Abstract

A theoretical investigation of rendered depth and angular errors, or Albertian errors, linked to natural eye movements in binocular head-mounted displays (HMDs) is presented for three possible eye-point locations: the center of the entrance pupil, the nodal point, and the center of rotation of the eye. A numerical quantification was conducted for both the pupil and the center of rotation of the eye under the assumption that the user will operate solely in either the near field under an associated instrumentation setting or the far field under a different setting. Under these conditions, the eyes are taken to gaze in the plane of the stereoscopic images. Across conditions, results show that the center of the entrance pupil minimizes rendered angular errors, while the center of rotation minimizes rendered position errors. Significantly, this investigation quantifies that under proper setting of the HMD and correct choice of the eye points, rendered depth and angular errors can be brought to be either negligible or within specification of even the most stringent applications in performance of tasks in either the near field or the far field.

© 2004 Optical Society of America

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References

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  1. J. P. Rolland, C. Meyer, K. Arthur, E. Rinalducci, “Methods of adjustments versus method of constant stimuli in the quantification of accuracy and precision of rendered depth in head-mounted displays,” Presence Teleoperators Virtual Environ. 11, 610–625 (2002).
    [CrossRef]
  2. J. E. Cutting, Perception with an Eye for Motion (MIT Press, Cambridge, Mass., 1986).
  3. J. D. Foley, A. van Dam, Fundamentals of Interactive Computer Graphics (Addison-Wesley, Reading, Mass., 1984).
  4. W. Robinett, J. P. Rolland, “A computational model for the stereoscopic optics of a head-mounted display,” Presence Teleoperators Virtual Environ. 1, 45–62 (1992).
  5. I. P. Howard, B. J. Rogers, Binocular Vision and Stere-opsis, No. 29 of Oxford Psychologic Series (Oxford U. Press, New York, 1995), pp. 591–593.
  6. R. L. Holloway, “Registration errors in augmented reality systems,” Ph.D. dissertation (University of North Carolina at Chapel Hill, Chapel Hill, N.Car., 1994) (unpublished).
  7. J. P. Rolland, D. Ariely, W. Gibson, “Towards quantifying depth and size perception in virtual environments,” Presence Teleoperators Virtual Environ. 4, 24–49 (1995).
  8. J. Siderov, R. S. Harwerth, “Precision of stereoscopic depth perception from double images,” Vision Res. 33, 1553–1560 (1993).
    [CrossRef] [PubMed]
  9. D. Brewster, “On the law of visible position in single and binocular vision, and on the representation of solid figures by the union of dissimilar plane pictures on the retina,” Trans. R. Soc. Edinburgh. 15, 349–368 (1844).
    [CrossRef]
  10. J. P. Wann, S. Rushton, M. Mon-Williams, “Natural problems for stereoscopic depth perception in virtual environments,” Vision Res. 35, 2731–2736 (1995).
    [CrossRef] [PubMed]
  11. K. N. Ogle, P. Boeder, “Distortion of stereoscopic spatial localization,” J. Opt. Soc. Am. 38, 723–733 (1948).
    [CrossRef] [PubMed]
  12. K. N. Ogle, “Spatial localization through binocular vision,” in The Eye (Academic, New York, 1962), Vol. 4, pp. 409–417.
  13. J. P. Rolland, “Head-mounted displays for virtual environments: the optical interface,” (invited paper), in International Lens Design Conference, Vol. 22 of 1994 OSA Proceedings Series (Optical Society of America, Washington, D.C., 1994), pp. 329–333.
  14. D. S. Goodman, “General principles of geometrical optics,” in Handbook of Optics, Vol. 1, 2nd ed., M. Bass, ed. (McGraw-Hill, New York, 1995), pp. 1.3–1.109.
  15. M. Ye, A. Bradley, L. N. Thibos, X. Zhang, “Interocular differences in transverse chromatic aberration determine chromostereopsis for small pupils,” Vision Res. 32, 1787–1796 (1991).
    [CrossRef]
  16. P. Simonet, M. C. W. Campbell, “Effect of illuminance on the directions of chromostereopsis and transverse chromatic aberration observed with natural pupils,” Ophthalmic Physiol. Opt. 10, 271–279 (1990).
    [CrossRef] [PubMed]
  17. R. B. Rabbetts, ed., Bennett and Rabbetts’ Clinal Visual Optics, 3rd ed. (Butterworth Heinemann, Oxford, UK, 1998), pp. 220–221.
  18. W. S. Stiles, B. H. Crawford, “The luminous efficiency of rays entering the eye pupil at different points,” Proc. R. Soc. London 112, 428–450 (1933).
    [CrossRef]
  19. C. Deering, “High resolution virtual reality,” Comput. Graph. 26(2), 195–202 (1992).
    [CrossRef]
  20. G. A. Fry, Geometrical optics (Chilton book company, Philadelphia, Pa., 1969).
  21. L. Vaissie, J. P. Rolland, “Eye-tracking integration in head-mounted displays,” U.S. patent6,433,760B1 (August13, 2002).
  22. J. P. Rolland, A. Yoshida, L. D. Davis, J. H. Reif, “High-resolution inset head-mounted display,” Appl. Opt. 37, 4183–4193 (1998).
    [CrossRef]
  23. J. P. Rolland, M. Krueger, A. Goon, “Multi-focal planes in head-mounted displays,” Appl. Opt. 39, 3209–3215 (2000).
    [CrossRef]
  24. J. P. Rolland, H. Fuchs, “Optical versus video see-through head-mounted displays,” in Fundamentals of Wearable Computers and Augmented Reality, W. Barfield, T. Caudell, eds. (Erlbaum, Mahwah, N.J., 2001), 113–156.
  25. D. B. Diner, D. H. Fender, Human Engineering in Stereoscopic Viewing Devices (Plenum, New York, 1993).
  26. L. Davis, J. Rolland, F. Hamza-Lup, Y. Ha, J. Norfleet, B. Pettitt, C. Imielinska, “Alice’s Adventures in Wonderland: a unique technology enabling a continuum of virtual environment experiences,” IEEE Comput. Graphics Appl. 23, 10–12 (2003).
    [CrossRef]
  27. K. R. Boff, L. Kaufman, J. P. Thomas, Handbook of Perception and Human Performance (Wiley, New York, 1986).

