Abstract

We have developed a digital holographic microscope (DHM), in a transmission mode, adapted to the quantitative study of cellular dynamics. Living cells in culture are optically probed by measuring the phase shift they produce on the transmitted wave front. The high temporal stability of the phase signal, equivalent to λ/1800, and the low acquisition time (∼20μs) enable to monitor cellular dynamics processes. An experimental procedure allowing to calculate both the integral refractive index and the cellular thickness (morphometry) from the measured phase shift is presented. Specifically, the method has been applied to study the dynamics of neurons in culture during a hypotonic stress. Such stress produces a paradoxical decrease of the phase which can be entirely resolved by applying the methodological approach described in this article; indeed the method allows to determine independently the thickness and the integral refractive index of cells.

© 2005 Optical Society of America

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References

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  1. P. Marquet , B. Rappaz , P. J. Magistretti , E. Cuche , Y. Emery , T. Colomb , and C. Depeursinge , “ Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy ,” Opt. Lett.   30 , 468 – 470 ( 2005 ).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [PubMed]
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    [Crossref] [PubMed]
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2005 (4)

2004 (1)

2003 (1)

F. Wehner , H. Olsen , H. Tinel , E. Kinne-Saffran , and R. K. Kinne , “ Cell volume regulation: osmolytes, osmolyte transport, and signal transduction ,” Rev. Physiol. Biochem. Pharmacol.   148 , 1 – 80 ( 2003 ).
[Crossref] [PubMed]

1999 (2)

1996 (3)

J. Beuthan , O. Minet , J. Helfmann , M. Herrig , and G. Muller , “ The spatial variation of the refractive index in biological cells ,” Phys. Med. Biol.   41 , 369 – 382 ( 1996 ).
[Crossref] [PubMed]

A. Dunn and R. Richards-Kortum , “ Three-dimensional computaton of light scattering from cells ,” IEEE J. Sel. Top. Quantum Electron.   2 , 898 – 905 ( 1996 ).
[Crossref]

J. Farinas and A. S. Verkman , “ Cell volume and plasma membrane osmotic water permeability in epithelial cell layers measured by interferometry ,” Biophys. J.   71 , 3511 – 3522 ( 1996 ).
[Crossref] [PubMed]

1993 (1)

G. J. Brewer , J. R. Torricelli , E. K. Evege , and P. J. Price , “ Optimized survival of hippocampal neurons in B27-supplemented Neurobasal, a new serum-free medium combination ,” J. Neurosci. Res.   35 , 567 – 576 ( 1993 ).
[Crossref] [PubMed]

1989 (1)

1985 (1)

F. Lanni , A. S. Waggoner , and D. L. Taylor , “ Structural organization of interphase 3T3 fibroblasts studied by total internal reflection fluorescence microscopy ,” J. Cell. Biol.   100 , 1091 – 1102 ( 1985 ).
[Crossref] [PubMed]

1980 (1)

K. J. Sweadner and S. M. Goldin , “ Active transport of sodium and potassium ions: mechanism, function, and regulation ,” N. Engl. J. Med.   302 , 777 – 783 ( 1980 ).
[Crossref] [PubMed]

1979 (1)

J. Bereiter-Hahn , C. H. Fox , and B. Thorell , “ Quantitative reflection contrast microscopy of living cells ,” J. Cell. Biol.   82 , 767 – 779 ( 1979 ).
[Crossref] [PubMed]

1952 (1)

H. G. Davies and M. H. F. Wilkins , “ Interference microscopy and mass determination ,” Nature   169 , 541 ( 1952 ).
[Crossref] [PubMed]

Allman, B. E.

C. L. Curl , C. J. Bellair , T. Harris , B. E. Allman , P. J. Harris , A. G. Stewart , A. Roberts , K. A. Nugent , and L. M. Delbridge , “ Refractive index measurement in viable cells using quantitative phase-amplitude microscopy and confocal microscopy ,” Cytometry A   65 , 88 – 92 ( 2005 ).
[PubMed]

Bellair, C. J.

C. L. Curl , C. J. Bellair , T. Harris , B. E. Allman , P. J. Harris , A. G. Stewart , A. Roberts , K. A. Nugent , and L. M. Delbridge , “ Refractive index measurement in viable cells using quantitative phase-amplitude microscopy and confocal microscopy ,” Cytometry A   65 , 88 – 92 ( 2005 ).
[PubMed]

Bereiter-Hahn, J.

