Abstract

We present a high-speed transport-of-intensity equation (TIE) quantitative phase microscopy technique, named TL-TIE, by combining an electrically tunable lens with a conventional transmission microscope. This permits the specimen at different focus position to be imaged in rapid succession, with constant magnification and no physically moving parts. The simplified image stack collection significantly reduces the acquisition time, allows for the diffraction-limited through-focus intensity stack collection at 15 frames per second, making dynamic TIE phase imaging possible. The technique is demonstrated by profiling of microlens array using optimal frequency selection scheme, and time-lapse imaging of live breast cancer cells by inversion the defocused phase optical transfer function to correct the phase blurring in traditional TIE. Experimental results illustrate its outstanding capability of the technique for quantitative phase imaging, through a simple, non-interferometric, high-speed, high-resolution, and unwrapping-free approach with prosperous applications in micro-optics, life sciences and bio-photonics.

© 2013 Optical Society of America

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2013 (2)

2012 (5)

2011 (3)

2010 (5)

2009 (1)

2008 (1)

2007 (2)

2005 (2)

J.  Luo, K.  Ying, P.  He, J.  Bai, “Properties of Savitzky–Golay digital differentiators,” Digit. Signal Process. 15(2), 122–136 (2005).
[CrossRef]

K.  Ishizuka, B.  Allman, “Phase measurement of atomic resolution image using transport of intensity equation,” J. Electron Microsc. (Tokyo) 54(3), 191–197 (2005).
[CrossRef] [PubMed]

2004 (4)

C. J.  Bellair, C. L.  Curl, B. E.  Allman, P. J.  Harris, A.  Roberts, L. M. D.  Delbridge, K. A.  Nugent, “Quantitative phase amplitude microscopy IV: imaging thick specimens,” J. Microsc. 214(1), 62–69 (2004).
[CrossRef] [PubMed]

C. J. R.  Sheppard, “Defocused transfer function for a partially coherent microscope and application to phase retrieval,” J. Opt. Soc. Am. A 21(5), 828–831 (2004).
[CrossRef] [PubMed]

M.  Beleggia, M. A.  Schofield, V. V.  Volkov, Y.  Zhu, “On the transport of intensity technique for phase retrieval,” Ultramicroscopy 102(1), 37–49 (2004).
[CrossRef] [PubMed]

D.  Paganin, A.  Barty, P. J.  McMahon, K. A.  Nugent, “Quantitative phase-amplitude microscopy. III. The effects of noise,” J. Microsc. 214(1), 51–61 (2004).
[CrossRef] [PubMed]

2002 (4)

E. D.  Barone-Nugent, A.  Barty, K. A.  Nugent, “Quantitative phase-amplitude microscopy I: optical microscopy,” J. Microsc. 206(3), 194–203 (2002).
[CrossRef] [PubMed]

U.  Schnars, P. O. J.  Werner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13(9), R85–R101 (2002).
[CrossRef]

C. J. R.  Sheppard, “Three-Dimensional Phase Imaging with the Intensity Transport Equation,” Appl. Opt. 41(28), 5951–5955 (2002).
[CrossRef] [PubMed]

V. V.  Volkov, Y.  Zhu, M.  De Graef, “A new symmetrized solution for phase retrieval using the transport of intensity equation,” Micron 33(5), 411–416 (2002).
[CrossRef] [PubMed]

2001 (1)

L. J.  Allen, M. P.  Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199(1-4), 65–75 (2001).
[CrossRef]

1999 (1)

1998 (2)

A.  Barty, K. A.  Nugent, D.  Paganin, A.  Roberts, “Quantitative optical phase microscopy,” Opt. Lett. 23(11), 817–819 (1998).
[CrossRef] [PubMed]

D.  Paganin, K. A.  Nugent, “Noninterferometric Phase Imaging with Partially Coherent Light,” Phys. Rev. Lett. 80(12), 2586–2589 (1998).
[CrossRef]

1997 (1)

T. E.  Gureyev, K. A.  Nugent, “Rapid quantitative phase imaging using the transport of intensity equation,” Opt. Commun. 133(1-6), 339–346 (1997).
[CrossRef]

1985 (1)

1983 (1)

1955 (2)

F.  Zernike, “How I Discovered Phase Contrast,” Science 121(3141), 345–349 (1955).
[CrossRef] [PubMed]

G.  Nomarski, “Differential microinterferometer with polarized waves,” J. Phys. Radium 16, 9s–13s (1955).

Acosta, E.

