Abstract

Coherent anti-Stokes Raman scattering (CARS) holography captures both the amplitude and the phase of the anti-Stokes field generated from a sample and can thus perform single-shot, chemically selective three-dimensional imaging. We present compressive CARS holography, a numerical technique based on the concept of compressive sensing, to improve the quality of reconstructed images by leveraging sparsity in the source distribution and reducing the out-of-focus background noise. In particular, we use the two-step iterative shrinkage threshold (TwIST) algorithm with an l1 norm regularizer to iteratively retrieve images from an off axis CARS digital hologram. It is shown that the use of compressive CARS holography enhances the CARS holographic imaging technique by reducing noise and thereby effectively emulating a higher axial resolution using only a single shot hologram.

© 2015 Optical Society of America

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References

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  1. D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
    [Crossref] [PubMed]
  2. E. Williams and J. Maynard, “Holographic imaging without the wavelength resolution limit,” Phys. Rev. Lett. 45(7), 554–557 (1980).
    [Crossref]
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    [Crossref] [PubMed]
  5. L. Onural and P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26(11), 261124 (1987).
    [Crossref]
  6. T. S. Huang, “Digital holography,” Proc. IEEE 59(9), 1335–1346 (1971).
    [Crossref]
  7. J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11(3), 77–79 (1967).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  10. A. J. Devaney, “Geophysical diffraction tomography,” IEEE Trans. Geosci. Rem. Sens. 22, 1–2 (1984).
  11. Q. Xu, K. Shi, H. Li, K. Choi, R. Horisaki, D. Brady, D. Psaltis, and Z. Liu, “Inline holographic coherent anti-Stokes Raman microscopy,” Opt. Express 18(8), 8213–8219 (2010).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]

2012 (2)

K. Shi, P. S. Edwards, J. Hu, Q. Xu, Y. Wang, D. Psaltis, and Z. Liu, “Holographic coherent anti-Stokes Raman scattering bio-imaging,” Biomed. Opt. Express 3(7), 1744–1749 (2012).
[Crossref] [PubMed]

P. S. Edwards, N. Mehta, K. Shi, Q. Xu, D. Psaltis, and Z. Liu, “Coherent anti-Stokes Raman scattering holography: theory and experiment,” J. Nonlinear Opt. Phys. Mater. 21(02), 1250028 (2012).
[Crossref]

2010 (2)

Q. Xu, K. Shi, H. Li, K. Choi, R. Horisaki, D. Brady, D. Psaltis, and Z. Liu, “Inline holographic coherent anti-Stokes Raman microscopy,” Opt. Express 18(8), 8213–8219 (2010).
[Crossref] [PubMed]

K. Shi, H. Li, Q. Xu, D. Psaltis, and Z. Liu, “Coherent anti-Stokes Raman holography for chemically selective single-shot nonscanning 3D imaging,” Phys. Rev. Lett. 104(9), 093902 (2010).
[Crossref] [PubMed]

2009 (2)

D. J. Brady, K. Choi, D. L. Marks, R. Horisaki, and S. Lim, “Compressive holography,” Opt. Express 17(15), 13040–13049 (2009).
[Crossref] [PubMed]

M. Jurna, J. P. Korterik, C. Otto, J. L. Herek, and H. L. Offerhaus, “Vibrational phase contrast microscopy by use of coherent anti-Stokes Raman scattering,” Phys. Rev. Lett. 103(4), 043905 (2009).
[Crossref] [PubMed]

2008 (1)

2007 (2)

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A New twIST: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process. 16(12), 2992–3004 (2007).
[Crossref] [PubMed]

M. Jurna, J. P. Korterik, C. Otto, and H. L. Offerhaus, “Shot noise limited heterodyne detection of CARS signals,” Opt. Express 15(23), 15207–15213 (2007).
[Crossref] [PubMed]

2006 (2)

D. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
[Crossref]

E. Candès, J. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59(8), 1207–1223 (2006).
[Crossref]

2004 (1)

I. Daubechies, M. Defrise, and C. De Mol, “An iterative thresholding algorithm for linear inverse problems with a sparsity constraint,” Commun. Pure Appl. Math. 57(11), 1413–1457 (2004).
[Crossref]

1994 (1)

1987 (1)

