Abstract

Exploration of nanoscale tissue structures is crucial in understanding biological processes. Although novel optical microscopy methods have been developed to probe cellular features beyond the diffraction limit, nanometer-scale quantification remains still inaccessible for in situ tissue. Here we demonstrate that, without actually resolving specific geometrical feature, OCT can be sensitive to tissue structural properties at the nanometer length scale. The statistical mass-density distribution in tissue is quantified by its autocorrelation function modeled by the Whittle-Mateŕn functional family. By measuring the wavelength-dependent backscattering coefficient μb(λ) and the scattering coefficient μs, we introduce a technique called inverse spectroscopic OCT (ISOCT) to quantify the mass-density correlation function. We find that the length scale of sensitivity of ISOCT ranges from ~30 to ~450 nm. Although these sub-diffractional length scales are below the spatial resolution of OCT and therefore not resolvable, they are nonetheless detectable. The sub-diffractional sensitivity is validated by 1) numerical simulations; 2) tissue phantom studies; and 3) ex vivo colon tissue measurements cross-validated by scanning electron microscopy (SEM). Finally, the 3D imaging capability of ISOCT is demonstrated with ex vivo rat buccal and human colon samples.

© 2013 OSA

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2012

2011

2010

O. Nadiarnykh, R. B. LaComb, M. A. Brewer, and P. J. Campagnola, “Alterations of the extracellular matrix in ovarian cancer studied by second harmonic generation imaging microscopy,” BMC Cancer10(1), 94 (2010).
[CrossRef] [PubMed]

F. E. Robles and A. Wax, “Measuring morphological features using light-scattering spectroscopy and Fourier-domain low-coherence interferometry,” Opt. Lett.35(3), 360–362 (2010).
[CrossRef] [PubMed]

2009

2008

A. Fercher, “Inverse Scattering, Dispersion, and Speckle in Optical Coherence Tomography,” Optical Coherence Tomography 119–146 (2008).

C. Xu, J. M. Schmitt, S. G. Carlier, and R. Virmani, “Characterization of atherosclerosis plaques by measuring both backscattering and attenuation coefficients in optical coherence tomography,” J. Biomed. Opt.13(3), 034003 (2008).
[CrossRef] [PubMed]

2007

C. J. R. Sheppard, “Fractal model of light scattering in biological tissue and cells,” Opt. Lett.32(2), 142–144 (2007).
[CrossRef] [PubMed]

I. Itzkan, L. Qiu, H. Fang, M. M. Zaman, E. Vitkin, I. C. Ghiran, S. Salahuddin, M. Modell, C. Andersson, L. M. Kimerer, P. B. Cipolloni, K. H. Lim, S. D. Freedman, I. Bigio, B. P. Sachs, E. B. Hanlon, and L. T. Perelman, “Confocal light absorption and scattering spectroscopic microscopy monitors organelles in live cells with no exogenous labels,” Proc. Natl. Acad. Sci. U.S.A.104(44), 17255–17260 (2007).
[CrossRef] [PubMed]

C. J. R. Sheppard, “Fractal model of light scattering in biological tissue and cells,” Opt. Lett.32(2), 142–144 (2007).
[CrossRef] [PubMed]

C. Lanctôt, T. Cheutin, M. Cremer, G. Cavalli, and T. Cremer, “Dynamic genome architecture in the nuclear space: regulation of gene expression in three dimensions,” Nat. Rev. Genet.8(2), 104–115 (2007).
[CrossRef] [PubMed]

2006

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods3(10), 793–796 (2006).
[CrossRef] [PubMed]

2005

2003

M. Cremer, K. Küpper, B. Wagler, L. Wizelman, J. von Hase, Y. Weiland, L. Kreja, J. Diebold, M. R. Speicher, and T. Cremer, “Inheritance of gene density-related higher order chromatin arrangements in normal and tumor cell nuclei,” J. Cell Biol.162(5), 809–820 (2003).
[CrossRef] [PubMed]

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography-principles and applications,” Rep. Prog. Phys.66(2), 239–303 (2003).
[CrossRef]

2002

B. Povazay, K. Bizheva, A. Unterhuber, B. Hermann, H. Sattmann, A. F. Fercher, W. Drexler, A. Apolonski, W. J. Wadsworth, J. C. Knight, P. S. Russell, M. Vetterlein, and E. Scherzer, “Submicrometer axial resolution optical coherence tomography,” Opt. Lett.27(20), 1800–1802 (2002).
[CrossRef] [PubMed]

