Abstract

Stereoscopic displays present different images to the two eyes and thereby create a compelling three-dimensional (3D) sensation. They are being developed for numerous applications including cinema, television, virtual prototyping, and medical imaging. However, stereoscopic displays cause perceptual distortions, performance decrements, and visual fatigue. These problems occur because some of the presented depth cues (i.e., perspective and binocular disparity) specify the intended 3D scene while focus cues (blur and accommodation) specify the fixed distance of the display itself. We have developed a stereoscopic display that circumvents these problems. It consists of a fast switchable lens synchronized to the display such that focus cues are nearly correct. The system has great potential for both basic vision research and display applications.

© 2009 OSA

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2009 (1)

2008 (2)

D. C. Hutchinson and H. W. Neal, “The design and implementation of a stereoscopic microdisplay television,” IEEE Trans. Consum. Electron. 54(2), 254–261 (2008).
[CrossRef]

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)

Y. Hu and R. A. Malthaner, “The feasibility of three-dimensional displays of the thorax for preoperative planning in the surgical treatment of lung cancer,” Eur. J. Cardiothorac. Surg. 31(3), 506–511 (2007).
[CrossRef] [PubMed]

2006 (1)

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 (3)

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,” Journal of Display Technology 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]

2004 (4)

M. Matsuki, H. Kani, F. Tatsugami, S. Yoshikawa, I. Narabayashi, S.-W. Lee, H. Shinohara, E. Nomura, and N. Tanigawa, “Preoperative assessment of vascular anatomy around the stomach by 3D imaging using MDCT before laparoscopy-assisted gastrectomy,” AJR Am. J. Roentgenol. 183(1), 145–151 (2004).
[PubMed]

L. M. J. Meesters, W. A. Ijsselsteijn, and P. J. H. Seuntiens, “A survey of perceptual evaluations and requirements of three-dimensional TV,” IEEE Trans. Circ. Syst. Video Tech. 14(3), 381–391 (2004).
[CrossRef]

A. Sullivan, “DepthCube solid-state 3D volumetric display,” Proc. SPIE 5291, 279 (2004).
[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]

2002 (1)

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

2000 (1)

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]

1996 (1)

A. Shiwa, K. Omura, and F. Kishino, “Proposal for a 3-D display with accommodative compensation: 3DDAC,” J. Soc. Inf. Disp. 4(4), 255–261 (1996).
[CrossRef]

1994 (1)

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

1987 (1)

1986 (2)

A. Bradley and I. Ohzawa, “A comparison of contrast detection and discrimination,” Vision Res. 26(6), 991–997 (1986).
[CrossRef] [PubMed]

B. G. Cumming and S. J. Judge, “Disparity-induced and blur-induced convergence eye movement and accommodation in the monkey,” J. Neurophysiol. 55(5), 896–914 (1986).
[PubMed]

1980 (1)

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

1977 (1)

W. N. Charman and H. Whitefoot, “Pupil diameter and depth-of-field of human eye as measured by laser speckle,” Opt. Acta (Lond.) 24, 1211–1216 (1977).
[CrossRef]

1972 (1)

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

1968 (1)

F. W. Campbell and J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. 197(3), 551–566 (1968).
[PubMed]

1957 (2)

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

E. F. Fincham and J. Walton, “The reciprocal actions of accommodation and convergence,” J. Physiol. 137(3), 488–508 (1957).
[PubMed]

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]

Banks, M. S.

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]

Bradley, A.

A. Bradley and I. Ohzawa, “A comparison of contrast detection and discrimination,” Vision Res. 26(6), 991–997 (1986).
[CrossRef] [PubMed]

Campbell, F. W.

F. W. Campbell and J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. 197(3), 551–566 (1968).
[PubMed]

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

Charman, W. N.

W. N. Charman and H. Whitefoot, “Pupil diameter and depth-of-field of human eye as measured by laser speckle,” Opt. Acta (Lond.) 24, 1211–1216 (1977).
[CrossRef]

Cumming, B. G.

B. G. Cumming and S. J. Judge, “Disparity-induced and blur-induced convergence eye movement and accommodation in the monkey,” J. Neurophysiol. 55(5), 896–914 (1986).
[PubMed]

Cupery, K. N.

