## Spherical aberration correction suitable for a wavefront controller

Optics Express, Vol. 17, Issue 16, pp. 14367-14373 (2009)

http://dx.doi.org/10.1364/OE.17.014367

Acrobat PDF (241 KB)

### Abstract

We propose a simple method to correct a large amount of spherical aberration caused by a refractive index mismatch. The method is based on inverse ray tracing and can generate correction phase patterns whose peak-to-valley values are minimized. We also demonstrated spherical aberration correction in a transparent acrylic block using a liquid-crystal-on-silicon spatial light modulator (LCOS-SLM). A distorted focal volume without correction was substantially improved with correction. This method is useful in cases where a large phase modulation is needed, such as when employing a high-NA lens or focusing a beam deep inside a sample.

© 2009 OSA

## 1. Introduction

1. M. J. Booth and T. Wilson, “Strategies for the compensation of specimen-induced spherical aberration in confocal microscopy of skin,” J. Microsc. **200**(Pt 1), 68–74 (2000). [CrossRef] [PubMed]

2. Y. Roichman, A. Waldron, E. Gardel, and D. G. Grier, “Optical traps with geometric aberrations,” Appl. Opt. **45**(15), 3425–3429 (2006). [CrossRef] [PubMed]

3. M. J. Booth, M. Schwertner, T. Wilson, M. Nakano, Y. Kawata, M. Nakabayashi, and S. Miyata, “Predictive aberration correction for multilayer optical data storage,” Appl. Phys. Lett. **88**(3), 031109 (2006). [CrossRef]

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

11. C. Mauclair, A. Mermillod-Blondin, N. Huot, E. Audouard, and R. Stoian, “Ultrafast laser writing of homogeneous longitudinal waveguides in glasses using dynamic wavefront correction,” Opt. Express **16**(8), 5481–5492 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-8-5481. [CrossRef] [PubMed]

*et al*. applied a genetic algorithm to generate pre-distortion patterns for multiphoton microscopy [12

12. L. Sherman, J. Y. Ye, O. Albert, and T. B. Norris, “Adaptive correction of depth-induced aberrations in multiphoton scanning microscopy using a deformable mirror,” J. Microsc. **206**(Pt 1), 65–71 (2002). [CrossRef] [PubMed]

13. M. J. Booth, M. A. A. Neil, and T. Wilson, “Aberration correction for confocal imaging in refractive-index-mismatched-media,” J. Microsc. **192**(2), 90–98 (1998). [CrossRef]

## 2. Calculation of pre-distortion patterns for aberration correction

*f*. The reference plane passes through the back principal point of an ideal objective lens whose focal length is

*f*. The back principal point

*C*is located at an intersection of the spherical reference plane and the optical axis in Fig. 1. The point D is the intersection of the optical axis and the interface between different materials. The pre-distortion pattern will be calculated as a distribution of optical path difference on this reference plane. When a plane wave enters the microscope objective and there is no refractive index mismatch, the wavefront outputted from the objective is coincident on the reference plane in shape and converges to an original focal point

*O*. Point

*O*’ is the desired focal point when a refractive material is set at a distance

*f*-

*d*from the principal point. Therefore, distance

*d*’ means the depth of the desired focal point. We assume that all rays incident on the reference plane are focused at the point

*O*’ after being given the pre-distortion. The optical path length of each ray from

*O*’ to the spherical reference plane can be calculated by using inverse ray tracing between those two points. In the inverse ray tracing procedure, the distance

*d*from

*O*to the surface of the material will be used as a parameter to control the PV value of the pre-distortion pattern. From now on, we call the depth

*d*the focus depth without refraction and the depth

*d*’ the focus depth with refraction.

*θ*

_{1}is the incident angle of the ray after correction,

*θ*

_{2}is the refraction angle of the same ray, and

*θ*is the ray angle when the refractive material is absent. Here,

*n*

_{1}and

*n*

_{2}are refractive indices before and after the interface, respectively. A pre-distortion pattern is defined as an optical path difference distribution between ray

*ABO*’ and ray

*CDO*’, that is

*Φ(θ)*-

*Φ(0)*.

*θ*

_{1}corresponding to a specific angle

*θ*. The relationship between

*θ*and

*θ*

_{1}is determined from

*θ*

_{1}for a specific angle

*θ*can be obtained by solving these equations. However, we took a different approach. By solving these equations for

*θ*, we get

*θ*

_{1}can be obtained by iteratively calculating

*θ*while changing

*θ*

_{1}until

*θ*is a desired angle as follow. Unless point

*O*’ is not much deeper than point

*O*,

*θ*

_{1}is larger than

*θ*, as shown in Fig. 1. Therefore, in the search procedure for

*θ*

_{1}, we set the initial value of

*θ*

_{1}to

*θ*and gradually increased the value of

*θ*

_{1}until

*θ*calculated from Eq. (5) reached the desired value. Then one can calculate a pre-distortion pattern

*Φ(θ)*-

*Φ(0)*for specific

*d*’ and

*d*. This pre-distortion pattern, in general, has a large PV value, which has to be minimized. This can be achieved by a search procedure in which

*Φ(θ)*-

*Φ(0)*is iteratively calculated as

*d*is varied until the PV value of the pre-distortion pattern is minimized.