Agour, M.

Allen, L. J.

L. J.  Allen, M. P.  Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199(1-4), 65–75 (2001).
[CrossRef]

Allman, B.

K.  Ishizuka, B.  Allman, “Phase measurement of atomic resolution image using transport of intensity equation,” J. Electron Microsc. (Tokyo) 54(3), 191–197 (2005).
[CrossRef] [PubMed]

Allman, B. E.

C. J.  Bellair, C. L.  Curl, B. E.  Allman, P. J.  Harris, A.  Roberts, L. M. D.  Delbridge, K. A.  Nugent, “Quantitative phase amplitude microscopy IV: imaging thick specimens,” J. Microsc. 214(1), 62–69 (2004).
[CrossRef] [PubMed]

Almoro, P. F.

Asundi, A.

Bai, J.

J.  Luo, K.  Ying, P.  He, J.  Bai, “Properties of Savitzky–Golay digital differentiators,” Digit. Signal Process. 15(2), 122–136 (2005).
[CrossRef]

Bai, X.

Barbastathis, G.

Barone-Nugent, E. D.

E. D.  Barone-Nugent, A.  Barty, K. A.  Nugent, “Quantitative phase-amplitude microscopy I: optical microscopy,” J. Microsc. 206(3), 194–203 (2002).
[CrossRef] [PubMed]

Barty, A.

D.  Paganin, A.  Barty, P. J.  McMahon, K. A.  Nugent, “Quantitative phase-amplitude microscopy. III. The effects of noise,” J. Microsc. 214(1), 51–61 (2004).
[CrossRef] [PubMed]

E. D.  Barone-Nugent, A.  Barty, K. A.  Nugent, “Quantitative phase-amplitude microscopy I: optical microscopy,” J. Microsc. 206(3), 194–203 (2002).
[CrossRef] [PubMed]

A.  Barty, K. A.  Nugent, D.  Paganin, A.  Roberts, “Quantitative optical phase microscopy,” Opt. Lett. 23(11), 817–819 (1998).
[CrossRef] [PubMed]

Beleggia, M.

M.  Beleggia, M. A.  Schofield, V. V.  Volkov, Y.  Zhu, “On the transport of intensity technique for phase retrieval,” Ultramicroscopy 102(1), 37–49 (2004).
[CrossRef] [PubMed]

Bellair, C. J.

C. J.  Bellair, C. L.  Curl, B. E.  Allman, P. J.  Harris, A.  Roberts, L. M. D.  Delbridge, K. A.  Nugent, “Quantitative phase amplitude microscopy IV: imaging thick specimens,” J. Microsc. 214(1), 62–69 (2004).
[CrossRef] [PubMed]

Bergmann, R. B.

Bhaduri, B.

Bie, R.

Boistel, R.

Camacho, L.

Chen, Q.

Choo, C. O.

Cloetens, P.

Cuche, E.

Cui, L.

Curl, C. L.

C. J.  Bellair, C. L.  Curl, B. E.  Allman, P. J.  Harris, A.  Roberts, L. M. D.  Delbridge, K. A.  Nugent, “Quantitative phase amplitude microscopy IV: imaging thick specimens,” J. Microsc. 214(1), 62–69 (2004).
[CrossRef] [PubMed]

De Graef, M.

V. V.  Volkov, Y.  Zhu, M.  De Graef, “A new symmetrized solution for phase retrieval using the transport of intensity equation,” Micron 33(5), 411–416 (2002).
[CrossRef] [PubMed]

Delbridge, L. M. D.

C. J.  Bellair, C. L.  Curl, B. E.  Allman, P. J.  Harris, A.  Roberts, L. M. D.  Delbridge, K. A.  Nugent, “Quantitative phase amplitude microscopy IV: imaging thick specimens,” J. Microsc. 214(1), 62–69 (2004).
[CrossRef] [PubMed]

Depeursinge, C.

