Abstract

We present a phase aberration correction method based on the correlation between the complex full-field and guide-star holograms in the context of digital holographic adaptive optics (DHAO). Removal of a global quadratic phase term before the correlation operation plays an important role in the correction. Correlation operation can remove the phase aberration at the entrance pupil plane and automatically refocus the corrected optical field. Except for the assumption that most aberrations lie at or close to the entrance pupil, the presented method does not impose any other constraints on the optical systems. Thus, it greatly enhances the flexibility of the optical design for DHAO systems in vision science and microscopy. Theoretical studies show that the previously proposed Fourier transform DHAO (FTDHAO) is just a special case of this general correction method, where the global quadratic phase term and a defocus term disappear. Hence, this correction method realizes the generalization of FTDHAO into arbitrary DHAO systems. The effectiveness and robustness of this method are demonstrated by simulations and experiments.

© 2013 Optical Society of America

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  1. H. W. Babcock, “The possibility of compensating astronomical seeing,” Publ. Astron. Soc. Pac. 65, 229–236 (1953).
    [CrossRef]
  2. M. A. van Dam, D. Le Mignant, and B. A. Macintosh, “Performance of the Keck observatory adaptive optics system,” Appl. Opt. 43, 5458–5467 (2004).
    [CrossRef]
  3. M. Hart, “Recent advances in astronomical adaptive optics,” Appl. Opt. 49, D17–D29 (2010).
    [CrossRef]
  4. J. Liang, B. Grimm, S. Goelz, and J. Bille, “Objective measurement of wave aberrations of the human eye with the use of a Hartmann-Shack wave-front sensor,” J. Opt. Soc. Am. A 11, 1949–1957 (1994).
    [CrossRef]
  5. J. Liang, D. R. Williams, and D. Miller, “Supernormal vision and high-resolution retinal imaging through adaptive optics,” J. Opt. Soc. Am. A 14, 2884–2892 (1997).
    [CrossRef]
  6. A. Roorda, F. Romero-Borja, W. J. Donnelly, H. Queener, T. J. Herbert, and M. C. W. Campbell, “Adaptive optics scanning laser ophthalmoscopy,” Opt. Express 10, 405–412 (2002).
    [CrossRef]
  7. K. M. Hampson, “Adaptive optics and vision,” J. Mod. Opt. 55, 3425–3467 (2008).
    [CrossRef]
  8. I. Iglesias, R. Ragazzoni, Y. Julien, and P. Artal, “Extended source pyramid wave-front sensor for the human eye,” Opt. Express 10, 419–428 (2002).
    [CrossRef]
  9. N. Doble, G. Yoon, L. Chen, P. Bierden, B. Singer, S. Olivier, and D. R. Williams, “Use of a microelectromechanical mirror for adaptive optics in the human eye,” Opt. Lett. 27, 1537–1539 (2002).
    [CrossRef]
  10. S. R. Chamot, C. Dainty, and S. Esposito, “Adaptive optics for ophthalmic applications using a pyramid wavefront sensor,” Opt. Express 14, 518–526 (2006).
    [CrossRef]
  11. Q. Mu, Z. Cao, D. Li, and L. Xuan, “Liquid crystal based adaptive optics system to compensate both low and high order aberrations in a model eye,” Opt. Express 15, 1946–1953 (2007).
    [CrossRef]
  12. M. J. Booth, D. Debarre, and A. Jesacher, “Adaptive optics for biomedical microscopy,” Opt. Photonics News 23, 22–29 (2012).
  13. M. J. Booth, “Adaptive optics in microscopy,” Phil. Trans. R. Soc. A 365, 2829–2843 (2007).
    [CrossRef]
  14. C. Liu and M. K. Kim, “Digital holographic adaptive optics for ocular imaging: proof of principle,” Opt. Lett. 36, 2710–2712 (2011).
    [CrossRef]
  15. U. Schnars and W. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179–181 (1994).
    [CrossRef]
  16. E. Cuche, P. Marquet, and C. Depeursinge, “Digital holography for quantitative phase-contrast imaging,” Opt. Lett. 24, 291–293 (1999).
    [CrossRef]
  17. C. Liu, D. Wang, and Y. Zhang, “Comparison and verification of numerical reconstruction methods in digital holography,” Opt. Eng. 48, 1058021 (2009).
  18. M. K. Kim, “Principles and techniques of digital holographic microscopy,” SPIE Rev. 1, 018005 (2010).
    [CrossRef]
  19. M. K. Kim, Digital Holographic Microscopy: Principles, Techniques, and Applications (Springer, 2011), pp. 55–93.
  20. C. Liu, X. Yu, and M. K. Kim, “Fourier transform digital holographic adaptive optics imaging system,” Appl. Opt. 51, 8449–8454 (2012).
    [CrossRef]
  21. F. Dubois, L. Joannes, and J. C. Legros, “Improved three-dimensional imaging with digital holography microscope with a source of partial spatial coherence,” Appl. Opt. 38, 7085–7094 (1999).
    [CrossRef]
  22. G. Pedrini and H. J. Tiziani, “Short-coherence digital microscopy by use of lensless holographic imaging system,” Appl. Opt. 41, 4489–4496 (2002).
    [CrossRef]
  23. M. K. Kim, “Adaptive optics by incoherent digital holography,” Opt. Lett. 37, 2694–2696 (2012).
    [CrossRef]
  24. M. K. Kim, “Incoherent digital holographic adaptive optics,” Appl. Opt. 52, A117–A130 (2013).
    [CrossRef]
  25. F. Dubois and C. Yourassowsky, “Full off-axis red-green-blue digital holographic microscope with LED illumination,” Opt. Lett. 37, 2190–2192 (2012).
    [CrossRef]
  26. R. Kelner and J. Rosen, “Spatially incoherent single channel digital Fourier holography,” Opt. Lett. 37, 3723–3725 (2012).
    [CrossRef]
  27. J. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005), pp. 105–107.
  28. L. Onural, “Some mathematical properties of the uniformly sampled quadratic phase function and associated issues in digital Fresnel diffraction simulation,” Opt. Eng. 43, 2557–2563 (2004).
    [CrossRef]
  29. N. Pavillon, C. S. Seelamantula, J. Kühn, M. Unser, and C. Depeursinge, “Suppression of the zero-order term in off-axis digital holography through nonlinear filtering,” Appl. Opt. 48, H186–H195 (2009).
    [CrossRef]

