Abstract

We observe imaging through windows comprising pairs of confocal lenslet arrays that have different focal lengths but that are otherwise identical. Image space is stretched in the longitudinal direction only. Such windows are examples of METATOYs, optical components that can change light-ray direction in ways that appear wave-optically forbidden.

© 2010 Optical Society of America

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References

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  1. J. Courtial, New J. Phys. 10, 083033 (2008).
    [CrossRef]
  2. J. Courtial, Opt. Commun. 282, 2634 (2009).
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  5. J. Courtial, Opt. Commun. 282, 2480 (2009).
    [CrossRef]
  6. A. C. Hamilton and J. Courtial, New J. Phys. 11, 013042(2009).
    [CrossRef]
  7. A. C. Hamilton, B. Sundar, J. Nelson, and J. Courtial, J. Opt. A 11, 085705 (2009).
    [CrossRef]
  8. M. Blair, L. Clark, E. A. Houston, G. Smith, J. Leach, A. C. Hamilton, and J. Courtial, Opt. Commun. 282, 4299(2009).
    [CrossRef]
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    [CrossRef] [PubMed]
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  11. R. Völkel, H. P. Herzig, P. Nussbaum, R. Dändliker, and W. B. Hugle, Opt. Eng. 35, 3323 (1996).
    [CrossRef]
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    [CrossRef]
  13. G. Lippmann and C. R. Hebd, Acad. Sci. 146, 446 (1908).
  14. T. Adelson and J. Y. A. Wang, IEEE Trans. Pattern Anal. Machine Intell. 14, 99 (1992).
    [CrossRef]
  15. R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Stanford Tech. Report CTSR 2005-02(2005).
  16. T. Okoshi, Proc. IEEE 68, 548 (1980).
    [CrossRef]
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    [CrossRef]
  18. D. Gabor, “Improvements in or relating to optical systems composed of lenticules,” UK patent 541,753 (1940).
  19. C. Hembd-Sölner, R. F. Stevens, and M. C. Hutley, J. Opt. A 1, 94 (1999).
    [CrossRef]
  20. P. Nussbaum, R. Völkel, H. P. Herzig, M. Eisner, and S. Haselbeck, Pure Appl. Opt. 6, 617 (1997).
    [CrossRef]
  21. W. Dultz, Appl. Opt. 23, 200 (1984).
    [CrossRef] [PubMed]
  22. J. Duparré, P. Schreiber, A. Matthes, E. Pshenay-Severin, A. Bräuer, A. Tünnermann, R. Völkel, M. Eisner, and T. Scharf, Opt. Express 13, 889 (2005).
    [CrossRef] [PubMed]

2009 (6)

J. Courtial, Opt. Commun. 282, 2480 (2009).
[CrossRef]

A. C. Hamilton and J. Courtial, New J. Phys. 11, 013042(2009).
[CrossRef]

A. C. Hamilton, B. Sundar, J. Nelson, and J. Courtial, J. Opt. A 11, 085705 (2009).
[CrossRef]

M. Blair, L. Clark, E. A. Houston, G. Smith, J. Leach, A. C. Hamilton, and J. Courtial, Opt. Commun. 282, 4299(2009).
[CrossRef]

B. Sundar, A. C. Hamilton, and J. Courtial, Opt. Lett. 34, 374 (2009).
[CrossRef] [PubMed]

J. Courtial, Opt. Commun. 282, 2634 (2009).
[CrossRef]

2008 (1)

J. Courtial, New J. Phys. 10, 083033 (2008).
[CrossRef]

2005 (1)

2002 (1)

R. F. Stevens and T. G. Harvey, J. Opt. A 4, S17 (2002).
[CrossRef]

1999 (1)

C. Hembd-Sölner, R. F. Stevens, and M. C. Hutley, J. Opt. A 1, 94 (1999).
[CrossRef]

1997 (1)

P. Nussbaum, R. Völkel, H. P. Herzig, M. Eisner, and S. Haselbeck, Pure Appl. Opt. 6, 617 (1997).
[CrossRef]

1996 (1)

R. Völkel, H. P. Herzig, P. Nussbaum, R. Dändliker, and W. B. Hugle, Opt. Eng. 35, 3323 (1996).
[CrossRef]

1994 (1)

M. C. Hutley, R. Hunt, R. F. Stevens, and P. Savander, Pure Appl. Opt. 3, 133 (1994).
[CrossRef]

1992 (1)

T. Adelson and J. Y. A. Wang, IEEE Trans. Pattern Anal. Machine Intell. 14, 99 (1992).
[CrossRef]

1991 (1)

R. F. Stevens and N. Davies, J. Photogr. Sci. 39, 199(1991).

1984 (1)

1980 (1)

T. Okoshi, Proc. IEEE 68, 548 (1980).
[CrossRef]

1979 (1)

1908 (1)

G. Lippmann and C. R. Hebd, Acad. Sci. 146, 446 (1908).

Adelson, T.

