Добавил:
Sekretar
kiopkiopkiop18@yandex.ru
t.me/Prokururor I Вовсе не секретарь, но почту проверяю
Опубликованный материал нарушает ваши авторские права? Сообщите нам.
Вуз:
Предмет:
Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_3921_Библиотеки_им_академика_М_И_Перельмана
.pdf
References 133
Furthermore, Thompson and Andrews [23] showed that combining speckle con-
trast values measured at various exposure times may lead to the prediction of laser
Doppler spectra. This would make multiple-exposure LSCPI equivalent to LDPI,
although at the expense of acquisition speed.
Probably there will be a future for both modalities, where the choice for a specific
technology will depend on the need for quantitative imaging. Since almost all
experience in LDPI has been gained with the use of scanning beam LDPI, the
introduction of both ffLDPI and LSCPI will make it necessary to reconsider existing
practices, protocols, and procedures.
References
1. Bonner, R. and Nossal, R. (1981) Model
for laser Doppler measurements of
blood-flow in tissue. Appl. Opt., 20 (12),
2097– 2107.
2. Draijer, M., Hondebrink, E., van
Leeuwen, T., and Steenbergen, W.
(2009) Review of laser speckle contrast
techniques for visualizing tissue perfu-
sion. Lasers Med. Sci., 24 (4), 639–651.
3. Leahy, M.J. (2009) Microvascular
blood flow: microcirculation imag-
ing, in Handbook of Biophotonics,
vol. 2, Chapter 26, (eds J. Popp and
V.V. Tuchin), Wiley-VCH Verlag
GmbH, pp. 403–444.
4. Atlan, M. and Gross, M. (2006) Laser
Doppler imaging, revisited. Rev. Sci.
Instrum., 77 (11), 116103.
5. Atlan, M. and Gross, M. (2007)
Wide-field fourier transform spectral
imaging. Appl. Phys. Lett., 91, 113510.
6. Atlan, M., Gross, M., Forget, B.C.,
Vitalis, T., Rancillac, A., and Dunn, A.K.
(2006) Frequency-domain wide-field
laser Doppler in vivo imaging. Opt. Lett.,
31 (18), 2762– 2764.
7. Atlan, M., Gross, M., Vitalis, T.,
Rancillac, A., Rossier, J., and Boccara,
A.C. (2008) High-speed wave-mixing
laser Doppler imaging in vivo. Opt. Lett.,
33 (8), 842– 844.
8. Gu, Q., Hayes-Gill, B.R., and Morgan,
S.P. (2008) Laser Doppler blood flow
complementary metal oxide semicon-
ductor imaging sensor with analog
on-chip processing. Appl. Opt., 47 (12),
2061– 2069.
9. Kongsavatsak, C., He, D.W.,
Hayes-Gill, B.R., Crowe, J.A., and
Morgan, S.P. (2008) Complemen-
tary metal-oxide-semiconductor
imaging array with laser Doppler
blood flow processing. Opt. Eng.,
47 (10), 14.
10. Draijer, M., Hondebrink, E., van
Leeuwen, T., and Steenbergen, W.
(2009) Twente optical perfusion camera:
system overview and performance for
video rate laser Doppler perfusion imag-
ing. Opt. Express, 17 (5), 3211 –3225.
11. Draijer, M., Hondebrink, E., van
Leeuwen, T., and Steenbergen, W.
(2009) Time domain algorithm for accel-
erated determination of the first order
moment of photo current fluctuations
in high speed laser Doppler perfusion
imaging. Med. Biol. Eng. Comput., 47
(10), 1103–1109.
12. Serov, A. and Lasser, T. (2005)
High-speed laser Doppler perfusion
imaging using an integrating CMOS
image sensor. Opt. Express, 13 (17),
6416– 6428.
13. Serov, A., Steinacher, B., and Lasser, T.
(2005) Full-field laser Doppler perfusion
imaging and monitoring with an intel-
ligent CMOS camera. Opt. Express, 13
(10), 3681–3689.