L. Onural and P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26(11), 261124 (1987).
[Crossref]

1984 (1)

A. J. Devaney, “Geophysical diffraction tomography,” IEEE Trans. Geosci. Rem. Sens. 22, 1–2 (1984).

1980 (1)

E. Williams and J. Maynard, “Holographic imaging without the wavelength resolution limit,” Phys. Rev. Lett. 45(7), 554–557 (1980).
[Crossref]

1971 (1)

T. S. Huang, “Digital holography,” Proc. IEEE 59(9), 1335–1346 (1971).
[Crossref]

1967 (1)

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11(3), 77–79 (1967).
[Crossref]

1962 (1)

1948 (1)

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[Crossref] [PubMed]

Bioucas-Dias, J. M.

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A New twIST: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process. 16(12), 2992–3004 (2007).
[Crossref] [PubMed]

Brady, D.

Brady, D. J.

Candès, E.

E. Candès, J. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59(8), 1207–1223 (2006).
[Crossref]

Centurion, M.

Choi, K.

Daubechies, I.

I. Daubechies, M. Defrise, and C. De Mol, “An iterative thresholding algorithm for linear inverse problems with a sparsity constraint,” Commun. Pure Appl. Math. 57(11), 1413–1457 (2004).
[Crossref]

De Mol, C.

I. Daubechies, M. Defrise, and C. De Mol, “An iterative thresholding algorithm for linear inverse problems with a sparsity constraint,” Commun. Pure Appl. Math. 57(11), 1413–1457 (2004).
[Crossref]

Defrise, M.

I. Daubechies, M. Defrise, and C. De Mol, “An iterative thresholding algorithm for linear inverse problems with a sparsity constraint,” Commun. Pure Appl. Math. 57(11), 1413–1457 (2004).
[Crossref]

Devaney, A. J.

A. J. Devaney, “Geophysical diffraction tomography,” IEEE Trans. Geosci. Rem. Sens. 22, 1–2 (1984).

Donoho, D.

D. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
[Crossref]

Edwards, P. S.

P. S. Edwards, N. Mehta, K. Shi, Q. Xu, D. Psaltis, and Z. Liu, “Coherent anti-Stokes Raman scattering holography: theory and experiment,” J. Nonlinear Opt. Phys. Mater. 21(02), 1250028 (2012).
[Crossref]

K. Shi, P. S. Edwards, J. Hu, Q. Xu, Y. Wang, D. Psaltis, and Z. Liu, “Holographic coherent anti-Stokes Raman scattering bio-imaging,” Biomed. Opt. Express 3(7), 1744–1749 (2012).
[Crossref] [PubMed]

Figueiredo, M. A. T.

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A New twIST: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process. 16(12), 2992–3004 (2007).
[Crossref] [PubMed]

Gabor, D.

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[Crossref] [PubMed]

Goodman, J. W.

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11(3), 77–79 (1967).
[Crossref]

Herek, J. L.

M. Jurna, J. P. Korterik, C. Otto, J. L. Herek, and H. L. Offerhaus, “Vibrational phase contrast microscopy by use of coherent anti-Stokes Raman scattering,” Phys. Rev. Lett. 103(4), 043905 (2009).
[Crossref] [PubMed]

Horisaki, R.

Hu, J.

Huang, T. S.

T. S. Huang, “Digital holography,” Proc. IEEE 59(9), 1335–1346 (1971).
[Crossref]

Jüptner, W.

Jurna, M.

M. Jurna, J. P. Korterik, C. Otto, J. L. Herek, and H. L. Offerhaus, “Vibrational phase contrast microscopy by use of coherent anti-Stokes Raman scattering,” Phys. Rev. Lett. 103(4), 043905 (2009).
[Crossref] [PubMed]

M. Jurna, J. P. Korterik, C. Otto, and H. L. Offerhaus, “Shot noise limited heterodyne detection of CARS signals,” Opt. Express 15(23), 15207–15213 (2007).
[Crossref] [PubMed]

Korterik, J. P.

