Abstract

Fast acquisition and high axial resolution are two primary requirements for three-dimensional micros copy. However, they are sometimes conflicting: imaging modalities such as confocal imaging can deliver superior resolution at the expense of sequential acquisition at different axial planes, which is a time-consuming process. Optical scanning holography (OSH) promises to deliver a good trade-off between these two goals. With just a single scan, we can capture the entire three-dimensional volume in a digital hologram; the data can then be processed to obtain the individual sections. An accurate modeling of the imaging system is key to devising an appropriate image reconstruction algorithm, especially for real data where random noise and other imaging imperfections must be taken into account. In this paper we dem onstrate sectional image reconstruction by applying an inverse imaging sectioning technique to experimental OSH data of biological specimens and visualizing the sections using the OSA Interactive Science Publishing software.

© 2009 Optical Society of America

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References

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  1. T. R. Corle and G. S. Kino, Confocal Scanning Optical Microscopy and Related Imaging Systems (Academic, 1996).
  2. Y. Shu, R. Chung, Z. Tan, J. Cheng, E. Y. Lam, K. S. Fung, and F. Wang, “Projection optics design for tilted projection of fringe patterns,” Opt. Eng. 47, 053002 (2008).
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    [CrossRef]
  4. D. Gabor, “A new microscope principle,” Nature 161, 777-778(1948).
  5. J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, 2004), 3rd ed.
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    [CrossRef]
  7. J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms ,” Appl. Phys. Lett. 11, 77-79 (1967).
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    [CrossRef]
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    [CrossRef]
  10. E. Y. Lam and J. W. Goodman, “Iterative statistical approach to blind image deconvolution,” J. Opt. Soc. Am. A 17, 1177-1184 (2000).
    [CrossRef]
  11. J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts & Company, 2007).
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    [CrossRef]
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    [CrossRef]
  17. G. Indebetouw, P. Klysubun, T. Kim, and T.-C. Poon, “Imaging properties of scanning holographic microscopy,” J. Opt. Soc. Am. A 17, 380-390 (2000).
    [CrossRef]
  18. T.-C. Poon, “Scanning holography and two-dimensional image processing by acousto-optic two-pupil synthesis,” J. Opt. Soc. Am. A 2, 521-527 (1985).
    [CrossRef]
  19. M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999), seventh ed.
  20. R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, 2000), 3rd ed.
  21. E. Y. Lam, “Noise in superresolution reconstruction,” Opt. Lett. 28, 2234-2236 (2003).
    [CrossRef]
  22. Z. Xu and E. Y. Lam, “Maximum a posteriori blind image deconvolution with Huber-Markov random-field regularization,” Opt. Lett. 34, 1453-1455 (2009).
    [CrossRef]
  23. X. Zhang, E. Y. Lam, T.-C. Poon, T. Kim, and Y. S. Kim, “Blind sectional image reconstruction for optical scanning holography,” submitted to Opt. Lett. .
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    [CrossRef]
  25. H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform: with Applications in Optics and Signal Processing, 1st ed. (Wiley, 2001).
  26. H. Kim, S.-W. Min, B. Lee, and T.-C. Poon, “Optical sectioning for optical scanning holography using phase-space filtering with wigner distribution functions,” Appl. Opt. 47, D164-D175 (2008).
    [CrossRef]
  27. L. Cohen, Time Frequency Analysis: Theory and Applications (Springer-Verlag, 2007), 1st ed.
  28. X. Zhang, E. Y. Lam, and T.-C. Poon, “Reconstruction of sectional images in holography using inverse imaging,” Opt. Express 16, 17215-17226 (2008).
    [CrossRef]
  29. X. Zhang, E. Y. Lam, and T.-C. Poon, “Fast iterative sectional image reconstruction in optical scanning holography,” in OSA Topical Meeting in Digital Holography and Three-Dimensional Imaging (2009).
  30. X. Zhang, T.-C. Poon, and E. Y. Lam, “An inverse imaging approach to sectional image reconstruction in optical scanning holography,” in International Topical Meeting on Information Photonics (2008).
  31. A. Ribés and F. Schmitt, “Linear inverse problems in imaging,” IEEE Sig. Proc. Mag. 25, 84-99 (2008).
  32. Y. Shen, E. Y. Lam, and N. Wong, “Binary image restoration by positive semidefinite programming,” Opt. Lett. 32, 121-123(2007).
    [CrossRef]
  33. G. Indebetouw, “Scanning holographic microscopy with spatially incoherent sources: Reconciling the holographic advantage with the sectioning advantage,” J. Opt. Soc. Am. A 26, 252-258 (2009).
    [CrossRef]

