Abstract

Vortex transmutation was predicted to take place when vortices interact with systems possessing discrete rotational symmetries of finite order [Phys. Rev. Lett. 95, 123901 (2005)]. Here we report what is believed to be the first experimental demonstration of vortex transmutation. We show that in free space, by simply inserting polygonal lenses into the optical path, the central vorticity of a coaxially incident optical vortex can be changed following the modular transmutation rule. We generate the wavefront at the exit face of the lenses with computer generated holograms and measure the output vorticity using the interference patterns at the focal plane. The results agree well with theoretical predictions.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. F. Nye and M. V. Berry, Proc. R. Soc. Lond. A 336, 165 (1974).
    [CrossRef]
  2. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
    [CrossRef]
  3. M. S. Soskin and M. V. Vasnetsov, Prog. Opt. 42, 219 (2001).
    [CrossRef]
  4. M. S. Soskin, V. N. Gorshkov, and M. V. Vasnetsov, Phys. Rev. A 56, 4064 (1997).
    [CrossRef]
  5. L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
    [CrossRef]
  6. M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
    [CrossRef]
  7. D. G. Grier, Nature 424, 810 (2003).
    [CrossRef]
  8. G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
    [CrossRef]
  9. E. Nagali, L. Sansoni, L. Marrucci, E. Santamato, and F. Sciarrino, Phys. Rev. A 81, 052317 (2010).
    [CrossRef]
  10. I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 103, 422 (1993).
    [CrossRef]
  11. G. Molina-Terriza, J. Recolons, J. P. Torres, L. Torner, and E. M. Wright, Phys. Rev. Lett. 87, 023902 (2001).
    [CrossRef]
  12. M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
    [CrossRef]
  13. N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, Opt. Lett. 17, 221 (1992).
    [CrossRef]
  14. N. Gao, C. Xie, C. Li, C. Jin, and M. Liu, Appl. Phys. Lett. 98, 151106 (2011).
    [CrossRef]
  15. C. Xie, X. Zhu, L. Shi, and M. Liu, Opt. Lett. 35, 1765 (2010).
    [CrossRef]
  16. L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
    [CrossRef]
  17. A. Ferrando, M. Zacares, M. Garcia-March, J. A. Monsoriu, and P. F. de Cordoba, Phys. Rev. Lett. 95, 123901 (2005).
    [CrossRef]
  18. A. Ferrando, Phys. Rev. E 72, 036612 (2005).
    [CrossRef]
  19. A. Ferrando, M. Zacares, and M. Garcia-March, Phys. Rev. Lett. 95, 043901 (2005).
    [CrossRef]
  20. V. M. Pérez-García, M. A. García-March, and A. Ferrando, Phys. Rev. A 75, 033618 (2007).
    [CrossRef]
  21. S. A. Collins, J. Opt. Soc. Am. 60, 1168 (1970).
    [CrossRef]
  22. J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, Phys. Rev. Lett. 105, 053904 (2010).
    [CrossRef]
  23. W. H. Lee, Appl. Opt. 13, 1677 (1974).
    [CrossRef]

2011

N. Gao, C. Xie, C. Li, C. Jin, and M. Liu, Appl. Phys. Lett. 98, 151106 (2011).
[CrossRef]

2010

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef]

C. Xie, X. Zhu, L. Shi, and M. Liu, Opt. Lett. 35, 1765 (2010).
[CrossRef]

E. Nagali, L. Sansoni, L. Marrucci, E. Santamato, and F. Sciarrino, Phys. Rev. A 81, 052317 (2010).
[CrossRef]

2007

G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

V. M. Pérez-García, M. A. García-March, and A. Ferrando, Phys. Rev. A 75, 033618 (2007).
[CrossRef]

2006

L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef]

2005

A. Ferrando, M. Zacares, M. Garcia-March, J. A. Monsoriu, and P. F. de Cordoba, Phys. Rev. Lett. 95, 123901 (2005).
[CrossRef]