2003

L. Davis, J. Rolland, F. Hamza-Lup, Y. Ha, J. Norfleet, B. Pettitt, C. Imielinska, “Alice’s Adventures in Wonderland: a unique technology enabling a continuum of virtual environment experiences,” IEEE Comput. Graphics Appl. 23, 10–12 (2003).
[CrossRef]

2002

J. P. Rolland, C. Meyer, K. Arthur, E. Rinalducci, “Methods of adjustments versus method of constant stimuli in the quantification of accuracy and precision of rendered depth in head-mounted displays,” Presence Teleoperators Virtual Environ. 11, 610–625 (2002).
[CrossRef]

2000

1998

1995

J. P. Rolland, D. Ariely, W. Gibson, “Towards quantifying depth and size perception in virtual environments,” Presence Teleoperators Virtual Environ. 4, 24–49 (1995).

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

1993

J. Siderov, R. S. Harwerth, “Precision of stereoscopic depth perception from double images,” Vision Res. 33, 1553–1560 (1993).
[CrossRef] [PubMed]

1992

W. Robinett, J. P. Rolland, “A computational model for the stereoscopic optics of a head-mounted display,” Presence Teleoperators Virtual Environ. 1, 45–62 (1992).

C. Deering, “High resolution virtual reality,” Comput. Graph. 26(2), 195–202 (1992).
[CrossRef]

1991

M. Ye, A. Bradley, L. N. Thibos, X. Zhang, “Interocular differences in transverse chromatic aberration determine chromostereopsis for small pupils,” Vision Res. 32, 1787–1796 (1991).
[CrossRef]

1990

P. Simonet, M. C. W. Campbell, “Effect of illuminance on the directions of chromostereopsis and transverse chromatic aberration observed with natural pupils,” Ophthalmic Physiol. Opt. 10, 271–279 (1990).
[CrossRef] [PubMed]

1948

1933

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

1844

D. Brewster, “On the law of visible position in single and binocular vision, and on the representation of solid figures by the union of dissimilar plane pictures on the retina,” Trans. R. Soc. Edinburgh. 15, 349–368 (1844).
[CrossRef]

Ariely, D.