M. Jurna, J. P. Korterik, C. Otto, J. L. Herek, and H. L. Offerhaus, “Vibrational phase contrast microscopy by use of coherent anti-Stokes Raman scattering,” Phys. Rev. Lett. 103(4), 043905 (2009).
[Crossref] [PubMed]

M. Jurna, J. P. Korterik, C. Otto, and H. L. Offerhaus, “Shot noise limited heterodyne detection of CARS signals,” Opt. Express 15(23), 15207–15213 (2007).
[Crossref] [PubMed]

Lawrence, R. W.

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11(3), 77–79 (1967).
[Crossref]

Leith, E. N.

Li, H.

Q. Xu, K. Shi, H. Li, K. Choi, R. Horisaki, D. Brady, D. Psaltis, and Z. Liu, “Inline holographic coherent anti-Stokes Raman microscopy,” Opt. Express 18(8), 8213–8219 (2010).
[Crossref] [PubMed]

K. Shi, H. Li, Q. Xu, D. Psaltis, and Z. Liu, “Coherent anti-Stokes Raman holography for chemically selective single-shot nonscanning 3D imaging,” Phys. Rev. Lett. 104(9), 093902 (2010).
[Crossref] [PubMed]

Lim, S.

Liu, Z.

K. Shi, P. S. Edwards, J. Hu, Q. Xu, Y. Wang, D. Psaltis, and Z. Liu, “Holographic coherent anti-Stokes Raman scattering bio-imaging,” Biomed. Opt. Express 3(7), 1744–1749 (2012).
[Crossref] [PubMed]

P. S. Edwards, N. Mehta, K. Shi, Q. Xu, D. Psaltis, and Z. Liu, “Coherent anti-Stokes Raman scattering holography: theory and experiment,” J. Nonlinear Opt. Phys. Mater. 21(02), 1250028 (2012).
[Crossref]

K. Shi, H. Li, Q. Xu, D. Psaltis, and Z. Liu, “Coherent anti-Stokes Raman holography for chemically selective single-shot nonscanning 3D imaging,” Phys. Rev. Lett. 104(9), 093902 (2010).
[Crossref] [PubMed]

Q. Xu, K. Shi, H. Li, K. Choi, R. Horisaki, D. Brady, D. Psaltis, and Z. Liu, “Inline holographic coherent anti-Stokes Raman microscopy,” Opt. Express 18(8), 8213–8219 (2010).
[Crossref] [PubMed]

Marks, D. L.

Maynard, J.

E. Williams and J. Maynard, “Holographic imaging without the wavelength resolution limit,” Phys. Rev. Lett. 45(7), 554–557 (1980).
[Crossref]

Mehta, N.

P. S. Edwards, N. Mehta, K. Shi, Q. Xu, D. Psaltis, and Z. Liu, “Coherent anti-Stokes Raman scattering holography: theory and experiment,” J. Nonlinear Opt. Phys. Mater. 21(02), 1250028 (2012).
[Crossref]

Offerhaus, H. L.

M. Jurna, J. P. Korterik, C. Otto, J. L. Herek, and H. L. Offerhaus, “Vibrational phase contrast microscopy by use of coherent anti-Stokes Raman scattering,” Phys. Rev. Lett. 103(4), 043905 (2009).
[Crossref] [PubMed]

M. Jurna, J. P. Korterik, C. Otto, and H. L. Offerhaus, “Shot noise limited heterodyne detection of CARS signals,” Opt. Express 15(23), 15207–15213 (2007).
[Crossref] [PubMed]

Onural, L.

L. Onural and P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26(11), 261124 (1987).
[Crossref]

Otto, C.

M. Jurna, J. P. Korterik, C. Otto, J. L. Herek, and H. L. Offerhaus, “Vibrational phase contrast microscopy by use of coherent anti-Stokes Raman scattering,” Phys. Rev. Lett. 103(4), 043905 (2009).
[Crossref] [PubMed]

M. Jurna, J. P. Korterik, C. Otto, and H. L. Offerhaus, “Shot noise limited heterodyne detection of CARS signals,” Opt. Express 15(23), 15207–15213 (2007).
[Crossref] [PubMed]

Psaltis, D.