A. Ferrando, Phys. Rev. E 72, 036612 (2005).
[CrossRef]

A. Ferrando, M. Zacares, and M. Garcia-March, Phys. Rev. Lett. 95, 043901 (2005).
[CrossRef]

2003

D. G. Grier, Nature 424, 810 (2003).
[CrossRef]

2002

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef]

2001

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef]

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

G. Molina-Terriza, J. Recolons, J. P. Torres, L. Torner, and E. M. Wright, Phys. Rev. Lett. 87, 023902 (2001).
[CrossRef]

1997

M. S. Soskin, V. N. Gorshkov, and M. V. Vasnetsov, Phys. Rev. A 56, 4064 (1997).
[CrossRef]

1994

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

1993

I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 103, 422 (1993).
[CrossRef]

1992

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, Opt. Lett. 17, 221 (1992).
[CrossRef]

1974

W. H. Lee, Appl. Opt. 13, 1677 (1974).
[CrossRef]

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

1970

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Arlt, J.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef]

Basistiy, I. V.

I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 103, 422 (1993).
[CrossRef]

Bazhenov, V. Y.

I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 103, 422 (1993).
[CrossRef]

Beijersbergen, M. W.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Berry, M. V.

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

Bryant, P. E.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef]

Chávez-Cerda, S.

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef]

Coerwinkel, R. P. C.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

Collins, S. A.

de Cordoba, P. F.

A. Ferrando, M. Zacares, M. Garcia-March, J. A. Monsoriu, and P. F. de Cordoba, Phys. Rev. Lett. 95, 123901 (2005).
[CrossRef]

Dholakia, K.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef]

Ferrando, A.

V. M. Pérez-García, M. A. García-March, and A. Ferrando, Phys. Rev. A 75, 033618 (2007).
[CrossRef]

A. Ferrando, Phys. Rev. E 72, 036612 (2005).
[CrossRef]

A. Ferrando, M. Zacares, M. Garcia-March, J. A. Monsoriu, and P. F. de Cordoba, Phys. Rev. Lett. 95, 123901 (2005).
[CrossRef]

A. Ferrando, M. Zacares, and M. Garcia-March, Phys. Rev. Lett. 95, 043901 (2005).
[CrossRef]

Fonseca, E. J. S.

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef]

Gao, N.

N. Gao, C. Xie, C. Li, C. Jin, and M. Liu, Appl. Phys. Lett. 98, 151106 (2011).
[CrossRef]

Garcia-March, M.

A. Ferrando, M. Zacares, M. Garcia-March, J. A. Monsoriu, and P. F. de Cordoba, Phys. Rev. Lett. 95, 123901 (2005).
[CrossRef]

A. Ferrando, M. Zacares, and M. Garcia-March, Phys. Rev. Lett. 95, 043901 (2005).
[CrossRef]

García-March, M. A.

V. M. Pérez-García, M. A. García-March, and A. Ferrando, Phys. Rev. A 75, 033618 (2007).
[CrossRef]

Gorshkov, V. N.

M. S. Soskin, V. N. Gorshkov, and M. V. Vasnetsov, Phys. Rev. A 56, 4064 (1997).
[CrossRef]

Grier, D. G.

D. G. Grier, Nature 424, 810 (2003).
[CrossRef]

Heckenberg, N. R.

Hickmann, J. M.

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef]

Jin, C.

N. Gao, C. Xie, C. Li, C. Jin, and M. Liu, Appl. Phys. Lett. 98, 151106 (2011).
[CrossRef]

Kristensen, M.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

Lee, W. H.

Li, C.

N. Gao, C. Xie, C. Li, C. Jin, and M. Liu, Appl. Phys. Lett. 98, 151106 (2011).
[CrossRef]

Liu, M.

N. Gao, C. Xie, C. Li, C. Jin, and M. Liu, Appl. Phys. Lett. 98, 151106 (2011).
[CrossRef]

C. Xie, X. Zhu, L. Shi, and M. Liu, Opt. Lett. 35, 1765 (2010).
[CrossRef]

MacDonald, M. P.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef]

Manzo, C.