J. P. Rolland, D. Ariely, W. Gibson, “Towards quantifying depth and size perception in virtual environments,” Presence Teleoperators Virtual Environ. 4, 24–49 (1995).

Arthur, K.

J. P. Rolland, C. Meyer, K. Arthur, E. Rinalducci, “Methods of adjustments versus method of constant stimuli in the quantification of accuracy and precision of rendered depth in head-mounted displays,” Presence Teleoperators Virtual Environ. 11, 610–625 (2002).
[CrossRef]

Boeder, P.

Boff, K. R.

K. R. Boff, L. Kaufman, J. P. Thomas, Handbook of Perception and Human Performance (Wiley, New York, 1986).

Bradley, A.

M. Ye, A. Bradley, L. N. Thibos, X. Zhang, “Interocular differences in transverse chromatic aberration determine chromostereopsis for small pupils,” Vision Res. 32, 1787–1796 (1991).
[CrossRef]

Brewster, D.

D. Brewster, “On the law of visible position in single and binocular vision, and on the representation of solid figures by the union of dissimilar plane pictures on the retina,” Trans. R. Soc. Edinburgh. 15, 349–368 (1844).
[CrossRef]

Campbell, M. C. W.

P. Simonet, M. C. W. Campbell, “Effect of illuminance on the directions of chromostereopsis and transverse chromatic aberration observed with natural pupils,” Ophthalmic Physiol. Opt. 10, 271–279 (1990).
[CrossRef] [PubMed]

Crawford, B. H.

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

Cutting, J. E.

J. E. Cutting, Perception with an Eye for Motion (MIT Press, Cambridge, Mass., 1986).

Davis, L.

L. Davis, J. Rolland, F. Hamza-Lup, Y. Ha, J. Norfleet, B. Pettitt, C. Imielinska, “Alice’s Adventures in Wonderland: a unique technology enabling a continuum of virtual environment experiences,” IEEE Comput. Graphics Appl. 23, 10–12 (2003).
[CrossRef]

Davis, L. D.

Deering, C.

C. Deering, “High resolution virtual reality,” Comput. Graph. 26(2), 195–202 (1992).
[CrossRef]

Diner, D. B.

D. B. Diner, D. H. Fender, Human Engineering in Stereoscopic Viewing Devices (Plenum, New York, 1993).

Fender, D. H.

D. B. Diner, D. H. Fender, Human Engineering in Stereoscopic Viewing Devices (Plenum, New York, 1993).

Foley, J. D.

J. D. Foley, A. van Dam, Fundamentals of Interactive Computer Graphics (Addison-Wesley, Reading, Mass., 1984).

Fry, G. A.

G. A. Fry, Geometrical optics (Chilton book company, Philadelphia, Pa., 1969).

Fuchs, H.

J. P. Rolland, H. Fuchs, “Optical versus video see-through head-mounted displays,” in Fundamentals of Wearable Computers and Augmented Reality, W. Barfield, T. Caudell, eds. (Erlbaum, Mahwah, N.J., 2001), 113–156.

Gibson, W.

J. P. Rolland, D. Ariely, W. Gibson, “Towards quantifying depth and size perception in virtual environments,” Presence Teleoperators Virtual Environ. 4, 24–49 (1995).

Goodman, D. S.

D. S. Goodman, “General principles of geometrical optics,” in Handbook of Optics, Vol. 1, 2nd ed., M. Bass, ed. (McGraw-Hill, New York, 1995), pp. 1.3–1.109.

Goon, A.

Ha, Y.

L. Davis, J. Rolland, F. Hamza-Lup, Y. Ha, J. Norfleet, B. Pettitt, C. Imielinska, “Alice’s Adventures in Wonderland: a unique technology enabling a continuum of virtual environment experiences,” IEEE Comput. Graphics Appl. 23, 10–12 (2003).
[CrossRef]

Hamza-Lup, F.

