Abstract

We theoretically and experimentally demonstrate how “vectograph” film may be used to create arbitrarily complex vector fields having broadband phase features such as optical vortices.

© 2009 Optical Society of America

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References

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  1. L. Lipton, Foundations of the Stereoscopic Cinema (Van Nostrand Reinhold, 1982).
  2. E. H. Land, J. Opt. Soc. Am. 30, 230 (1940).
    [CrossRef]
  3. RIS--Stereo Imaging Group, “Outlook for StereoJet Three-Dimensional Printing,” www.rowland.harvard.edu/organization
  4. J. J. Scarpetti, P. M. DuBois, R. M. Friedhoff, and V. K. Walworth, J. Imaging Sci. Technol. 42, 307 (1998).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  11. M. Vasnetsov and K. Staliunas, Optical Vortices, in Horizons in Horizons in World Physics Vol. 228 (Nova Science, 1999).
  12. G. A. Swartzlander, Jr., Opt. Lett. 31, 2042 (2006).
    [CrossRef] [PubMed]
  13. G. A. Swartzlander Jr., E. L. Ford, R. S. Abdul-Malik, L. M. Close, M. A. Peters, D. M. Palacios, and D. W. Wilson, Opt. Express 14, 10200 (2008).
    [CrossRef]
  14. J. F. Nye, Proc. R. Soc. London 389, 279 (1983).
    [CrossRef]
  15. J. F. Nye and J. V. Hajnal, Proc. R. Soc. London 409, 21 (1987).
    [CrossRef]
  16. M. S. Soskin and M. V. Vasnetsov, Prog. Opt. 42, 219 (2001).
    [CrossRef]
  17. E. Hasman, G. Biener, A. Niv, and V. Kleiner, Prog. Opt. 47, 215 (2005).
    [CrossRef]
  18. M. Stalder and M. Schadt, Opt. Lett. 21, 1948 (1996).
    [CrossRef] [PubMed]
  19. R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
    [CrossRef] [PubMed]
  20. A. Shoham, R. Vander, and S. G. Lipson, Opt. Lett. 31, 3405 (2006).
    [CrossRef] [PubMed]

2008

G. A. Swartzlander Jr., E. L. Ford, R. S. Abdul-Malik, L. M. Close, M. A. Peters, D. M. Palacios, and D. W. Wilson, Opt. Express 14, 10200 (2008).
[CrossRef]

2006

2005

E. Hasman, G. Biener, A. Niv, and V. Kleiner, Prog. Opt. 47, 215 (2005).
[CrossRef]

2003

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

2001

M. S. Soskin and M. V. Vasnetsov, Prog. Opt. 42, 219 (2001).
[CrossRef]

1998

J. J. Scarpetti, P. M. DuBois, R. M. Friedhoff, and V. K. Walworth, J. Imaging Sci. Technol. 42, 307 (1998).

Z. S. Sacks, D. Rozas, and G. A. Swartzlander, Jr., J. Opt. Soc. Am. B 15, 2226 (1998).
[CrossRef]

1997

1996

1987

J. F. Nye and J. V. Hajnal, Proc. R. Soc. London 409, 21 (1987).
[CrossRef]

1983

J. F. Nye, Proc. R. Soc. London 389, 279 (1983).
[CrossRef]

1974

J. F. Nye and M. V. Berry, Proc. R. Soc. London 336, 165 (1974).
[CrossRef]

1969

1940

Abdul-Malik, R. S.

G. A. Swartzlander Jr., E. L. Ford, R. S. Abdul-Malik, L. M. Close, M. A. Peters, D. M. Palacios, and D. W. Wilson, Opt. Express 14, 10200 (2008).
[CrossRef]

Allen, L.

Arnold, A. C.

L. A. Levin and A. C. Arnold, Neuro-Ophthalmology: The Practical Guide, (Thieme, 2005).

Berry, M. V.

J. F. Nye and M. V. Berry, Proc. R. Soc. London 336, 165 (1974).
[CrossRef]

Biener, G.