Ding, H.

Falldorf, C.

García, J.

Gillette, M. U.

Gorthi, S. S.

Guigay, J. P.

Gureyev, T. E.

T. E.  Gureyev, K. A.  Nugent, “Rapid quantitative phase imaging using the transport of intensity equation,” Opt. Commun. 133(1-6), 339–346 (1997).
[CrossRef]

Hanson, S. G.

Harris, P. J.

C. J.  Bellair, C. L.  Curl, B. E.  Allman, P. J.  Harris, A.  Roberts, L. M. D.  Delbridge, K. A.  Nugent, “Quantitative phase amplitude microscopy IV: imaging thick specimens,” J. Microsc. 214(1), 62–69 (2004).
[CrossRef] [PubMed]

He, P.

J.  Luo, K.  Ying, P.  He, J.  Bai, “Properties of Savitzky–Golay digital differentiators,” Digit. Signal Process. 15(2), 122–136 (2005).
[CrossRef]

Ishizuka, K.

K.  Ishizuka, B.  Allman, “Phase measurement of atomic resolution image using transport of intensity equation,” J. Electron Microsc. (Tokyo) 54(3), 191–197 (2005).
[CrossRef] [PubMed]

Iwai, H.

Kou, S. S.

Langer, M.

Luo, J.

J.  Luo, K.  Ying, P.  He, J.  Bai, “Properties of Savitzky–Golay digital differentiators,” Digit. Signal Process. 15(2), 122–136 (2005).
[CrossRef]

Luo, Y.

Marquet, P.

McMahon, P. J.

D.  Paganin, A.  Barty, P. J.  McMahon, K. A.  Nugent, “Quantitative phase-amplitude microscopy. III. The effects of noise,” J. Microsc. 214(1), 51–61 (2004).
[CrossRef] [PubMed]

Micó, V.

Millet, L.

Mir, M.

Miwa, M.

Nomarski, G.

G.  Nomarski, “Differential microinterferometer with polarized waves,” J. Phys. Radium 16, 9s–13s (1955).

Nugent, K. A.

D.  Paganin, A.  Barty, P. J.  McMahon, K. A.  Nugent, “Quantitative phase-amplitude microscopy. III. The effects of noise,” J. Microsc. 214(1), 51–61 (2004).
[CrossRef] [PubMed]

C. J.  Bellair, C. L.  Curl, B. E.  Allman, P. J.  Harris, A.  Roberts, L. M. D.  Delbridge, K. A.  Nugent, “Quantitative phase amplitude microscopy IV: imaging thick specimens,” J. Microsc. 214(1), 62–69 (2004).
[CrossRef] [PubMed]

E. D.  Barone-Nugent, A.  Barty, K. A.  Nugent, “Quantitative phase-amplitude microscopy I: optical microscopy,” J. Microsc. 206(3), 194–203 (2002).
[CrossRef] [PubMed]

D.  Paganin, K. A.  Nugent, “Noninterferometric Phase Imaging with Partially Coherent Light,” Phys. Rev. Lett. 80(12), 2586–2589 (1998).
[CrossRef]

A.  Barty, K. A.  Nugent, D.  Paganin, A.  Roberts, “Quantitative optical phase microscopy,” Opt. Lett. 23(11), 817–819 (1998).
[CrossRef] [PubMed]

T. E.  Gureyev, K. A.  Nugent, “Rapid quantitative phase imaging using the transport of intensity equation,” Opt. Commun. 133(1-6), 339–346 (1997).
[CrossRef]

Osten, W.

Oxley, M. P.

L. J.  Allen, M. P.  Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199(1-4), 65–75 (2001).
[CrossRef]

Paganin, D.

D.  Paganin, A.  Barty, P. J.  McMahon, K. A.  Nugent, “Quantitative phase-amplitude microscopy. III. The effects of noise,” J. Microsc. 214(1), 51–61 (2004).
[CrossRef] [PubMed]

A.  Barty, K. A.  Nugent, D.  Paganin, A.  Roberts, “Quantitative optical phase microscopy,” Opt. Lett. 23(11), 817–819 (1998).
[CrossRef] [PubMed]

D.  Paganin, K. A.  Nugent, “Noninterferometric Phase Imaging with Partially Coherent Light,” Phys. Rev. Lett. 80(12), 2586–2589 (1998).
[CrossRef]

Pedrini, G.

