## Phase plates for generation of variable amounts of primary spherical aberration |

Optics Express, Vol. 19, Issue 14, pp. 13171-13178 (2011)

http://dx.doi.org/10.1364/OE.19.013171

Acrobat PDF (1019 KB)

### Abstract

We discuss a set of phase plate-pairs for the generation of variable amounts of primary spherical aberration. The surface descriptions of these optical plates are provided, and their aberration-generating properties are verified with real ray-tracing. These plate-pairs are robust in that they allow large tolerances to spacing as well as errors in the relative displacement of the plates. Both primary spherical aberration (*r ^{4}
*) and Zernike spherical aberration (6

*r*-

^{4}*6r*can be generated. The amount of spherical aberration is proportional to the plate-pair displacement and in our example it reaches up to 48 waves (~8 waves Zernike) for a clear aperture of 25 mm.

^{2}+ 1)© 2011 OSA

## 1. Introduction

1. P. S. Tsai, B. Migliori, K. Campbell, T. N. Kim, Z. Kam, A. Groisman, and D. Kleinfeld, “Spherical aberration correction in nonlinear microscopy and optical ablation using a transparent deformable membrane,” Appl. Phys. Lett. **91**(19), 191102 (2007). [CrossRef]

2. E. Theofanidou, L. Wilson, W. Hossack, and J. Arlt, “Spherical aberration correction for optical tweezers,” Opt. Commun. **236**(1-3), 145–150 (2004). [CrossRef]

3. J. Knittel, H. Richter, M. Hain, S. Somalingam, and T. Tschudi, “Liquid crystal lens for spherical aberration compensation in blu-ray disc systems,” IEE Proc. Sci. Meas. Technol. **152**(1), 15–18 (2005). [CrossRef]

4. P. Mouroulis, “Depth of field extension with spherical optics,” Opt. Express **16**(17), 12995–13004 (2008). [CrossRef] [PubMed]

5. M. Schwertner, M. J. Booth, T. Tanaka, T. Wilson, and S. Kawata, “Spherical aberration correction system using an adaptive optics deformable mirror,” Opt. Commun. **263**(2), 147–151 (2006). [CrossRef]

1. P. S. Tsai, B. Migliori, K. Campbell, T. N. Kim, Z. Kam, A. Groisman, and D. Kleinfeld, “Spherical aberration correction in nonlinear microscopy and optical ablation using a transparent deformable membrane,” Appl. Phys. Lett. **91**(19), 191102 (2007). [CrossRef]

3. J. Knittel, H. Richter, M. Hain, S. Somalingam, and T. Tschudi, “Liquid crystal lens for spherical aberration compensation in blu-ray disc systems,” IEE Proc. Sci. Meas. Technol. **152**(1), 15–18 (2005). [CrossRef]

6. R. A. Buchroeder and R. B. Hooker, “Aberration generator,” Appl. Opt. **14**(10), 2476–2479 (1975). [CrossRef] [PubMed]

6. R. A. Buchroeder and R. B. Hooker, “Aberration generator,” Appl. Opt. **14**(10), 2476–2479 (1975). [CrossRef] [PubMed]

9. A. W. Lohmann, “A new class of varifocal lenses,” Appl. Opt. **9**(7), 1669–1671 (1970). [CrossRef] [PubMed]

10. S. Bará, Z. Jaroszewicz, A. Kołodziejczyk, and V. Moreno, “Determination of basic grids for subtractive moire patterns,” Appl. Opt. **30**(10), 1258–1262 (1991). [CrossRef] [PubMed]

13. J. M. Burch and D. C. Williams, “Varifocal moiré zone plates for straightness measurement,” Appl. Opt. **16**(9), 2445–2450 (1977). [CrossRef] [PubMed]

14. N. López-Gil, H. C. Howland, B. Howland, N. Charman, and R. Applegate, “Generation of third order spherical and coma aberrations by use of radially symmetrical fourth order lenses,” J. Opt. Soc. Am. A **15**(9), 2563–2571 (1998). [CrossRef]

15. I. A. Palusinski, J. M. Sasián, and J. E. Greivenkamp, “Lateral-shift variable aberration generators,” Appl. Opt. **38**(1), 86–90 (1999). [CrossRef] [PubMed]