T. Adelson and J. Y. A. Wang, IEEE Trans. Pattern Anal. Machine Intell. 14, 99 (1992).
[CrossRef]

Anderson, R. H.

Blair, M.

M. Blair, L. Clark, E. A. Houston, G. Smith, J. Leach, A. C. Hamilton, and J. Courtial, Opt. Commun. 282, 4299(2009).
[CrossRef]

Bräuer, A.

Brédif, M.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Stanford Tech. Report CTSR 2005-02(2005).

Clark, L.

M. Blair, L. Clark, E. A. Houston, G. Smith, J. Leach, A. C. Hamilton, and J. Courtial, Opt. Commun. 282, 4299(2009).
[CrossRef]

Courtial, J.

A. C. Hamilton, B. Sundar, J. Nelson, and J. Courtial, J. Opt. A 11, 085705 (2009).
[CrossRef]

J. Courtial, Opt. Commun. 282, 2634 (2009).
[CrossRef]

J. Courtial, Opt. Commun. 282, 2480 (2009).
[CrossRef]

A. C. Hamilton and J. Courtial, New J. Phys. 11, 013042(2009).
[CrossRef]

M. Blair, L. Clark, E. A. Houston, G. Smith, J. Leach, A. C. Hamilton, and J. Courtial, Opt. Commun. 282, 4299(2009).
[CrossRef]

B. Sundar, A. C. Hamilton, and J. Courtial, Opt. Lett. 34, 374 (2009).
[CrossRef] [PubMed]

J. Courtial, New J. Phys. 10, 083033 (2008).
[CrossRef]

Dändliker, R.

R. Völkel, H. P. Herzig, P. Nussbaum, R. Dändliker, and W. B. Hugle, Opt. Eng. 35, 3323 (1996).
[CrossRef]

Davies, N.

R. F. Stevens and N. Davies, J. Photogr. Sci. 39, 199(1991).

Dultz, W.

Duparré, J.

Duval, G.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Stanford Tech. Report CTSR 2005-02(2005).

Eisner, M.

Gabor, D.

D. Gabor, “Improvements in or relating to optical systems composed of lenticules,” UK patent 541,753 (1940).

Hamilton, A. C.

A. C. Hamilton, B. Sundar, J. Nelson, and J. Courtial, J. Opt. A 11, 085705 (2009).
[CrossRef]

A. C. Hamilton and J. Courtial, New J. Phys. 11, 013042(2009).
[CrossRef]

M. Blair, L. Clark, E. A. Houston, G. Smith, J. Leach, A. C. Hamilton, and J. Courtial, Opt. Commun. 282, 4299(2009).
[CrossRef]

B. Sundar, A. C. Hamilton, and J. Courtial, Opt. Lett. 34, 374 (2009).
[CrossRef] [PubMed]

Hanrahan, P.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Stanford Tech. Report CTSR 2005-02(2005).

Harvey, T. G.

R. F. Stevens and T. G. Harvey, J. Opt. A 4, S17 (2002).
[CrossRef]

Haselbeck, S.

P. Nussbaum, R. Völkel, H. P. Herzig, M. Eisner, and S. Haselbeck, Pure Appl. Opt. 6, 617 (1997).
[CrossRef]

Hebd, C. R.

G. Lippmann and C. R. Hebd, Acad. Sci. 146, 446 (1908).

Hembd-Sölner, C.

C. Hembd-Sölner, R. F. Stevens, and M. C. Hutley, J. Opt. A 1, 94 (1999).
[CrossRef]

Herzig, H. P.

P. Nussbaum, R. Völkel, H. P. Herzig, M. Eisner, and S. Haselbeck, Pure Appl. Opt. 6, 617 (1997).
[CrossRef]

R. Völkel, H. P. Herzig, P. Nussbaum, R. Dändliker, and W. B. Hugle, Opt. Eng. 35, 3323 (1996).
[CrossRef]

Horowitz, M.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Stanford Tech. Report CTSR 2005-02(2005).

Houston, E. A.

M. Blair, L. Clark, E. A. Houston, G. Smith, J. Leach, A. C. Hamilton, and J. Courtial, Opt. Commun. 282, 4299(2009).
[CrossRef]

Hugle, W. B.

R. Völkel, H. P. Herzig, P. Nussbaum, R. Dändliker, and W. B. Hugle, Opt. Eng. 35, 3323 (1996).
[CrossRef]

Hunt, R.