Pham, H.

Popescu, G.

Qu, W.

Reed Teague, M.

Roberts, A.

C. J.  Bellair, C. L.  Curl, B. E.  Allman, P. J.  Harris, A.  Roberts, L. M. D.  Delbridge, K. A.  Nugent, “Quantitative phase amplitude microscopy IV: imaging thick specimens,” J. Microsc. 214(1), 62–69 (2004).
[CrossRef] [PubMed]

A.  Barty, K. A.  Nugent, D.  Paganin, A.  Roberts, “Quantitative optical phase microscopy,” Opt. Lett. 23(11), 817–819 (1998).
[CrossRef] [PubMed]

Rogers, J.

Schnars, U.

U.  Schnars, P. O. J.  Werner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13(9), R85–R101 (2002).
[CrossRef]

Schofield, M. A.

M.  Beleggia, M. A.  Schofield, V. V.  Volkov, Y.  Zhu, “On the transport of intensity technique for phase retrieval,” Ultramicroscopy 102(1), 37–49 (2004).
[CrossRef] [PubMed]

Schonbrun, E.

Sheppard, C. J. R.

Singh, V. R.

Soto, M.

Streibl, N.

Tangella, K.

Tian, L.

Unarunotai, S.

v Kopylow, C.

Volkov, V. V.

M.  Beleggia, M. A.  Schofield, V. V.  Volkov, Y.  Zhu, “On the transport of intensity technique for phase retrieval,” Ultramicroscopy 102(1), 37–49 (2004).
[CrossRef] [PubMed]

V. V.  Volkov, Y.  Zhu, M.  De Graef, “A new symmetrized solution for phase retrieval using the transport of intensity equation,” Micron 33(5), 411–416 (2002).
[CrossRef] [PubMed]

Waller, L.

Wang, Z.

Werner, P. O. J.

U.  Schnars, P. O. J.  Werner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13(9), R85–R101 (2002).
[CrossRef]

Xue, B.

Xue, W.

Yamashita, Y.

Yamauchi, T.

Yang, S. Y.

Ying, K.

J.  Luo, K.  Ying, P.  He, J.  Bai, “Properties of Savitzky–Golay digital differentiators,” Digit. Signal Process. 15(2), 122–136 (2005).
[CrossRef]

Yingjie, Y.

Yu, Y.

Yuan, X.-H.

Zalevsky, Z.

Zernike, F.

F.  Zernike, “How I Discovered Phase Contrast,” Science 121(3141), 345–349 (1955).
[CrossRef] [PubMed]

Zhang, L.

Zhao, M.

Zheng, S.

Zhou, F.

Zhu, Y.

M.  Beleggia, M. A.  Schofield, V. V.  Volkov, Y.  Zhu, “On the transport of intensity technique for phase retrieval,” Ultramicroscopy 102(1), 37–49 (2004).
[CrossRef] [PubMed]

V. V.  Volkov, Y.  Zhu, M.  De Graef, “A new symmetrized solution for phase retrieval using the transport of intensity equation,” Micron 33(5), 411–416 (2002).
[CrossRef] [PubMed]

Zuo, C.

Appl. Opt. (4)

Biomed. Opt. Express (1)

Digit. Signal Process. (1)

J.  Luo, K.  Ying, P.  He, J.  Bai, “Properties of Savitzky–Golay digital differentiators,” Digit. Signal Process. 15(2), 122–136 (2005).
[CrossRef]

J. Electron Microsc. (Tokyo) (1)

K.  Ishizuka, B.  Allman, “Phase measurement of atomic resolution image using transport of intensity equation,” J. Electron Microsc. (Tokyo) 54(3), 191–197 (2005).
[CrossRef] [PubMed]

J. Microsc. (3)

C. J.  Bellair, C. L.  Curl, B. E.  Allman, P. J.  Harris, A.  Roberts, L. M. D.  Delbridge, K. A.  Nugent, “Quantitative phase amplitude microscopy IV: imaging thick specimens,” J. Microsc. 214(1), 62–69 (2004).
[CrossRef] [PubMed]