K. Shi, P. S. Edwards, J. Hu, Q. Xu, Y. Wang, D. Psaltis, and Z. Liu, “Holographic coherent anti-Stokes Raman scattering bio-imaging,” Biomed. Opt. Express 3(7), 1744–1749 (2012).
[Crossref] [PubMed]

P. S. Edwards, N. Mehta, K. Shi, Q. Xu, D. Psaltis, and Z. Liu, “Coherent anti-Stokes Raman scattering holography: theory and experiment,” J. Nonlinear Opt. Phys. Mater. 21(02), 1250028 (2012).
[Crossref]

K. Shi, H. Li, Q. Xu, D. Psaltis, and Z. Liu, “Coherent anti-Stokes Raman holography for chemically selective single-shot nonscanning 3D imaging,” Phys. Rev. Lett. 104(9), 093902 (2010).
[Crossref] [PubMed]

Q. Xu, K. Shi, H. Li, K. Choi, R. Horisaki, D. Brady, D. Psaltis, and Z. Liu, “Inline holographic coherent anti-Stokes Raman microscopy,” Opt. Express 18(8), 8213–8219 (2010).
[Crossref] [PubMed]

Y. Pu, M. Centurion, and D. Psaltis, “Harmonic holography: a new holographic principle,” Appl. Opt. 47(4), A103–A110 (2008).
[Crossref] [PubMed]

Pu, Y.

Romberg, J.

E. Candès, J. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59(8), 1207–1223 (2006).
[Crossref]

Schnars, U.

Scott, P. D.

L. Onural and P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26(11), 261124 (1987).
[Crossref]

Shi, K.

P. S. Edwards, N. Mehta, K. Shi, Q. Xu, D. Psaltis, and Z. Liu, “Coherent anti-Stokes Raman scattering holography: theory and experiment,” J. Nonlinear Opt. Phys. Mater. 21(02), 1250028 (2012).
[Crossref]

K. Shi, P. S. Edwards, J. Hu, Q. Xu, Y. Wang, D. Psaltis, and Z. Liu, “Holographic coherent anti-Stokes Raman scattering bio-imaging,” Biomed. Opt. Express 3(7), 1744–1749 (2012).
[Crossref] [PubMed]

Q. Xu, K. Shi, H. Li, K. Choi, R. Horisaki, D. Brady, D. Psaltis, and Z. Liu, “Inline holographic coherent anti-Stokes Raman microscopy,” Opt. Express 18(8), 8213–8219 (2010).
[Crossref] [PubMed]

K. Shi, H. Li, Q. Xu, D. Psaltis, and Z. Liu, “Coherent anti-Stokes Raman holography for chemically selective single-shot nonscanning 3D imaging,” Phys. Rev. Lett. 104(9), 093902 (2010).
[Crossref] [PubMed]

Tao, T.

E. Candès, J. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59(8), 1207–1223 (2006).
[Crossref]

Upatnieks, J.

Wang, Y.

Williams, E.

E. Williams and J. Maynard, “Holographic imaging without the wavelength resolution limit,” Phys. Rev. Lett. 45(7), 554–557 (1980).
[Crossref]

Xu, Q.

P. S. Edwards, N. Mehta, K. Shi, Q. Xu, D. Psaltis, and Z. Liu, “Coherent anti-Stokes Raman scattering holography: theory and experiment,” J. Nonlinear Opt. Phys. Mater. 21(02), 1250028 (2012).
[Crossref]

K. Shi, P. S. Edwards, J. Hu, Q. Xu, Y. Wang, D. Psaltis, and Z. Liu, “Holographic coherent anti-Stokes Raman scattering bio-imaging,” Biomed. Opt. Express 3(7), 1744–1749 (2012).
[Crossref] [PubMed]

Q. Xu, K. Shi, H. Li, K. Choi, R. Horisaki, D. Brady, D. Psaltis, and Z. Liu, “Inline holographic coherent anti-Stokes Raman microscopy,” Opt. Express 18(8), 8213–8219 (2010).
[Crossref] [PubMed]

K. Shi, H. Li, Q. Xu, D. Psaltis, and Z. Liu, “Coherent anti-Stokes Raman holography for chemically selective single-shot nonscanning 3D imaging,” Phys. Rev. Lett. 104(9), 093902 (2010).
[Crossref] [PubMed]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11(3), 77–79 (1967).
[Crossref]

Biomed. Opt. Express (1)

Commun. Pure Appl. Math. (2)