L. Davis, J. Rolland, F. Hamza-Lup, Y. Ha, J. Norfleet, B. Pettitt, C. Imielinska, “Alice’s Adventures in Wonderland: a unique technology enabling a continuum of virtual environment experiences,” IEEE Comput. Graphics Appl. 23, 10–12 (2003).
[CrossRef]

Harwerth, R. S.

J. Siderov, R. S. Harwerth, “Precision of stereoscopic depth perception from double images,” Vision Res. 33, 1553–1560 (1993).
[CrossRef] [PubMed]

Holloway, R. L.

R. L. Holloway, “Registration errors in augmented reality systems,” Ph.D. dissertation (University of North Carolina at Chapel Hill, Chapel Hill, N.Car., 1994) (unpublished).

Howard, I. P.

I. P. Howard, B. J. Rogers, Binocular Vision and Stere-opsis, No. 29 of Oxford Psychologic Series (Oxford U. Press, New York, 1995), pp. 591–593.

Imielinska, C.

L. Davis, J. Rolland, F. Hamza-Lup, Y. Ha, J. Norfleet, B. Pettitt, C. Imielinska, “Alice’s Adventures in Wonderland: a unique technology enabling a continuum of virtual environment experiences,” IEEE Comput. Graphics Appl. 23, 10–12 (2003).
[CrossRef]

Kaufman, L.

K. R. Boff, L. Kaufman, J. P. Thomas, Handbook of Perception and Human Performance (Wiley, New York, 1986).

Krueger, M.

Meyer, C.

J. P. Rolland, C. Meyer, K. Arthur, E. Rinalducci, “Methods of adjustments versus method of constant stimuli in the quantification of accuracy and precision of rendered depth in head-mounted displays,” Presence Teleoperators Virtual Environ. 11, 610–625 (2002).
[CrossRef]

Mon-Williams, M.

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

Norfleet, J.

L. Davis, J. Rolland, F. Hamza-Lup, Y. Ha, J. Norfleet, B. Pettitt, C. Imielinska, “Alice’s Adventures in Wonderland: a unique technology enabling a continuum of virtual environment experiences,” IEEE Comput. Graphics Appl. 23, 10–12 (2003).
[CrossRef]

Ogle, K. N.

K. N. Ogle, P. Boeder, “Distortion of stereoscopic spatial localization,” J. Opt. Soc. Am. 38, 723–733 (1948).
[CrossRef] [PubMed]

K. N. Ogle, “Spatial localization through binocular vision,” in The Eye (Academic, New York, 1962), Vol. 4, pp. 409–417.

Pettitt, B.

L. Davis, J. Rolland, F. Hamza-Lup, Y. Ha, J. Norfleet, B. Pettitt, C. Imielinska, “Alice’s Adventures in Wonderland: a unique technology enabling a continuum of virtual environment experiences,” IEEE Comput. Graphics Appl. 23, 10–12 (2003).
[CrossRef]

Reif, J. H.

Rinalducci, E.

J. P. Rolland, C. Meyer, K. Arthur, E. Rinalducci, “Methods of adjustments versus method of constant stimuli in the quantification of accuracy and precision of rendered depth in head-mounted displays,” Presence Teleoperators Virtual Environ. 11, 610–625 (2002).
[CrossRef]

Robinett, W.

W. Robinett, J. P. Rolland, “A computational model for the stereoscopic optics of a head-mounted display,” Presence Teleoperators Virtual Environ. 1, 45–62 (1992).

Rogers, B. J.

I. P. Howard, B. J. Rogers, Binocular Vision and Stere-opsis, No. 29 of Oxford Psychologic Series (Oxford U. Press, New York, 1995), pp. 591–593.

Rolland, J.

L. Davis, J. Rolland, F. Hamza-Lup, Y. Ha, J. Norfleet, B. Pettitt, C. Imielinska, “Alice’s Adventures in Wonderland: a unique technology enabling a continuum of virtual environment experiences,” IEEE Comput. Graphics Appl. 23, 10–12 (2003).
[CrossRef]

Rolland, J. P.