L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef]

Marrucci, L.

E. Nagali, L. Sansoni, L. Marrucci, E. Santamato, and F. Sciarrino, Phys. Rev. A 81, 052317 (2010).
[CrossRef]

L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef]

McDuff, R.

Molina-Terriza, G.

G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

G. Molina-Terriza, J. Recolons, J. P. Torres, L. Torner, and E. M. Wright, Phys. Rev. Lett. 87, 023902 (2001).
[CrossRef]

Monsoriu, J. A.

A. Ferrando, M. Zacares, M. Garcia-March, J. A. Monsoriu, and P. F. de Cordoba, Phys. Rev. Lett. 95, 123901 (2005).
[CrossRef]

Nagali, E.

E. Nagali, L. Sansoni, L. Marrucci, E. Santamato, and F. Sciarrino, Phys. Rev. A 81, 052317 (2010).
[CrossRef]

Nye, J. F.

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

Paparo, D.

L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef]

Paterson, L.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef]

Pérez-García, V. M.

V. M. Pérez-García, M. A. García-March, and A. Ferrando, Phys. Rev. A 75, 033618 (2007).
[CrossRef]

Recolons, J.

G. Molina-Terriza, J. Recolons, J. P. Torres, L. Torner, and E. M. Wright, Phys. Rev. Lett. 87, 023902 (2001).
[CrossRef]

Sansoni, L.

E. Nagali, L. Sansoni, L. Marrucci, E. Santamato, and F. Sciarrino, Phys. Rev. A 81, 052317 (2010).
[CrossRef]

Santamato, E.

E. Nagali, L. Sansoni, L. Marrucci, E. Santamato, and F. Sciarrino, Phys. Rev. A 81, 052317 (2010).
[CrossRef]

Sciarrino, F.

E. Nagali, L. Sansoni, L. Marrucci, E. Santamato, and F. Sciarrino, Phys. Rev. A 81, 052317 (2010).
[CrossRef]

Shi, L.

Sibbett, W.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef]

Smith, C. P.

Soares, W. C.

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef]

Soskin, M. S.

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

M. S. Soskin, V. N. Gorshkov, and M. V. Vasnetsov, Phys. Rev. A 56, 4064 (1997).
[CrossRef]

I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 103, 422 (1993).
[CrossRef]

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Torner, L.

G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

G. Molina-Terriza, J. Recolons, J. P. Torres, L. Torner, and E. M. Wright, Phys. Rev. Lett. 87, 023902 (2001).
[CrossRef]

Torres, J. P.

G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

G. Molina-Terriza, J. Recolons, J. P. Torres, L. Torner, and E. M. Wright, Phys. Rev. Lett. 87, 023902 (2001).
[CrossRef]

Vasnetsov, M. V.

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

M. S. Soskin, V. N. Gorshkov, and M. V. Vasnetsov, Phys. Rev. A 56, 4064 (1997).
[CrossRef]

I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 103, 422 (1993).
[CrossRef]

Volke-Sepulveda, K.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef]

White, A. G.

Woerdman, J. P.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Wright, E. M.

G. Molina-Terriza, J. Recolons, J. P. Torres, L. Torner, and E. M. Wright, Phys. Rev. Lett. 87, 023902 (2001).
[CrossRef]

Xie, C.

N. Gao, C. Xie, C. Li, C. Jin, and M. Liu, Appl. Phys. Lett. 98, 151106 (2011).
[CrossRef]

C. Xie, X. Zhu, L. Shi, and M. Liu, Opt. Lett. 35, 1765 (2010).
[CrossRef]

Zacares, M.

A. Ferrando, M. Zacares, and M. Garcia-March, Phys. Rev. Lett. 95, 043901 (2005).
[CrossRef]

A. Ferrando, M. Zacares, M. Garcia-March, J. A. Monsoriu, and P. F. de Cordoba, Phys. Rev. Lett. 95, 123901 (2005).
[CrossRef]

Zhu, X.