J. Bereiter-Hahn , C. H. Fox , and B. Thorell , “ Quantitative reflection contrast microscopy of living cells ,” J. Cell. Biol.   82 , 767 – 779 ( 1979 ).
[Crossref] [PubMed]

Beuthan, J.

J. Beuthan , O. Minet , J. Helfmann , M. Herrig , and G. Muller , “ The spatial variation of the refractive index in biological cells ,” Phys. Med. Biol.   41 , 369 – 382 ( 1996 ).
[Crossref] [PubMed]

Bolin, F.

Brewer, G. J.

G. J. Brewer , J. R. Torricelli , E. K. Evege , and P. J. Price , “ Optimized survival of hippocampal neurons in B27-supplemented Neurobasal, a new serum-free medium combination ,” J. Neurosci. Res.   35 , 567 – 576 ( 1993 ).
[Crossref] [PubMed]

Carl, D.

Colomb, T.

Cuche, E.

Curl, C. L.

C. L. Curl , C. J. Bellair , T. Harris , B. E. Allman , P. J. Harris , A. G. Stewart , A. Roberts , K. A. Nugent , and L. M. Delbridge , “ Refractive index measurement in viable cells using quantitative phase-amplitude microscopy and confocal microscopy ,” Cytometry A   65 , 88 – 92 ( 2005 ).
[PubMed]

Dasari, R. R.

Davies, H. G.

H. G. Davies and M. H. F. Wilkins , “ Interference microscopy and mass determination ,” Nature   169 , 541 ( 1952 ).
[Crossref] [PubMed]

Delbridge, L. M.

C. L. Curl , C. J. Bellair , T. Harris , B. E. Allman , P. J. Harris , A. G. Stewart , A. Roberts , K. A. Nugent , and L. M. Delbridge , “ Refractive index measurement in viable cells using quantitative phase-amplitude microscopy and confocal microscopy ,” Cytometry A   65 , 88 – 92 ( 2005 ).
[PubMed]

Depeursinge, C.

Dunn, A.

A. Dunn and R. Richards-Kortum , “ Three-dimensional computaton of light scattering from cells ,” IEEE J. Sel. Top. Quantum Electron.   2 , 898 – 905 ( 1996 ).
[Crossref]

Emery, Y.

Evege, E. K.

G. J. Brewer , J. R. Torricelli , E. K. Evege , and P. J. Price , “ Optimized survival of hippocampal neurons in B27-supplemented Neurobasal, a new serum-free medium combination ,” J. Neurosci. Res.   35 , 567 – 576 ( 1993 ).
[Crossref] [PubMed]

Farinas, J.

J. Farinas and A. S. Verkman , “ Cell volume and plasma membrane osmotic water permeability in epithelial cell layers measured by interferometry ,” Biophys. J.   71 , 3511 – 3522 ( 1996 ).
[Crossref] [PubMed]

Feld, M. S.

Ference, R.

Fox, C. H.

J. Bereiter-Hahn , C. H. Fox , and B. Thorell , “ Quantitative reflection contrast microscopy of living cells ,” J. Cell. Biol.   82 , 767 – 779 ( 1979 ).
[Crossref] [PubMed]

Goldin, S. M.

K. J. Sweadner and S. M. Goldin , “ Active transport of sodium and potassium ions: mechanism, function, and regulation ,” N. Engl. J. Med.   302 , 777 – 783 ( 1980 ).
[Crossref] [PubMed]

Harris, P. J.

C. L. Curl , C. J. Bellair , T. Harris , B. E. Allman , P. J. Harris , A. G. Stewart , A. Roberts , K. A. Nugent , and L. M. Delbridge , “ Refractive index measurement in viable cells using quantitative phase-amplitude microscopy and confocal microscopy ,” Cytometry A   65 , 88 – 92 ( 2005 ).
[PubMed]

Harris, T.

C. L. Curl , C. J. Bellair , T. Harris , B. E. Allman , P. J. Harris , A. G. Stewart , A. Roberts , K. A. Nugent , and L. M. Delbridge , “ Refractive index measurement in viable cells using quantitative phase-amplitude microscopy and confocal microscopy ,” Cytometry A   65 , 88 – 92 ( 2005 ).
[PubMed]

He, A.