14. Raabe, A., De Ville, D.V., Leutenegger,
M., Szelenyi, A., Hattingen, E., Gerlach,
R., Seifert, V., Hauger, C., Lopez, A.,
Leitgeb, R., Unser, M., Martin-Williams,
E.J., and Lasser, T. (2009) Laser Doppler
imaging for intraoperative human
brain mapping. Neuroimage, 44 (4),
1284– 1289.
15. Schlosser, S., Wirth, R., Plock, J.A.,
Serov, A., Banic, A., and Erni, D. (2010)
https://t.me/medicina_free
134 6 Fast Full-Field Laser Doppler Perfusion Imaging
Application of a new laser Doppler
imaging system in planning and moni-
toring of surgical flaps. J. Biomed. Opt.,
15 (3), 036023– 036026.
16. Serov, A., Steenbergen, W., and de Mul,
F. (2002) Laser Doppler perfusion imag-
ing with a complimentary metal oxide
semiconductor image sensor. Opt. Lett.,
27 (5), 300– 302.
17. van Herpt, H., Draijer, M., Hondebrink,
E., Nieuwenhuis, M., Beerthuizen, G.,
van Leeuwen, T., and Steenbergen, W.
(2010) Burn imaging with a whole field
laser Doppler perfusion imager based on
a CMOS imaging array. Burns, 36 (3),
389– 396.
18. Droog, E.J., Steenbergen, W., and
Sjoberg, F. (2001) Measurement
of depth of burns by laser Doppler
perfusion imaging. Burns, 27 (6),
561– 568.
19. Nilsson, G.E., Tenland, T., and
Oberg, P.A. (1980) New instrument
for continuous measurement of
tissue blood-flow by light beating
spectroscopy. IEEE Trans. Biomed.
Eng., 27 (1), 12–19.
20. Nilsson, G.E., Tenland, T., and Oberg,
P.A. (1980) Evaluation of a laser Doppler
flowmeter for measurement of tissue
blood-flow. IEEE Trans. Biomed. Eng., 27
(10), 597 –604.
21. Binzoni, T. and Van De Ville, D. (2008)
Full-field laser-Doppler imaging and
its physiological significance for tissue
blood perfusion. Phys. Med. Biol., 53
(23), 6673 –6694.
22. Draijer, M.J., Hondebrink, E.,
Larsson, M., van Leeuwen, T.G.,
and Steenbergen, W. (2010) Relation
between the contrast in time integrated
dynamic speckle patterns an the power
spectral density of their temporal inten-
sity fluctuations. Opt. Express, 18 (21),
21883– 21891.
23. Thompson, O.B. and Andrews, M.K.
(2010) Tissue perfusion measurements:
multiple-exposure laser speckle analysis
generates laser Doppler-like spectra.
J. Biomed. Opt., 15 (2), 027015.
https://t.me/medicina_free
135
7
Speckle Effects in Laser Doppler Perfusion Imaging
Wiendelt Steenbergen
7.1
Introduction
For those observing laser light, speckles are an inevitable phenomenon. Images
of static objects illuminated by laser light with a sufficient coherence length
are characterized by a grainy or speckled structure, or in other words, they are
composed of speckles. Speckles on the retina are always ‘‘in focus,’’ even when the
object plane is not imaged on the retina.
When laser light is scattered off a partially dynamic object, for instance, a
scattering medium with slow internal motion of scattering centers, such as many
biological samples, the speckle pattern exhibits slow changes in time. Faster motion
of scatterers will generate more rapid speckle motion and, above a certain typical
speed of scatterers, the speckle motion is too fast to be observed by the naked eye.
However, a photodetector that is sufficiently fast will still be able to record the
associated intensity fluctuations.
