(2), 328–340 (2005).
[CrossRef]

Ohta, K.

T. Shibata, T. Kawai, K. Ohta, M. Otsuki, N. Miyake, Y. Yoshihara, and T. Iwasaki, “Stereoscopic 3-D display with optical correction for the reduction of the discrepancy between accommodation and convergence,” J. Soc. Inf. Disp. 13(8), 665–671 (2005).
[CrossRef]

Okano, F.

M. Emoto, T. Niida, and F. Okano, “Repeated vergence adaptation causes the decline of visual functions in watching stereoscopic television,” J. Disp. Technol. 1(2), 328–340 (2005).
[CrossRef]

Otsuki, M.

T. Shibata, T. Kawai, K. Ohta, M. Otsuki, N. Miyake, Y. Yoshihara, and T. Iwasaki, “Stereoscopic 3-D display with optical correction for the reduction of the discrepancy between accommodation and convergence,” J. Soc. Inf. Disp. 13(8), 665–671 (2005).
[CrossRef]

Owens, D. A.

D. A. Owens, “A comparison of accommodative responsiveness and contrast sensitivity for sinusoidal gratings,” Vision Res. 20(2), 159–167 (1980).
[CrossRef] [PubMed]

Phillips, S.

V. V. Krishnan, S. Phillips, and L. Stark, “Frequency analysis of accommodation, accommodative vergence and disparity vergence,” Vision Res. 13(8), 1545–1554 (1973).
[CrossRef] [PubMed]

Porter, J.

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[PubMed]

Ravikumar, S.

Richmond, M. J.

G. E. Favalora, J. Napoli, D. M. Hall, R. K. Dorval, M. G. Giovinco, M. J. Richmond, and et al.., “100 million-voxel volumetric display,” Proc. SPIE 712, 300–312 (2002).
[CrossRef]

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]

Schowengerdt, B. T.

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

Schwiegerling, J.

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

Seibel, E. J.

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

Shibata, T.

T. Shibata, J. Kim, D. M. Hoffman, and M. S. Banks, “The zone of comfort: predicting visual discomfort with stereo displays,” J. Vis. 11(8), 1–29 (2011).
[CrossRef] [PubMed]

T. Shibata, T. Kawai, K. Ohta, M. Otsuki, N. Miyake, Y. Yoshihara, and T. Iwasaki, “Stereoscopic 3-D display with optical correction for the reduction of the discrepancy between accommodation and convergence,” J. Soc. Inf. Disp. 13(8), 665–671 (2005).
[CrossRef]

Stark, L.

V. V. Krishnan, S. Phillips, and L. Stark, “Frequency analysis of accommodation, accommodative vergence and disparity vergence,” Vision Res. 13(8), 1545–1554 (1973).
[CrossRef] [PubMed]

Sullivan, A.

A. Sullivan, “Depth cube solid-state 3D volumetric display,” Proc. SPIE 5291, 279–284 (2004).
[CrossRef]

Suyama, S.

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).

Takada, H.

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).

Tan, B.

Thibos, L. N.

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W. N. Charman and J. Tucker, “Accommodation as a function of object form,” Am. J. Optom. Physiol. Opt. 55(2), 84–92 (1978).
[PubMed]

Wann, J. P.

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]

Watt, S. J.

K. J. MacKenzie, D. M. Hoffman, and S. J. Watt, “Accommodation to multiple-focal-plane displays: Implications for improving stereoscopic displays and for accommodation control,” J. Vis. 10(8), 1–20 (2010).
[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] [PubMed]

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[CrossRef]

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G. Y. Yoon and D. R. Williams, “Visual performance after correcting the monochromatic and chromatic aberrations of the eye,” J. Opt. Soc. Am. A 19(2), 266–275 (2002).
[CrossRef] [PubMed]

D. R. Williams, G. Y. Yoon, J. Porter, A. Guirao, H. Hofer, and I. Cox, “Visual benefit of correcting higher order aberrations of the eye visual benefit of correcting higher order aberrations of the eye,” J. Refract. Surg. 16(5), S554–S559 (2000).
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[CrossRef] [PubMed]

Yoon, G. Y.

G. Y. Yoon and D. R. Williams, “Visual performance after correcting the monochromatic and chromatic aberrations of the eye,” J. Opt. Soc. Am. A 19(2), 266–275 (2002).
[CrossRef] [PubMed]

D. R. Williams, G. Y. Yoon, J. Porter, A. Guirao, H. Hofer, and I. Cox, “Visual benefit of correcting higher order aberrations of the eye visual benefit of correcting higher order aberrations of the eye,” J. Refract. Surg. 16(5), S554–S559 (2000).
[PubMed]

Yoshihara, Y.