Appl. Opt.

Appl. Phys. Lett.

N. Gao, C. Xie, C. Li, C. Jin, and M. Liu, Appl. Phys. Lett. 98, 151106 (2011).
[CrossRef]

J. Opt. Soc. Am.

Nat. Phys.

G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

Nature

D. G. Grier, Nature 424, 810 (2003).
[CrossRef]

Opt. Commun.

I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 103, 422 (1993).
[CrossRef]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

Opt. Lett.

Phys. Rev. A

V. M. Pérez-García, M. A. García-March, and A. Ferrando, Phys. Rev. A 75, 033618 (2007).
[CrossRef]

E. Nagali, L. Sansoni, L. Marrucci, E. Santamato, and F. Sciarrino, Phys. Rev. A 81, 052317 (2010).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

M. S. Soskin, V. N. Gorshkov, and M. V. Vasnetsov, Phys. Rev. A 56, 4064 (1997).
[CrossRef]

Phys. Rev. E

A. Ferrando, Phys. Rev. E 72, 036612 (2005).
[CrossRef]

Phys. Rev. Lett.

A. Ferrando, M. Zacares, and M. Garcia-March, Phys. Rev. Lett. 95, 043901 (2005).
[CrossRef]

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef]

L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef]

A. Ferrando, M. Zacares, M. Garcia-March, J. A. Monsoriu, and P. F. de Cordoba, Phys. Rev. Lett. 95, 123901 (2005).
[CrossRef]

G. Molina-Terriza, J. Recolons, J. P. Torres, L. Torner, and E. M. Wright, Phys. Rev. Lett. 87, 023902 (2001).
[CrossRef]

Proc. R. Soc. Lond. A

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

Prog. Opt.

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

Science

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef]

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1.

(a) Schematic of the vortex transmutation setup. A vortex beam with vorticity li illuminates the aperture, and the output vorticity lo is obtained at the observation plane; (b) Phase profiles of the PLs’ transmittance functions.

Fig. 2.
Fig. 2.

Intensity (left column) and phase (right column) profile at the central region of the focal plane of the PLs illuminated by input vortex beams with (a) n=3, li=1; (b) n=3, li=2; (c) n=3, li=3; (d) n=3, li=4; (e) n=4, li=5; (f) n=5, li=5; (g) n=6, li=5 and (h) n=7, li=5. In the simulations, the wavelength of the input beam is 355 nm, the focal length of the PLs is 10 cm, and the actual size of the images is 80μm×80μm.

Fig. 3.
Fig. 3.

Schematic diagram of the experimental setup for the demonstration of optical vortex transmutation in free space. The inset illustrates the structure of the CGHs. The upper part is the aperture, and the lower part is the LG.

Fig. 4.
Fig. 4.

Microscopic images of the CGHs (left column) and the diffraction patterns without (middle column) and with (right column) the reference beam, with the parameters (a) n=3, li=1; (b) n=3, li=2; (c) n=3, li=3; (d) n=3, li=4; (e) n=4, li=5; (f) n=5, li=5; (g) n=6, li=5 and (h) n=7, li=5. The size of the microscopic images are 2.6μm×2.6μm and that of the CCD recorded images are 110μm×110μm.

Equations (5)

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

Uo(xo,yo)Ui(xi,yi)exp{ik2C[D(xi2+yi2)2(xixo+yiyo)+A(xo2+yo2)]}dxidyi,
lo=li+sn(sZ),where|lo|n/2,
tPL(ρ)=exp[ikρ2cos2(φnφ/2π2π/nπ/n)/2f],
Uo(r,z)=iAλztPL(ρ)exp(iliφ)exp(ik2z|rρ|2)dρ,
tCGH(ρ)=m=sin(mπ/2)mπexp[im·arg(UPL)],

Metrics