The dynamic speckle pattern, which is the result of the interaction of coherent
light with red blood cells moving within a static tissue matrix, and the associated
fluctuations of the light intensity of the detector are an essential aspect of laser
Doppler perfusion monitoring (LDPM) and laser Doppler perfusion imaging
(LDPI). In the past, some confusion has been caused by the parallel use of
‘‘speckle flowmetry’’ [1–4] and ‘‘laser Doppler flowmetry’’ [5, 6] for the same
method in which the intensity fluctuation signal is recorded and a perfusion signal
is derived from its power spectrum. Although not all speckle motion is caused by
the Doppler effect, intensity fluctuations in laser Doppler methods are essentially
caused by speckle motion. The distinction between ‘‘Doppler’’ and ‘‘speckle’’ may
be described as follows: dynamic speckle is the phenomenon that is being recorded,
while Doppler effect provides the framework for the interpretation of intensity
fluctuations in terms of perfusion.
Microcirculation Imaging, First Edition. Edited by Martin J. Leahy.
2012 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2012 by Wiley-VCH Verlag GmbH & Co. KGaA.
https://t.me/medicina_free
136 7 Speckle Effects in Laser Doppler Perfusion Imaging
7.2
What Are Speckles? Basic Properties
Speckles are the result of the interference of a very large number of light waves.
A condition for obtaining observable speckles is that the phases of these waves
remain fairly constant within a certain time scale, or in other words, the waves
should be sufficiently coherent. Without such correlation, no interference can be
observed by the eye or with a normal photodetector or imaging array. A second
condition is that these multiple waves have a certain angular spread. The situation
is illustrated in Figure 7.1a for spherical waves emitted from a plane such as
an optically rough reflector illuminated by coherent light. Here, optically rough
means a roughness on the scale of the wavelength of light used. Because of the
roughness of the screen, a perfectly smooth wave front hitting the screen will lead
to a spatial randomization of the phases of the reflected wave. We can also regard
this as a collection of spherical waves, with mutually random phases. Since the
light is coherent, the waves, although they have a random distribution of phases,
are coherent too and are therefore able to interfere. If a screen is placed at a certain
distance from the rough surface, the waves arrive as planar waves. The phase of
each wave varies with the position on the screen, and the phase difference between
two points on the screen will be larger for skew waves than for waves that are
almost perpendicular. Therefore, at each location on the screen, the local electric
field and the intensity are the result of the addition of many electric fields with
mutual phase differences that vary with screen position. The result is the speckle
pattern as shown in Figure 7.1b, which was generated by observing light emitted by
a paper that was illuminated by a He–Ne laser. Actually, two interference patterns
are formed, each associated with two perpendicular polarizations of the incident
Ω
Screen
(
a
)(
b
)
Figure 7.1 (a) Waves emitted by an optically rough surface
and hitting a distant screen at an angular spread given by
solid angle . The phases of the waves vary with the posi-
tion on the screen. (b) The resulting interference pattern on
screen.
https://t.me/medicina_free
7.2 What Are Speckles? Basic Properties 137
light. The speckle pattern shown here is one of the two, selected by placing a
linear polarizer between the paper and the screen. This is called polarized speckle.
It is important to realize that the above principle also holds for coherent waves
backscattered from turbid media, such as tissue, as long as the difference in the
diffuse path lengths of the interfering photons is less than the coherence length
of the light. The visibility of the interference pattern decays exponentially with
increasing optical path difference.
The basic properties of speckle patterns have been investigated by Goodman
[7, 8]. The most relevant for the topic of this chapter are briefly mentioned here.
We restrict ourselves to the case of a single polarized speckle pattern.
7.2.1
Distributions of Field Amplitude and Intensity
Since speckle is formed by the amplitude addition of many coherent waves whose
phases are randomized, the local field complex amplitude can be described by a
phasor that results from the addition of many phasors, as shown in Figure 7.2.
Because speckle is the result of the addition of a large number of randomly
oriented phasors, the resulting amplitude has a circular Gaussian distribution in
the complex plane. That the resulting distribution is Gaussian follows from the
central limit theorem, which is applicable to this situation. As a consequence of
the Gaussian distribution of the complex field amplitude, the intensity distribution
has an exponential (or Poisson) distribution.