E. M. Granger and K. N. Cupery, “Optical merit function (SQF), which correlates with subjective image judgments,” Photographic Science and Engineering 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).
[CrossRef]

Dorval, R. K.

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

Emoto, M.

M. Emoto, T. Niida, and F. Okano, “Repeated vergence adaptation causes the decline of visual functions in watching stereoscopic television,” Journal of Display Technology 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]

Favalora, G. E.

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

Field, D. J.

Fincham, E. F.

E. F. Fincham and J. Walton, “The reciprocal actions of accommodation and convergence,” J. Physiol. 137(3), 488–508 (1957).
[PubMed]

Giovinco, M. G.

G. E. Favalora, J. Napoli, D. M. Hall, R. K. Dorval, M. G. Giovinco, M. J. Richmond, and ., “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), 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,” Photographic Science and Engineering 16, 221–230 (1972).

Hall, D. M.

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

Hoffman, D. M.

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]

Hu, Y.

Y. Hu and R. A. Malthaner, “The feasibility of three-dimensional displays of the thorax for preoperative planning in the surgical treatment of lung cancer,” Eur. J. Cardiothorac. Surg. 31(3), 506–511 (2007).
[CrossRef] [PubMed]

Hua, H.

Hutchinson, D. C.

D. C. Hutchinson and H. W. Neal, “The design and implementation of a stereoscopic microdisplay television,” IEEE Trans. Consum. Electron. 54(2), 254–261 (2008).
[CrossRef]

Ijsselsteijn, W. A.

L. M. J. Meesters, W. A. Ijsselsteijn, and P. J. H. Seuntiens, “A survey of perceptual evaluations and requirements of three-dimensional TV,” IEEE Trans. Circ. Syst. Video Tech. 14(3), 381–391 (2004).
[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]

Judge, S. J.

B. G. Cumming and S. J. Judge, “Disparity-induced and blur-induced convergence eye movement and accommodation in the monkey,” J. Neurophysiol. 55(5), 896–914 (1986).
[PubMed]

Kani, H.

M. Matsuki, H. Kani, F. Tatsugami, S. Yoshikawa, I. Narabayashi, S.-W. Lee, H. Shinohara, E. Nomura, and N. Tanigawa, “Preoperative assessment of vascular anatomy around the stomach by 3D imaging using MDCT before laparoscopy-assisted gastrectomy,” AJR Am. J. Roentgenol. 183(1), 145–151 (2004).
[PubMed]

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]

Kishino, F.

A. Shiwa, K. Omura, and F. Kishino, “Proposal for a 3-D display with accommodative compensation: 3DDAC,” J. Soc. Inf. Disp. 4(4), 255–261 (1996).
[CrossRef]

Kruger, P. B.

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

Lee, S.-W.

M. Matsuki, H. Kani, F. Tatsugami, S. Yoshikawa, I. Narabayashi, S.-W. Lee, H. Shinohara, E. Nomura, and N. Tanigawa, “Preoperative assessment of vascular anatomy around the stomach by 3D imaging using MDCT before laparoscopy-assisted gastrectomy,” AJR Am. J. Roentgenol. 183(1), 145–151 (2004).
[PubMed]

Liu, S.

Malthaner, R. A.

Y. Hu and R. A. Malthaner, “The feasibility of three-dimensional displays of the thorax for preoperative planning in the surgical treatment of lung cancer,” Eur. J. Cardiothorac. Surg. 31(3), 506–511 (2007).
[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]

Matsuki, M.

M. Matsuki, H. Kani, F. Tatsugami, S. Yoshikawa, I. Narabayashi, S.-W. Lee, H. Shinohara, E. Nomura, and N. Tanigawa, “Preoperative assessment of vascular anatomy around the stomach by 3D imaging using MDCT before laparoscopy-assisted gastrectomy,” AJR Am. J. Roentgenol. 183(1), 145–151 (2004).
[PubMed]

Meesters, L. M. J.

L. M. J. Meesters, W. A. Ijsselsteijn, and P. J. H. Seuntiens, “A survey of perceptual evaluations and requirements of three-dimensional TV,” IEEE Trans. Circ. Syst. Video Tech. 14(3), 381–391 (2004).
[CrossRef]

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]

Napoli, J.

