In the investigations of inhomogeneous media, availability of methods to study the interior of the material without affecting it is valuable. Optical coherence tomography provides such a functionality by providing depth resolved images of semi-transparent objects non-invasively. This is especially useful in medicine and is used not only in research but also in clinical practice. Optical coherence tomography characterizes each cross section by its reflectance. The basic physics principle underlying optical coherence tomography is low-coherence interferometry, which is combined with lateral scanning to produce cross sections. It is clearly desirable to obtain more detailed information regarding each cross section, if available. We have developed a system which measures the fluctuation spectra at all depths in low-coherence interferometry. By providing more information for each cross section, this can in principle be effective in tissue characterization and pathological diagnosis. The system uses the time dependence of the low-coherence interferometry data to obtain the fluctuation spectrum at each depth. Additionally, noise reduction is applied to obtain the spectra without unwanted noise, such as shot-noise, which can swamp the signal. The measurement system is applied to samples with no external stimuli, and depth resolved thermal fluctuation spectra of the samples are obtained. These spectra are compared with their corresponding theoretical expectations and are found to agree. The measurement system requires dualizing the detectors in the low-coherence interferometer but otherwise requires little additional equipment. The measurements were performed in ten to a hundred seconds.

1.
N.
Tanno
,
T.
Ichikawa
, and
A.
Saeki
, “
Lightwave reflection measurement
,” Japanese patent 2010042 (
1990
).
2.
D.
Huang
 et al, “
Optical coherence tomography
,”
Science
254
,
1178
1181
(
1991
).
3.
A. F.
Fercher
,
W.
Drexler
,
C. K.
Hitzenberger
, and
T.
Lasser
, “
Optical coherence tomography—Principles and applications
,”
Rep. Prog. Phys.
66
,
239
303
(
2003
).
4.
A. F.
Fercher
,
C. K.
Hitzenberger
,
G.
Kamp
, and
S. Y.
Elzaiat
, “
Measurement of intraocular distances by backscattering spectral interferometry
,”
Opt. Commun.
117
,
43
48
(
1995
).
5.
G.
Hausler
and
M. W.
Lindner
, “
‘Coherence radar’ and ‘spectral radar’—New tools for dermatological diagnosis
,”
J. Biomed. Opt.
3
,
21
31
(
1998
).
6.
T.
Mitsui
, “
Dynamic range of optical reflectometry with spectral interferometry
,”
Jpn. J. Appl. Phys., Part 1
38
,
6133
6137
(
1999
).
7.
R.
Leitgeb
,
C. K.
Hitzenberger
, and
A.
Fercher
, “
Performance of Fourier domain vs. time domain optical coherence’ tomography
,”
Opt. Express
11
,
889
894
(
2003
).
8.
J. F.
de Boer
 et al, “
Improved signal-to-noise ratio in spectral-domain compared with time-domain optical coherence tomography
,”
Opt. Lett.
28
,
2067
2069
(
2003
).
9.
R. K.
Wang
, “
In vivo full range complex Fourier domain optical coherence tomography
,”
Appl. Phys. Lett.
90
,
054103
(
2007
).
10.
L.
An
and
R. K.
Wang
, “
Use of a scanner to modulate spatial interferograms for in vivo full-range Fourier-domain optical coherence tomography
,”
Opt. Lett.
32
,
3423
3425
(
2007
).
11.
X. J.
Wang
,
T. E.
Milner
, and
J. S.
Nelson
, “
Characterization of fluid-flow velocity by optical Doppler tomography
,”
Opt. Lett.
20
,
1337
1339
(
1995
).
12.
S.
Makita
 et al, “
Optical coherence angiography
,”
Opt. Express
14
,
7821
7840
(
2006
).
13.
R. K.
Wang
,
S. L.
Jacques
,
Z.
Ma
,
S.
Hurst
,
S. R.
Hanson
, and
A.
Gruber
, “
Three dimensional optical angiography
,”
Opt. Express
15
,
4083
4097
(
2007
).
14.
A. Q.
Zhang
,
Q. Q.
Zhang
,
C. L.
Chen
, and
R. K.
Wang
, “
Methods and algorithms for optical coherence tomography-based angiography: A review and comparison
,”
J. Biomed. Opt.
20
,
100901
(
2015
).
15.
Light Scattering by Liquid Surfaces and Complementary Techniques
, edited by
D.
Langevin
(
Marcel Dekker
,
New York
,
1992
).
16.
M.
Szkulmowski
,
A.
Szkulmowska
,
T.
Bajraszewski
,
A.
Kowalczyk
, and
M.
Wojtkowski
, “
Flow velocity estimation using joint spectral and time domain optical coherence tomography
,”
Opt. Express
16
,
6008
6025
(
2008
).
17.
J. M.
Schmitt
, “
OCT elastography: Imaging microscopic deformation and strain of tissue
,”
Opt. Express
3
,
199
211
(
1998
).
18.
K. V.
Larin
and
D. D.
Sampson
, “
Optical coherence elastography—OCT at network in tissue biomechanics
,”
Opt. Express
8
,
1172
1202
(
2017
).
19.
P.
Cicuta
and
L.
Hopkinson
, “
Recent developments of surface light scattering as a tool for optical-rheology of polymer monolayers
,”
Colloids Surf., A
233
,
97
107
(
2004
).
20.
L. M. C.
Sagis
, “
Dynamic properties of interfaces in soft matter: Experiments and theory
,”
Rev. Mod. Phys.
83
,
1367
1403
(
2011
).
21.
W. H.
Press
,
S. A.
Teukolsky
,
W. T.
Vetterling
, and
B. P.
Flannery
,
Numerical Recipes: The Art of Scientific Computing
, 3rd ed. (
Cambridge University Press
,
New York
,
2007
).
22.
E. A.
Swanson
 et al, “
High-speed optical coherence domain reflectometry
,”
Opt. Lett.
17
,
151
153
(
1992
).
23.
T.
Mitsui
and
K.
Aoki
, “
Direct optical observations of surface thermal motions at sub-shot noise levels
,”
Phys. Rev. E
80
,
020602(R)
(
2009
).
24.
25.
W. M.
Haynes
,
CRC Handbook of Chemistry and Physics
, 92nd ed. (
CRC Press
,
Baton Rouge
,
2011
).
26.
V. G.
Levich
,
Physicochemical Hydrodynamics
(
Prentice-Hall
,
Englewood Cliffs
,
1962
).
27.
M. A.
Bouchiat
and
J.
Meunier
, “
Power spectrum of fluctuations thermally excited on free surface of a simple liquid
,”
J. Phys.
32
,
561
571
(
1971
).
28.
J.
Jackle
, “
The spectrum of surface waves on viscoelastic liquids of arbitrary depth
,”
J. Phys.: Condens. Matter
10
,
7121
7131
(
1998
).
29.
T.
Mitsui
and
K.
Aoki
, “
Measurements of liquid surface fluctuations at sub-shot-noise levels with Michelson interferometry
,”
Phys. Rev. E
87
,
042403
(
2013
).
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