T. Shibata, T. Kawai, K. Ohta, M. Otsuki, N. Miyake, Y. Yoshihara, and T. Iwasaki, “Stereoscopic 3-D display with optical correction for the reduction of the discrepancy between accommodation and convergence,” J. Soc. Inf. Disp. 13(8), 665–671 (2005).
[CrossRef]

ACM Trans. Graph.

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]

Am. J. Ophthalmol.

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

Am. J. Optom. Physiol. Opt.

W. N. Charman and J. Tucker, “Accommodation as a function of object form,” Am. J. Optom. Physiol. Opt. 55(2), 84–92 (1978).
[PubMed]

J. Disp. Technol.

M. Emoto, T. Niida, and F. Okano, “Repeated vergence adaptation causes the decline of visual functions in watching stereoscopic television,” J. Disp. Technol. 1(2), 328–340 (2005).
[CrossRef]

J. Imaging Sci. Technol.

M. Lambooij, W. IJsselsteijn, M. Fortuin, and I. Heynderickx, “Visual discomfort and visual fatigue of stereoscopic displays: a review,” J. Imaging Sci. Technol. 53(3), 030201 (2009).
[CrossRef]

J. Opt. Soc. Am. A

J. Refract. Surg.

D. R. Williams, G. Y. Yoon, J. Porter, A. Guirao, H. Hofer, and I. Cox, “Visual benefit of correcting higher order aberrations of the eye visual benefit of correcting higher order aberrations of the eye,” J. Refract. Surg. 16(5), S554–S559 (2000).
[PubMed]

J. Soc. Inf. Disp.

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

T. Shibata, T. Kawai, K. Ohta, M. Otsuki, N. Miyake, Y. Yoshihara, and T. Iwasaki, “Stereoscopic 3-D display with optical correction for the reduction of the discrepancy between accommodation and convergence,” J. Soc. Inf. Disp. 13(8), 665–671 (2005).
[CrossRef]

J. Vis.

M. A. Georgeson, K. A. May, T. C. A. Freeman, and G. S. Hesse, “From filters to features: scale-space analysis of edge and blur coding in human vision,” J. Vis. 7(13), 7, 1–21 (2007).
[CrossRef] [PubMed]

T. Shibata, J. Kim, D. M. Hoffman, and M. S. Banks, “The zone of comfort: predicting visual discomfort with stereo displays,” J. Vis. 11(8), 1–29 (2011).
[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] [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), 33, 1–30 (2008).
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[CrossRef] [PubMed]

K. J. MacKenzie, D. M. Hoffman, and S. J. Watt, “Accommodation to multiple-focal-plane displays: Implications for improving stereoscopic displays and for accommodation control,” J. Vis. 10(8), 1–20 (2010).
[CrossRef] [PubMed]

Jpn. J. Appl. Phys.

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).

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E. M. Granger and K. N. Cupery, “Optical merit function (SQF), which correlates with subjective image judgments,” Photogr. Sci. Eng. 16, 221–230 (1972).

Proc. SPIE

A. Sullivan, “Depth cube solid-state 3D volumetric display,” Proc. SPIE 5291, 279–284 (2004).
[CrossRef]

G. E. Favalora, J. Napoli, D. M. Hall, R. K. Dorval, M. G. Giovinco, M. J. Richmond, and et al.., “100 million-voxel volumetric display,” Proc. SPIE 712, 300–312 (2002).
[CrossRef]

Vision Res.

D. A. Owens, “A comparison of accommodative responsiveness and contrast sensitivity for sinusoidal gratings,” Vision Res. 20(2), 159–167 (1980).
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S. Mathews and P. B. Kruger, “Spatiotemporal transfer function of human accommodation,” Vision Res. 34(15), 1965–1980 (1994).
[CrossRef] [PubMed]

V. V. Krishnan, S. Phillips, and L. Stark, “Frequency analysis of accommodation, accommodative vergence and disparity vergence,” Vision Res. 13(8), 1545–1554 (1973).
[CrossRef] [PubMed]

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).
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D. J. Field and N. Brady, “Visual sensitivity, blur and the sources of variability in the amplitude spectra of natural scenes,” Vision Res. 37(23), 3367–3383 (1997).
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Figures (10)

Fig. 1
Fig. 1

Multi-plane display and depth-weighted blending. Left panel: Parameters of multi-plane display. Two planes at distances in diopters of Dn and Df are used to display images to the eye. To simulate a distance Ds (also in diopters), a depth-weighted blending rule is used to determine the intensities In and If for the near and far image planes, respectively. The image points on those planes are aligned such that they sum on the viewer’s retina to create the desired intensity. The viewer’s eye is focused at some distance (not indicated) that affects the formation of the retinal images from the near and far planes. Right panel: The intensities In and If proscribed by the linear depth-weighted blending rule (Eq. (1) to simulate distance Ds (in diopters). The green and red lines represent respectively the intensities In and If.