7.2.2
Speckle Contrast
The speckle contrast quantifies the visibility of the speckles, or the modulation
depth of the speckle pattern. For a statistically homogeneous static speckle pattern,
the contrast is defined as
K ≡
σ
I
I
(7.1)
where σ
I
is the standard deviation of the intensity I and
denotes spatial averaging.
Re(A)
Im(A)
Figure 7.2 Complex amplitude (gray pha-
sor) of the local field as a result of the
addition of multiple phasors.
https://t.me/medicina_free
138 7 Speckle Effects in Laser Doppler Perfusion Imaging
For a single linearly polarized speckle pattern, caused by a static object, the
Poisson intensity distribution leads to a value K = 1, which means that the
standard deviation of the intensity fluctuations is equal to the average intensity.
This fact is important later in this chapter.
7.2.3
Speckle Size
Owing to the stochastic nature of laser speckle patterns, speckle size can only
be expressed in terms of an average size, to be derived from a function that
describes the distribution of the width or diameter of the speckles. For laser
Doppler flowmetry, the speckle area, or coherence area, appears to be the quantity
of relevance. It is not exactly defined which feature in a speckle pattern such as in
Figure 7.1 can be called ‘‘a speckle.’’ Therefore, we analyze the complete speckle
pattern in terms of the spatial correlation function R
I
(x) ≡
I(x)I (x + x)
/
I
2
of the intensity distribution I(x). Here we have assumed that the speckle pattern
is statistically homogeneous and isotropic. While R
I
(x) can be analyzed in terms
of speckle width or speckle area in various ways, the expression for the area of one
speckle that is most relevant for laser Doppler flowmetry can be shown [9] to be
A
speckle
= 2π
∞
0
R
I
(x)xdx (7.2)
A
speckle
can be regarded as an ‘‘effective speckle area’’ because a dynamic speckle
pattern that would consist of areas of uniform intensity with an area of exactly
A
speckle
will generate the same photocurrentfluctuations as the real dynamicspeckle
pattern.
The spatial correlation function R
I
(x) is related to the angular intensity distribu-
tion of the incoming light and therefore to the intensity distribution I
x
, y
in the
light-emitting plane. The wider this distribution function, for instance expressed
by the solid angle in Figure 7.1, the smaller the speckles will be. This relation is
obtained in two steps. First, for light that has a Gaussian amplitude distribution,
the spatial correlations of the intensity R
I
(x) and the field amplitude R
E
(x) are
related by
R
I
(x) =
I
2
+
R
E
(x)
2
(7.3)
which is called Siegert’s relation. The observation plane and the source plane, as
shown schematically in Figure 7.3, are related by the Zernike –Van Cittert theorem
[10]. This theorem states that R
E
(x) and I
x
, y
are related in the same manner
as the electric field amplitude distribution E(x,y)inthexy-plane would be related
to the electric field amplitude distribution E(x
, y
) in the x’y’-plane, with amplitude
distribution E(x
, y
) mathematically equal to the intensity distribution I(x
, y
). This
fact mathematically links the problem of coherence of randomly phased waves
emitted by a plane to the phenomenon of diffraction. Hence, R
E
(x), or the more
https://t.me/medicina_free
7.3 Significance of Speckles in LDPI 139
Dx
Detector surface
Surface of medium
x′
y′
y
x
I(x’,y’)
Z
f
1
f
1
f
0
f
0
R
E
(∆x)
Figure 7.3 Definition of coordinates on the surface of the
medium and on the detector surface. f
1
and f
0
refer to two
different fractions in which the light can be divided, such as
Doppler shifted and non-Doppler shifted light.
general form R
E
(x, y) and I
x
, y
are related by
R
E
(X, Y) =
source
I(x
, y
)exp
−i
2π
λZ
(x
x + y
y)
dx
dy
source
I(x
, y
)dx
dy
(7.4)
Now, if we know the intensity distribution I
x
, y
of the light emitted at the source
plane, we can calculate R
E
(x) with Eq. (7.4), R
I
(x) with Eq. (7.3), and eventually
A
speckle
using Eq. (7.2). Remember that this ‘‘source’’ can be a tissue that diffusely
and specularly reflects some of the light that it is illuminated with.