Helfmann, J.

J. Beuthan , O. Minet , J. Helfmann , M. Herrig , and G. Muller , “ The spatial variation of the refractive index in biological cells ,” Phys. Med. Biol.   41 , 369 – 382 ( 1996 ).
[Crossref] [PubMed]

Herrig, M.

J. Beuthan , O. Minet , J. Helfmann , M. Herrig , and G. Muller , “ The spatial variation of the refractive index in biological cells ,” Phys. Med. Biol.   41 , 369 – 382 ( 1996 ).
[Crossref] [PubMed]

Ikeda, T.

Kemper, B.

Kinne, R. K.

F. Wehner , H. Olsen , H. Tinel , E. Kinne-Saffran , and R. K. Kinne , “ Cell volume regulation: osmolytes, osmolyte transport, and signal transduction ,” Rev. Physiol. Biochem. Pharmacol.   148 , 1 – 80 ( 2003 ).
[Crossref] [PubMed]

Kinne-Saffran, E.

F. Wehner , H. Olsen , H. Tinel , E. Kinne-Saffran , and R. K. Kinne , “ Cell volume regulation: osmolytes, osmolyte transport, and signal transduction ,” Rev. Physiol. Biochem. Pharmacol.   148 , 1 – 80 ( 2003 ).
[Crossref] [PubMed]

Lai, J.

Lanni, F.

F. Lanni , A. S. Waggoner , and D. L. Taylor , “ Structural organization of interphase 3T3 fibroblasts studied by total internal reflection fluorescence microscopy ,” J. Cell. Biol.   100 , 1091 – 1102 ( 1985 ).
[Crossref] [PubMed]

Li, Z.

Magistretti, P. J.

Marquet, P.

Minet, O.

J. Beuthan , O. Minet , J. Helfmann , M. Herrig , and G. Muller , “ The spatial variation of the refractive index in biological cells ,” Phys. Med. Biol.   41 , 369 – 382 ( 1996 ).
[Crossref] [PubMed]

Muller, G.

J. Beuthan , O. Minet , J. Helfmann , M. Herrig , and G. Muller , “ The spatial variation of the refractive index in biological cells ,” Phys. Med. Biol.   41 , 369 – 382 ( 1996 ).
[Crossref] [PubMed]

Nugent, K. A.

C. L. Curl , C. J. Bellair , T. Harris , B. E. Allman , P. J. Harris , A. G. Stewart , A. Roberts , K. A. Nugent , and L. M. Delbridge , “ Refractive index measurement in viable cells using quantitative phase-amplitude microscopy and confocal microscopy ,” Cytometry A   65 , 88 – 92 ( 2005 ).
[PubMed]

Olsen, H.

F. Wehner , H. Olsen , H. Tinel , E. Kinne-Saffran , and R. K. Kinne , “ Cell volume regulation: osmolytes, osmolyte transport, and signal transduction ,” Rev. Physiol. Biochem. Pharmacol.   148 , 1 – 80 ( 2003 ).
[Crossref] [PubMed]

Popescu, G.

Preuss, L.

Price, P. J.

G. J. Brewer , J. R. Torricelli , E. K. Evege , and P. J. Price , “ Optimized survival of hippocampal neurons in B27-supplemented Neurobasal, a new serum-free medium combination ,” J. Neurosci. Res.   35 , 567 – 576 ( 1993 ).
[Crossref] [PubMed]

Rappaz, B.

Richards-Kortum, R.

A. Dunn and R. Richards-Kortum , “ Three-dimensional computaton of light scattering from cells ,” IEEE J. Sel. Top. Quantum Electron.   2 , 898 – 905 ( 1996 ).
[Crossref]

Roberts, A.

C. L. Curl , C. J. Bellair , T. Harris , B. E. Allman , P. J. Harris , A. G. Stewart , A. Roberts , K. A. Nugent , and L. M. Delbridge , “ Refractive index measurement in viable cells using quantitative phase-amplitude microscopy and confocal microscopy ,” Cytometry A   65 , 88 – 92 ( 2005 ).
[PubMed]

Stewart, A. G.