E. D.  Barone-Nugent, A.  Barty, K. A.  Nugent, “Quantitative phase-amplitude microscopy I: optical microscopy,” J. Microsc. 206(3), 194–203 (2002).
[CrossRef] [PubMed]

D.  Paganin, A.  Barty, P. J.  McMahon, K. A.  Nugent, “Quantitative phase-amplitude microscopy. III. The effects of noise,” J. Microsc. 214(1), 51–61 (2004).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

J. Phys. Radium (1)

G.  Nomarski, “Differential microinterferometer with polarized waves,” J. Phys. Radium 16, 9s–13s (1955).

Meas. Sci. Technol. (1)

U.  Schnars, P. O. J.  Werner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13(9), R85–R101 (2002).
[CrossRef]

Micron (1)

V. V.  Volkov, Y.  Zhu, M.  De Graef, “A new symmetrized solution for phase retrieval using the transport of intensity equation,” Micron 33(5), 411–416 (2002).
[CrossRef] [PubMed]

Opt. Commun. (2)

L. J.  Allen, M. P.  Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199(1-4), 65–75 (2001).
[CrossRef]

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T.  Yamauchi, H.  Iwai, M.  Miwa, Y.  Yamashita, “Low-coherent quantitative phase microscope for nanometer-scale measurement of living cells morphology,” Opt. Express 16(16), 12227–12238 (2008).
[CrossRef] [PubMed]

R.  Bie, X.-H.  Yuan, M.  Zhao, L.  Zhang, “Method for estimating the axial intensity derivative in the TIE with higher order intensity derivatives and noise suppression,” Opt. Express 20(7), 8186–8191 (2012).
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B.  Xue, S.  Zheng, L.  Cui, X.  Bai, F.  Zhou, “Transport of intensity phase imaging from multiple intensities measured in unequally-spaced planes,” Opt. Express 19(21), 20244–20250 (2011).
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S.  Zheng, B.  Xue, W.  Xue, X.  Bai, F.  Zhou, “Transport of intensity phase imaging from multiple noisy intensities measured in unequally-spaced planes,” Opt. Express 20(2), 972–985 (2012).
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L.  Waller, L.  Tian, G.  Barbastathis, “Transport of intensity phase-amplitude imaging with higher order intensity derivatives,” Opt. Express 18(12), 12552–12561 (2010).
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C.  Zuo, Q.  Chen, Y.  Yu, A.  Asundi, “Transport-of-intensity phase imaging using Savitzky-Golay differentiation filter--theory and applications,” Opt. Express 21(5), 5346–5362 (2013).
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[CrossRef] [PubMed]

Other (2)

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J. W. Goodman, Introduction To Fourier Optics, 3th ed. (Roberts & Company Publishers, 2005).

Supplementary Material (3)

» Media 1: MOV (2466 KB)     
» Media 2: MOV (2691 KB)     
» Media 3: MOV (9340 KB)     

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Figures (7)

Fig. 1
Fig. 1

Schematic setup for TL-TIE system. A 4f system with OL/ETL located at the Fourier plane is attached to Olympus IX71 bright field microscope. The Fourier lens L1 relays the back focal plane of the objective onto the OL/ETL. Fourier lens L2 reconstructs the final image at the CCD plane, which is conjugated with the image plane. The shift of the object plane with equal magnification can be realized adjusting the focal length of ETL.

Fig. 2
Fig. 2

Defocusing characterization of the tunable lens and the TL-TIE system. (a) Measured focal length calibration curve of the ETL as a function of current. The region in the dashed box (magnified in the inset) shows good linearity of response. (b) The theoretical [Eq. (5)], simulated, and measured focus-shift curves of the TL-TIE system.

Fig. 3
Fig. 3

Simulations and real performance of TL-TIE systems with a 40x objective (NA = 0.6). (a) Simulated spot diagrams. (b) Simulated MTF. (c) PSF measured using a 500 nm pinhole without the TL-TIE relay system. (d) Measured PSF of the whole TL-TIE system. The cross-sectional slices are fitted by the Gaussian function.