For the simple case of a circular homogeneous source, we find that
A
speckle
=
λ
2
(7.5)
with angle being the solid angle of the incoming light. Equation (7.5) is a rule of
thumb often used for estimating the speckle size when is approximately known.
7.3
Significance of Speckles in LDPI
In the previous section, we only took into account the properties of static speckle
patterns. In LDPI, we deal with dynamic speckle patterns, with sometimes a certain
static component. The presence of a static component in the speckle pattern will
https://t.me/medicina_free
140 7 Speckle Effects in Laser Doppler Perfusion Imaging
12 3
N
A
speckl
e
Figure 7.4 Instantaneous speckle pattern with speckle area
A
spec
and an equivalent instantaneous ‘‘speckle pattern’’
consisting of N speckles with equal area A
speckle
and uni-
form intensity within each speckle.
depend on the nature of the medium in which the light is scattered. If the medium
contains moving particles at a sufficient concentration, all light will be Doppler
shifted, leading to a completely dynamic speckle pattern. If a part of the light, which
is diffusely scattered by the medium,has not undergone a Doppler shift, a part of the
speckle pattern will be static. Here, we first assume a completely dynamic speckle
pattern, generated only by Doppler-shifted light. We now analyze the consequence
of the speckled nature of the intensity distribution on the photodetector. Instead
of a natural speckle pattern as shown in Figure 7.4, we now assume an equivalent
pattern such as the one shown in Figure 7.4, consisting of N speckles with equal
area A
speckle
and uniform intensity. ‘‘Equivalent’’ here means that both speckle
patterns will generate the same photocurrent fluctuations.
We assume that all speckles are statistically identical, having the same average
intensity
i
sp
and distribution of intensity fluctuations δi
sp
(t). The photocurrent
generated by any speckle can then be written as i
sp
(t) =
i
sp
+ δi
sp
(t). The current
i
tot
(t) generated by the total speckle pattern is the sum of the currents of the
individual speckles. For the variance of the total photocurrent we find
i
2
tot
=
N
j=1
N
k=1
i
j
(
t
)
i
k
(
t
)
= N
2
i
sp
2
+ N
δi
2
sp
= N
2
i
sp
2
+ N
i
sp
2
(7.6)
This result is obtained if we assume that the intensity fluctuations of all speckles
are mutually uncorrelated. In fact, this could be called the definition of the speckle
concept within the framework of laser Doppler flowmetry. The second step in Eq.
(7.6) can be made, thanks to the Poisson intensity distribution of speckle patterns.
We earlier invoked this property to conclude that for polarized speckle the contrast
K = 1. While this was stated for the spatial variations in a static speckle pattern, it
also holds for the temporal fluctuations at one position within a dynamic speckle
pattern, that is, there is a Poisson intensity distribution in space and time. The first
term of the right-hand side of Eq. (7.6) is related to the DC part of the photocurrent,
while the second term is caused by the photocurrent fluctuations. From Eq. (7.6),
it follows that the modulation depth of the total photodetector current is
M ≡
i
2
AC
i
DC
2
=
1
N
(7.7)
https://t.me/medicina_free
7.4 Further Analysis of the Consequence of Speckle in LDPI 141
For a mixed static–dynamic speckle pattern, generated by light of which a fraction
f has been Doppler shifted, it can be shown [9] that
M =
1
N
f (2 − f ) (7.8)
For simplicity, we have assumed that the spatial intensity distributions on the tissue
surface of Doppler-shifted light and nonshifted light are identical. In general, this
will not be the case because Doppler-shifted photons will, on average, have a wider
path length distribution and a wider intensity distribution at the tissue surface.