C. L. Curl , C. J. Bellair , T. Harris , B. E. Allman , P. J. Harris , A. G. Stewart , A. Roberts , K. A. Nugent , and L. M. Delbridge , “ Refractive index measurement in viable cells using quantitative phase-amplitude microscopy and confocal microscopy ,” Cytometry A   65 , 88 – 92 ( 2005 ).
[PubMed]

Sweadner, K. J.

K. J. Sweadner and S. M. Goldin , “ Active transport of sodium and potassium ions: mechanism, function, and regulation ,” N. Engl. J. Med.   302 , 777 – 783 ( 1980 ).
[Crossref] [PubMed]

Taylor, D. L.

F. Lanni , A. S. Waggoner , and D. L. Taylor , “ Structural organization of interphase 3T3 fibroblasts studied by total internal reflection fluorescence microscopy ,” J. Cell. Biol.   100 , 1091 – 1102 ( 1985 ).
[Crossref] [PubMed]

Taylor, R.

Thorell, B.

J. Bereiter-Hahn , C. H. Fox , and B. Thorell , “ Quantitative reflection contrast microscopy of living cells ,” J. Cell. Biol.   82 , 767 – 779 ( 1979 ).
[Crossref] [PubMed]

Tinel, H.

F. Wehner , H. Olsen , H. Tinel , E. Kinne-Saffran , and R. K. Kinne , “ Cell volume regulation: osmolytes, osmolyte transport, and signal transduction ,” Rev. Physiol. Biochem. Pharmacol.   148 , 1 – 80 ( 2003 ).
[Crossref] [PubMed]

Torricelli, J. R.

G. J. Brewer , J. R. Torricelli , E. K. Evege , and P. J. Price , “ Optimized survival of hippocampal neurons in B27-supplemented Neurobasal, a new serum-free medium combination ,” J. Neurosci. Res.   35 , 567 – 576 ( 1993 ).
[Crossref] [PubMed]

Verkman, A. S.

J. Farinas and A. S. Verkman , “ Cell volume and plasma membrane osmotic water permeability in epithelial cell layers measured by interferometry ,” Biophys. J.   71 , 3511 – 3522 ( 1996 ).
[Crossref] [PubMed]

von Bally, G.

Waggoner, A. S.

F. Lanni , A. S. Waggoner , and D. L. Taylor , “ Structural organization of interphase 3T3 fibroblasts studied by total internal reflection fluorescence microscopy ,” J. Cell. Biol.   100 , 1091 – 1102 ( 1985 ).
[Crossref] [PubMed]

Wang, C.

Wehner, F.

F. Wehner , H. Olsen , H. Tinel , E. Kinne-Saffran , and R. K. Kinne , “ Cell volume regulation: osmolytes, osmolyte transport, and signal transduction ,” Rev. Physiol. Biochem. Pharmacol.   148 , 1 – 80 ( 2003 ).
[Crossref] [PubMed]

Wernicke, G.

Wilkins, M. H. F.

H. G. Davies and M. H. F. Wilkins , “ Interference microscopy and mass determination ,” Nature   169 , 541 ( 1952 ).
[Crossref] [PubMed]

Appl. Opt. (4)

Biophys. J. (1)

J. Farinas and A. S. Verkman , “ Cell volume and plasma membrane osmotic water permeability in epithelial cell layers measured by interferometry ,” Biophys. J.   71 , 3511 – 3522 ( 1996 ).
[Crossref] [PubMed]

Cytometry A (1)

C. L. Curl , C. J. Bellair , T. Harris , B. E. Allman , P. J. Harris , A. G. Stewart , A. Roberts , K. A. Nugent , and L. M. Delbridge , “ Refractive index measurement in viable cells using quantitative phase-amplitude microscopy and confocal microscopy ,” Cytometry A   65 , 88 – 92 ( 2005 ).
[PubMed]

IEEE J. Sel. Top. Quantum Electron. (1)

A. Dunn and R. Richards-Kortum , “ Three-dimensional computaton of light scattering from cells ,” IEEE J. Sel. Top. Quantum Electron.   2 , 898 – 905 ( 1996 ).
[Crossref]

J. Cell. Biol. (2)

F. Lanni , A. S. Waggoner , and D. L. Taylor , “ Structural organization of interphase 3T3 fibroblasts studied by total internal reflection fluorescence microscopy ,” J. Cell. Biol.   100 , 1091 – 1102 ( 1985 ).
[Crossref] [PubMed]

