Abstract

Traditional wavefront-sensor-based adaptive optics (AO) techniques face numerous challenges that cause poor performance in scattering samples. Sensorless closed-loop AO techniques overcome these challenges by optimizing an image metric at different states of a deformable mirror (DM). This requires acquisition of a series of images continuously for optimization − an arduous task in dynamic in vivo samples. We present a technique where the different states of the DM are instead simulated using computational adaptive optics (CAO). The optimal wavefront is estimated by performing CAO on an initial volume to minimize an image metric, and then the pattern is translated to the DM. In this paper, we have demonstrated this technique on a spectral-domain optical coherence microscope for three applications: real-time depth-wise aberration correction, single-shot volumetric aberration correction, and extension of depth-of-focus. Our technique overcomes the disadvantages of sensor-based AO, reduces the number of image acquisitions compared to traditional sensorless AO, and retains the advantages of both computational and hardware-based AO.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2019 (2)

J. A. Mulligan, X. Feng, and S. G. Adie, “Quantitative reconstruction of time-varying 3D cell forces with traction force optical coherence microscopy,” Sci. Rep. 9, 4086 (2019).
[Crossref]

F. A. South, Y.-Z. Liu, P.-C. Huang, T. Kohlfarber, and S. A. Boppart, “Local wavefront mapping in tissue using computational adaptive optics OCT,” Opt. Lett. 44, 1186–1189 (2019).
[Crossref] [PubMed]

2018 (6)

2017 (1)

2016 (7)

P. Pande, Y.-Z. Liu, F. A. South, and S. A. Boppart, “Automated computational aberration correction method for broadband interferometric imaging techniques,” Opt. Lett. 41, 3324–3327 (2016).
[Crossref] [PubMed]

D. Hillmann, H. Spahr, C. Hain, H. Sudkamp, G. Franke, C. Pfäffle, C. Winter, and G. Hüttmann, “Aberration-free volumetric high-speed imaging of in vivo retina,” Sci. Rep. 6, 35209 (2016).
[Crossref]

U. Böhm, S. W. Hell, and R. Schmidt, “4Pi-RESOLFT nanoscopy,” Nat. Commun. 7, 10504 (2016).
[Crossref] [PubMed]

M. Cua, D. J. Wahl, Y. Zhao, S. Lee, S. Bonora, R. J. Zawadzki, Y. Jian, and M. V. Sarunic, “Coherence-gated sensorless adaptive optics multiphoton retinal imaging,” Sci. Reports 6, 32223 (2016).
[Crossref]

F. Fogel, I. Waldspurger, and A. d’Aspremont, “Phase retrieval for imaging problems,” Math. Program. Comput. 8, 311–335 (2016).
[Crossref]

R. S. Jonnal, O. P. Kocaoglu, R. J. Zawadzki, Z. Liu, D. T. Miller, and J. S. Werner, “A review of adaptive optics optical coherence tomography: technical advances, scientific applications, and the future,” Invest. Ophthalmol. Vis. Sci. 57, OCT51–OCT68 (2016).
[Crossref]

Y. Jian, S. Lee, M. J. Ju, M. Heisler, W. Ding, R. J. Zawadzki, S. Bonora, and M. V. Sarunic, “Lens-based wavefront sensorless adaptive optics swept source OCT,” Sci. Reports 6, 27620 (2016).
[Crossref]

2015 (5)

N. D. Shemonski, F. A. South, Y.-Z. Liu, S. G. Adie, P. S. Carney, and S. A. Boppart, “Computational high-resolution optical imaging of the living human retina,” Nat. Photonics 9, 440–443 (2015).
[Crossref]

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging: a contemporary overview,” IEEE Signal Process. Mag. 32, 87–109 (2015).
[Crossref]

K. F. Tehrani, J. Xu, Y. Zhang, P. Shen, and P. Kner, “Adaptive optics stochastic optical reconstruction microscopy (AO-STORM) using a genetic algorithm,” Opt. Express 23, 13677–13692 (2015).
[Crossref] [PubMed]

H. R. Verstraete, S. Wahls, J. Kalkman, and M. Verhaegen, “Model-based sensor-less wavefront aberration correction in optical coherence tomography,” Opt. Lett. 40, 5722–5725 (2015).
[Crossref] [PubMed]