2013 (1)

2012 (5)

2011 (1)

2010 (2)

M. Hart, “Recent advances in astronomical adaptive optics,” Appl. Opt. 49, D17–D29 (2010).
[CrossRef]

M. K. Kim, “Principles and techniques of digital holographic microscopy,” SPIE Rev. 1, 018005 (2010).
[CrossRef]

2009 (2)

C. Liu, D. Wang, and Y. Zhang, “Comparison and verification of numerical reconstruction methods in digital holography,” Opt. Eng. 48, 1058021 (2009).

N. Pavillon, C. S. Seelamantula, J. Kühn, M. Unser, and C. Depeursinge, “Suppression of the zero-order term in off-axis digital holography through nonlinear filtering,” Appl. Opt. 48, H186–H195 (2009).
[CrossRef]

2008 (1)

K. M. Hampson, “Adaptive optics and vision,” J. Mod. Opt. 55, 3425–3467 (2008).
[CrossRef]

2007 (2)

2006 (1)

2004 (2)

L. Onural, “Some mathematical properties of the uniformly sampled quadratic phase function and associated issues in digital Fresnel diffraction simulation,” Opt. Eng. 43, 2557–2563 (2004).
[CrossRef]

M. A. van Dam, D. Le Mignant, and B. A. Macintosh, “Performance of the Keck observatory adaptive optics system,” Appl. Opt. 43, 5458–5467 (2004).
[CrossRef]

2002 (4)

1999 (2)

1997 (1)

1994 (2)

1953 (1)

H. W. Babcock, “The possibility of compensating astronomical seeing,” Publ. Astron. Soc. Pac. 65, 229–236 (1953).
[CrossRef]

Artal, P.