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

Narabayashi, I.

M. Matsuki, H. Kani, F. Tatsugami, S. Yoshikawa, I. Narabayashi, S.-W. Lee, H. Shinohara, E. Nomura, and N. Tanigawa, “Preoperative assessment of vascular anatomy around the stomach by 3D imaging using MDCT before laparoscopy-assisted gastrectomy,” AJR Am. J. Roentgenol. 183(1), 145–151 (2004).
[PubMed]

Neal, H. W.

D. C. Hutchinson and H. W. Neal, “The design and implementation of a stereoscopic microdisplay television,” IEEE Trans. Consum. Electron. 54(2), 254–261 (2008).
[CrossRef]

Niida, T.

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

Nomura, E.

M. Matsuki, H. Kani, F. Tatsugami, S. Yoshikawa, I. Narabayashi, S.-W. Lee, H. Shinohara, E. Nomura, and N. Tanigawa, “Preoperative assessment of vascular anatomy around the stomach by 3D imaging using MDCT before laparoscopy-assisted gastrectomy,” AJR Am. J. Roentgenol. 183(1), 145–151 (2004).
[PubMed]

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]

Ohzawa, I.

A. Bradley and I. Ohzawa, “A comparison of contrast detection and discrimination,” Vision Res. 26(6), 991–997 (1986).
[CrossRef] [PubMed]

Okano, F.

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

Omura, K.

A. Shiwa, K. Omura, and F. Kishino, “Proposal for a 3-D display with accommodative compensation: 3DDAC,” J. Soc. Inf. Disp. 4(4), 255–261 (1996).
[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]

Richmond, M. J.

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

Robson, J. G.

F. W. Campbell and J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. 197(3), 551–566 (1968).
[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]

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]

Seuntiens, P. J. H.

L. M. J. Meesters, W. A. Ijsselsteijn, and P. J. H. Seuntiens, “A survey of perceptual evaluations and requirements of three-dimensional TV,” IEEE Trans. Circ. Syst. Video Tech. 14(3), 381–391 (2004).
[CrossRef]

Shibata, 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]

Shinohara, H.

M. Matsuki, H. Kani, F. Tatsugami, S. Yoshikawa, I. Narabayashi, S.-W. Lee, H. Shinohara, E. Nomura, and N. Tanigawa, “Preoperative assessment of vascular anatomy around the stomach by 3D imaging using MDCT before laparoscopy-assisted gastrectomy,” AJR Am. J. Roentgenol. 183(1), 145–151 (2004).
[PubMed]

Shiwa, A.

A. Shiwa, K. Omura, and F. Kishino, “Proposal for a 3-D display with accommodative compensation: 3DDAC,” J. Soc. Inf. Disp. 4(4), 255–261 (1996).
[CrossRef]

Sullivan, A.

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

Suyama, S.

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Supplementary Material (1)

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Figures (7)

Fig. 1
Fig. 1

Vergence distance and accommodation distance in natural viewing and with conventional stereoscopic displays. a) Plan view of a viewer and two objects in the natural environment. The viewer is fixating the far object and not the near object. The lines of sight to the far object intersect at the object. The distance to the intersection is the vergence distance. The distance to which the eye must be focused to form a sharp retinal image of the object is the focal distance; the distance to which the eyes are focused is the accommodation distance. b) Simulation of a conventional stereoscopic display of the same pair of objects. The display screen is at the same distance as the simulated far object so the vergence and focal distance of the image of the far object are the same as in a. However, the near object is presented on the display screen so its focal distance is no longer equal to the vergence distance, resulting in vergence-accommodation conflict and incorrect blur. c) Photograph of two objects like the ones depicted in a with the camera focused on the far object. Note the blurred image of the near object and the nearer parts of the ground plane. d) Photograph of two objects in which the focal distance is effectively the same as in a conventional stereoscopic display. Note the sharp image of the near object and the ground plane. e) Plot showing range of comfortable vergence-accommodative stimuli. The abscissa represents the simulated distance, and the ordinate represents the focal distance. Stimuli that fall within the red zone will be comfortable to fuse and focus [10,12]

Fig. 2
Fig. 2

The high-speed switchable lens. a) Schematic of the lens. The first polarizer produces vertically polarized light that is then either rotated, or not, through 90° by the first ferroelectric liquid-crystal polarization (FLC1) switch. The first lens focuses the two polarization states differently. A second FLC and lens produces two more possible focal lengths for each of the first polarization states creating four focal states in all. b) Photograph of the lens assembly. c and d) Images of four dolls at different distances with the lens in two different focal states. e) Overhead view of the lens, eye, and CRT. The viewing frustum is indicated by the tan shading. The focal distances associated with the four lens states are indicated by the horizontal lines.

