## Subaperture correlation based digital adaptive optics for full field optical coherence tomography |

Optics Express, Vol. 21, Issue 9, pp. 10850-10866 (2013)

http://dx.doi.org/10.1364/OE.21.010850

Acrobat PDF (2820 KB)

### Abstract

This paper proposes a sub-aperture correlation based numerical phase correction method for interferometric full field imaging systems provided the complex object field information can be extracted. This method corrects for the wavefront aberration at the pupil/ Fourier transform plane without the need of any adaptive optics, spatial light modulators (SLM) and additional cameras. We show that this method does not require the knowledge of any system parameters. In the simulation study, we consider a full field swept source OCT (FF SSOCT) system to show the working principle of the algorithm. Experimental results are presented for a technical and biological sample to demonstrate the proof of the principle.

© 2013 OSA

## 1. Introduction

1. B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. **17**(5), S573–S577 (2001). [PubMed]

3. M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. U.S.A. **103**(46), 17137–17142 (2006). [CrossRef] [PubMed]

4. M. Pircher and R. J. Zawadzki, “Combining adaptive optics with optical coherence tomography: Unveiling the cellular structure of the human retina in vivo,” Expert Rev. Ophthalmol. **2**(6), 1019–1035 (2007). [CrossRef]

5. K. Sasaki, K. Kurokawa, S. Makita, and Y. Yasuno, “Extended depth of focus adaptive optics spectral domain optical coherence tomography,” Biomed. Opt. Express **3**(10), 2353–2370 (2012). [CrossRef] [PubMed]

7. N. Ji, D. E. Milkie, and E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods **7**(2), 141–147 (2010). [CrossRef] [PubMed]

8. T. Haist, J. Hafner, M. Warber, and W. Osten, “Scene-based wavefront correction with spatial light modulators,” Proc. SPIE **7064**, 70640M, 70640M-11 (2008). [CrossRef]

9. A. E. Tippie and J. R. Fienup, “Sub-Aperture Techniques Applied to Phase-Error Correction in Digital Holography,” in *Digital Holography and Three-Dimensional Imaging*, OSA Techinal Digest (CD) (Optical Society of America, 2011), paper DMA4. http://www.opticsinfobase.org/abstract.cfm?URI=DH-2011-DMA4 [CrossRef]

10. S. T. Thurman and J. R. Fienup, “Phase-error correction in digital holography,” J. Opt. Soc. Am. A **25**(4), 983–994 (2008). [CrossRef] [PubMed]

11. S. G. Adie, B. W. Graf, A. Ahmad, P. S. Carney, and S. A. Boppart, “Computational adaptive optics for broadband optical interferometric tomography of biological tissue,” Proc. Natl. Acad. Sci. U.S.A. **109**(19), 7175–7180 (2012). [CrossRef] [PubMed]

## 2. Theory

14. M. Rueckel and W. Denk, “Properties of coherence-gated wavefront sensing,” J. Opt. Soc. Am. A **24**(11), 3517–3529 (2007). [CrossRef] [PubMed]

16. M. Guizar-Sicairos, S. T. Thurman, and J. R. Fienup, “Efficient subpixel image registration algorithms,” Opt. Lett. **33**(2), 156–158 (2008). [CrossRef] [PubMed]

## 3. Computer simulation

*K*no longer stands for the number of subapertures but defines the size of each subaperture as

7. N. Ji, D. E. Milkie, and E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods **7**(2), 141–147 (2010). [CrossRef] [PubMed]

*K*= 5, 7 9 and 11. Also, increasing the percentage of overlap to more than 50 percent between subapertures does not significantly reduce the residual phase error. This is due to the redundancy of data caused by the overlap. We can see that for

*K*= 3 the residual rms errors are lower for the cases of more than 50 percent overlap as compared to the 50 percent overlap case. But still the residual rms errors are higher than in the non overlapping case. On the other hand, for

*K*= 13, the residual rms errors for the cases of more than 50 percent overlap are higher than both the 50 percent overlap and the non-overlapping case. Since both

*K*= 3 and

*K*= 13 fall in the regimes where the approximations and assumptions of the presented algorithm are no longer valid, it is difficult to explain the exact reasons behind the observed differences. Nevertheless, in Fig. 6 we can see that the condition

*N*is the size of the aperture in pixels. From Eq. (9) we can estimate the quadratic phase error. This method is simple and fast as compared to the defocus correction method based on sharpness optimization which requires long iterations.