J. Bereiter-Hahn , C. H. Fox , and B. Thorell , “ Quantitative reflection contrast microscopy of living cells ,” J. Cell. Biol.   82 , 767 – 779 ( 1979 ).
[Crossref] [PubMed]

J. Neurosci. Res. (1)

G. J. Brewer , J. R. Torricelli , E. K. Evege , and P. J. Price , “ Optimized survival of hippocampal neurons in B27-supplemented Neurobasal, a new serum-free medium combination ,” J. Neurosci. Res.   35 , 567 – 576 ( 1993 ).
[Crossref] [PubMed]

N. Engl. J. Med. (1)

K. J. Sweadner and S. M. Goldin , “ Active transport of sodium and potassium ions: mechanism, function, and regulation ,” N. Engl. J. Med.   302 , 777 – 783 ( 1980 ).
[Crossref] [PubMed]

Nature (1)

H. G. Davies and M. H. F. Wilkins , “ Interference microscopy and mass determination ,” Nature   169 , 541 ( 1952 ).
[Crossref] [PubMed]

Opt. Lett. (2)

Phys. Med. Biol. (1)

J. Beuthan , O. Minet , J. Helfmann , M. Herrig , and G. Muller , “ The spatial variation of the refractive index in biological cells ,” Phys. Med. Biol.   41 , 369 – 382 ( 1996 ).
[Crossref] [PubMed]

Rev. Physiol. Biochem. Pharmacol. (1)

F. Wehner , H. Olsen , H. Tinel , E. Kinne-Saffran , and R. K. Kinne , “ Cell volume regulation: osmolytes, osmolyte transport, and signal transduction ,” Rev. Physiol. Biochem. Pharmacol.   148 , 1 – 80 ( 2003 ).
[Crossref] [PubMed]

Other (1)

M. Born and E. Wolf , eds., “ Principles of Optics ,” ( Cambridge University Press , 1999 ), pp. 467 – 472 .

Supplementary Material (3)

» Media 1: MOV (842 KB)     
» Media 2: MOV (738 KB)     
» Media 3: MOV (862 KB)     

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Figures (9)

Fig. 1.
Fig. 1.

(A) Basic configuration for digital holographic microscopy (DHM). A VCSEL laser diode produces the coherent light (λ = 658 nm) which is divided by a beam splitter (BS). The specimen (S) is illuminated by one beam through a condenser (C). A microscope objective (MO) collects the transmitted light and forms the object wave (O) which interferes with a reference beam (R) to produce the hologram recorded by the digital CCD camera (Basler A101f). Fig. 1. (B) Typical example of a hologram acquired by the camera (1024 × 1024 pixels). The scale bar indicates the size of the hologram recorded on the CCD camera chip.

Fig. 2.
Fig. 2.

(A.) Diagram of the perfusion chamber used to monitor neurons in culture. h: cell thickness; ni: cellular refractive index; D: perfusion chamber height; nm: perfusion solution refractive index. (B.) 3D perspective representation of the quantitative phase contrast image of 3 neurons in culture observed with a 63x MO (NA=0.8). Each pixel represents a quantitative measurement of the cellular optical path length (OPL). The scale (at right) relates the OPL (in degree) to the morphology (in μm) using the measured mean value of the neuronal cell body refractive index nc¯ = 1.3774 (see results).

Fig. 3.
Fig. 3.

Nycodenz (HistodenzTM, C19H26I3N3O9, MW 821.14), the hydrophilic molecule used to shift the refractive index.

Fig. 4.
Fig. 4.

The “decoupling procedure”. The graphic shows the phase signal (averaged over the 2995 pixel neuronal surface delineated by the red contour line, inset) plotted versus perfusion time. Rectangles on the bottom indicate when the standard solution (black) or the decoupling solution (dashed) are perfused. Comparison of the phase signal recorded in 1 and 2 allows for the separate measurement of the integral refractive index and the cellular thickness of the specimen. The peaks in the phase signal are artifacts produced by the perfusion solutions switches. Each point of the phase time course results from the reconstruction of a single hologram. The temporal fluctuation of the phase signal ≡ 0.2°. Inset: for the determination of the neuronal surface see the text.