16. T. Hellmuth, A. Bich, R. Börret, A. Holschbach, and A. Kelm, “Variable phaseplates for focus invariant optical systems,” Proc. SPIE **5962**, 596215 (2005). [CrossRef]

*n*, a lateral displacement

*Δ*of the reference frame gives rise to the appearance of all aberration terms of orders

*p*equal to or smaller than

*n*, whose coefficients are proportional to the powers Δ

*of the lateral displacement, as can be straightforwardly deduced [17*

^{n-p}17. A. Guirao, D. R. Williams, and I. G. Cox, “Effect of rotation and translation on the expected benefits of an ideal method to correct the eye’s higher order aberrations,” J. Opt. Soc. Am. A **18**(5), 1003–1015 (2001). [CrossRef]

*n*cancels out, and some amounts of lower order terms are produced. The above mentioned phase plates (except the Alvarez-Humphrey and Lohmann lens) generate some amounts of undesired lower order aberrations. This drawback was first overcome for non symmetric aberrations with rotating pairs of phase plates [18

18. E. Acosta and S. Bará, “Variable aberration generators using rotated Zernike plates,” J. Opt. Soc. Am. A **22**(9), 1993–1996 (2005). [CrossRef] [PubMed]

1. P. S. Tsai, B. Migliori, K. Campbell, T. N. Kim, Z. Kam, A. Groisman, and D. Kleinfeld, “Spherical aberration correction in nonlinear microscopy and optical ablation using a transparent deformable membrane,” Appl. Phys. Lett. **91**(19), 191102 (2007). [CrossRef]

5. M. Schwertner, M. J. Booth, T. Tanaka, T. Wilson, and S. Kawata, “Spherical aberration correction system using an adaptive optics deformable mirror,” Opt. Commun. **263**(2), 147–151 (2006). [CrossRef]

19. B. M. Pixton and J. E. Greivenkamp, “Spherical aberration gauge for human vision,” Appl. Opt. **49**(30), 5906–5913 (2010). [CrossRef] [PubMed]

*r*) or Zernike spherical aberration

^{4}*(6r*that is proportional to the plate-pair displacement. The simulation results performed in Zemax, optical design software, show ample tolerances to errors in the plate spacing and displacements, and insignificant aberration residual due to other modes.

^{4}- 6r^{2}+ 1)## 2. Theory

*a*can take any real value. The second surface of the first phase plate is flat.

*A*by

*–A*. If we assuming parallel light illumination, then when both plates are in contact and displaced by an amount

*Δ*in opposite directions along the X coordinate, the resulting optical path difference is proportional to the equivalent thickness of the set in the overlapping region, this is,where

*n*represents the refractive index of the plate and

*n’*that of the surrounding medium. In Eq. (2) some constant phase terms have been neglected and a simple optical path addition has been used to obtain the final optical path difference.

*Δ*, the optical path difference becomes,Thus, when both pairs of plates are stacked together a linear combination of spherical aberration and defocus proportional to the relative displacement

*Δ*is obtained,where

*a = 0*only primary spherical aberration is obtained whereas with

*a = 1*some defocus is introduced which minimizes the OPD variance (being in fact proportional to Zernike polynomial

14. N. López-Gil, H. C. Howland, B. Howland, N. Charman, and R. Applegate, “Generation of third order spherical and coma aberrations by use of radially symmetrical fourth order lenses,” J. Opt. Soc. Am. A **15**(9), 2563–2571 (1998). [CrossRef]

15. I. A. Palusinski, J. M. Sasián, and J. E. Greivenkamp, “Lateral-shift variable aberration generators,” Appl. Opt. **38**(1), 86–90 (1999). [CrossRef] [PubMed]

19. B. M. Pixton and J. E. Greivenkamp, “Spherical aberration gauge for human vision,” Appl. Opt. **49**(30), 5906–5913 (2010). [CrossRef] [PubMed]

*r*and

^{4}*r*terms while cancelling lower order terms.

^{2}## 3. Numerical simulations

*a = 1*were modelled in Zemax optical design software. We used BK7 glass for plates in air and a wavelength of 0.6563μm. Each plate is a square of about 50 mm in side and a thickness of

*A*is set to 0.02 to obtain up to

*Δ*of

*Δ = 10mm*(where about 48 waves of spherical aberration can be achieved).