The problem is treated in its full complexity by Steenbergen and coworkers [9].
This reference provide a theory for the general case that all photons can be divided
into fractions according to relevant criteria, for instance, Doppler shifted versus
nonshifted and photons with large penetration depth versus photons with small
penetration depth.
Suppose that we can divide the detected light in a static fraction f
0
and
Doppler-shifted fractions f
1
,f
2, ...
, f
N
whose sum, by definition, is 1 – f
0
.The
situation for two fractions is indicated in Figure 7.3. Now, for the modulation depth
of the photodetector signal we find
M = 2
M
i
f
0
f
i
A
0i
speckle
A
det
+
M
i=1
M
j=1
f
i
f
j
A
ij
speckle
A
det
(7.9)
Here, A
ij
speckle
is the so-called fractional speckle area, which can be calculated from
the field correlation functions R
i
E
(x) and R
j
E
(x) of each fraction f
i
and f
j
as
A
ij
coh
= 2π
∞
0
R
i
E
(x)R
∗j
E
(x)x dx (7.10)
For each fraction i, the field correlation function R
i
E
(x) can be obtained from
the intensity distribution I
i
x
, y
of that fraction, by using Eq. (7.4). This theory
will allow us to predict signal levels generated by light composed of the arbitrary
fraction of Doppler-shifted light and to calculate the relative contribution of each
fraction to the total photodetector current.
7.4
Further Analysis of the Consequence of Speckle in LDPI
From Eqs. (7.5) and (7.6), it can be concluded that the number of speckles N
involved in signal generation, and therefore the speckle size, determines the
overall response of the system. How can the number of speckles N involved in
speckle generation vary? The LDPI geometry that we will consider here is that of a
scanning laser beam and a lens that images the tissue onto a photodetector. The
situation is depicted in Figure 7.5. For a given optical system, the solid angle is
constant. However, the effective detector size A
det
will vary with the tissue optical
properties as indicated in the figure, and therefore N will vary. For a given detector
area and a given average light intensity, small speckles (large N) generate small
https://t.me/medicina_free
142 7 Speckle Effects in Laser Doppler Perfusion Imaging
A
det
A
det
N small in case of
High absorption or
high scattering or
superficial photons
N large in case of
Low absorption or
low scattering or
deep photons
Ω
Figure 7.5 Essentials of a laser Doppler perfusion imager.
Two effective detector sizes A
det
are indicated, associated
with high or low levels of scattering and/or absorption and
with photons with a large or small penetration depth.
photocurrent fluctuations and large speckles (small N) generate large fluctuations
of the photocurrent. Furthermore, from our theory [9], it can be concluded that
if a certain category of photons generates by itself speckles smaller than the
average size, its contribution to the total photocurrent fluctuations will be relatively
suppressed. Such a category could be the photons that reached at least a certain
depth. This category will occupy a larger detector area than the superficial photons,
and the associated value of N will be relatively large.
For scanning beam LDPI devices without a lens, the solid angle will vary
with tissue optical properties or photon penetration depth, and in this case, A
det
is
determined by the physical size of the photodetector. It has been shown [11] that
the conclusions drawn in this chapter also hold for this configuration.
Hence, we restrict ourselves to the category of scanning beam perfusion imagers
[12, 13]. The conclusions will not hold for the recent wide-field LDPI devices with
high-speed cameras [14 –18]. In these, the number of speckles N will only depend
on the properties of the imaging system.
The above concept is now elaborated for the following properties of scanning
beam LDPI devices:
•
The overall sensitivity of a laser Doppler system in relation to the beam size and
the tissue optical properties.
•
The depth sensitivity of LDPI.
•
The width of the power spectrum of photocurrent fluctuations.
7.4.1
Overall Sensitivity
As a measure of sensitivity, we take the modulation depth of the photodetector
signal, as defined in Eq. (7.7). The overall sensitivity of an LDPI system for a range
https://t.me/medicina_free
Соседние файлы в папке Библиотека им академика М.И. Перельмана