J. P. Rolland, C. Meyer, K. Arthur, E. Rinalducci, “Methods of adjustments versus method of constant stimuli in the quantification of accuracy and precision of rendered depth in head-mounted displays,” Presence Teleoperators Virtual Environ. 11, 610–625 (2002).
[CrossRef]

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

J. P. Rolland, A. Yoshida, L. D. Davis, J. H. Reif, “High-resolution inset head-mounted display,” Appl. Opt. 37, 4183–4193 (1998).
[CrossRef]

J. P. Rolland, D. Ariely, W. Gibson, “Towards quantifying depth and size perception in virtual environments,” Presence Teleoperators Virtual Environ. 4, 24–49 (1995).

W. Robinett, J. P. Rolland, “A computational model for the stereoscopic optics of a head-mounted display,” Presence Teleoperators Virtual Environ. 1, 45–62 (1992).

J. P. Rolland, “Head-mounted displays for virtual environments: the optical interface,” (invited paper), in International Lens Design Conference, Vol. 22 of 1994 OSA Proceedings Series (Optical Society of America, Washington, D.C., 1994), pp. 329–333.

L. Vaissie, J. P. Rolland, “Eye-tracking integration in head-mounted displays,” U.S. patent6,433,760B1 (August13, 2002).

J. P. Rolland, H. Fuchs, “Optical versus video see-through head-mounted displays,” in Fundamentals of Wearable Computers and Augmented Reality, W. Barfield, T. Caudell, eds. (Erlbaum, Mahwah, N.J., 2001), 113–156.

Rushton, S.

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

Siderov, J.

J. Siderov, R. S. Harwerth, “Precision of stereoscopic depth perception from double images,” Vision Res. 33, 1553–1560 (1993).
[CrossRef] [PubMed]

Simonet, P.

P. Simonet, M. C. W. Campbell, “Effect of illuminance on the directions of chromostereopsis and transverse chromatic aberration observed with natural pupils,” Ophthalmic Physiol. Opt. 10, 271–279 (1990).
[CrossRef] [PubMed]

Stiles, W. S.

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

Thibos, L. N.

M. Ye, A. Bradley, L. N. Thibos, X. Zhang, “Interocular differences in transverse chromatic aberration determine chromostereopsis for small pupils,” Vision Res. 32, 1787–1796 (1991).
[CrossRef]

Thomas, J. P.

K. R. Boff, L. Kaufman, J. P. Thomas, Handbook of Perception and Human Performance (Wiley, New York, 1986).

Vaissie, L.

L. Vaissie, J. P. Rolland, “Eye-tracking integration in head-mounted displays,” U.S. patent6,433,760B1 (August13, 2002).

van Dam, A.

J. D. Foley, A. van Dam, Fundamentals of Interactive Computer Graphics (Addison-Wesley, Reading, Mass., 1984).

Wann, J. P.

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

Ye, M.

M. Ye, A. Bradley, L. N. Thibos, X. Zhang, “Interocular differences in transverse chromatic aberration determine chromostereopsis for small pupils,” Vision Res. 32, 1787–1796 (1991).
[CrossRef]

Yoshida, A.

Zhang, X.

M. Ye, A. Bradley, L. N. Thibos, X. Zhang, “Interocular differences in transverse chromatic aberration determine chromostereopsis for small pupils,” Vision Res. 32, 1787–1796 (1991).
[CrossRef]

Appl. Opt.

Comput. Graph.

C. Deering, “High resolution virtual reality,” Comput. Graph. 26(2), 195–202 (1992).
[CrossRef]

IEEE Comput. Graphics Appl.

L. Davis, J. Rolland, F. Hamza-Lup, Y. Ha, J. Norfleet, B. Pettitt, C. Imielinska, “Alice’s Adventures in Wonderland: a unique technology enabling a continuum of virtual environment experiences,” IEEE Comput. Graphics Appl. 23, 10–12 (2003).
[CrossRef]

J. Opt. Soc. Am.

Ophthalmic Physiol. Opt.

