Abstract

Rotating point spread functions (PSFs) present invariant features that continuously rotate with defocus and are important in diverse applications such as computational imaging and atom/particle trapping. However, their transfer function efficiency is typically very low. We generate highly efficient rotating PSFs by tailoring the range of invariant rotation to the specific application. The PSF design involves an optimization procedure that applies constraints in the Gauss-Laguerre modal plane, the spatial domain, and the Fourier domain. We observed over thirty times improvement in transfer function efficiency. Experiments with a phase-only spatial light modulator demonstrate the potential of high-efficiency rotating PSFs.

© 2008 Optical Society of America

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References

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  1. Y. Y. Schechner, R. Piestun, and J. Shamir, "Wave propagation with rotating intensity distributions," Phys. Rev. E 54, R50-R53 (1996).
    [CrossRef]
  2. V. V. Kotlyar, V. A. Soifer, and S. N. Khonina, "An algorithm for the generation of laser beams with longitudinal periodicity: rotating images," J. Mod. Opt. 44, 1409-1416 (1997).
    [CrossRef]
  3. R. Piestun, Y. Y. Schechner, and J. Shamir, "Propagation-invariant wave fields with finite energy," J. Opt. Soc. Am. A 17, 294-303 (2000).
    [CrossRef]
  4. S. N. Khonina, V. V. Kotlyar, V. A. Soifer, M. Honkanen, J. Lautanen, and J. Turunen, "Generation of rotating Gauss-Laguerre modes with binary-phase diffractive optics," J. Mod. Opt. 46, 227-238 (1999).
  5. E. G. Abramochkin and V. G. Volostnikov, "Spiral light beams," Phys.-Usp. 47, 1177-1203 (2004).
    [CrossRef]
  6. A. Y. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, "Angular momentum of a rotating light beam," Opt. Comm. 249, 367-378 (2005).
    [CrossRef]
  7. N. B. Simpson, L. Allen, and M. J. Padgett, "Optical tweezers and optical spanners with Laguerre-Gaussian modes," J. of Mod. Opt. 43, 2485-2491 (1996).
    [CrossRef]
  8. M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, "Creation and manipulation of three-dimensional optically trapped structures," Science 296, 1101-1103 (2002).
    [CrossRef] [PubMed]
  9. R. Grimm, M. Weidemuller, and Y. B. Ovchinnikov, "Optical dipole traps for neutral atoms," Adv. At. Mol. Opt. Phys. 42, 95-170 (2000).
    [CrossRef]
  10. A. Greengard, Y. Y. Schechner, and R. Piestun, "Depth from diffracted rotation," Opt. Lett. 31, 181-183 (2006).
    [CrossRef] [PubMed]
  11. W. H. Lee, "Computer-generated holograms: techniques and applications," in Progress in Optics, E. Wolf, ed. (Elsevier, 1978), Chap. 3.
  12. R. Piestun, B. Spektor, and J. Shamir, "Wave fields in three dimensions: analysis and synthesis," J. Opt. Soc. Am. A 13, 1837-1848 (1996).
    [CrossRef]
  13. R. Piestun and J. Shamir, "Control of wave-front propagation with diffractive elements," Opt. Lett. 19, 771-773 (1994).
    [CrossRef] [PubMed]

2006

2005

A. Y. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, "Angular momentum of a rotating light beam," Opt. Comm. 249, 367-378 (2005).
[CrossRef]

2004

E. G. Abramochkin and V. G. Volostnikov, "Spiral light beams," Phys.-Usp. 47, 1177-1203 (2004).
[CrossRef]

2002

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, "Creation and manipulation of three-dimensional optically trapped structures," Science 296, 1101-1103 (2002).
[CrossRef] [PubMed]

2000

R. Grimm, M. Weidemuller, and Y. B. Ovchinnikov, "Optical dipole traps for neutral atoms," Adv. At. Mol. Opt. Phys. 42, 95-170 (2000).
[CrossRef]

R. Piestun, Y. Y. Schechner, and J. Shamir, "Propagation-invariant wave fields with finite energy," J. Opt. Soc. Am. A 17, 294-303 (2000).
[CrossRef]

1999

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, M. Honkanen, J. Lautanen, and J. Turunen, "Generation of rotating Gauss-Laguerre modes with binary-phase diffractive optics," J. Mod. Opt. 46, 227-238 (1999).