E. Hasman, G. Biener, A. Niv, and V. Kleiner, Prog. Opt. 47, 215 (2005).
[CrossRef]

Close, L. M.

G. A. Swartzlander Jr., E. L. Ford, R. S. Abdul-Malik, L. M. Close, M. A. Peters, D. M. Palacios, and D. W. Wilson, Opt. Express 14, 10200 (2008).
[CrossRef]

Dholakia, K.

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

DuBois, P. M.

J. J. Scarpetti, P. M. DuBois, R. M. Friedhoff, and V. K. Walworth, J. Imaging Sci. Technol. 42, 307 (1998).

Ford, E. L.

G. A. Swartzlander Jr., E. L. Ford, R. S. Abdul-Malik, L. M. Close, M. A. Peters, D. M. Palacios, and D. W. Wilson, Opt. Express 14, 10200 (2008).
[CrossRef]

Friedhoff, R. M.

J. J. Scarpetti, P. M. DuBois, R. M. Friedhoff, and V. K. Walworth, J. Imaging Sci. Technol. 42, 307 (1998).

Hajnal, J. V.

J. F. Nye and J. V. Hajnal, Proc. R. Soc. London 409, 21 (1987).
[CrossRef]

Hasman, E.

E. Hasman, G. Biener, A. Niv, and V. Kleiner, Prog. Opt. 47, 215 (2005).
[CrossRef]

Kleiner, V.

E. Hasman, G. Biener, A. Niv, and V. Kleiner, Prog. Opt. 47, 215 (2005).
[CrossRef]

Land, E. H.

Law, C. T.

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Levin, L. A.

L. A. Levin and A. C. Arnold, Neuro-Ophthalmology: The Practical Guide, (Thieme, 2005).

Lipson, S. G.

Lipton, L.

L. Lipton, Foundations of the Stereoscopic Cinema (Van Nostrand Reinhold, 1982).

Marathay, A. S.

Niv, A.

E. Hasman, G. Biener, A. Niv, and V. Kleiner, Prog. Opt. 47, 215 (2005).
[CrossRef]

Nye, J. F.

J. F. Nye and J. V. Hajnal, Proc. R. Soc. London 409, 21 (1987).
[CrossRef]

J. F. Nye, Proc. R. Soc. London 389, 279 (1983).
[CrossRef]

J. F. Nye and M. V. Berry, Proc. R. Soc. London 336, 165 (1974).
[CrossRef]

Padgett, M. J.

Palacios, D. M.

G. A. Swartzlander Jr., E. L. Ford, R. S. Abdul-Malik, L. M. Close, M. A. Peters, D. M. Palacios, and D. W. Wilson, Opt. Express 14, 10200 (2008).
[CrossRef]

Peters, M. A.

G. A. Swartzlander Jr., E. L. Ford, R. S. Abdul-Malik, L. M. Close, M. A. Peters, D. M. Palacios, and D. W. Wilson, Opt. Express 14, 10200 (2008).
[CrossRef]

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Rozas, D.

Sacks, Z. S.

Scarpetti, J. J.

J. J. Scarpetti, P. M. DuBois, R. M. Friedhoff, and V. K. Walworth, J. Imaging Sci. Technol. 42, 307 (1998).

Schadt, M.

Shoham, A.

Simpson, N. B.

Soskin, M. S.

M. S. Soskin and M. V. Vasnetsov, Prog. Opt. 42, 219 (2001).
[CrossRef]

Stalder, M.

Staliunas, K.

M. Vasnetsov and K. Staliunas, Optical Vortices, in Horizons in Horizons in World Physics Vol. 228 (Nova Science, 1999).

Swartzlander, G. A.

Vander, R.

Vasnetsov, M.

M. Vasnetsov and K. Staliunas, Optical Vortices, in Horizons in Horizons in World Physics Vol. 228 (Nova Science, 1999).

Vasnetsov, M. V.