2009 (2)

2008 (4)

H. Kim, S.-W. Min, B. Lee, and T.-C. Poon, “Optical sectioning for optical scanning holography using phase-space filtering with wigner distribution functions,” Appl. Opt. 47, D164-D175 (2008).
[CrossRef]

X. Zhang, E. Y. Lam, and T.-C. Poon, “Reconstruction of sectional images in holography using inverse imaging,” Opt. Express 16, 17215-17226 (2008).
[CrossRef]

Y. Shu, R. Chung, Z. Tan, J. Cheng, E. Y. Lam, K. S. Fung, and F. Wang, “Projection optics design for tilted projection of fringe patterns,” Opt. Eng. 47, 053002 (2008).

A. Ribés and F. Schmitt, “Linear inverse problems in imaging,” IEEE Sig. Proc. Mag. 25, 84-99 (2008).

2007 (1)

2006 (2)

2003 (2)

2002 (1)

2000 (2)

1997 (1)

1995 (1)

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, and Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338-1344 (1995).

1992 (1)

1985 (1)

1978 (1)

1967 (1)

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

1966 (1)

C. Knox, “Holographic microscopy as a technique for recording dynamic microscopic subjects,” Science 153, 989-990 (1966).
[CrossRef]

1948 (1)

D. Gabor, “A new microscope principle,” Nature 161, 777-778(1948).

Athey, B. D.

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999), seventh ed.

Bracewell, R. N.

R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, 2000), 3rd ed.

Cheng, J.

Y. Shu, R. Chung, Z. Tan, J. Cheng, E. Y. Lam, K. S. Fung, and F. Wang, “Projection optics design for tilted projection of fringe patterns,” Opt. Eng. 47, 053002 (2008).

Chien, W.-C.

Chung, R.

Y. Shu, R. Chung, Z. Tan, J. Cheng, E. Y. Lam, K. S. Fung, and F. Wang, “Projection optics design for tilted projection of fringe patterns,” Opt. Eng. 47, 053002 (2008).

Cohen, L.

L. Cohen, Time Frequency Analysis: Theory and Applications (Springer-Verlag, 2007), 1st ed.

Corle, T. R.

T. R. Corle and G. S. Kino, Confocal Scanning Optical Microscopy and Related Imaging Systems (Academic, 1996).

Dilworth, D. S.

Doh, K.

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, and Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338-1344 (1995).

Duncan, B. D.

Fung, K. S.

Y. Shu, R. Chung, Z. Tan, J. Cheng, E. Y. Lam, K. S. Fung, and F. Wang, “Projection optics design for tilted projection of fringe patterns,” Opt. Eng. 47, 053002 (2008).

Gabor, D.

D. Gabor, “A new microscope principle,” Nature 161, 777-778(1948).

Goodman, J. W.

E. Y. Lam and J. W. Goodman, “Iterative statistical approach to blind image deconvolution,” J. Opt. Soc. Am. A 17, 1177-1184 (2000).
[CrossRef]

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

J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, 2004), 3rd ed.

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts & Company, 2007).

Huisken, J.

Indebetouw, G.

Kim, H.

Kim, T.

Kim, Y. S.

X. Zhang, E. Y. Lam, T.-C. Poon, T. Kim, and Y. S. Kim, “Blind sectional image reconstruction for optical scanning holography,” submitted to Opt. Lett. .

Kino, G. S.

T. R. Corle and G. S. Kino, Confocal Scanning Optical Microscopy and Related Imaging Systems (Academic, 1996).

Klysubun, P.

Knox, C.

C. Knox, “Holographic microscopy as a technique for recording dynamic microscopic subjects,” Science 153, 989-990 (1966).
[CrossRef]

Kutay, M. A.

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform: with Applications in Optics and Signal Processing, 1st ed. (Wiley, 2001).

Lam, E. Y.