*Δ = 0mm*for the first pair and

*Δ = 0.01mm*for the second pair, 2)

*Δ = 5mm*for the first pair and

*Δ = 5.01mm*for the second one, and 3)

*Δ = 10mm*for the first pair and

*Δ = 10.01mm*for the second one. In addition, in these three cases the following random values for plate rotations about the axes X,Y, and Z were included in the simulation:

- a) The first plate was rotated 0.1 degrees about X, −0.05 about Y and 0.3 about Z
- b) The second plate was rotated −0.2 degrees about X, 0.04 about Y and 0.1 about Z
- c) The third plate was rotated 0.05 degrees about X, −1.1 about Y and 0.2 about Z
- d) The fourth plate was rotated 0.8 degrees about X, 0.05 about Y and 0.1 about Z

## 4. Conclusion

## Acknowledgments

## References and links

1. | P. S. Tsai, B. Migliori, K. Campbell, T. N. Kim, Z. Kam, A. Groisman, and D. Kleinfeld, “Spherical aberration correction in nonlinear microscopy and optical ablation using a transparent deformable membrane,” Appl. Phys. Lett. |

2. | E. Theofanidou, L. Wilson, W. Hossack, and J. Arlt, “Spherical aberration correction for optical tweezers,” Opt. Commun. |

3. | J. Knittel, H. Richter, M. Hain, S. Somalingam, and T. Tschudi, “Liquid crystal lens for spherical aberration compensation in blu-ray disc systems,” IEE Proc. Sci. Meas. Technol. |

4. | P. Mouroulis, “Depth of field extension with spherical optics,” Opt. Express |

5. | M. Schwertner, M. J. Booth, T. Tanaka, T. Wilson, and S. Kawata, “Spherical aberration correction system using an adaptive optics deformable mirror,” Opt. Commun. |

6. | R. A. Buchroeder and R. B. Hooker, “Aberration generator,” Appl. Opt. |

7. | L. W. Alvarez and W. E. Humphrey, “Variable power lens and system,” U.S. Patent 3,507,565 (1970). |

8. | L. W. Alvarez, “Two-element variable-power spherical lens,” U.S. Patent 3,305,294 (1967). |

9. | A. W. Lohmann, “A new class of varifocal lenses,” Appl. Opt. |

10. | S. Bará, Z. Jaroszewicz, A. Kołodziejczyk, and V. Moreno, “Determination of basic grids for subtractive moire patterns,” Appl. Opt. |

11. | A. W. Lohmann and D. P. Paris, “Variable Fresnel zone pattern,” Appl. Opt. |

12. | A. Kołodziejczyk and Z. Jaroszewicz, “Diffractive elements of variable optical power and high diffraction efficiency,” Appl. Opt. |

13. | J. M. Burch and D. C. Williams, “Varifocal moiré zone plates for straightness measurement,” Appl. Opt. |

14. | N. López-Gil, H. C. Howland, B. Howland, N. Charman, and R. Applegate, “Generation of third order spherical and coma aberrations by use of radially symmetrical fourth order lenses,” J. Opt. Soc. Am. A |

15. | I. A. Palusinski, J. M. Sasián, and J. E. Greivenkamp, “Lateral-shift variable aberration generators,” Appl. Opt. |

16. | T. Hellmuth, A. Bich, R. Börret, A. Holschbach, and A. Kelm, “Variable phaseplates for focus invariant optical systems,” Proc. SPIE |

17. | A. Guirao, D. R. Williams, and I. G. Cox, “Effect of rotation and translation on the expected benefits of an ideal method to correct the eye’s higher order aberrations,” J. Opt. Soc. Am. A |

18. | E. Acosta and S. Bará, “Variable aberration generators using rotated Zernike plates,” J. Opt. Soc. Am. A |

19. | B. M. Pixton and J. E. Greivenkamp, “Spherical aberration gauge for human vision,” Appl. Opt. |

**OCIS Codes**

(220.0220) Optical design and fabrication : Optical design and fabrication

(220.1000) Optical design and fabrication : Aberration compensation

**ToC Category:**

Optical Design and Fabrication

**History**

Original Manuscript: May 3, 2011

Revised Manuscript: June 3, 2011

Manuscript Accepted: June 10, 2011

Published: June 22, 2011

**Citation**

Eva Acosta and José Sasián, "Phase plates for generation of variable amounts of primary spherical aberration," Opt. Express **19**, 13171-13178 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-14-13171