1997

V. V. Kotlyar, V. A. Soifer, and S. N. Khonina, "An algorithm for the generation of laser beams with longitudinal periodicity: rotating images," J. Mod. Opt. 44, 1409-1416 (1997).
[CrossRef]

1996

R. Piestun, B. Spektor, and J. Shamir, "Wave fields in three dimensions: analysis and synthesis," J. Opt. Soc. Am. A 13, 1837-1848 (1996).
[CrossRef]

N. B. Simpson, L. Allen, and M. J. Padgett, "Optical tweezers and optical spanners with Laguerre-Gaussian modes," J. of Mod. Opt. 43, 2485-2491 (1996).
[CrossRef]

Y. Y. Schechner, R. Piestun, and J. Shamir, "Wave propagation with rotating intensity distributions," Phys. Rev. E 54, R50-R53 (1996).
[CrossRef]

1994

Abramochkin, E. G.

E. G. Abramochkin and V. G. Volostnikov, "Spiral light beams," Phys.-Usp. 47, 1177-1203 (2004).
[CrossRef]

Allen, L.

N. B. Simpson, L. Allen, and M. J. Padgett, "Optical tweezers and optical spanners with Laguerre-Gaussian modes," J. of Mod. Opt. 43, 2485-2491 (1996).
[CrossRef]

Arlt, J.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, "Creation and manipulation of three-dimensional optically trapped structures," Science 296, 1101-1103 (2002).
[CrossRef] [PubMed]

Bekshaev, A. Y.

A. Y. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, "Angular momentum of a rotating light beam," Opt. Comm. 249, 367-378 (2005).
[CrossRef]

Dholakia, K.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, "Creation and manipulation of three-dimensional optically trapped structures," Science 296, 1101-1103 (2002).
[CrossRef] [PubMed]

Greengard, A.

Grimm, R.

R. Grimm, M. Weidemuller, and Y. B. Ovchinnikov, "Optical dipole traps for neutral atoms," Adv. At. Mol. Opt. Phys. 42, 95-170 (2000).
[CrossRef]

Honkanen, M.

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, M. Honkanen, J. Lautanen, and J. Turunen, "Generation of rotating Gauss-Laguerre modes with binary-phase diffractive optics," J. Mod. Opt. 46, 227-238 (1999).

Khonina, S. N.

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, M. Honkanen, J. Lautanen, and J. Turunen, "Generation of rotating Gauss-Laguerre modes with binary-phase diffractive optics," J. Mod. Opt. 46, 227-238 (1999).

V. V. Kotlyar, V. A. Soifer, and S. N. Khonina, "An algorithm for the generation of laser beams with longitudinal periodicity: rotating images," J. Mod. Opt. 44, 1409-1416 (1997).
[CrossRef]

Kotlyar, V. V.

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, M. Honkanen, J. Lautanen, and J. Turunen, "Generation of rotating Gauss-Laguerre modes with binary-phase diffractive optics," J. Mod. Opt. 46, 227-238 (1999).

V. V. Kotlyar, V. A. Soifer, and S. N. Khonina, "An algorithm for the generation of laser beams with longitudinal periodicity: rotating images," J. Mod. Opt. 44, 1409-1416 (1997).
[CrossRef]

Lautanen, J.

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, M. Honkanen, J. Lautanen, and J. Turunen, "Generation of rotating Gauss-Laguerre modes with binary-phase diffractive optics," J. Mod. Opt. 46, 227-238 (1999).

MacDonald, M. P.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, "Creation and manipulation of three-dimensional optically trapped structures," Science 296, 1101-1103 (2002).
[CrossRef] [PubMed]

Ovchinnikov, Y. B.

R. Grimm, M. Weidemuller, and Y. B. Ovchinnikov, "Optical dipole traps for neutral atoms," Adv. At. Mol. Opt. Phys. 42, 95-170 (2000).
[CrossRef]

Padgett, M. J.

N. B. Simpson, L. Allen, and M. J. Padgett, "Optical tweezers and optical spanners with Laguerre-Gaussian modes," J. of Mod. Opt. 43, 2485-2491 (1996).
[CrossRef]

Paterson, L.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, "Creation and manipulation of three-dimensional optically trapped structures," Science 296, 1101-1103 (2002).
[CrossRef] [PubMed]

Piestun, R.

Schechner, Y. Y.

Shamir, J.

Sibbett, W.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, "Creation and manipulation of three-dimensional optically trapped structures," Science 296, 1101-1103 (2002).
[CrossRef] [PubMed]

Simpson, N. B.

N. B. Simpson, L. Allen, and M. J. Padgett, "Optical tweezers and optical spanners with Laguerre-Gaussian modes," J. of Mod. Opt. 43, 2485-2491 (1996).
[CrossRef]

Soifer, V. A.

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, M. Honkanen, J. Lautanen, and J. Turunen, "Generation of rotating Gauss-Laguerre modes with binary-phase diffractive optics," J. Mod. Opt. 46, 227-238 (1999).

V. V. Kotlyar, V. A. Soifer, and S. N. Khonina, "An algorithm for the generation of laser beams with longitudinal periodicity: rotating images," J. Mod. Opt. 44, 1409-1416 (1997).
[CrossRef]

Soskin, M. S.