## 3. Experimental set-up

14. T. Inoue, H. Tanaka, N. Fukuchi, M. Takumi, N. Matsumoto, T. Hara, N. Yoshida, Y. Igasaki, and Y. Kobayashi, “LCOS spatial light modulator controlled by 12-bit signals for optical phase-only modulation,” Proc. SPIE **6487**, 64870Y (2007). [CrossRef]

*f*= 3.6 mm). The telescope scaled down the size of the incident beam to match the size of the objective’s pupil diameter of 4 mm. In order to use SLM’s active area effectively, a combination of plano-convex lenses with focal lengths of 200 mm (L2) and 100 mm (L3) was used as the telescope. Thus, the effective area of the LCOS-SLM was imaged approximately onto the objective’s entrance pupil, making an area of 400 pixels in diameter effectively available. The modulated beam was focused into an acrylic block with a refractive index of

*n*

_{2}= 1.49 (Mitsubishi Rayon, ShinkoliteL, 302), which was placed in air (

*n*

_{1}= 1.0). The focal spot was monitored from the side of the acrylic block. An observation area of 60 μm × 60 μm was expanded onto a CCD camera (Sony, XC-ST30) by using a microscope objective (Mitsutoyo, MPlanNIR50, N.A. = 0.42), an extension tube (5 cm length), and an extender (Pentax, 2-EX). The acrylic block contained blue pigment, which enabled us to observe the focal spot through scattered light.

## 4. Results

*d*’ = 100 μm, (b)

*d*’ = 500 μm, and (c)

*d*’ = 1000 μm from the interface of the acrylic block are shown in Fig. 3. These results show that the intensity distributions of the focal spots spread asymmetrically in both radial and longitudinal directions. The asymmetry and the extent of spreading became worse at increasing focusing depths. This spreading, of course, caused the reduction in peak optical density.

*d*, were set to 64 μm, 319 μm, and 638 μm for the cases

*d*’ = 100 μm,

*d*’ = 500 μm, and

*d*’ = 1000 μm, respectively. The intensity distributions of the corrected focal spots were symmetrical and similar to each other. Their beam waists were narrow compared with those obtained without correction. For example, the lateral full width at half maximum (FWHM) of the focal spot when

*d*’ = 1000 μm was corrected from 2 μm to 1 μm, and the longitudinal FWHM was corrected from 36 μm to 7 μm. From these results, it can be concluded that this correction method worked effectively, even when the beam was focused deep inside the sample.

## 5. Discussion

## 6. Conclusion

## Acknowledgments

## References and links

1. | M. J. Booth and T. Wilson, “Strategies for the compensation of specimen-induced spherical aberration in confocal microscopy of skin,” J. Microsc. |

2. | Y. Roichman, A. Waldron, E. Gardel, and D. G. Grier, “Optical traps with geometric aberrations,” Appl. Opt. |

3. | M. J. Booth, M. Schwertner, T. Wilson, M. Nakano, Y. Kawata, M. Nakabayashi, and S. Miyata, “Predictive aberration correction for multilayer optical data storage,” Appl. Phys. Lett. |

4. | S. Taccheo, G. Della Valle, R. Osellame, G. Cerullo, N. Chiodo, P. Laporta, O. Svelto, A. Killi, U. Morgner, M. Lederer, and D. Kopf, “Er:Yb-doped waveguide laser fabricated by femtosecond laser pulses,” Opt. Lett. |

5. | J. P. McDonald, V. R. Mistry, K. E. Ray, and S. M. Yalisove, “Femtosecond pulsed laser direct write production of nano- and microfluidic channels,” Appl. Phys. Lett. |

6. | K. Miura, J. Qiu, H. Inouye, T. Mitsuyu, and K. Hirao, “Photowritten optical waveguides in various glasses with ultrashort pulse laser,” Appl. Phys. Lett. |

7. | N. Takeshima, Y. Narita, S. Tanaka, Y. Kuroiwa, and K. Hirao, “Fabrication of high-efficiency diffraction gratings in glass,” Opt. Lett. |

8. | D. Homoelle, S. Wielandy, A. L. Gaeta, N. F. Borrelli, and C. Smith, “Infrared photosensitivity in silica glasses exposed to femtosecond laser pulses,” Opt. Lett. |

9. | A. M. Streltsov and N. F. Borrelli, “Fabrication and analysis of a directional coupler written in glass by nanojoule femtosecond laser pulses,” Opt. Lett. |

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

11. | C. Mauclair, A. Mermillod-Blondin, N. Huot, E. Audouard, and R. Stoian, “Ultrafast laser writing of homogeneous longitudinal waveguides in glasses using dynamic wavefront correction,” Opt. Express |