A. Roorda and J. L. Duncan, “Adaptive optics ophthalmoscopy,” Annu. Rev. Vis. Sci. 1, 19–50 (2015).
[Crossref]

2014 (4)

2013 (4)

2012 (3)

2011 (2)

V. Lakshminarayanan and A. Fleck, “Zernike polynomials: a guide,” J. Mod. Opt. 58, 545–561 (2011).
[Crossref]

A. Thayil and M. J. Booth, “Self calibration of sensorless adaptive optical microscopes,” J. Eur. Opt. Soc. 6, 11045 (2011).
[Crossref]

2010 (3)

P. Kner, L. Winoto, D. A. Agard, and J. W. Sedat, “Closed loop adaptive optics for microscopy without a wavefront sensor,” Proc. SPIE 7570, 757006 (2010).
[Crossref]

J.-W. Cha, J. Ballesta, and P. T. So, “Shack-Hartmann wavefront-sensor-based adaptive optics system for multiphoton microscopy,” J. Biomed. Opt. 15, 046022 (2010).
[Crossref] [PubMed]

S. Tuohy and A. G. Podoleanu, “Depth-resolved wavefront aberrations using a coherence-gated Shack-Hartmann wavefront sensor,” Opt. Express 18, 3458–3476 (2010).
[Crossref] [PubMed]

2009 (5)

D. Débarre, E. J. Botcherby, T. Watanabe, S. Srinivas, M. J. Booth, and T. Wilson, “Image-based adaptive optics for two-photon microscopy,” Opt. Lett. 34, 2495–2497 (2009).
[Crossref] [PubMed]

N. Olivier, D. Débarre, and E. Beaurepaire, “Dynamic aberration correction for multiharmonic microscopy,” Opt. Lett. 34, 3145–3147 (2009).
[Crossref] [PubMed]

K. N. Walker and R. K. Tyson, “Wavefront correction using a Fourier-based image sharpness metric,” Proc. SPIE 7468, 74680O (2009).
[Crossref]

N. Ji, D. E. Milkie, and E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods 7, 141 (2009).
[Crossref] [PubMed]

J. M. Girkin, S. Poland, and A. J. Wright, “Adaptive optics for deeper imaging of biological samples,” Curr. Opin. Biotechnol. 20, 106–110 (2009).
[Crossref] [PubMed]

2008 (1)

2007 (1)

M. J. Booth, “Adaptive optics in microscopy,” Philos. Transactions Royal Soc. Lond. A: Math. Phys. Eng. Sci. 365, 2829–2843 (2007).
[Crossref]

2006 (3)

M. J. Rust, M. Bates, and X. Zhuang, “Stochastic optical reconstruction microscopy (STORM) provides subdiffraction-limit image resolution,” Nat. Methods 3, 793 (2006).
[Crossref] [PubMed]

S. T. Hess, T. P. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91, 4258–4272 (2006).
[Crossref] [PubMed]

T. Colomb, F. Montfort, J. Kühn, N. Aspert, E. Cuche, A. Marian, F. Charrière, S. Bourquin, P. Marquet, and C. Depeursinge, “Numerical parametric lens for shifting, magnification, and complete aberration compensation in digital holographic microscopy,” J. Opt. Soc. Am. A 23, 3177–3190 (2006).
[Crossref]

2005 (2)

2004 (1)

B. M. Hanser, M. G. Gustafsson, D. Agard, and J. W. Sedat, “Phase-retrieved pupil functions in wide-field fluorescence microscopy,” J. Microsc. 216, 32–48 (2004).
[Crossref] [PubMed]

2003 (3)

2002 (4)

A. Roorda, F. Romero-Borja, W. J. Donnelly, H. Queener, T. J. Hebert, and M. C. Campbell, “Adaptive optics scanning laser ophthalmoscopy,” Opt. Express 10, 405–412 (2002).
[Crossref] [PubMed]

M. J. Booth, M. A. Neil, R. Juškaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. 99, 5788–5792 (2002).
[Crossref] [PubMed]

X. Li and W. Jiang, “Comparing zonal reconstruction algorithms and modal reconstruction algorithms in adaptive optics system,” Proc. SPIE 4825, 121–131 (2002).
[Crossref]

L. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, “Standards for reporting the optical aberrations of eyes,” J. Refract. Surg. 18, S652–S660 (2002).
[PubMed]

2001 (1)

Z. Kam, B. Hanser, M. Gustafsson, D. Agard, and J. Sedat, “Computational adaptive optics for live three-dimensional biological imaging,” Proc. Natl. Acad. Sci. U. S. A. 98, 3790–3795 (2001).
[Crossref] [PubMed]

2000 (3)

1997 (1)

1982 (1)

1974 (1)

1873 (1)

E. Abbe, “Beiträge zur theorie des mikroskops und der mikroskopischen wahrnehmung,” Arch. für mikroskopische Anat. 9, 413–418 (1873).
[Crossref]

Abbe, E.