Fig. 4
Fig. 4

(Media 1) Microlens array characterization using OFS. (a-e) Recorded intensity images with defocus distance 15, 5, 0, −5, −15 μm, respectively. (f) Quantitative phase recovered by OFS. (g) Digital hologram captured by a DHM system. The carrier fringes can be easily seen in the magnified area. (h) Unwrapped phase of DHM. (i) 3D rendering of the OFS result. (j) Line profiles corresponding to the red solid line in (f) and the black dotted line in (h), respectively.

Fig. 5
Fig. 5

Phase retrieval comparison under severely noisy conditions. (a-c) Intensity images with defocus distance 5, 0, −5μm after adding artificial noise. (d) Phase recovered by traditional TIE with 2-plane separation of ± 1μm. (e) Phase recovered by 9th-order TIE (9th-degree SGDF). (f) Phase recovered by 1st-order TIE (1st-degree SGDF). (g) Phase recovered by OFS. The lower-right portion of each image shows the corresponding digitally rewrapped phase within range [π,π) . (h) The cross-sectional profiles corresponding to the blue and red lines in (f) and (g), respectively. (i) The magnified area corresponding to the boxed region in (e).

Fig. 6
Fig. 6

Experiment validation of IDPOTF method. (a-c) Intensity images with defocus distance −2.5, 0, 2.5 μm (d) Phase map recovered by traditional TIE. (e) Phase map recovered by IDPOTF. The insets show the magnified areas corresponding to boxed regions. (f) TIE phase CTF and DPOTF for defocus distance 2.5, and 0.5 μm . (g) The intensity distributions along the blue solid line and the red dotted line shown in (d) and (e).

Fig. 7
Fig. 7

Time-lapse quantitative phase imaging of an individual MCF-7 using TL-TIE. (a-c) Intensity images with defocus distance −2.5, 0, 2.5 μm (d) Phase map recovered through IDPOTF (Media 2). (e) Digitally simulated DIC image from (d) (Media 2). (f) 3D pseudo-color rendering of the cell thickness (Media 3).

Equations (19)

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u Δz (x,y)= F 1 { F{ u 0 (x,y) } H Δz (u,v) },
H Δz (u,v)=exp[ iπλΔz( u 2 + v 2 ) ],
t l (ξ,η)=exp[ iπ λ f c ( ξ 2 + η 2 ) ],
f c = f ETL f OL f ETL + f OL d .
Δz= f 2 f c = f 2 ( f ETL + f OL d ) f ETL f OL .
k I( r ) z =[ I( r )ϕ( r ) ],
k I z = 2 ψ,
( I 1 ψ )= 2 ϕ.
k I I z = 2 ϕ,
I( r ) z I Δz ( r ) I Δz ( r ) 2Δz .
I( r ) z j=n n a j I jΔz ( r ) Δz .
I ^ Δz ( u ) I ^ Δz ( u ) 4 =πΔzλ u 2 ψ ^ ( u ).
T TIE (u)=πΔzλ u 2 .
T p ( u )= 1 2 T p ( 3 ) ( u,η )sin( 2πΔzη )dη .
I ^ z (u)= I ^ 0 (u)+2[ sin(πλz u 2 )πλz u 2 cos(πλz u 2 ) ]F{ I 0 ( r )φ( r ) } cos(πλz u 2 ) λz 2π F{ [ I 0 ( r )φ( r ) ] }.
F{ I(r) z } j=n n a j I ^ jΔz (u) Δz = 1 Δz j=n n a j I ^ 0 (u) + 1 Δz j=n n a j [ sin(πλjΔz u 2 )πλjΔz u 2 cos(πλjΔz u 2 ) ] F{ I 0 ( r )φ( r ) } λ 2π j=n n a j jcos(πλjΔz u 2 ) F{ [ I 0 ( r )φ( r ) ] }.
j=n n a j [ sin(πλjΔz u 2 )πλjΔz u 2 cos(πλjΔz u 2 ) ] 0;
j=n n a j jcos(πλjΔz u 2 ) 1.
F{ I(r) z } λ 2π F{ [ I( r )φ( r ) ] }.

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