S. M. Pupa, S. Ménard, S. Forti, and E. Tagliabue, “New insights into the role of extracellular matrix during tumor onset and progression,” J. Cell. Physiol.192(3), 259–267 (2002).
[CrossRef] [PubMed]

R. K. Wang, “Signal degradation by multiple scattering in optical coherence tomography of dense tissue: a Monte Carlo study towards optical clearing of biotissues,” Phys. Med. Biol.47(13), 2281–2299 (2002).
[CrossRef] [PubMed]

2001

N. Théret, O. Musso, B. Turlin, D. Lotrian, P. Bioulac-Sage, J. P. Campion, K. Boudjéma, and B. Clément, “Increased extracellular matrix remodeling is associated with tumor progression in human hepatocellular carcinomas,” Hepatology34(1), 82–88 (2001).
[CrossRef] [PubMed]

M. Moscoso, J. B. Keller, and G. Papanicolaou, “Depolarization and blurring of optical images by biological tissue,” J. Opt. Soc. Am. A18(4), 948–960 (2001).
[CrossRef] [PubMed]

2000

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc.198(2), 82–87 (2000).
[CrossRef] [PubMed]

1999

J. M. Schmitt, S. H. Xiang, and K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt.4(1), 95–105 (1999).
[CrossRef] [PubMed]

1997

C. Matzler, “Autocorrelation functions of granular media with free arrangement of spheres, spherical shells or ellipsoids,” J. Appl. Phys.81(3), 1509–1517 (1997).
[CrossRef]

1996

1994

1991

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and et, “Optical coherence tomography,” Science254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

1984

A. Lewis, M. Isaacson, A. Harootunian, and A. Muray, “Development of a 500 Å spatial resolution light microscope: I. light is efficiently transmitted through λ/16 diameter apertures,” Ultramicroscopy13(3), 227–231 (1984).
[CrossRef]

1954

H. G. Davies, M. H. F. Wilkins, J. Chayen, and L. F. La Cour, “The use of the interference microscope to determine dry mass in living cells and as a quantitative cytochemical method,” Quarterly J.Microscopical Sciences (New York)3, 271–304 (1954).

R. Barer and S. Tkaczyk, “Refractive index of concentrated protein solutions,” Nature173(4409), 821–822 (1954).
[CrossRef] [PubMed]

1941

L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J.93, 70–83 (1941).
[CrossRef]

Akkin, T.

Andersson, C.

I. Itzkan, L. Qiu, H. Fang, M. M. Zaman, E. Vitkin, I. C. Ghiran, S. Salahuddin, M. Modell, C. Andersson, L. M. Kimerer, P. B. Cipolloni, K. H. Lim, S. D. Freedman, I. Bigio, B. P. Sachs, E. B. Hanlon, and L. T. Perelman, “Confocal light absorption and scattering spectroscopic microscopy monitors organelles in live cells with no exogenous labels,” Proc. Natl. Acad. Sci. U.S.A.104(44), 17255–17260 (2007).
[CrossRef] [PubMed]

Apolonski, A.

Backman, V.

J. Yi, Q. Wei, H. F. Zhang, and V. Backman, “Structured interference optical coherence tomography,” Opt. Lett.37(15), 3048–3050 (2012).
[CrossRef] [PubMed]

A. J. Radosevich, J. Yi, J. D. Rogers, and V. Backman, “Structural length-scale sensitivities of diffuse reflectance in continuous random media under the Born approximation,” Opt. Lett.37, 5220–5222 (2012).
[CrossRef] [PubMed]

A. J. Gomes, S. Ruderman, M. DelaCruz, R. K. Wali, H. K. Roy, and V. Backman, “In vivo measurement of the shape of the tissue-refractive-index correlation function and its application to detection of colorectal field carcinogenesis,” J. Biomed. Opt.17(4), 047005 (2012).
[CrossRef] [PubMed]

J. Yi and V. Backman, “Imaging a full set of optical scattering properties of biological tissue by inverse spectroscopic optical coherence tomography,” Opt. Lett.37(21), 4443–4445 (2012).
[CrossRef] [PubMed]

A. J. Radosevich, N. N. Mutyal, V. Turzhitsky, J. D. Rogers, J. Yi, A. Taflove, and V. Backman, “Measurement of the spatial backscattering impulse-response at short length scales with polarized enhanced backscattering,” Opt. Lett.36(24), 4737–4739 (2011).
[CrossRef] [PubMed]

J. D. Rogers, İ. R. Capoğlu, and V. Backman, “Nonscalar elastic light scattering from continuous random media in the Born approximation,” Opt. Lett.34(12), 1891–1893 (2009).
[CrossRef] [PubMed]

İ. R. Capoğlu, J. D. Rogers, A. Taflove, and V. Backman, “Accuracy of the Born approximation in calculating the scattering coefficient of biological continuous random media,” Opt. Lett.34(17), 2679–2681 (2009).
[CrossRef] [PubMed]

Barer, R.