E. Abbe, “Beiträge zur theorie des mikroskops und der mikroskopischen wahrnehmung,” Arch. für mikroskopische Anat. 9, 413–418 (1873).
[Crossref]

Adie, S. G.

J. A. Mulligan, X. Feng, and S. G. Adie, “Quantitative reconstruction of time-varying 3D cell forces with traction force optical coherence microscopy,” Sci. Rep. 9, 4086 (2019).
[Crossref]

S. Liu, J. A. Mulligan, and S. G. Adie, “Volumetric optical coherence microscopy with a high space-bandwidth-time product enabled by hybrid adaptive optics,” Biomed. Opt. Express 9, 3137–3152 (2018).
[Crossref] [PubMed]

N. D. Shemonski, F. A. South, Y.-Z. Liu, S. G. Adie, P. S. Carney, and S. A. Boppart, “Computational high-resolution optical imaging of the living human retina,” Nat. Photonics 9, 440–443 (2015).
[Crossref]

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K. Wang, D. E. Milkie, A. Saxena, P. Engerer, T. Misgeld, M. E. Bronner, J. Mumm, and E. Betzig, “Rapid adaptive optical recovery of optimal resolution over large volumes,” Nat. Methods 11, 625–628 (2014).
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N. Ji, D. E. Milkie, and E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods 7, 141 (2009).
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Miller, J.

Misgeld, T.

K. Wang, D. E. Milkie, A. Saxena, P. Engerer, T. Misgeld, M. E. Bronner, J. Mumm, and E. Betzig, “Rapid adaptive optical recovery of optimal resolution over large volumes,” Nat. Methods 11, 625–628 (2014).
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Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light. Sci. Appl. 7, 17141 (2018).
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K. Wang, D. E. Milkie, A. Saxena, P. Engerer, T. Misgeld, M. E. Bronner, J. Mumm, and E. Betzig, “Rapid adaptive optical recovery of optimal resolution over large volumes,” Nat. Methods 11, 625–628 (2014).
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B. M. Hanser, M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase retrieval for high-numerical-aperture optical systems,” Opt. Lett. 28, 801–803 (2003).
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Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging: a contemporary overview,” IEEE Signal Process. Mag. 32, 87–109 (2015).
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Sudkamp, H.

D. Hillmann, H. Spahr, C. Hain, H. Sudkamp, G. Franke, C. Pfäffle, C. Winter, and G. Hüttmann, “Aberration-free volumetric high-speed imaging of in vivo retina,” Sci. Rep. 6, 35209 (2016).
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Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light. Sci. Appl. 7, 17141 (2018).
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D. Hillmann, H. Spahr, C. Hain, H. Sudkamp, G. Franke, C. Pfäffle, C. Winter, and G. Hüttmann, “Aberration-free volumetric high-speed imaging of in vivo retina,” Sci. Rep. 6, 35209 (2016).
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J. M. Girkin, S. Poland, and A. J. Wright, “Adaptive optics for deeper imaging of biological samples,” Curr. Opin. Biotechnol. 20, 106–110 (2009).
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Xu, Y.