Fig. 3
Fig. 3

Two display configurations. a) Schematic of the optical system with two CRTs, one for each eye, viewed through mirrors. Separate lens assemblies for each eye. With the CRT running at 180Hz, the refresh rate is 45Hz for each eye. Photosensors detect light on the CRT and through control electronics synchronize the lens assemblies to the CRTs. b) Photograph of the system in the two-display configuration. c) Schematic of the system with one CRT and two lens assemblies. Images are presented time sequentially to the two eyes by using liquid-crystal shutter glasses that alternately block and pass light to the eyes. Photosensors again detect light from the CRT to enable synchronization of the lens assemblies and shutter glasses [29] with the CRT. Eight sub-frames are presented for each volumetric frame, four per eye. With the CRT running at 180Hz, the refresh rate is therefore 22.5Hz per eye. d) Photograph of the display in the one-display configuration. A video of the display in action can be viewed in Fig. 5.

Fig. 4
Fig. 4

Images of a real scene recorded through the switchable lens assembly. The four focal states are shown. The distances of each of the focused objects from the lens were (a) 285 mm for Stalin, (b) 375mm for Brezhnev, (c) 590mm for Gorbachev, and (d) 970mm for Yeltsin.

Fig. 5
Fig. 5

(Media 1) The video shows images captured through the system with the lens assembly in each of its four focal states. The simulated scene consists of four letter-acuity charts placed on a ground plane at different distances from the viewer. The first segment of the video shows the effect of refocusing the camera used to record the video when the switchable lens is inactive and the display becomes a conventional display; in this case, all the charts are a fixed focal distance from the camera, so they go in and out of focus simultaneously. The second segment of the video shows the effect of refocusing the camera when the switchable lens is activated; the various charts go in and out of focus separately. The third and fourth segments show an object moving in depth. In the third, the switchable lens is inactivated so the object remains equally focused as it moves in depth. In the fourth, the lens is activated, so the object goes in and out of focus appropriately.

Fig. 6
Fig. 6

Modulation transfer of the switchable lens system. Modulation transfer is plotted as a function of spatial frequency for the four focal states of the system. We printed test patterns of high-contrast square-wave gratings that ranged from 5 to 63 cpd. To measure the MTFs, we used a Canon 20D dSLR camera with a Canon 50mm, f/1.8 prime lens (set at f/4.0). The direct measurements determined the MTF of the camera plus any attenuation in the printing process. Then with the same camera, we photographed the same test patterns at the same magnification through the switchable lens system. We set the system in one of its four states and made the measurements, and then repeated this for the other focal states. The plotted MTFs are the MTFs for imaging through the switchable lens system divided by the MTFs for imaging with the camera alone. Error bars represent standard deviations. There is some variation in modulation transfer across the four focal states, but the MTFs are similar to that of a high-quality digital camera.

Fig. 7
Fig. 7

Retinal-image contrast with the multi-focal display for different types of optics, spatial frequencies, and separations of the focal planes. Each panel plots plane separation in diopters on the abscissa and the position of the simulated object on the ordinate. Color (see color bar) represents modulation transfer (contrast in the retinal image divided by incident contrast). In constructing the figure, we assumed that the eye has accommodated precisely to the simulated distance. The upper row shows the calculations for diffraction-limited optics with a 4-mm aperture. The lower row shows the calculations for typical human optics (left eye of author DMH) with a 4-mm pupil; the transfer properties were determined by wave-front measurements with a Shack-Hartmann sensor. The left, middle, and right columns show the results for spatial frequencies of 3, 6, and 18 cpd, respectively.

Equations (2)

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(2N1)Δ
In=[1(DnDs)(DnDf)]IsIf=[(DnDs)(DnDf)]Is

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