R. Barer and S. Tkaczyk, “Refractive index of concentrated protein solutions,” Nature173(4409), 821–822 (1954).
[CrossRef] [PubMed]

Bates, M.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods3(10), 793–796 (2006).
[CrossRef] [PubMed]

Betzig, E.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

Bigio, I.

I. Itzkan, L. Qiu, H. Fang, M. M. Zaman, E. Vitkin, I. C. Ghiran, S. Salahuddin, M. Modell, C. Andersson, L. M. Kimerer, P. B. Cipolloni, K. H. Lim, S. D. Freedman, I. Bigio, B. P. Sachs, E. B. Hanlon, and L. T. Perelman, “Confocal light absorption and scattering spectroscopic microscopy monitors organelles in live cells with no exogenous labels,” Proc. Natl. Acad. Sci. U.S.A.104(44), 17255–17260 (2007).
[CrossRef] [PubMed]

Bioulac-Sage, P.

N. Théret, O. Musso, B. Turlin, D. Lotrian, P. Bioulac-Sage, J. P. Campion, K. Boudjéma, and B. Clément, “Increased extracellular matrix remodeling is associated with tumor progression in human hepatocellular carcinomas,” Hepatology34(1), 82–88 (2001).
[CrossRef] [PubMed]

Bizheva, K.

Bonifacino, J. S.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

Boudjéma, K.

N. Théret, O. Musso, B. Turlin, D. Lotrian, P. Bioulac-Sage, J. P. Campion, K. Boudjéma, and B. Clément, “Increased extracellular matrix remodeling is associated with tumor progression in human hepatocellular carcinomas,” Hepatology34(1), 82–88 (2001).
[CrossRef] [PubMed]

Bouma, B. E.

L. Liu, J. A. Gardecki, S. K. Nadkarni, J. D. Toussaint, Y. Yagi, B. E. Bouma, and G. J. Tearney, “Imaging the subcellular structure of human coronary atherosclerosis using micro-optical coherence tomography,” Nat. Med.17(8), 1010–1014 (2011).
[CrossRef] [PubMed]

Brewer, M. A.

O. Nadiarnykh, R. B. LaComb, M. A. Brewer, and P. J. Campagnola, “Alterations of the extracellular matrix in ovarian cancer studied by second harmonic generation imaging microscopy,” BMC Cancer10(1), 94 (2010).
[CrossRef] [PubMed]

Campagnola, P. J.

O. Nadiarnykh, R. B. LaComb, M. A. Brewer, and P. J. Campagnola, “Alterations of the extracellular matrix in ovarian cancer studied by second harmonic generation imaging microscopy,” BMC Cancer10(1), 94 (2010).
[CrossRef] [PubMed]

Campion, J. P.

N. Théret, O. Musso, B. Turlin, D. Lotrian, P. Bioulac-Sage, J. P. Campion, K. Boudjéma, and B. Clément, “Increased extracellular matrix remodeling is associated with tumor progression in human hepatocellular carcinomas,” Hepatology34(1), 82–88 (2001).
[CrossRef] [PubMed]

Capoglu, I. R.

Carlier, S. G.

C. Xu, J. M. Schmitt, S. G. Carlier, and R. Virmani, “Characterization of atherosclerosis plaques by measuring both backscattering and attenuation coefficients in optical coherence tomography,” J. Biomed. Opt.13(3), 034003 (2008).
[CrossRef] [PubMed]

Cavalli, G.

C. Lanctôt, T. Cheutin, M. Cremer, G. Cavalli, and T. Cremer, “Dynamic genome architecture in the nuclear space: regulation of gene expression in three dimensions,” Nat. Rev. Genet.8(2), 104–115 (2007).
[CrossRef] [PubMed]

Cense, B.

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and et, “Optical coherence tomography,” Science254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Chayen, J.

H. G. Davies, M. H. F. Wilkins, J. Chayen, and L. F. La Cour, “The use of the interference microscope to determine dry mass in living cells and as a quantitative cytochemical method,” Quarterly J.Microscopical Sciences (New York)3, 271–304 (1954).

Cheutin, T.

C. Lanctôt, T. Cheutin, M. Cremer, G. Cavalli, and T. Cremer, “Dynamic genome architecture in the nuclear space: regulation of gene expression in three dimensions,” Nat. Rev. Genet.8(2), 104–115 (2007).
[CrossRef] [PubMed]

Cipolloni, P. B.