## 4. Experimental results

*f*= 40 mm) in both the sample and the reference arm. The sample consisted of a layer of plastic, a film of dried milk and an USAF resolution test target (RTT). A thin film of dried milk was used to produce scattering and diffuse reflection. The plastic layer of non uniform thickness and structure to create random aberration was created by heating a plastic used for compact disc (CD) cases. The output beam from the sweeping laser source (Superlum BroadSweeper 840-M) incident on the lens L1 is of diameter 10 mm and the field of view on the sample is ~2 mm. The power incident on sample is 5 mW. The RTT surface was in focus while imaging. The image of the sample formed by L2 is transferred to the camera plane using a telescope formed by lens L3 and L4 with effective magnification of 2.5

## 5. Discussion and conclusion

10. S. T. Thurman and J. R. Fienup, “Phase-error correction in digital holography,” J. Opt. Soc. Am. A **25**(4), 983–994 (2008). [CrossRef] [PubMed]

11. S. G. Adie, B. W. Graf, A. Ahmad, P. S. Carney, and S. A. Boppart, “Computational adaptive optics for broadband optical interferometric tomography of biological tissue,” Proc. Natl. Acad. Sci. U.S.A. **109**(19), 7175–7180 (2012). [CrossRef] [PubMed]

18. D. Hillmann, G. Franke, C. Lührs, P. Koch, and G. Hüttmann, “Efficient holoscopy image reconstruction,” Opt. Express **20**(19), 21247–21263 (2012). [CrossRef] [PubMed]

## 6. Appendix A

19. V. N. Mahajan and G. M. Dai, “Orthonormal polynomials in wavefront analysis: analytical solution,” J. Opt. Soc. Am. A **24**(9), 2994–3016 (2007). [CrossRef] [PubMed]

## Acknowledgments

## References and links

1. | B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. |

2. | J. L. Beverage, R. V. Shack, and M. R. Descour, “Measurement of the three-dimensional microscope point spread function using a Shack-Hartmann wavefront sensor,” J. Microsc. |

3. | M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. U.S.A. |

4. | M. Pircher and R. J. Zawadzki, “Combining adaptive optics with optical coherence tomography: Unveiling the cellular structure of the human retina in vivo,” Expert Rev. Ophthalmol. |

5. | K. Sasaki, K. Kurokawa, S. Makita, and Y. Yasuno, “Extended depth of focus adaptive optics spectral domain optical coherence tomography,” Biomed. Opt. Express |

6. | L. A. Poyneer, “Scene-based Shack-Hartmann wave-front sensing: analysis and simulation,” Appl. Opt. |

7. | N. Ji, D. E. Milkie, and E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods |

8. | T. Haist, J. Hafner, M. Warber, and W. Osten, “Scene-based wavefront correction with spatial light modulators,” Proc. SPIE |

9. | A. E. Tippie and J. R. Fienup, “Sub-Aperture Techniques Applied to Phase-Error Correction in Digital Holography,” in |

10. | S. T. Thurman and J. R. Fienup, “Phase-error correction in digital holography,” J. Opt. Soc. Am. A |

11. | S. G. Adie, B. W. Graf, A. Ahmad, P. S. Carney, and S. A. Boppart, “Computational adaptive optics for broadband optical interferometric tomography of biological tissue,” Proc. Natl. Acad. Sci. U.S.A. |

12. | P. Hariharan, |

13. | D. Malacara, |

14. | M. Rueckel and W. Denk, “Properties of coherence-gated wavefront sensing,” J. Opt. Soc. Am. A |

15. | W. Drexler and J. G. Fujimoto, |

16. | M. Guizar-Sicairos, S. T. Thurman, and J. R. Fienup, “Efficient subpixel image registration algorithms,” Opt. Lett. |

17. | A. E. Tippie, A. Kumar, and J. R. Fienup, “High-resolution synthetic-aperture digital holography with digital phase and pupil correction,” Opt. Express |

18. | D. Hillmann, G. Franke, C. Lührs, P. Koch, and G. Hüttmann, “Efficient holoscopy image reconstruction,” Opt. Express |

19. | V. N. Mahajan and G. M. Dai, “Orthonormal polynomials in wavefront analysis: analytical solution,” J. Opt. Soc. Am. A |