Z. Xu and E. Y. Lam, “Maximum a posteriori blind image deconvolution with Huber-Markov random-field regularization,” Opt. Lett. 34, 1453-1455 (2009).
[CrossRef]

X. Zhang, E. Y. Lam, and T.-C. Poon, “Reconstruction of sectional images in holography using inverse imaging,” Opt. Express 16, 17215-17226 (2008).
[CrossRef]

Y. Shu, R. Chung, Z. Tan, J. Cheng, E. Y. Lam, K. S. Fung, and F. Wang, “Projection optics design for tilted projection of fringe patterns,” Opt. Eng. 47, 053002 (2008).

Y. Shen, E. Y. Lam, and N. Wong, “Binary image restoration by positive semidefinite programming,” Opt. Lett. 32, 121-123(2007).
[CrossRef]

E. Y. Lam, “Noise in superresolution reconstruction,” Opt. Lett. 28, 2234-2236 (2003).
[CrossRef]

E. Y. Lam and J. W. Goodman, “Iterative statistical approach to blind image deconvolution,” J. Opt. Soc. Am. A 17, 1177-1184 (2000).
[CrossRef]

X. Zhang, E. Y. Lam, T.-C. Poon, T. Kim, and Y. S. Kim, “Blind sectional image reconstruction for optical scanning holography,” submitted to Opt. Lett. .

X. Zhang, E. Y. Lam, and T.-C. Poon, “Fast iterative sectional image reconstruction in optical scanning holography,” in OSA Topical Meeting in Digital Holography and Three-Dimensional Imaging (2009).

X. Zhang, T.-C. Poon, and E. Y. Lam, “An inverse imaging approach to sectional image reconstruction in optical scanning holography,” in International Topical Meeting on Information Photonics (2008).

Lawrence, R. W.

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

Lee, B.

Leith, E. N.

Lohmann, A. W.

Martínez-Corral, M.

Mills, K. D.

Min, S.-W.

Ozaktas, H. M.

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform: with Applications in Optics and Signal Processing, 1st ed. (Wiley, 2001).

Poon, T.-C.

H. Kim, S.-W. Min, B. Lee, and T.-C. Poon, “Optical sectioning for optical scanning holography using phase-space filtering with wigner distribution functions,” Appl. Opt. 47, D164-D175 (2008).
[CrossRef]

X. Zhang, E. Y. Lam, and T.-C. Poon, “Reconstruction of sectional images in holography using inverse imaging,” Opt. Express 16, 17215-17226 (2008).
[CrossRef]

G. Indebetouw, P. Klysubun, T. Kim, and T.-C. Poon, “Imaging properties of scanning holographic microscopy,” J. Opt. Soc. Am. A 17, 380-390 (2000).
[CrossRef]

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, and Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338-1344 (1995).

B. D. Duncan and T.-C. Poon, “Gaussian beam analysis of optical scanning holography,” J. Opt. Soc. Am. A 9, 229-236(1992).
[CrossRef]

T.-C. Poon, “Scanning holography and two-dimensional image processing by acousto-optic two-pupil synthesis,” J. Opt. Soc. Am. A 2, 521-527 (1985).
[CrossRef]

X. Zhang, E. Y. Lam, T.-C. Poon, T. Kim, and Y. S. Kim, “Blind sectional image reconstruction for optical scanning holography,” submitted to Opt. Lett. .

X. Zhang, E. Y. Lam, and T.-C. Poon, “Fast iterative sectional image reconstruction in optical scanning holography,” in OSA Topical Meeting in Digital Holography and Three-Dimensional Imaging (2009).

X. Zhang, T.-C. Poon, and E. Y. Lam, “An inverse imaging approach to sectional image reconstruction in optical scanning holography,” in International Topical Meeting on Information Photonics (2008).

T.-C. Poon, Optical Scanning Holography with MATLAB (Springer, 2007).

Rhodes, W. T.

Ribés, A.

A. Ribés and F. Schmitt, “Linear inverse problems in imaging,” IEEE Sig. Proc. Mag. 25, 84-99 (2008).

Schilling, B.

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, and Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338-1344 (1995).

Schmitt, F.

A. Ribés and F. Schmitt, “Linear inverse problems in imaging,” IEEE Sig. Proc. Mag. 25, 84-99 (2008).

Shen, Y.

Shinoda, K.

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, and Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338-1344 (1995).

Shu, Y.

Y. Shu, R. Chung, Z. Tan, J. Cheng, E. Y. Lam, K. S. Fung, and F. Wang, “Projection optics design for tilted projection of fringe patterns,” Opt. Eng. 47, 053002 (2008).