Babcock, H. W.

H. W. Babcock, “The possibility of compensating astronomical seeing,” Publ. Astron. Soc. Pac. 65, 229–236 (1953).
[CrossRef]

Bierden, P.

Bille, J.

Booth, M. J.

M. J. Booth, D. Debarre, and A. Jesacher, “Adaptive optics for biomedical microscopy,” Opt. Photonics News 23, 22–29 (2012).

M. J. Booth, “Adaptive optics in microscopy,” Phil. Trans. R. Soc. A 365, 2829–2843 (2007).
[CrossRef]

Campbell, M. C. W.

Cao, Z.

Chamot, S. R.

Chen, L.

Cuche, E.

Dainty, C.

Debarre, D.

M. J. Booth, D. Debarre, and A. Jesacher, “Adaptive optics for biomedical microscopy,” Opt. Photonics News 23, 22–29 (2012).

Depeursinge, C.

Doble, N.

Donnelly, W. J.

Dubois, F.

Esposito, S.

Goelz, S.

Goodman, J.

J. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005), pp. 105–107.

Grimm, B.

Hampson, K. M.

K. M. Hampson, “Adaptive optics and vision,” J. Mod. Opt. 55, 3425–3467 (2008).
[CrossRef]

Hart, M.

Herbert, T. J.

Iglesias, I.

Jesacher, A.

M. J. Booth, D. Debarre, and A. Jesacher, “Adaptive optics for biomedical microscopy,” Opt. Photonics News 23, 22–29 (2012).

Joannes, L.

Julien, Y.

Jüptner, W.

Kelner, R.

Kim, M. K.

Kühn, J.

Le Mignant, D.

Legros, J. C.

Li, D.

Liang, J.

Liu, C.

Macintosh, B. A.

Marquet, P.

Miller, D.

Mu, Q.

Olivier, S.

Onural, L.

L. Onural, “Some mathematical properties of the uniformly sampled quadratic phase function and associated issues in digital Fresnel diffraction simulation,” Opt. Eng. 43, 2557–2563 (2004).
[CrossRef]

Pavillon, N.

Pedrini, G.

Queener, H.

Ragazzoni, R.

Romero-Borja, F.

Roorda, A.

Rosen, J.

Schnars, U.

Seelamantula, C. S.

Singer, B.

Tiziani, H. J.

Unser, M.

van Dam, M. A.

Wang, D.

C. Liu, D. Wang, and Y. Zhang, “Comparison and verification of numerical reconstruction methods in digital holography,” Opt. Eng. 48, 1058021 (2009).

Williams, D. R.

Xuan, L.

Yoon, G.

Yourassowsky, C.

Yu, X.

Zhang, Y.

C. Liu, D. Wang, and Y. Zhang, “Comparison and verification of numerical reconstruction methods in digital holography,” Opt. Eng. 48, 1058021 (2009).

Appl. Opt. (8)

J. Mod. Opt. (1)

K. M. Hampson, “Adaptive optics and vision,” J. Mod. Opt. 55, 3425–3467 (2008).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Eng. (2)

L. Onural, “Some mathematical properties of the uniformly sampled quadratic phase function and associated issues in digital Fresnel diffraction simulation,” Opt. Eng. 43, 2557–2563 (2004).
[CrossRef]

C. Liu, D. Wang, and Y. Zhang, “Comparison and verification of numerical reconstruction methods in digital holography,” Opt. Eng. 48, 1058021 (2009).

Opt. Express (4)

Opt. Lett. (6)

Opt. Photonics News (1)

M. J. Booth, D. Debarre, and A. Jesacher, “Adaptive optics for biomedical microscopy,” Opt. Photonics News 23, 22–29 (2012).