A. Y. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, "Angular momentum of a rotating light beam," Opt. Comm. 249, 367-378 (2005).
[CrossRef]

Spektor, B.

Turunen, J.

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, M. Honkanen, J. Lautanen, and J. Turunen, "Generation of rotating Gauss-Laguerre modes with binary-phase diffractive optics," J. Mod. Opt. 46, 227-238 (1999).

Vasnetsov, M. V.

A. Y. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, "Angular momentum of a rotating light beam," Opt. Comm. 249, 367-378 (2005).
[CrossRef]

Volke-Sepulveda, K.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, "Creation and manipulation of three-dimensional optically trapped structures," Science 296, 1101-1103 (2002).
[CrossRef] [PubMed]

Volostnikov, V. G.

E. G. Abramochkin and V. G. Volostnikov, "Spiral light beams," Phys.-Usp. 47, 1177-1203 (2004).
[CrossRef]

Weidemuller, M.

R. Grimm, M. Weidemuller, and Y. B. Ovchinnikov, "Optical dipole traps for neutral atoms," Adv. At. Mol. Opt. Phys. 42, 95-170 (2000).
[CrossRef]

Adv. At. Mol. Opt. Phys.

R. Grimm, M. Weidemuller, and Y. B. Ovchinnikov, "Optical dipole traps for neutral atoms," Adv. At. Mol. Opt. Phys. 42, 95-170 (2000).
[CrossRef]

J. Mod. Opt.

V. V. Kotlyar, V. A. Soifer, and S. N. Khonina, "An algorithm for the generation of laser beams with longitudinal periodicity: rotating images," J. Mod. Opt. 44, 1409-1416 (1997).
[CrossRef]

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, M. Honkanen, J. Lautanen, and J. Turunen, "Generation of rotating Gauss-Laguerre modes with binary-phase diffractive optics," J. Mod. Opt. 46, 227-238 (1999).

J. of Mod. Opt.

N. B. Simpson, L. Allen, and M. J. Padgett, "Optical tweezers and optical spanners with Laguerre-Gaussian modes," J. of Mod. Opt. 43, 2485-2491 (1996).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Comm.

A. Y. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, "Angular momentum of a rotating light beam," Opt. Comm. 249, 367-378 (2005).
[CrossRef]

Opt. Lett.

Phys. Rev. E

Y. Y. Schechner, R. Piestun, and J. Shamir, "Wave propagation with rotating intensity distributions," Phys. Rev. E 54, R50-R53 (1996).
[CrossRef]

Science

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, "Creation and manipulation of three-dimensional optically trapped structures," Science 296, 1101-1103 (2002).
[CrossRef] [PubMed]

Usp.

E. G. Abramochkin and V. G. Volostnikov, "Spiral light beams," Phys.-Usp. 47, 1177-1203 (2004).
[CrossRef]

Other

W. H. Lee, "Computer-generated holograms: techniques and applications," in Progress in Optics, E. Wolf, ed. (Elsevier, 1978), Chap. 3.

Supplementary Material (5)

» Media 1: MOV (58 KB)     
» Media 2: MOV (44 KB)     
» Media 3: MOV (41 KB)     
» Media 4: MOV (94 KB)     
» Media 5: MOV (3448 KB)     

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Figures (4)

Fig. 1.
Fig. 1.

Transfer functions of (a) rotating PSF, (b) HER-PSF initial estimate, and (c) HER-PSF. (d), (e), and (f) are the GL modal plane decompositions of the transfer functions in (a), (b), and (c), respectively. The transfer functions of the HER-PSF initial estimate and the HER-PSF form a cloud around the line in (d).

Fig. 2.
Fig. 2.

Movies of different rotating PSFs: (a) Exact rotating PSF, (b) HER-PSF initial estimate, (c) HER-PSF, and (d) the experimental implementation of HER-PSF. HER-PSF has over 30 times higher efficiency than the exact rotating PSF. [Media 1][Media 2][Media 3][Media 4]

Fig. 3.
Fig. 3.

Movie of the evolutions of (a) mask phase, (b) GL modal plane, (c) main lobe peak intensity, and (d) mask transparency in the iterative optimization procedure.[Media 5]

Fig. 4.
Fig. 4.

A HER-PSF mask designed for a wavelength of 550nm, when used with the wavelengths 500nm and 600nm, exhibits (a) same rotation rates as function of defocus parameter (ψ) and (b) slightly different rotation rates as a function of depth (NA=0.71).

Equations (2)

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d ( m , n ) = k = 1 N [ ( m m k ) 2 + ( n n k ) 2 ] p ,
T = x y H i ( x , y ) x y C ( x , y ) ,

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