Stelzer, E. H. K.

Suzuki, Y.

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, and Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338-1344 (1995).

Swoger, J.

Tan, Z.

Y. Shu, R. Chung, Z. Tan, J. Cheng, E. Y. Lam, K. S. Fung, and F. Wang, “Projection optics design for tilted projection of fringe patterns,” Opt. Eng. 47, 053002 (2008).

Wang, F.

Y. Shu, R. Chung, Z. Tan, J. Cheng, E. Y. Lam, K. S. Fung, and F. Wang, “Projection optics design for tilted projection of fringe patterns,” Opt. Eng. 47, 053002 (2008).

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999), seventh ed.

Wong, N.

Wu, M.

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, and Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338-1344 (1995).

Xu, Z.

Yamaguchi, I.

Zalevsky, Z.

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform: with Applications in Optics and Signal Processing, 1st ed. (Wiley, 2001).

Zhang, T.

Zhang, X.

X. Zhang, E. Y. Lam, and T.-C. Poon, “Reconstruction of sectional images in holography using inverse imaging,” Opt. Express 16, 17215-17226 (2008).
[CrossRef]

X. Zhang, E. Y. Lam, and T.-C. Poon, “Fast iterative sectional image reconstruction in optical scanning holography,” in OSA Topical Meeting in Digital Holography and Three-Dimensional Imaging (2009).

X. Zhang, T.-C. Poon, and E. Y. Lam, “An inverse imaging approach to sectional image reconstruction in optical scanning holography,” in International Topical Meeting on Information Photonics (2008).

X. Zhang, E. Y. Lam, T.-C. Poon, T. Kim, and Y. S. Kim, “Blind sectional image reconstruction for optical scanning holography,” submitted to Opt. Lett. .

Zhong, W.

Appl. Opt. (3)

Digital image formation from electronically detected holograms (1)

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

IEEE Sig. Proc. Mag. (1)

A. Ribés and F. Schmitt, “Linear inverse problems in imaging,” IEEE Sig. Proc. Mag. 25, 84-99 (2008).

J. Opt. Soc. Am. A (8)

Nature (1)

D. Gabor, “A new microscope principle,” Nature 161, 777-778(1948).

Opt. Eng. (2)

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, and Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338-1344 (1995).

Y. Shu, R. Chung, Z. Tan, J. Cheng, E. Y. Lam, K. S. Fung, and F. Wang, “Projection optics design for tilted projection of fringe patterns,” Opt. Eng. 47, 053002 (2008).

Opt. Express (1)

Opt. Lett. (5)

Science (1)

C. Knox, “Holographic microscopy as a technique for recording dynamic microscopic subjects,” Science 153, 989-990 (1966).
[CrossRef]

Other (10)

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform: with Applications in Optics and Signal Processing, 1st ed. (Wiley, 2001).

L. Cohen, Time Frequency Analysis: Theory and Applications (Springer-Verlag, 2007), 1st ed.

X. Zhang, E. Y. Lam, and T.-C. Poon, “Fast iterative sectional image reconstruction in optical scanning holography,” in OSA Topical Meeting in Digital Holography and Three-Dimensional Imaging (2009).

X. Zhang, T.-C. Poon, and E. Y. Lam, “An inverse imaging approach to sectional image reconstruction in optical scanning holography,” in International Topical Meeting on Information Photonics (2008).

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999), seventh ed.

R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, 2000), 3rd ed.

T.-C. Poon, Optical Scanning Holography with MATLAB (Springer, 2007).

T. R. Corle and G. S. Kino, Confocal Scanning Optical Microscopy and Related Imaging Systems (Academic, 1996).

J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, 2004), 3rd ed.

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts & Company, 2007).

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Figures (5)

Fig. 1
Fig. 1

Optical scanning holography system architecture.

Fig. 2
Fig. 2

Holograms of a point object captured experimentally: (a) sine hologram, cosine hologram. Online readers can see the full set of the sine holograms at View 1 and the cosine holograms at View 2.

Fig. 3
Fig. 3

Reconstructed point source at z = 85 μm . (a) Reconstruction using the theoretical impulse response. (b) Magnified image of the yellow box in (a). The reconstruction at various depths can be accessed online at View 3 and View 4.