Phil. Trans. R. Soc. A (1)

M. J. Booth, “Adaptive optics in microscopy,” Phil. Trans. R. Soc. A 365, 2829–2843 (2007).
[CrossRef]

Publ. Astron. Soc. Pac. (1)

H. W. Babcock, “The possibility of compensating astronomical seeing,” Publ. Astron. Soc. Pac. 65, 229–236 (1953).
[CrossRef]

SPIE Rev. (1)

M. K. Kim, “Principles and techniques of digital holographic microscopy,” SPIE Rev. 1, 018005 (2010).
[CrossRef]

Other (2)

M. K. Kim, Digital Holographic Microscopy: Principles, Techniques, and Applications (Springer, 2011), pp. 55–93.

J. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005), pp. 105–107.

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Figures (10)

Fig. 1.
Fig. 1.

Coordinates for a two-lens optical system.

Fig. 2.
Fig. 2.

Simulation example where the defocus term Φd exists and the global quadratic phase term Φq is unity. (a),(b) Simulated amplitude and phase. The phase maps are represented by blue-white-red color map that corresponds to [π,π]. (c) Optical field at the CCD plane without aberrator in place. (d) Focused image of (c). (e) Simulated phase aberration Φ. (f) Full-field aberrated hologram at the CCD plane. (g) Focused image of (f). (h) Full-field phase profile at the pupil with aberration. (i) Guide-star hologram, i.e., the amplitude PSF of the system. (j) General pupil function that is the FT of (i). (k) Corrected field at the pupil. (l) Corrected image from (k).

Fig. 3.
Fig. 3.

Simulation example where Φq exists while Φd is unity. (a) Undistorted optical field at CCD plane. (b) Distorted field at the CCD plane. (c) Distorted field at the pupil. (d) Amplitude PSF of the system. (e) General pupil function. (f) Corrected image.

Fig. 4.
Fig. 4.

Demonstration of the effect of Φq on the corrected image. (a) Measured aberration at the pupil when Φq is not eliminated. (b) Measured aberration at the pupil when Φq is partially eliminated. (c) Image corrected by (a). (d) Image corrected by (b).

Fig. 5.
Fig. 5.

Simulation example where both Φq and Φd exist. (a) Distorted optical field at the CCD plane. (b) Distorted image. (c) Distorted field at the pupil. (d) Amplitude PSF of the system. (e) General pupil function. (f) Corrected image.

Fig. 6.
Fig. 6.

Schematic diagram of the experimental apparatus. S, sample; L1–L3, lens; A, aberrator; BS1-4, beam splitters.

Fig. 7.
Fig. 7.

Experimental example where the defocus term Φd exists while the global quadratic phase term Φq is unity. (a) Hologram without aberration. (b) Amplitude at the CCD plane. (c) Undistorted field at the pupil. (d) Undistorted image. (e) Distorted hologram. (f) Distorted field at the CCD plane. (g) Distorted field at the pupil. (h) Distorted image. (i) Guide-star hologram. (j) Amplitude PSF of the system. (k) General pupil function. (l) Corrected image.

Fig. 8.
Fig. 8.

Experimental example where Φq exists while Φd takes unity. (a) Undistorted image. (b) Distorted image. (c) Distorted full field at the pupil. (d) Amplitude PSF of the system. (e) Measured aberration. (f) Corrected image.

Fig. 9.
Fig. 9.

Experimental demonstration of the effect of Φq on the corrected image. (a) Measured aberration at the pupil when Φq is not eliminated. (b) Measured aberration at the pupil when Φq is partially eliminated. (c) Image corrected by (a). (d) Image corrected by (b).

Fig. 10.
Fig. 10.

Experimental example where both Φq and Φd exist. (a) Distorted optical field at CCD plane. (b) Distorted image. (c) Distorted field at the pupil. (d) Amplitude PSF of the system. (e) Phase map of the FT of (d). (f) Corrected image.