I. Itzkan, L. Qiu, H. Fang, M. M. Zaman, E. Vitkin, I. C. Ghiran, S. Salahuddin, M. Modell, C. Andersson, L. M. Kimerer, P. B. Cipolloni, K. H. Lim, S. D. Freedman, I. Bigio, B. P. Sachs, E. B. Hanlon, and L. T. Perelman, “Confocal light absorption and scattering spectroscopic microscopy monitors organelles in live cells with no exogenous labels,” Proc. Natl. Acad. Sci. U.S.A.104(44), 17255–17260 (2007).
[CrossRef] [PubMed]

Clément, B.

N. Théret, O. Musso, B. Turlin, D. Lotrian, P. Bioulac-Sage, J. P. Campion, K. Boudjéma, and B. Clément, “Increased extracellular matrix remodeling is associated with tumor progression in human hepatocellular carcinomas,” Hepatology34(1), 82–88 (2001).
[CrossRef] [PubMed]

Cremer, M.

C. Lanctôt, T. Cheutin, M. Cremer, G. Cavalli, and T. Cremer, “Dynamic genome architecture in the nuclear space: regulation of gene expression in three dimensions,” Nat. Rev. Genet.8(2), 104–115 (2007).
[CrossRef] [PubMed]

M. Cremer, K. Küpper, B. Wagler, L. Wizelman, J. von Hase, Y. Weiland, L. Kreja, J. Diebold, M. R. Speicher, and T. Cremer, “Inheritance of gene density-related higher order chromatin arrangements in normal and tumor cell nuclei,” J. Cell Biol.162(5), 809–820 (2003).
[CrossRef] [PubMed]

Cremer, T.

C. Lanctôt, T. Cheutin, M. Cremer, G. Cavalli, and T. Cremer, “Dynamic genome architecture in the nuclear space: regulation of gene expression in three dimensions,” Nat. Rev. Genet.8(2), 104–115 (2007).
[CrossRef] [PubMed]

M. Cremer, K. Küpper, B. Wagler, L. Wizelman, J. von Hase, Y. Weiland, L. Kreja, J. Diebold, M. R. Speicher, and T. Cremer, “Inheritance of gene density-related higher order chromatin arrangements in normal and tumor cell nuclei,” J. Cell Biol.162(5), 809–820 (2003).
[CrossRef] [PubMed]

Davidson, M. W.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science313(5793), 1642–1645 (2006).
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Davies, H. G.

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Supplementary Material (1)

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Figures (8)

Fig. 1
Fig. 1

Illustration of the principle of ISOCT. (Left figure) An example of a numerically generated R.I. random medium (50x50x15 μm in xyz), whose correlation function is defined by Eq. (1) with D = 2.4, lc = 0.9μm. (Middle figure) Conventional FDOCT reconstructs the A-scan profile by an IFT on the entire spectrum. Top middle figure is an example of an A-scan signal (green) simulated from the R.I. fluctuation (Δ R.I.) (blue). The R.I. fluctuation was taken from the numerical R.I. medium. The calculated correlation function (c.f.) based on the A-scan profile does not represent the R.I. correlation function. (Right figure) The optical properties including μb and μs were used to inversely recover the correlation functional form. Both the OCT spectrum (top right) and the A-scan correlation function (bottom middle) were averaged over 10 A-scan signals.

Fig. 2
Fig. 2

(a) Example of the W-M correlation functions. The spatial displacement ρ on the x-axis is normalized by lc and the correlation function is normalized by Nc; (b-c) corresponding backscattering coefficient and reflection ratio spectrum. μb is normalized by k and Nc.

Fig. 3
Fig. 3

ISOCT data processing in three steps. Step 1: Based on Beer’s law, the square of the OCT A-line signal follows exponential decay so that the decay rate is proportional to μs. The heterogeneity of μb(z) can also be recovered by Eq. (10); Step 2: By doing STFT, the μb(z) spectrum is extracted and fitted with a power law. D(z) is obtained by Eq. (5). Step 3: lc(z) is calculated by Eq. (6) or (7).

Fig. 4
Fig. 4

(a-b) Perturbation of R.I. correlation function at lower and upper length scale, rmin and rmax. (c-d) D value change (%) as a function of rmin and rmax. The 5% sensitivity threshold is labeled for better comparison. D and lc are configured to be 2.8 and 1μm, respectively.