Fig. 4
Fig. 4

Sections reconstructed by the conventional method. (a) Reconstructed section at z = 85 μm . (b) Reconstructed section at z = 120 μm . The full set of the reconstruction is given online at View 5.

Fig. 5
Fig. 5

Reconstructed sections by inverse imaging. The full set of the reconstruction is given online at View 6.

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Equations (18)

Equations on this page are rendered with MathJax. Learn more.

H ( k x , k y ; z ) = exp { j z 2 k 0 ( k x 2 + k y 2 ) } × p 1 * ( x ˜ , y ˜ ) p 2 ( x ˜ + f k 0 k x , y ˜ + f k 0 k y ) exp { j z f ( x ˜ k x + y ˜ k y ) } d x ˜ d y ˜ ,
H ( k x , k y ; z ) | OSH = exp { j z 2 k 0 ( k x 2 + k y 2 ) } exp { j z f ( f k 0 k x 2 f k 0 k y 2 ) } = exp { j z 2 k 0 ( k x 2 + k y 2 ) } exp { j z k 0 ( k x 2 + k y 2 ) } = exp { j z 2 k 0 ( k x 2 + k y 2 ) } ,
h ( x , y ; z ) | OSH = 1 4 π 2 H ( k x , k y ; z ) | OSH exp { j ( k x x + k y y ) } d k x d k y = 1 4 π 2 exp { j k 0 2 z ( x 2 + y 2 ) } × exp { j ( z 2 k 0 k x 2 k x x + k 0 2 z x 2 + z 2 k 0 k y 2 k y y + k 0 2 z y 2 ) } d k x d k y = 1 4 π 2 exp { j k 0 2 z ( x 2 + y 2 ) } exp { j z 2 k 0 ( k ^ x 2 + k ^ y 2 ) } d k ^ x d k ^ y .
exp { j z 2 k 0 k ^ x 2 } d k ^ x = cos ( z 2 k 0 k ^ x 2 ) d k ^ x j sin ( z 2 k 0 k ^ x 2 ) d k ^ x ,
cos ( z 2 k 0 k ^ x 2 ) d k ^ x = sin ( z 2 k 0 k ^ x 2 ) d k ^ x = 2 k 0 π z cos π k ˜ x 2 d k ˜ x = k 0 π z .
h ( x , y ; z ) | OSH = exp { j k 0 2 z ( x 2 + y 2 ) } · 1 4 π 2 · ( k 0 π z j k 0 π z ) 2 = exp { j k 0 2 z ( x 2 + y 2 ) } · 1 4 π 2 · ( 2 j k 0 π z ) = j k 0 2 π z exp { j k 0 2 z ( x 2 + y 2 ) } ,
g ( x , y ) = ( | O ( x , y , z ) | 2 * h ( x , y ; z ) ) d z ,
i = 1 N ( | O ( x , y , z i ) | 2 * h ( x , y ; z i ) ) ,
h * ( x , y ; z ) = h ( x , y ; z ) = j k 0 2 π z exp { j k 0 2 z ( x 2 + y 2 ) } ,
F { h ( x , y ; z ) * h * ( x , y ; z ) } = F { h ( x , y ; z ) } F { h * ( x , y ; z ) } = H ( k x , k y ; z ) H * ( k x , k y ; z ) = 1.
g ( x , y ) * h * ( x , y ; z 1 ) = i = 1 N ( | O ( x , y , z i ) | 2 * h ( x , y ; z i ) ) * h * ( x , y ; z 1 ) = | O ( x , y , z 1 ) | 2 + i = 2 N | O ( x , y , z i ) | 2 * h ( x , y ; z i ) * h * ( x , y ; z 1 ) .
W ( k x , k y ) = H * ( k x , k y ; z 1 ) | H ( k x , k y ; z 1 ) | 2 + P imag ( k x , k y ) P real ( k x , k y ) P imag ( k x , k y ) ,
g = i = 1 N H i ϕ i + η ,
g = H ϕ + η ,
H = H 1 H 2 H N and ϕ = ϕ 1 ϕ 2 ϕ N .
ϕ ^ = arg min H ϕ g 2 + μ g 2 ,
ϕ ^ = H T ( H H T + μ I ) 1 g ,
| O i ( x , y ; z ) | 2 = δ ( x , y ) δ ( z z i ) for i = 1 , , N .

Metrics