M. S. Soskin and M. V. Vasnetsov, Prog. Opt. 42, 219 (2001).
[CrossRef]

Walworth, V. K.

J. J. Scarpetti, P. M. DuBois, R. M. Friedhoff, and V. K. Walworth, J. Imaging Sci. Technol. 42, 307 (1998).

Wilson, D. W.

G. A. Swartzlander Jr., E. L. Ford, R. S. Abdul-Malik, L. M. Close, M. A. Peters, D. M. Palacios, and D. W. Wilson, Opt. Express 14, 10200 (2008).
[CrossRef]

J. Imaging Sci. Technol.

J. J. Scarpetti, P. M. DuBois, R. M. Friedhoff, and V. K. Walworth, J. Imaging Sci. Technol. 42, 307 (1998).

J. Opt. Soc. Am.

J. Opt. Soc. Am. B

Opt. Express

G. A. Swartzlander Jr., E. L. Ford, R. S. Abdul-Malik, L. M. Close, M. A. Peters, D. M. Palacios, and D. W. Wilson, Opt. Express 14, 10200 (2008).
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Proc. R. Soc. London

J. F. Nye, Proc. R. Soc. London 389, 279 (1983).
[CrossRef]

J. F. Nye and J. V. Hajnal, Proc. R. Soc. London 409, 21 (1987).
[CrossRef]

J. F. Nye and M. V. Berry, Proc. R. Soc. London 336, 165 (1974).
[CrossRef]

Prog. Opt.

M. S. Soskin and M. V. Vasnetsov, Prog. Opt. 42, 219 (2001).
[CrossRef]

E. Hasman, G. Biener, A. Niv, and V. Kleiner, Prog. Opt. 47, 215 (2005).
[CrossRef]

Other

M. Vasnetsov and K. Staliunas, Optical Vortices, in Horizons in Horizons in World Physics Vol. 228 (Nova Science, 1999).

RIS--Stereo Imaging Group, “Outlook for StereoJet Three-Dimensional Printing,” www.rowland.harvard.edu/organization

L. A. Levin and A. C. Arnold, Neuro-Ophthalmology: The Practical Guide, (Thieme, 2005).

L. Lipton, Foundations of the Stereoscopic Cinema (Van Nostrand Reinhold, 1982).

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Figures (3)

Fig. 1
Fig. 1

Optical configuration in a rotated reference frame comprising a light source, a beam expander, polarizers, a quarter-wave plate, vectographs, and a detector.

Fig. 2
Fig. 2

(a) Vectograph image functions f ( x , y ) and g ( x , y ) , (b) Jones matrix amplitude M i , j ( x , y ) , and (c) phase Φ i , j ( x , y ) . Grayscale maps (in color online) are shown.

Fig. 3
Fig. 3

Experimental images using StereoJet masks (a) with and (b) without a quarter-wave plate. Respective computed amplitude and phase profiles are shown in (c),(d) and (e),(f).

Equations (9)

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

M f = [ f 1 ( x , y ) 0 0 f 2 ( x , y ) ] , M g = [ g 1 ( x , y ) 0 0 g 2 ( x , y ) ] ,
M f , α = π 4 = M t rot ( α ) M f M rot ( α ) = 1 2 [ f 1 + f 2 f 1 f 2 f 1 f 2 f 1 + f 2 ] ,
M rot ( α ) = [ cos ( α ) sin ( α ) sin ( α ) cos ( α ) ] .
M sys = M g , α M QWP M f , α = [ M x , x M y , x M x , y M y , y ] ,
f 1 = ( 1 + f ) 2 , f 2 = 1 f 1 ,
g 1 = ( 1 + g ) 2 , g 2 = 1 g 1 ,
M sys = 1 4 [ 1 + i f g f + i g g + i f i + f g ] .
f ( x , y ) + i g ( x , y ) = A ( r ) exp ( i m θ ) .
f ( x , y ) = A ( r ) cos ( m θ ) , g ( x , y ) = A ( r ) sin ( m θ ) .

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