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### References

- P. S. Tsai, B. Migliori, K. Campbell, T. N. Kim, Z. Kam, A. Groisman, and D. Kleinfeld, “Spherical aberration correction in nonlinear microscopy and optical ablation using a transparent deformable membrane,” Appl. Phys. Lett. 91(19), 191102 (2007). [CrossRef]
- E. Theofanidou, L. Wilson, W. Hossack, and J. Arlt, “Spherical aberration correction for optical tweezers,” Opt. Commun. 236(1-3), 145–150 (2004). [CrossRef]
- J. Knittel, H. Richter, M. Hain, S. Somalingam, and T. Tschudi, “Liquid crystal lens for spherical aberration compensation in blu-ray disc systems,” IEE Proc. Sci. Meas. Technol. 152(1), 15–18 (2005). [CrossRef]
- P. Mouroulis, “Depth of field extension with spherical optics,” Opt. Express 16(17), 12995–13004 (2008). [CrossRef] [PubMed]
- M. Schwertner, M. J. Booth, T. Tanaka, T. Wilson, and S. Kawata, “Spherical aberration correction system using an adaptive optics deformable mirror,” Opt. Commun. 263(2), 147–151 (2006). [CrossRef]
- R. A. Buchroeder and R. B. Hooker, “Aberration generator,” Appl. Opt. 14(10), 2476–2479 (1975). [CrossRef] [PubMed]
- L. W. Alvarez and W. E. Humphrey, “Variable power lens and system,” U.S. Patent 3,507,565 (1970).
- L. W. Alvarez, “Two-element variable-power spherical lens,” U.S. Patent 3,305,294 (1967).
- A. W. Lohmann, “A new class of varifocal lenses,” Appl. Opt. 9(7), 1669–1671 (1970). [CrossRef] [PubMed]
- S. Bará, Z. Jaroszewicz, A. Kołodziejczyk, and V. Moreno, “Determination of basic grids for subtractive moire patterns,” Appl. Opt. 30(10), 1258–1262 (1991). [CrossRef] [PubMed]
- A. W. Lohmann and D. P. Paris, “Variable Fresnel zone pattern,” Appl. Opt. 6(9), 1567–1570 (1967). [CrossRef] [PubMed]
- A. Kołodziejczyk and Z. Jaroszewicz, “Diffractive elements of variable optical power and high diffraction efficiency,” Appl. Opt. 32(23), 4317–4322 (1993). [CrossRef] [PubMed]
- J. M. Burch and D. C. Williams, “Varifocal moiré zone plates for straightness measurement,” Appl. Opt. 16(9), 2445–2450 (1977). [CrossRef] [PubMed]
- N. López-Gil, H. C. Howland, B. Howland, N. Charman, and R. Applegate, “Generation of third order spherical and coma aberrations by use of radially symmetrical fourth order lenses,” J. Opt. Soc. Am. A 15(9), 2563–2571 (1998). [CrossRef]
- I. A. Palusinski, J. M. Sasián, and J. E. Greivenkamp, “Lateral-shift variable aberration generators,” Appl. Opt. 38(1), 86–90 (1999). [CrossRef] [PubMed]
- T. Hellmuth, A. Bich, R. Börret, A. Holschbach, and A. Kelm, “Variable phaseplates for focus invariant optical systems,” Proc. SPIE 5962, 596215 (2005). [CrossRef]
- A. Guirao, D. R. Williams, and I. G. Cox, “Effect of rotation and translation on the expected benefits of an ideal method to correct the eye’s higher order aberrations,” J. Opt. Soc. Am. A 18(5), 1003–1015 (2001). [CrossRef]
- E. Acosta and S. Bará, “Variable aberration generators using rotated Zernike plates,” J. Opt. Soc. Am. A 22(9), 1993–1996 (2005). [CrossRef] [PubMed]
- B. M. Pixton and J. E. Greivenkamp, “Spherical aberration gauge for human vision,” Appl. Opt. 49(30), 5906–5913 (2010). [CrossRef] [PubMed]

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