**OCIS Codes**

(100.2000) Image processing : Digital image processing

(100.3020) Image processing : Image reconstruction-restoration

(110.0180) Imaging systems : Microscopy

(110.4500) Imaging systems : Optical coherence tomography

(110.1085) Imaging systems : Adaptive imaging

(100.3175) Image processing : Interferometric imaging

**ToC Category:**

Image Processing

**History**

Original Manuscript: February 28, 2013

Revised Manuscript: April 17, 2013

Manuscript Accepted: April 23, 2013

Published: April 26, 2013

**Virtual Issues**

Vol. 8, Iss. 6 *Virtual Journal for Biomedical Optics*

**Citation**

Abhishek Kumar, Wolfgang Drexler, and Rainer A. Leitgeb, "Subaperture correlation based digital adaptive optics for full field optical coherence tomography," Opt. Express **21**, 10850-10866 (2013)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-21-9-10850

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### References

- B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg.17(5), S573–S577 (2001). [PubMed]
- J. L. Beverage, R. V. Shack, and M. R. Descour, “Measurement of the three-dimensional microscope point spread function using a Shack-Hartmann wavefront sensor,” J. Microsc.205(1), 61–75 (2002). [CrossRef] [PubMed]
- M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. U.S.A.103(46), 17137–17142 (2006). [CrossRef] [PubMed]
- M. Pircher and R. J. Zawadzki, “Combining adaptive optics with optical coherence tomography: Unveiling the cellular structure of the human retina in vivo,” Expert Rev. Ophthalmol.2(6), 1019–1035 (2007). [CrossRef]
- K. Sasaki, K. Kurokawa, S. Makita, and Y. Yasuno, “Extended depth of focus adaptive optics spectral domain optical coherence tomography,” Biomed. Opt. Express3(10), 2353–2370 (2012). [CrossRef] [PubMed]
- L. A. Poyneer, “Scene-based Shack-Hartmann wave-front sensing: analysis and simulation,” Appl. Opt.42(29), 5807–5815 (2003). [CrossRef] [PubMed]
- N. Ji, D. E. Milkie, and E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods7(2), 141–147 (2010). [CrossRef] [PubMed]
- T. Haist, J. Hafner, M. Warber, and W. Osten, “Scene-based wavefront correction with spatial light modulators,” Proc. SPIE7064, 70640M, 70640M-11 (2008). [CrossRef]
- A. E. Tippie and J. R. Fienup, “Sub-Aperture Techniques Applied to Phase-Error Correction in Digital Holography,” in Digital Holography and Three-Dimensional Imaging, OSA Techinal Digest (CD) (Optical Society of America, 2011), paper DMA4. http://www.opticsinfobase.org/abstract.cfm?URI=DH-2011-DMA4 [CrossRef]
- S. T. Thurman and J. R. Fienup, “Phase-error correction in digital holography,” J. Opt. Soc. Am. A25(4), 983–994 (2008). [CrossRef] [PubMed]
- S. G. Adie, B. W. Graf, A. Ahmad, P. S. Carney, and S. A. Boppart, “Computational adaptive optics for broadband optical interferometric tomography of biological tissue,” Proc. Natl. Acad. Sci. U.S.A.109(19), 7175–7180 (2012). [CrossRef] [PubMed]
- P. Hariharan, Optical Interferometry (Academic, 2003).
- D. Malacara, Optical Shop Testing (Wiley, 1992).
- M. Rueckel and W. Denk, “Properties of coherence-gated wavefront sensing,” J. Opt. Soc. Am. A24(11), 3517–3529 (2007). [CrossRef] [PubMed]
- W. Drexler and J. G. Fujimoto, Optical Coherence Tomography: Technology and Applications (Springer, 2008).
- M. Guizar-Sicairos, S. T. Thurman, and J. R. Fienup, “Efficient subpixel image registration algorithms,” Opt. Lett.33(2), 156–158 (2008). [CrossRef] [PubMed]
- A. E. Tippie, A. Kumar, and J. R. Fienup, “High-resolution synthetic-aperture digital holography with digital phase and pupil correction,” Opt. Express19(13), 12027–12038 (2011). [CrossRef] [PubMed]
- D. Hillmann, G. Franke, C. Lührs, P. Koch, and G. Hüttmann, “Efficient holoscopy image reconstruction,” Opt. Express20(19), 21247–21263 (2012). [CrossRef] [PubMed]
- V. N. Mahajan and G. M. Dai, “Orthonormal polynomials in wavefront analysis: analytical solution,” J. Opt. Soc. Am. A24(9), 2994–3016 (2007). [CrossRef] [PubMed]

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