E. Candès, J. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59(8), 1207–1223 (2006).
[Crossref]

I. Daubechies, M. Defrise, and C. De Mol, “An iterative thresholding algorithm for linear inverse problems with a sparsity constraint,” Commun. Pure Appl. Math. 57(11), 1413–1457 (2004).
[Crossref]

IEEE Trans. Geosci. Rem. Sens. (1)

A. J. Devaney, “Geophysical diffraction tomography,” IEEE Trans. Geosci. Rem. Sens. 22, 1–2 (1984).

IEEE Trans. Image Process. (1)

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A New twIST: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process. 16(12), 2992–3004 (2007).
[Crossref] [PubMed]

IEEE Trans. Inf. Theory (1)

D. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
[Crossref]

J. Nonlinear Opt. Phys. Mater. (1)

P. S. Edwards, N. Mehta, K. Shi, Q. Xu, D. Psaltis, and Z. Liu, “Coherent anti-Stokes Raman scattering holography: theory and experiment,” J. Nonlinear Opt. Phys. Mater. 21(02), 1250028 (2012).
[Crossref]

J. Opt. Soc. Am. (1)

Nature (1)

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[Crossref] [PubMed]

Opt. Eng. (1)

L. Onural and P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26(11), 261124 (1987).
[Crossref]

Opt. Express (3)

Phys. Rev. Lett. (3)

K. Shi, H. Li, Q. Xu, D. Psaltis, and Z. Liu, “Coherent anti-Stokes Raman holography for chemically selective single-shot nonscanning 3D imaging,” Phys. Rev. Lett. 104(9), 093902 (2010).
[Crossref] [PubMed]

E. Williams and J. Maynard, “Holographic imaging without the wavelength resolution limit,” Phys. Rev. Lett. 45(7), 554–557 (1980).
[Crossref]

M. Jurna, J. P. Korterik, C. Otto, J. L. Herek, and H. L. Offerhaus, “Vibrational phase contrast microscopy by use of coherent anti-Stokes Raman scattering,” Phys. Rev. Lett. 103(4), 043905 (2009).
[Crossref] [PubMed]

Proc. IEEE (1)

T. S. Huang, “Digital holography,” Proc. IEEE 59(9), 1335–1346 (1971).
[Crossref]

Other (1)

P. Hariharan, Optical Holography: Principles, techniques and applications. Cambridge University, (1996).

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Figures (5)

Fig. 1
Fig. 1 (a) Schematic diagram of CARS holography (b) Central part (256x256 pixels) of a recorded CARS hologram; (c) DC filtered two dimensional Fourier transform (amplitude) of the hologram in (b); (d) A digitally filtered and re-centered sideband; (e) Reconstructed CARS field (amplitude) at the recording plane.
Fig. 2
Fig. 2 Image reconstruction using conventional digital propagation. The nine polystyrene microspheres are visible, but are surrounded by out-of-focus background contributions.
Fig. 3
Fig. 3 Compressive sensing based image reconstruction using the l1 regularization. The diffraction noise is suppressed and the spheres signal can clearly be seen to be localized at different depth positions. Red arrow indicates spheres used for SNR analysis in Fig. 4.
Fig. 4
Fig. 4 Axial localization using compressive CARS holography. (a) and (b) show SNR for two spheres (indicated by red arrows in Fig. 3 along the z depth position using conventional digital back-propagation algorithm and compressive reconstruction, respectively. (c) and (d) show the x-z cross section of the lower sphere using digital back-propagation and the compressive reconstruction, respectively.
Fig. 5
Fig. 5 (a-e) Compressive CARS holographic reconstruction of HeLa cells at various depths.

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A ˜ a s ( u , v , L ) A p 2 A s * 0 L d z e i Δ k z ( χ ˜ ( 3 ) ( u , v , z ) e i ( L z ) ( k x 2 + k y 2 ) / ( 2 k a s ) )
A ˜ a s ( u , v ) = 0 L d z H ( u , v , z ) X ˜ ( 3 ) ( u , v , z ) or , A ˜ a s ( u , v ) = l [ n , m X ( 3 ) ( n Δ x , m Δ y , l Δ z ) e i 2 π ( u n Δ x + v m Δ y ) ] e i Δ k l Δ z e i π λ a s ( L l Δ z ) ( u 2 + v 2 )

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