M. C. Hutley, R. Hunt, R. F. Stevens, and P. Savander, Pure Appl. Opt. 3, 133 (1994).
[CrossRef]

Hutley, M. C.

C. Hembd-Sölner, R. F. Stevens, and M. C. Hutley, J. Opt. A 1, 94 (1999).
[CrossRef]

M. C. Hutley, R. Hunt, R. F. Stevens, and P. Savander, Pure Appl. Opt. 3, 133 (1994).
[CrossRef]

M. C. Hutley and R. F. Stevens, in Microlens Arrays, M.C.Hutley, ed., IOP Short Meetings Series No. 30 (Institute of Physics, 1991), pp. 147–154.

Leach, J.

M. Blair, L. Clark, E. A. Houston, G. Smith, J. Leach, A. C. Hamilton, and J. Courtial, Opt. Commun. 282, 4299(2009).
[CrossRef]

Levoy, M.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Stanford Tech. Report CTSR 2005-02(2005).

Lippmann, G.

G. Lippmann and C. R. Hebd, Acad. Sci. 146, 446 (1908).

Matthes, A.

Nelson, J.

A. C. Hamilton, B. Sundar, J. Nelson, and J. Courtial, J. Opt. A 11, 085705 (2009).
[CrossRef]

Ng, R.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Stanford Tech. Report CTSR 2005-02(2005).

Nussbaum, P.

P. Nussbaum, R. Völkel, H. P. Herzig, M. Eisner, and S. Haselbeck, Pure Appl. Opt. 6, 617 (1997).
[CrossRef]

R. Völkel, H. P. Herzig, P. Nussbaum, R. Dändliker, and W. B. Hugle, Opt. Eng. 35, 3323 (1996).
[CrossRef]

Okoshi, T.

T. Okoshi, Proc. IEEE 68, 548 (1980).
[CrossRef]

Pshenay-Severin, E.

Savander, P.

M. C. Hutley, R. Hunt, R. F. Stevens, and P. Savander, Pure Appl. Opt. 3, 133 (1994).
[CrossRef]

Scharf, T.

Schreiber, P.

Smith, G.

M. Blair, L. Clark, E. A. Houston, G. Smith, J. Leach, A. C. Hamilton, and J. Courtial, Opt. Commun. 282, 4299(2009).
[CrossRef]

Stevens, R. F.

R. F. Stevens and T. G. Harvey, J. Opt. A 4, S17 (2002).
[CrossRef]

C. Hembd-Sölner, R. F. Stevens, and M. C. Hutley, J. Opt. A 1, 94 (1999).
[CrossRef]

M. C. Hutley, R. Hunt, R. F. Stevens, and P. Savander, Pure Appl. Opt. 3, 133 (1994).
[CrossRef]

R. F. Stevens and N. Davies, J. Photogr. Sci. 39, 199(1991).

M. C. Hutley and R. F. Stevens, in Microlens Arrays, M.C.Hutley, ed., IOP Short Meetings Series No. 30 (Institute of Physics, 1991), pp. 147–154.

Sundar, B.

A. C. Hamilton, B. Sundar, J. Nelson, and J. Courtial, J. Opt. A 11, 085705 (2009).
[CrossRef]

B. Sundar, A. C. Hamilton, and J. Courtial, Opt. Lett. 34, 374 (2009).
[CrossRef] [PubMed]

Tünnermann, A.

Völkel, R.

J. Duparré, P. Schreiber, A. Matthes, E. Pshenay-Severin, A. Bräuer, A. Tünnermann, R. Völkel, M. Eisner, and T. Scharf, Opt. Express 13, 889 (2005).
[CrossRef] [PubMed]

P. Nussbaum, R. Völkel, H. P. Herzig, M. Eisner, and S. Haselbeck, Pure Appl. Opt. 6, 617 (1997).
[CrossRef]

R. Völkel, H. P. Herzig, P. Nussbaum, R. Dändliker, and W. B. Hugle, Opt. Eng. 35, 3323 (1996).
[CrossRef]

Wang, J. Y. A.

T. Adelson and J. Y. A. Wang, IEEE Trans. Pattern Anal. Machine Intell. 14, 99 (1992).
[CrossRef]

Acad. Sci. (1)

G. Lippmann and C. R. Hebd, Acad. Sci. 146, 446 (1908).

Appl. Opt. (2)

IEEE Trans. Pattern Anal. Machine Intell. (1)