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S. You, H. Tu, E. J. Chaney, Y. Sun, Y. Zhao, A. J. Bower, Y.-Z. Liu, M. Marjanovic, S. Sinha, Y. Pu, and et al., “Intravital imaging by simultaneous label-free autofluorescence-multiharmonic microscopy,” Nat. Commun. 9, 2125 (2018).
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R. S. Jonnal, O. P. Kocaoglu, R. J. Zawadzki, Z. Liu, D. T. Miller, and J. S. Werner, “A review of adaptive optics optical coherence tomography: technical advances, scientific applications, and the future,” Invest. Ophthalmol. Vis. Sci. 57, OCT51–OCT68 (2016).
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M. Cua, D. J. Wahl, Y. Zhao, S. Lee, S. Bonora, R. J. Zawadzki, Y. Jian, and M. V. Sarunic, “Coherence-gated sensorless adaptive optics multiphoton retinal imaging,” Sci. Reports 6, 32223 (2016).
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Y. Jian, J. Xu, M. A. Gradowski, S. Bonora, R. J. Zawadzki, and M. V. Sarunic, “Wavefront sensorless adaptive optics optical coherence tomography for in vivo retinal imaging in mice,” Biomed. Opt. Express 5, 547–559 (2014).
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Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light. Sci. Appl. 7, 17141 (2018).
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S. You, H. Tu, E. J. Chaney, Y. Sun, Y. Zhao, A. J. Bower, Y.-Z. Liu, M. Marjanovic, S. Sinha, Y. Pu, and et al., “Intravital imaging by simultaneous label-free autofluorescence-multiharmonic microscopy,” Nat. Commun. 9, 2125 (2018).
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M. Cua, D. J. Wahl, Y. Zhao, S. Lee, S. Bonora, R. J. Zawadzki, Y. Jian, and M. V. Sarunic, “Coherence-gated sensorless adaptive optics multiphoton retinal imaging,” Sci. Reports 6, 32223 (2016).
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G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7, 739 (2013).
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M. J. Rust, M. Bates, and X. Zhuang, “Stochastic optical reconstruction microscopy (STORM) provides subdiffraction-limit image resolution,” Nat. Methods 3, 793 (2006).
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A. Roorda and J. L. Duncan, “Adaptive optics ophthalmoscopy,” Annu. Rev. Vis. Sci. 1, 19–50 (2015).
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Appl. Opt. (3)

Arch. für mikroskopische Anat. (1)

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Biomed. Opt. Express (6)

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S. T. Hess, T. P. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91, 4258–4272 (2006).
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Curr. Opin. Biotechnol. (1)

J. M. Girkin, S. Poland, and A. J. Wright, “Adaptive optics for deeper imaging of biological samples,” Curr. Opin. Biotechnol. 20, 106–110 (2009).
[Crossref] [PubMed]

IEEE Signal Process. Mag. (1)

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging: a contemporary overview,” IEEE Signal Process. Mag. 32, 87–109 (2015).
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Invest. Ophthalmol. Vis. Sci. (1)

R. S. Jonnal, O. P. Kocaoglu, R. J. Zawadzki, Z. Liu, D. T. Miller, and J. S. Werner, “A review of adaptive optics optical coherence tomography: technical advances, scientific applications, and the future,” Invest. Ophthalmol. Vis. Sci. 57, OCT51–OCT68 (2016).
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J. Biomed. Opt. (1)

J.-W. Cha, J. Ballesta, and P. T. So, “Shack-Hartmann wavefront-sensor-based adaptive optics system for multiphoton microscopy,” J. Biomed. Opt. 15, 046022 (2010).
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J. Eur. Opt. Soc. (1)

A. Thayil and M. J. Booth, “Self calibration of sensorless adaptive optical microscopes,” J. Eur. Opt. Soc. 6, 11045 (2011).
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B. M. Hanser, M. G. Gustafsson, D. Agard, and J. W. Sedat, “Phase-retrieved pupil functions in wide-field fluorescence microscopy,” J. Microsc. 216, 32–48 (2004).
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L. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, “Standards for reporting the optical aberrations of eyes,” J. Refract. Surg. 18, S652–S660 (2002).
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Light. Sci. Appl. (2)

Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light. Sci. Appl. 7, 17141 (2018).
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M. J. Booth, “Adaptive optical microscopy: the ongoing quest for a perfect image,” Light. Sci. Appl. 3, e165 (2014).
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Math. Program. Comput. (1)

F. Fogel, I. Waldspurger, and A. d’Aspremont, “Phase retrieval for imaging problems,” Math. Program. Comput. 8, 311–335 (2016).
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Nat. Commun. (2)