Equations (21)

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G(x3,x0)=+dx2exp[jπλd3(x3x2)2]exp(jπλf2x22){exp(jπλd2x22)+dx1A(x0)×exp[jπλd1(x1x0)2]P(x1)Φ(x1)exp(jπλf1x12)exp(jπλd2x12)exp(j2πλd2x1x2)}=exp(jπλd3x32)exp(jπλd1x02)A(x0)+dx1P(x1)Φ(x1)exp[jπλ(1d1+1d21f1)x12]exp(j2πλd1x0x1)×[+dx2exp(jπλd2x22)exp(jπλd3x22)exp(jπλf2x22)exp(j2π1λd2x2x1)exp(j2πλd3x2x3)]=exp(jπλd3x32)exp(jπλd1x02)A(x0)+dx1P(x1)Φ(x1)exp[jπλ(1d1+1d21f1)x12]exp(j2πλd1x0x1)×{+dx2exp[jπλ(1d2+1d31f2)x22]exp[j2πλ(x1d2+x3d3)x2]},
β=11d1+1d21f1andγ=11d2+1d31f2.
G(x3,x0)=exp(jπλd3x32)exp(jπλd1x02)A(x0)+dx1P(x1)Φ(x1)exp(jπλβx12)exp(j2πλd1x0x1)×{+dx2exp(jπλγx22)exp[j2πλ(x1d2+x3d3)x2]}=exp[jπλ(1d3γd32)x32]exp(jπλd1x02)A(x0)+dx1P(x1)Φ(x1)exp[jπλ(1βγd22)x12]exp[j2π(γx3λd2d3+x0λd1)x1].
P1(x1)=P(x1)Φ(x1)Φd(x1),
Φd(x1)=exp[jπλ(1βγd22)x12],
G(x3,x0)=exp[jπλ(1d3γd32)x32]exp(jπλd1x02)A(x0)T(γd1d2d3x3+x0),
T(γd1d2d3x3+x0)=FT{P1(x1)}|fx=1λd1(γd1d2d3x3+x0),
O(x3)=Φq(x3)+dx0exp[jπλd1(x02)]A(x0)T(γd1d2d3x3+x0),
Φq(x3)=exp[jπλ(1d3γd32)x32].
G1(x3)=A0T(γd1d2d3x3).
O1(x3)=+dx0exp[jπλd1(x02)]A(x0)T(γd1d2d3x3+x0).
O1G1(x3)=A0++dαdx0exp[jπλd1(x02)]A(x0)T(γd1d2d3x3+x0+γd1d2d3α)T*(γd1d2d3α)=d2d3A0γd1++dαdx0exp[jπλd1(x02)]A(x0)T(γd1d2d3x3+x0+α)T*(α),
T(x0+γd1d2d3x3+α)=+dηP1(η)exp[j2πλd1η(x0+γd1d2d3x3+α)]
T*(α)=+dxP1*(x)exp(j2πλd1αx).
O1G1(x3)=d2d3A0γd1++dαdx0exp[jπλd1(x02)]A(x0)×{+dηP1(η)exp[j2πλd1η(x0+γd1d2d3x3+α)]+dxP1*(x)exp(j2πλd1αx)}=d2d3A0γd1+dx0exp[jπλd1(x02)]A(x0)×++dxdηP1*(x)P1(η)exp[j2πλd1η(x0+γd1d2d3x3)]{+dαexp[j2πλd1(xη)α]}=λd2d3A0γ+dx0exp(jπλd1x02)A(x0)++dxdηP1*(x)P1(η)exp[j2πλd1η(x0+γd1d2d3x3)]δ(xη)=λd2d3A0γ+dx0exp(jπλd1x02)A(x0)+dxP1*(x)P1(x)exp[j2πλd1x(x0+γd1d2d3x3)]=λd2d3A0γ+dx0exp(jπλd1x02)A(x0)+dxP(x)exp[j2πλd1x(x0+γd1d2d3x3)],
O1G1(x3)=IFT{FT{O1(x3)}FT*{G1(x3)}},
FT{G(x3,0)}=A0FT{exp[jπλ(1d3γd32)x32]T(γd1d2d3x3)}=A0FT{exp[jπλ(1d3γd32)(λd2d3γ)2fx2]}FT{FT{P1(x1)}(fx)}=A0γd2jλ(d3γ)exp[jπγ2λ(d3γ)d22x12]P1(x1),
fx=γλd2d3x3.
Δfx=Δfy=γλd2d3Δx3.
Δx1=λd2d3NγΔx3andΔy1=λd2d3MγΔx3.
D2λd2d34γΔx3.

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