Speckle contrast optical tomography
Speckle contrast optical tomography system provided with at least one point source and multiple detectors, means for providing different source positions, the point source having a coherence length of at least the source position-detector distance and means for arranging the source position-detector pairs over a sample to be inspected, the system being further provided with means for measuring the speckle contrast; the speckle contrast system of the invention thus capable of obtaining 3D images.
1. A speckle contrast optical tomography system comprising:
a plurality of point sources each adapted to generate light, each of the plurality of point sources located at a respective first location over a sample to be examined;
a plurality of detectors located at respective second locations relative to the sample; and
wherein the plurality of point sources and the plurality of detectors are arranged over a tissue volume of the sample in an arrangement that defines a plurality of source position-detector pairs adapted to examine the tissue volume;
the speckle contrast optical tomography system further comprising:
a processing device adapted to:
determine a speckle contrast between each of the plurality of source position-detector pairs, after light transverses the tissue volume, both in the absence of flow and in the presence of flow, thereby generating speckle contrast data;
correct the speckle contrast data for shot-noise error and intensity gradients; and
construct a speckle contrast forward model by performing the following steps:
computing a field autocorrelation for the plurality of source positions and the plurality of detectors;
computing the speckle contrast for the plurality of source positions and the plurality of detectors;
computing a difference value defining a relationship between the speckle contrast corrected for shot noise and intensity gradients and a baseline speckle contrast measurement value; and
determining a linear system of equations having a solution that provides a flow contrast, based at least in part on the difference value.
2. The speckle contrast optical tomography system of claim 1 , wherein:
the field autocorrelation for the plurality of point sources and the plurality of detectors is computed using a first equation, the first equation being defined as follows:
−∇. D∇G ( r,τ )+(μ a +⅓(μ s′ k 0 ) 2 <Δr 2 ( r,τ )>) G ( r,τ )= q 0 ( r )
wherein
G(r,τ) is an un-normalized field autocorrelation,
D, μ a , μ s′ , and k 0 are a diffusion coefficient, an absorption coefficient, a reduced scattering coefficient and a magnitude of wave vector, respectively;
g 0 (r) is a respective first location of a point source, wherein r is a set of spatial co-ordinates;
<Δr 2 (r,τ) > is a mean square displacement which models Brownian motion as well as a random flow given by 6D B τ and V 2 τ 2 , respectively;
D B is a particle diffusion coefficient in cm 2 /sec; and
V is a random flow with a unit of velocity;
the speckle contrast for the plurality of point sources and the plurality of detectors is computed based on the computed field autocorrelation and a second equation defined as follows:
K
=
2
β
T
∫
0
T
g
1
2
(
r
,
τ
)
(
1
-
τ
T
)
ⅆ
τ
wherein
g
1
(
r
,
τ
)
=
G
(
r
,
τ
)
G
(
r
,
0
)
is a normalized field autocorrelation;
τ is a correlation time;
T is an exposure time of a detector array; and
β is 0.5; and
the difference value indicating the relationship between the speckle contrast corrected for shot noise and integrity gradients and the baseline speckle contrast measurement value is computed using a third equation defined as follows:
K
c
2
-
K
co
2
=
-
4
β
T
∫
0
T
c
v
τ
2
(
1
-
τ
T
)
g
1
0
(
r
,
τ
)
G
(
r
,
0
)
[
∫
G
(
r
′
,
r
d
,
τ
)
G
1
0
(
r
′
,
r
s
,
τ
)
Δ
V
2
ⅆ
r
′
]
ⅆ
τ
wherein
K c is the speckle contrast corrected for shot noise and intensity gradients;
r s and r d are spatial coordinates of the plurality of point sources and the plurality of detectors, respectively;
K co is the baseline speckle contrast value;
g 1 0 and G 1 0 correspond to a baseline situation; and
C v =⅓(μ s′ k 0 ) 2; and
wherein the third equation is discretized in a source-detector geometry to obtain a linear system of equations whose solution provides a flow contrast ΔV 2 .
3. A speckle contrast optical tomography system comprising:
a laser point source adapted to generate light;
a plurality of detectors arranged over a sample to be examined; and
a plurality of galvanometric mirrors adapted to provide a plurality of source positions for scanning the source over the sample;
wherein the plurality of galvanometric mirrors and the plurality of detectors are arranged over a tissue volume of the sample in an arrangement that defines a plurality of source position-detector pairs adapted to examine the tissue volume;
wherein the laser point source has a coherence length of at least a source position-detector distance;
the speckle contrast optical tomography system further comprising:
a processing device adapted to:
determine a speckle contrast between each of the plurality of source position-detector pairs, after light transverses the tissue volume, both in the absence of flow and in the presence of flow, thereby generating speckle contrast data;
correct the speckle contrast data for shot-noise error and intensity gradients; and
construct a speckle contrast forward model by performing the following steps:
computing a field autocorrelation for the plurality of source positions and the plurality of detectors;
computing the speckle contrast for the plurality of source positions and the plurality of detectors;
computing a difference value defining a relationship between the speckle contrast corrected for shot noise and intensity gradients and a baseline speckle contrast measurement value; and
determining a linear system of equations having a solution that provides a flow contrast, based at least in part on the difference value.