P. Simonet, M. C. W. Campbell, “Effect of illuminance on the directions of chromostereopsis and transverse chromatic aberration observed with natural pupils,” Ophthalmic Physiol. Opt. 10, 271–279 (1990).
[CrossRef] [PubMed]

Presence Teleoperators Virtual Environ.

J. P. Rolland, C. Meyer, K. Arthur, E. Rinalducci, “Methods of adjustments versus method of constant stimuli in the quantification of accuracy and precision of rendered depth in head-mounted displays,” Presence Teleoperators Virtual Environ. 11, 610–625 (2002).
[CrossRef]

W. Robinett, J. P. Rolland, “A computational model for the stereoscopic optics of a head-mounted display,” Presence Teleoperators Virtual Environ. 1, 45–62 (1992).

J. P. Rolland, D. Ariely, W. Gibson, “Towards quantifying depth and size perception in virtual environments,” Presence Teleoperators Virtual Environ. 4, 24–49 (1995).

Proc. R. Soc. London

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

Trans. R. Soc. Edinburgh.

D. Brewster, “On the law of visible position in single and binocular vision, and on the representation of solid figures by the union of dissimilar plane pictures on the retina,” Trans. R. Soc. Edinburgh. 15, 349–368 (1844).
[CrossRef]

Vision Res.

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

J. Siderov, R. S. Harwerth, “Precision of stereoscopic depth perception from double images,” Vision Res. 33, 1553–1560 (1993).
[CrossRef] [PubMed]

M. Ye, A. Bradley, L. N. Thibos, X. Zhang, “Interocular differences in transverse chromatic aberration determine chromostereopsis for small pupils,” Vision Res. 32, 1787–1796 (1991).
[CrossRef]

Other

R. B. Rabbetts, ed., Bennett and Rabbetts’ Clinal Visual Optics, 3rd ed. (Butterworth Heinemann, Oxford, UK, 1998), pp. 220–221.

K. N. Ogle, “Spatial localization through binocular vision,” in The Eye (Academic, New York, 1962), Vol. 4, pp. 409–417.

J. P. Rolland, “Head-mounted displays for virtual environments: the optical interface,” (invited paper), in International Lens Design Conference, Vol. 22 of 1994 OSA Proceedings Series (Optical Society of America, Washington, D.C., 1994), pp. 329–333.

D. S. Goodman, “General principles of geometrical optics,” in Handbook of Optics, Vol. 1, 2nd ed., M. Bass, ed. (McGraw-Hill, New York, 1995), pp. 1.3–1.109.

I. P. Howard, B. J. Rogers, Binocular Vision and Stere-opsis, No. 29 of Oxford Psychologic Series (Oxford U. Press, New York, 1995), pp. 591–593.

R. L. Holloway, “Registration errors in augmented reality systems,” Ph.D. dissertation (University of North Carolina at Chapel Hill, Chapel Hill, N.Car., 1994) (unpublished).

J. E. Cutting, Perception with an Eye for Motion (MIT Press, Cambridge, Mass., 1986).

J. D. Foley, A. van Dam, Fundamentals of Interactive Computer Graphics (Addison-Wesley, Reading, Mass., 1984).

K. R. Boff, L. Kaufman, J. P. Thomas, Handbook of Perception and Human Performance (Wiley, New York, 1986).

G. A. Fry, Geometrical optics (Chilton book company, Philadelphia, Pa., 1969).

L. Vaissie, J. P. Rolland, “Eye-tracking integration in head-mounted displays,” U.S. patent6,433,760B1 (August13, 2002).

J. P. Rolland, H. Fuchs, “Optical versus video see-through head-mounted displays,” in Fundamentals of Wearable Computers and Augmented Reality, W. Barfield, T. Caudell, eds. (Erlbaum, Mahwah, N.J., 2001), 113–156.

D. B. Diner, D. H. Fender, Human Engineering in Stereoscopic Viewing Devices (Plenum, New York, 1993).

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Figures (9)

Fig. 1
Fig. 1

Definition of the frame of coordinates. The centers of rotation of the eyes were chosen as the eye points for illustration purposes; point B (not shown) coincides with P.