12. | L. Sherman, J. Y. Ye, O. Albert, and T. B. Norris, “Adaptive correction of depth-induced aberrations in multiphoton scanning microscopy using a deformable mirror,” J. Microsc. |

13. | M. J. Booth, M. A. A. Neil, and T. Wilson, “Aberration correction for confocal imaging in refractive-index-mismatched-media,” J. Microsc. |

14. | T. Inoue, H. Tanaka, N. Fukuchi, M. Takumi, N. Matsumoto, T. Hara, N. Yoshida, Y. Igasaki, and Y. Kobayashi, “LCOS spatial light modulator controlled by 12-bit signals for optical phase-only modulation,” Proc. SPIE |

**OCIS Codes**

(220.1000) Optical design and fabrication : Aberration compensation

(230.6120) Optical devices : Spatial light modulators

**ToC Category:**

Optical Design and Fabrication

**History**

Original Manuscript: May 29, 2009

Revised Manuscript: July 24, 2009

Manuscript Accepted: July 27, 2009

Published: July 31, 2009

**Citation**

Haruyasu Itoh, Naoya Matsumoto, and Takashi Inoue, "Spherical aberration correction suitable for a wavefront controller," Opt. Express **17**, 14367-14373 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-16-14367

Sort: Year | Journal | Reset

### References

- M. J. Booth and T. Wilson, “Strategies for the compensation of specimen-induced spherical aberration in confocal microscopy of skin,” J. Microsc. 200(Pt 1), 68–74 (2000). [CrossRef] [PubMed]
- Y. Roichman, A. Waldron, E. Gardel, and D. G. Grier, “Optical traps with geometric aberrations,” Appl. Opt. 45(15), 3425–3429 (2006). [CrossRef] [PubMed]
- M. J. Booth, M. Schwertner, T. Wilson, M. Nakano, Y. Kawata, M. Nakabayashi, and S. Miyata, “Predictive aberration correction for multilayer optical data storage,” Appl. Phys. Lett. 88(3), 031109 (2006). [CrossRef]
- S. Taccheo, G. Della Valle, R. Osellame, G. Cerullo, N. Chiodo, P. Laporta, O. Svelto, A. Killi, U. Morgner, M. Lederer, and D. Kopf, “Er:Yb-doped waveguide laser fabricated by femtosecond laser pulses,” Opt. Lett. 29(22), 2626–2628 (2004). [CrossRef] [PubMed]
- J. P. McDonald, V. R. Mistry, K. E. Ray, and S. M. Yalisove, “Femtosecond pulsed laser direct write production of nano- and microfluidic channels,” Appl. Phys. Lett. 88(18), 183113–183115 (2006). [CrossRef]
- K. Miura, J. Qiu, H. Inouye, T. Mitsuyu, and K. Hirao, “Photowritten optical waveguides in various glasses with ultrashort pulse laser,” Appl. Phys. Lett. 71(23), 3329–3331 (1997). [CrossRef]
- N. Takeshima, Y. Narita, S. Tanaka, Y. Kuroiwa, and K. Hirao, “Fabrication of high-efficiency diffraction gratings in glass,” Opt. Lett. 30(4), 352–354 (2005). [CrossRef] [PubMed]
- D. Homoelle, S. Wielandy, A. L. Gaeta, N. F. Borrelli, and C. Smith, “Infrared photosensitivity in silica glasses exposed to femtosecond laser pulses,” Opt. Lett. 24(18), 1311–1313 (1999). [CrossRef]
- A. M. Streltsov and N. F. Borrelli, “Fabrication and analysis of a directional coupler written in glass by nanojoule femtosecond laser pulses,” Opt. Lett. 26(1), 42–43 (2001). [CrossRef]
- E. Theofanidou, L. Wilson, W. J. Hossack, and J. Arlt, “Spherical aberration correction for optical tweezers,” Opt. Commun. 236(1-3), 145–150 (2004). [CrossRef]
- C. Mauclair, A. Mermillod-Blondin, N. Huot, E. Audouard, and R. Stoian, “Ultrafast laser writing of homogeneous longitudinal waveguides in glasses using dynamic wavefront correction,” Opt. Express 16(8), 5481–5492 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-8-5481 . [CrossRef] [PubMed]
- L. Sherman, J. Y. Ye, O. Albert, and T. B. Norris, “Adaptive correction of depth-induced aberrations in multiphoton scanning microscopy using a deformable mirror,” J. Microsc. 206(Pt 1), 65–71 (2002). [CrossRef] [PubMed]
- M. J. Booth, M. A. A. Neil, and T. Wilson, “Aberration correction for confocal imaging in refractive-index-mismatched-media,” J. Microsc. 192(2), 90–98 (1998). [CrossRef]
- T. Inoue, H. Tanaka, N. Fukuchi, M. Takumi, N. Matsumoto, T. Hara, N. Yoshida, Y. Igasaki, and Y. Kobayashi, “LCOS spatial light modulator controlled by 12-bit signals for optical phase-only modulation,” Proc. SPIE 6487, 64870Y (2007). [CrossRef]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.