U. Böhm, S. W. Hell, and R. Schmidt, “4Pi-RESOLFT nanoscopy,” Nat. Commun. 7, 10504 (2016).
[Crossref] [PubMed]

S. You, H. Tu, E. J. Chaney, Y. Sun, Y. Zhao, A. J. Bower, Y.-Z. Liu, M. Marjanovic, S. Sinha, Y. Pu, and et al., “Intravital imaging by simultaneous label-free autofluorescence-multiharmonic microscopy,” Nat. Commun. 9, 2125 (2018).
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Nat. Methods (3)

N. Ji, D. E. Milkie, and E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods 7, 141 (2009).
[Crossref] [PubMed]

M. J. Rust, M. Bates, and X. Zhuang, “Stochastic optical reconstruction microscopy (STORM) provides subdiffraction-limit image resolution,” Nat. Methods 3, 793 (2006).
[Crossref] [PubMed]

K. Wang, D. E. Milkie, A. Saxena, P. Engerer, T. Misgeld, M. E. Bronner, J. Mumm, and E. Betzig, “Rapid adaptive optical recovery of optimal resolution over large volumes,” Nat. Methods 11, 625–628 (2014).
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Nat. Photonics (2)

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7, 739 (2013).
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N. D. Shemonski, F. A. South, Y.-Z. Liu, S. G. Adie, P. S. Carney, and S. A. Boppart, “Computational high-resolution optical imaging of the living human retina,” Nat. Photonics 9, 440–443 (2015).
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Opt. Express (6)

Opt. Lett. (9)

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F. A. South, Y.-Z. Liu, P.-C. Huang, T. Kohlfarber, and S. A. Boppart, “Local wavefront mapping in tissue using computational adaptive optics OCT,” Opt. Lett. 44, 1186–1189 (2019).
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Philos. Transactions Royal Soc. Lond. A: Math. Phys. Eng. Sci. (1)

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Figures (8)