Fig. 5
Fig. 5

Sensitivity analysis of D measurement on changes at sub-diffractional length scales. (a) The volume fraction of the phantom spheres forms a power law to the diameters. The composition of different solutions were changed so that D ± S.E. were plotted against the largest sphere sizes removed (b) or added (c) in the phantom solutions. The initial compositions for (b) and (c) were from 30nm to 1μm and from 0.08 to 0.36μm, respectively.

Fig. 6
Fig. 6

OCT and tomographic D maps from phantoms. Gray scale OCT image and pseudo-color D map in low length scale (a-b) and upper length scale phantom studies. Bar = 200µm.

Fig. 7
Fig. 7

R.I. Correlation function measurement on human colon biopsy. (a) SEM image of a colon cross-section. The resolution is 40nm. Bar = 10μm. (b) The ISOCT measurement on D ± SE and lc ± SE in terms of penetration depth. The boundary of the cells and the collagen network is around 50μm depth from the surface. (c-d) The comparison between the correlation function obtained by the SEM image (c) and ISOCT (d). The 2D image autocorrelation function (a.c.f) ± SE from SEM is calculated from different regions on the image with image dimension 5x5μm. The ISOCT R.I. correlation functions were calculated using averaged value of D and lc from Epi and LP. Epi: epithelium, LP: lamina propria.

Fig. 8
Fig. 8

Three dimensional capability of measuring D. (a-b) OCT image and map of D values calculated by ISOCT on rat buccal biopsy ex vivo. The boundaries of KE, SE and SE, SM is labeled in blue. Bar = 200μm. (c-e) Histogram of D in three distinct layers: keratinized epithelium (KE), stratified epithelium (SE) and sub-mucosa (SM). (f) Three dimensional D distribution overlaid with morphology on human colon biopsies (Media 1). Dimension: 2x2x1mm in x,y,z.

Equations (23)

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C n (ρ)= N c 2 (5D)/2 ( ρ l c ) (D3)/2 K (D3)/2 ( ρ l c ),
σ n 2 ={ N c ×|Γ((D3)/2)|D>3 N c × 2 (5D)/2 ( ρ l l c ) (D3)/2 K (D3)/2 ( ρ l l c )0<D3 ,
n= n 0 +εχ
μ b = N c 8 π Γ(D/2) k 4 l c 3 (1+ (2k l c ) 2 ) D/2 .
μ b 2 3D N c π Γ(D/2) l c 3D k 4D (k l c 1).
α= 16Γ(D/2) k 6 l c 6 Γ(D/23) · [ (1+(2 k 2 l c 2 (D/22)1) ×2 k 2 l c 2 (D/23))(1+2 k 2 l c 2 (D/2+1) +4 k 4 l c 4 (43D/2+ D 2 /4)) (1+4 k 2 l c 2 ) 1D/2 ][ (1+ [2k l c ] 2 ) D/2 ].
α Γ(D/2) Γ(D/21) (2k l c ) 2D (k l c 1&D>2).
I 2 (z)=r I 0 2 μ b (z) 4π Lexp( μ s ·2nz),
ln[ I(z) I 0 ]= 1 2 ln( rL 4π )+ 1 2 ln[ μ b (z)]nz· μ s .
μ b (z)=(4π I 2 (z)/rL I 0 2 )exp( μ s 2nz),
C n = C n ACF(G),
C n = C n ACF(δG),
μ b (k)= k 3 0 C n (ρ)sin(2kρ)ρdρ,
Φ( k s )=FT[ C n (ρ)]= N c l c 3 Γ(D/2) π 3/2 (1+ k s 2 l c 2 ) D/2 ,
Φ= N c l c 3 Γ(3/2) π 3/2 (1+4 [k l c sin(θ/2)] 2 ) 3/2 .
p(θ)= (1+2 k 2 l c 2 ) 1+4 k 2 l c 2 4 k 2 l c 2 1 2 k 4 l c 4 1 (1+4[k l c sin (θ/2) 2 ]) 3/2 .
p(θ)= 1 g 2 4π 1 (1+ g 2 2gcos(θ)) 3/2 ,
n Δ l = n Δ G,
FT( C n )=|FT( n Δ G) | 2 =|FT( n Δ )×FT(G) | 2 =|FT( n Δ ) | 2 ×|FT(G) | 2 =FT( C n )×FT(ACF(G)),
C n = C n ACF(G).
n Δ h = n Δ n Δ G,
FT( C n )=|FT( n Δ n Δ G) | 2 =|FT( n Δ δ n Δ G) | 2 =|FT( n Δ (δG)) | 2 =|FT( n Δ ) | 2 ×|FT(δG) | 2 =FT( C n )×FT(ACF(δG)),
C n = C n ACF(δG).

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