Fig. 5.
Fig. 5.

(A.) Real-time monitoring of the phase signal of 3 neurons observed during a hypotonic shock. Inset: quantitative phase contrast image of the monitored neurons. The phase mean values of the colored rectangles are plotted versus perfusion time. The black bar denotes perfusion of the hypotonic solution for 5 minutes. Scale bar in the inset image: 10 μm. Fig 5 (B). (862 KB) MOVIE: Temporal evolution of the spatial distribution of phase of the central neuron on the inset image in A when the hypotonic solution is perfused. Each point of the phase time courses results from the reconstruction of a single hologram. The temporal fluctuations of the phase signals are 0.473°, 0.232°, 0.252° for the left, right and middle cell, respectively.

Fig. 6.
Fig. 6.

Quantitative phase images of two neuronal cell bodies before (panel A, “standard”) and 3 minutes after the onset of the hypotonic shock (panel B, “hypotonic”). C. Color-coded distribution of phase difference resulting from the subtraction of the “standard” image from the “hypotonic” image. Neuronal cell body boundaries have been identified by a gradient-based edge detection algorithm.

Fig. 7.
Fig. 7.

(756 KB) MOVIE: Temporal evolution of the phase difference of the central neuron on the inset image Fig. 5 (A) when a hypotonic solution is applied to a neuron. The black bar denotes perfusion of the hypotonic solution. The phase image acquired at time t=0 was subtracted from all the other images of the movie.

Fig. 8.
Fig. 8.

Morphometry of 2 cell bodies before (panel A) and 3 minutes after the onset (panel B) of a hypotonic shock. Here the z-axis (cellular thickness) is expressed in micrometers. These values where obtained using the results of the decoupling procedure. C. Color-coded distribution of thickness variations resulting from the subtraction of the “standard” image to the “hypotonic” image.

Fig. 9.
Fig. 9.

(883 KB) MOVIE: Temporal dynamics of the cell morphometry (red plot) and of the mean integral refractive index (values in blue) of the central neuron on the inset image Fig. 5(A) when a hypotonic shock is applied (black rectangle).

Tables (1)

Tables Icon

Table 1. Result of the decoupling procedure applied to the two neurons illustrated in Fig. 8 before (standard) and 3 mn after the beginning of the perfusion with the hypotonic solution (hypotonic). Scell: cell surface; Vcell: cell volume. Beta quantifies the swelling of the cell due to the application of the hypotonic solution (see text). Results are expressed as mean ± standard deviation. Cell 1: cell on top of Fig. 8, cell 2: cell on bottom of Fig. 8.

Equations (12)

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

OPL i = 0 h i n c , i ( z ) d z + n m ( D h i ) = ( n ̅ c , i n m ) h i + n m D ,
φ 1 , i = 2 π λ ( n ̅ c , i n m ) h i ,
φ 2 , i = 2 π λ ( n ̅ c , i ( n m + δ n ) ) h i
n ̅ c , i = δ n φ 1 , i ( φ 1 , i φ 2 , i ) + n m ,
h i = λ 2 π ( φ 1 , i φ 2 , i ) δ n = λ 2 π φ 1 , i ( n ̅ c , i n m )
V cell N Cell S Pixel M 2 h ̅ Cell ,
β ( n ̅ c ( β ) n m ) = λ 2 π φ Tot V 0 ,
φ Tot = i S Cell φ i 2 π λ ( n ̅ c ( β ) n m ) V ,
n ̅ c ( β ) = ( 1 r β ) n cyt ( β ) + r β n solid ,
n cyt N x N H 2 O = 1 + N H 2 O α H 2 O + x N x α x 1 1 3 ( N H 2 O α H 2 O + x N x α x ) ,
n cyt ( β cyt ) = 1 + { β cyt ( 1 p H 2 O ) β cyt } C H 2 O α H 2 O + 1 β cyt x N x α x 1 1 3 ( { β cyt ( 1 p H 2 O ) β cyt } C H 2 O α H 2 O + 1 β cyt x N x α x ) =
1 + { β cyt 1 β cyt } C H 2 O α H 2 O + C β cyt 1 1 3 ( { β cyt 1 β cyt } C H 2 O α H 2 O + C β cyt ) ,

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