Fig. 2
Fig. 2

The results of Liu and Hua [16]. The accommodative distance that maximizes the area under the MTF is plotted as a function of the ratio of pixel intensities on two image planes, one at 0D and the other at 0.6D (indicated by arrows on right). The intensity ratio is I0.6 / (I0.6 + I0) where I0.6 and I0 are the intensities at the 0.6D and 0D planes, respectively. The black diagonal line represents the linear weighting rule. The blue curve represents Liu and Hua’s findings from Table 2 in their paper.

Fig. 3
Fig. 3

Modulation transfer as a function of accommodative distance for different spatial frequencies. The monochromatic (550nm) stimulus is presented on one plane at 0D. The eye is diffraction limited with a 4mm pupil. Different symbols represent different spatial frequencies. The position of the image plane is indicated by the arrow in the lower left.

Fig. 4
Fig. 4

Modulation transfer as a function of accommodation distance for a two-plane display. The model eye is diffraction limited with a 4mm pupil. The stimulus is monochromatic (550nm). The planes are positioned at 0 and 0.6D (indicated by arrows). The intensity ratio and spatial frequency associated with each set of data are given in the legend.

Fig. 5
Fig. 5

Area MTF as a function of accommodation distance for a two-plane display. The model eye is diffraction limited with a 4mm pupil. The stimulus is monochromatic (550nm) and contains all spatial frequencies at equal contrast from 0 to 30 cpd. The planes are positioned at 0 and 0.6 D (indicated by arrows). MTF area was calculated from 0 to 30cpd for intensity ratios of 0.5, 0.25, and 0.

Fig. 6
Fig. 6

Accommodation distance that maximizes MTF area for each intensity ratio. The model eye is diffraction-limited with a 4mm pupil. The stimulus is monochromatic (550nm). The stimulus consisted of one spatial frequency at 4, 9, or 21cpd, or contained all spatial frequencies at equal contrast from 0 to 30 cpd. The image planes were positioned at 0 and 0.6D as indicated by the arrows.

Fig. 7
Fig. 7

The neural transfer function (NTF). The NTF is the effective contrast of the neural image divided by retinal-image contrast at different spatial frequencies. Adapted from [21].

Fig. 8
Fig. 8

Accommodation distance that maximizes the area under the weighted MTF for each intensity ratio. The model eye is a typical human eye with a 4mm pupil. The stimulus is white. The stimulus consisted of one spatial frequency at 4, 9, or 21cpd, or contained all spatial frequencies from 0 to 30cpd with amplitudes proportional to 1/f. The image planes were positioned at 0 and 0.6D as indicated by the arrows.

Fig. 9
Fig. 9

Contrast change as a function of accommodation change for different displays. Each panel plots the distance to which the eye is accommodated on the abscissa and the MTF area on the ordinate. Different colors represent different positions of the stimulus: black for 0D, blue for 0.15D, red for 0.3D, green for 0.45D, and purple for 0.6D. The parameters of the model eye are given in Table 1. Upper left: MTF area (a measure of retinal-image contrast) as a function of accommodation for a white, broadband stimulus with 1/f spectrum presented at five different distances in the real world. The function has been weighted by the NTF of Fig. 7. Upper right: Contrast as a function of accommodation for the same stimulus presented on a multi-plane display with the image planes at 0 and 0.6D and the linear, depth-weighted blending rule. Lower left: Contrast as a function of accommodation for the same stimulus using Liu and Hua’s non-linear blending rule [16]. Lower right: Contrast as a function of accommodation for the same stimulus using a box-function blending rule. The box rule assigned an intensity ratio of 0 for all simulated distances of 0-0.3D and of 1 for all simulated distances of 0.3-0.6D.

Fig. 10
Fig. 10

Perceived optical quality for a thin white line receding in depth. We calculated Visual Strehl ratios (observed PSF peak divided by PSF peak for well-focused, diffraction-limited eye, where the PSFs have been weighted by the NTF [35]) for different horizontal positions along the line. Black, blue, red, and green symbols represent, respectively, the ratios for a real-world stimulus, a multi-plane stimulus with the linear blending rule, a multi-plane stimulus with Liu and Hua’s non-linear blending rule [16], and a multi-plane stimulus with a box-function rule. The panels show the results when the eye is accommodated to 0D (the far end of the line), 0.15, 0.3, 0.45, and 0.6D (the near end of the line). The parameters of the model eye are given in Table 1.

Tables (1)

Tables Icon

Table 1 Aberration Vector of Model Eye*

Equations (3)

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

I n =[ 1 ( D n D s ) ( D n D f ) ] I s I f =[ ( D n D s ) ( D n D f ) ] I s .
r M 0.6 (f)+(1r) M 0 (f)
r(x,y)=o(x,y)*p(x,y)

Metrics