Fig. 1
Fig. 1 Comparison of sensor-based AO, traditional sensorless AO, and AutoAO. The red lines represent the closed-loop involved in finding the optimal DM pattern for imaging. Det: Image Detector. DM: Deformable Mirror. PC: Computing Unit. WFS: Wavefront Sensor.
Fig. 2
Fig. 2 (a) Schematic diagram of the spectral domain AO OCM system. (b) Flowchart of the AutoAO algorithm. The steps with the dashed edges describes optional post-processing steps. (c) The Tikhonov-regularized inverse interaction matrix, α−1, mapping Wn to An and the offset, ξ.
Fig. 3
Fig. 3 Depth-wise aberration correction. (a) En face OCM images of a tissue-mimicking phantom made from a translucent plastic sheet before (top row) and after correction (bottom row) at different depths with respect to (w.r.t.) the focal plane. The color scales are normalized for the focal plane in each row. The top row corresponds to en face images from the same volume. Each image in the bottom row is from a different volume shown at the plane of optimization. Scale bar: 20 μm. (b) Zernike polynomial weights sent to the DM, An, corresponding to the images acquired in the bottom row of (a). (c) Patterns sent to the DM corresponding to the weights in (b) to acquire the images in the bottom row of (a). (d) Comparing the energy of the acquired signals before and after optimization. The black line corresponds to the original volume, the points in the blue line are from the corresponding optimized volumes calculated at the plane of optimization. (e) Histograms of the optical field for each plane before and after optimization where the original signal occurrences are in dark blue and the optimized signal occurrences are in light blue. The black and red arrows represent the possible noise and signal levels of the en face images respectively. Note that the y-axes are in logarithmic scale.
Fig. 4
Fig. 4 Volumetric aberration correction. En face OCM images of a tissue-mimicking phantom made from a translucent plastic sheet before (First row), after correction with DM (second row), and post-correction with CAO on planes in the second row (third row) at different depths spaced 3 pixels (or 9 μm) apart. Scale bar: 10 μm.
Fig. 5
Fig. 5 Analysis of volumetric aberration correction. (a) Histograms of the optical field for a 150-μm section before and after optimization (before correction with CAO) where the original signal occurrences are in dark red and the optimized signal occurrences are in light red. (b) The maximum signal magnitude at each pixel calculated for each of the en face images shown in Fig. 4. The black line corresponds to the aberrated image, the solid red line corresponds to the image corrected with AutoAO before correction with CAO, and the dotted red line corresponds to the metric after CAO. (c) Comparing the energy of the acquired signals before and after optimization. The black and red lines correspond to the original and optimized volumes, respectively. (d) Time taken for estimating the optimal phase correction mask when different number of depths are chosen for optimization. The solid line passes through the median value of 100 measurements. (e) Phase correction mask generated by AutoAO algorithm (top), corresponding pattern sent to the DM (bottom).
Fig. 6
Fig. 6 Volumetric aberration correction in a biological sample. (a) Cross-section OCM images (superposition of 10 slow-axis frames) of a tissue section from a salmon before (left) and after correction (right). The yellow arrows highlight the difference before and after correction with AutoAO. The plot below shows the mean energy per plane (for the entire 300 × 300 μm2 transverse region) before (red) and after (black) correction. Scale bars: 100 μm. (b) Pattern sent to the DM to achieve correction. (c) En face OCM images before correction (top), after correction (middle), and the corrected images post-CAO (bottom), each spaced 30 μm apart along the z-axis. The yellow arrows highlight the difference before and after correction with AutoAO, where the features are aberration free and have apparent increase in signal. Scale bar: 100 μm.
Fig. 7
Fig. 7 Extension of depth-of-focus. (a) Cross-section OCM images of the tissue mimicking phantom made of a translucent plastic sheet for different states of the DM. The color scales for each image are normalized to the maximum value in the plane. Scale bars: 20 μm. (b) Comparing the energy of the acquired signals for different aberration states on the DM. The black line corresponds to a flat DM profile, the red and green dotted lines correspond to astigmatic and spherically aberrated beams, respectively, and the blue solid line corresponds to the optimally aberrated profile generated by AutoAO. The gray dotted horizontal line corresponds to a 23 dB drop in the mean energy of the plane. From the intersection of this line to the four curves, the axial depth-of-fields from the graph for the flat, astigmatic, spherically aberrated, and the optimized beams are 144, 159, 168, and 177 μm, respectively. (c) The optimized pattern sent to the DM. (d) PSF measured at different aberration states shown at depths spaced 9 μm apart, measured on a silicone phantom with sparsely distributed iron-oxide nanoparticles. Each tile is 7.25 × 7.25 μm2. (e) En face OCM images for the flat, astigmatic, spherical, and optimized aberration profiles generated by the DM. Axial locations z1 to z7 are depths spaced 15 μm apart. The arrows point to notable features to help visually align the images in each column. Scale bar: 20 μm.
Fig. 8
Fig. 8 Comparing en face images of the translucent plastic sheet from the flat DM profile with the beam profile optimized for extending the depth-of-focus after correction with CAO for depths z′1 to z′7, each spaced 15 μm apart. The third row is the histogram of the signals for the planes shown where the black and gray bars correspond to the flat and optimized DM profiles, respectively. Scale bar: 20 μm.

Equations (11)

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S ¯ ( z , x , y ) = [ Q x , Q y ] 1 { exp [ j Φ ( z , Q x , Q y ) ] [ x , y ] [ S ( z , x , y ) ] } Φ ( z , Q x , Q y ) = m , n W n ( z ) Z n ( Q x , Q y )
W ^ 4 ( z k ) = argmin { 𝒥 [ S ˜ ( z k , x , y ) ] 𝒥 [ S ( z k , x , y ) ] 1 }
S ˜ ( z k , x , y ) = [ Q x , Q y ] 1 { exp [ j W 4 ( z k ) Z 4 ( Q x , Q y ) ] × [ x , y ] [ S ( z k , x , y ) ] }
𝒥 [ S ( z k , x , y ) ] = x , y | S ( z k , x , y ) S * ( z k , x , y ) | 1 4
W ^ n = argmin { [ S ˜ ( z , x , y ) ] [ S ˜ ( z , x , y ) ] 1 }
W n = α A n + ξ
DW [ z k , S ( z , x , y ) ] = x , y | S ( z k , x , y ) S * ( z k , x , y ) | 1 4
Vol [ S ( z , x , y ) ] = x , y , z | S ( z , x , y ) S * ( z , x , y ) | 1 4
𝒦 [ z , S ( z , x , y ) ] = x , y | S ( z , x , y ) S * ( z , x , y ) | 1 2
DOF [ S ( z , x , y ) ] = 1 N z z ( 𝒦 [ z , S ( z , x , y ) ] μ z ) 2
μ z = 0.8 max z 𝒦 [ z , S ( z , x , y ) ]

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