T. Adelson and J. Y. A. Wang, IEEE Trans. Pattern Anal. Machine Intell. 14, 99 (1992).
[CrossRef]

J. Opt. A (3)

R. F. Stevens and T. G. Harvey, J. Opt. A 4, S17 (2002).
[CrossRef]

C. Hembd-Sölner, R. F. Stevens, and M. C. Hutley, J. Opt. A 1, 94 (1999).
[CrossRef]

A. C. Hamilton, B. Sundar, J. Nelson, and J. Courtial, J. Opt. A 11, 085705 (2009).
[CrossRef]

J. Photogr. Sci. (1)

R. F. Stevens and N. Davies, J. Photogr. Sci. 39, 199(1991).

New J. Phys. (2)

J. Courtial, New J. Phys. 10, 083033 (2008).
[CrossRef]

A. C. Hamilton and J. Courtial, New J. Phys. 11, 013042(2009).
[CrossRef]

Opt. Commun. (3)

J. Courtial, Opt. Commun. 282, 2634 (2009).
[CrossRef]

J. Courtial, Opt. Commun. 282, 2480 (2009).
[CrossRef]

M. Blair, L. Clark, E. A. Houston, G. Smith, J. Leach, A. C. Hamilton, and J. Courtial, Opt. Commun. 282, 4299(2009).
[CrossRef]

Opt. Eng. (1)

R. Völkel, H. P. Herzig, P. Nussbaum, R. Dändliker, and W. B. Hugle, Opt. Eng. 35, 3323 (1996).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Proc. IEEE (1)

T. Okoshi, Proc. IEEE 68, 548 (1980).
[CrossRef]

Pure Appl. Opt. (2)

M. C. Hutley, R. Hunt, R. F. Stevens, and P. Savander, Pure Appl. Opt. 3, 133 (1994).
[CrossRef]

P. Nussbaum, R. Völkel, H. P. Herzig, M. Eisner, and S. Haselbeck, Pure Appl. Opt. 6, 617 (1997).
[CrossRef]

Other (3)

D. Gabor, “Improvements in or relating to optical systems composed of lenticules,” UK patent 541,753 (1940).

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Stanford Tech. Report CTSR 2005-02(2005).

M. C. Hutley and R. F. Stevens, in Microlens Arrays, M.C.Hutley, ed., IOP Short Meetings Series No. 30 (Institute of Physics, 1991), pp. 147–154.

Supplementary Material (3)

» Media 1: MOV (2333 KB)     
» Media 2: MOV (1810 KB)     
» Media 3: MOV (2457 KB)     

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Figures (5)

Fig. 1
Fig. 1

Schematic top view of the experimental setup for Figs. 2, 4. B, W, and W are, respectively, the black knight, the white knight, and the image of the white knight formed by the CLAs. c, o, and i are the camera, object, and image distances, respectively. The sketch is not to scale.

Fig. 2
Fig. 2

Confirmation of the image position through focusing. The image of the white chess piece created by the CLAs ( η = 0.57 ) goes in and out of focus together with the black chess piece as the position of the focus plane changes. The focusing plane is a distance Δ z in front of the black chess piece; the measured object and image distances are o = 70 mm and i = 34 mm ( i / o = 0.49 ). The photos shown here are from a movie (Media 1).

Fig. 3
Fig. 3

Horizontal parallax. As the camera is moved left and right (a distance Δ x out of the default position), the image (produced by CLAs with η = 0.57 ) of the white chess piece does not move relative to the black chess piece. Out-of-focus additional “ghost” images [2] of the white knight are visible, most notably in the rightmost frame to the right of the black knight. The measured object and image distances are, respectively, o = 70 mm and i = 34 mm ( i / o = 0.49 ). The photos are part of a movie (Media 2).

Fig. 4
Fig. 4

Vertical parallax. As the camera is moved upward ( Δ y is the height above the default position), the image of the white chess piece does not move relative to the black chess piece. When seen from above ( Δ y > 0 ), the image of the white chess piece appears to be seen from below; this is due to the image being pseudoscopic, and, therefore, in this case, “hollow” (like the bust in the hollow-bust optical illusion [21]). Here this effect is enhanced because the depth of the image is stretched. This is particularly apparent in the corresponding movie (Media 3). The pictures were taken using CLAs with η = 1.7 ; measured object and image distances are o = 56 mm and i = 100 mm , respectively ( i / o = 1.8 ).

Fig. 5
Fig. 5

Pseudoscopic imaging. Two white chess pieces at different object distances ( o 1 = 76 mm and o 2 = 90 mm ) are being imaged by CLAs ( η = 1.7 ). For comparison, two black chess pieces have been placed in the corresponding image planes ( i 1 = 140 mm and i 2 = 150 mm ). From the camera position ( 480 mm in front of the CLAs), the images of the two white chess pieces overlap, and so do the two black chess pieces. However, whereas the black chess piece in front (the knight) obscures the one behind (the pawn), the image behind (of the white pawn) obscures that in front.

Equations (2)

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η = f 2 f 1 ,
i o = η .

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