Fig. 2
Fig. 2

Top view of the stereoscopic vision model presented in Fig. 1.

Fig. 3
Fig. 3

Angular errors for θgL=0° and ϕg=0°, case 1, far field. Angular errors (a) when the centers of rotation of the eyes are taken as the eye points and (b) when the centers of pupils of the eyes are taken as the eye points. (c) Top and side views of the observation direction of the eyes.

Fig. 4
Fig. 4

Angular errors for θgL=0° and ϕg=15°, case 1, far field; (a)–(c) as in Fig. 3.

Fig. 5
Fig. 5

Angular errors for θgL=0° and ϕg=0°, case 1, near field. Angular errors (a) when the centers of rotation of the eyes are taken as the eye points and (b) when the centers of pupils of the eyes are taken as the eye points. Depth errors (c) with centers of rotation of the eyes as the eye points and (d) with centers of pupils of eyes as the eye points. (e) Top and side views of the observation direction of the eyes.

Fig. 6
Fig. 6

Angular errors for α=0° and ϕg=0°, case 2, far field; (a)–(c) as in Fig. 3.

Fig. 7
Fig. 7

Angular errors for α=0° and ϕg=10°, case 2, far field; (a)–(c) as in Fig. 3.

Fig. 8
Fig. 8

Angular errors for α=0° and ϕg=0°, case 2, near field; (a)–(e) as in Fig. 5.

Fig. 9
Fig. 9

Angular errors for α=0° and ϕg=10°, case 2, near field; (a)–(e) as in Fig. 5.

Tables (5)

Tables Icon

Table 1 Simulation Parameters

Tables Icon

Table 2 Angular Errors as θgL and ϕg Vary for Case 1, Far Field, for D=10, zg=10, α=0

Tables Icon

Table 3 Angular and Depth Errors as θgL and ϕg Vary for Case 1, Near Field, for D=1, zg=1, α=0

Tables Icon

Table 4 Angular Errors as ϕg and α Vary for Case 2, Far Field, for D=10, zg=10, θgL=-θgR

Tables Icon

Table 5 Angular and Depth Errors as ϕg and α Vary for Case 2, Near Field, for D=1, zg=1, θgL=-θgR

Equations (28)

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

AngE=arccosOP  OPOP  OP,
DepthE=|zP-zP|/cos(ϕg).
VLPD tan θBLcos ϕB-S2, D tan ϕB, D,
VRPD tan θBRcos ϕB+S2, D tan ϕB, D.
ELP=k1 ELVPL,
ERP=k1 ERVPR,(k1, k1)R2.
k1=k1=S cos(ϕB)D(tan θBL-tan θBR).
xP=S2+S tan θBR(tan θBL-tan θBR),
yP=S sin ϕB(tan θBL-tan θBR),
zP=r+S cos ϕBD(tan θBL-tan θBR) (D-r).
VLP(D-r)(xp+S/2)zp-r-S2, (D-r)ypzp-r, D,
VRP(D-r)(xp-S/2)zp-r+S2, (D-r)ypzp-r, D.
OPLrPsin θgL-S/2rPcos θgLsin ϕgrPcos θgLcos ϕg.
OPRrPsin θgR+S/2rPcos θgRsin ϕgrPcos θgRcos ϕg.
PLP=k2 PLVLP,
PRP=k2 PRVRP,(k2, k2)R2.
cd=Mk2k2=abab k2k2,
c=rP(sin θgR-sin θgL)+S,
a=D tan θBLcos ϕB-rPsin θgL,
b=-D tan θBRcos ϕB-rPsin θgR,
d=rPcos ϕg(cos θgR-cos θgL),
a=D-rPcos θgLcos ϕg,
b=-(D-rPcos θgRcos ϕg).
k2=bc-dbdet(M),
k2=ad-cadet(M).
xP=rPsin θgR+S2+k2D tan θgRcos(ϕg+α)-rPsin θgR,
yP=rPcos θgRsin ϕg+k2((D tan(ϕg+α)-rPcos θgRsin ϕg),
zP=rPcos θgRcos ϕg+k2(D-rPcos θgRcos ϕg).

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