4. The speckle contrast optical tomography system of claim 3 , wherein:
the field autocorrelation for the plurality of source positions and the plurality of detectors is computed using a first equation, the first equation being defined as follows:
−∇· D∇G ( r,τ )+(μ a +⅓(μ s′ k 0 ) 2<Δ r 2 ( r,τ )>) G ( r,τ )= q 0 ( r )
wherein
G(r,τ) is an un-normalized field autocorrelation,
D, μ a , μ s′ , and k 0 are a diffusion coefficient, an absorption coefficient, a reduced scattering coefficient and a magnitude of wave vector, respectively;
q 0 (r) is a source position wherein r is a set of spatial co-ordinates;
<Δr 2 (r,τ)> is a mean square displacement which models Brownian motion as well as a random flow given by 6D B τ and V 2 τ 2 , respectively;
D B is a particle diffusion coefficient in cm 2 /sec; and
V is a random flow with a unit of velocity;
the speckle contrast for the plurality of source positions and the plurality of detectors is computed based on the computed field autocorrelation and a second equation defined as follows:
K
=
2
β
T
∫
0
T
g
1
2
(
r
,
τ
)
(
1
-
τ
T
)
ⅆ
τ
wherein
g
1
(
r
,
τ
)
=
G
(
r
,
τ
)
G
(
r
,
0
)
is a normalized field autocorrelation;
τ is a correlation time;
T is an exposure time of a detector array; and
β is 0.5; and
the difference value indicating the relationship between the speckle contrast corrected for shot noise and intensity gradient and the baseline speckle contrast measurement value is computed using a third equation defined as follows:
K
c
2
-
K
co
2
=
-
4
β
T
∫
0
T
c
v
τ
2
(
1
-
τ
T
)
g
1
0
(
r
,
τ
)
G
(
r
,
0
)
[
∫
G
(
r
′
,
r
d
,
τ
)
G
1
0
(
r
′
,
r
s
,
τ
)
Δ
V
2
ⅆ
r
′
]
ⅆ
τ
wherein
K c is the speckle contrast corrected for shot noise and intensity gradient;
r s and r d are spatial coordinates of the plurality of source positions and the plurality of detectors, respectively;
K co is the baseline speckle contrast value;
g 1 0 and G 1 0 correspond to a baseline situation; and
c v =⅓(μ s′ k 0 ) 2 ; and
wherein the third equation is discretized in a source-detector geometry to obtain a linear system of equations whose solution provides a flow contrast ΔV 2 .
5. A speckle contrast optical tomography system comprising:
a laser adapted to generate light;
a plurality of detectors arranged over a volume of a sample to be examined;
a plurality of optical fibers adapted to guide the light from the laser to a plurality of source positions;
wherein the laser has a coherence length of at least a source position-detector distance;
wherein the plurality of detectors and the plurality of source positions are arranged over a tissue volume of the sample in an arrangement that defines a plurality of source position-detector pairs adapted to examine the tissue volume;
the speckle contrast optical tomography system further including:
a processing device adapted to:
measure a speckle contrast for each of the plurality of source position-detector pairs, after the light transverses the tissue volume, both in the absence of flow and in the presence of flow, to generate speckle contrast data;
correct the speckle contrast data for shot-noise error and intensity gradients; and
construct a speckle contrast forward model for the speckle contrast optical tomography system by performing the following steps:
computing a field autocorrelation for the plurality of source positions and the plurality of detectors;
computing the speckle contrast for the plurality of source positions and the plurality of detectors;
computing a difference value defining a relationship between the speckle contrast corrected for shot noise and intensity gradients and a baseline speckle contrast measurement value; and
determining a linear system of equations having a solution that provides a flow contrast, based at least in part on the difference value.
6. The speckle contrast optical tomography system of claim 5 , wherein:
the field autocorrelation for multiplicity of light sources and detectors is computed using a first equation defined as follows:
−∇· D∇G ( r,τ )+(μ a +⅓(μ s′ k 0 ) 2<Δ r 2 ( r,τ )>) G ( r,τ )= q 0 ( r ) ( I )
wherein
G(r,τ) is an un-normalized field autocorrelation;
D, μ a ,μ s′ , and k 0 are a diffusion coefficient, an absorption coefficient, a reduced scattering coefficient and a magnitude of wave vector, respectively;
q 0 (r) is a point source wherein r is a set of spatial co-ordinates;
<Δr 2 (r,τ)> is a mean square displacement which models Brownian motion as well as a random flow given by 6D B τ and
V 2 τ 2 respectively′
D B is a particle diffusion coefficient in cm 2 /sec; and
V is a random flow with unit of velocity;
the speckle contrast for the plurality of light sources and the plurality of detectors is computed using the computed field autocorrelation and a second equation defined as follows:
K
=
2
β
T
∫
0
T
g
1
2
(
r
,
τ
)
(
1
-
τ
T
)
ⅆ
τ
wherein
g
1
(
r
,
τ
)
=
G
(
r
,
τ
)
G
(
r
,
0
)
is a normalized field autocorrelation;
τ is a correlation time;
T is an exposure time of a detector array; and
β is 0.5; and
the difference value indicating the relationship between the speckle contrast measurement corrected for shot noise and intensity gradient and the baseline speckle contrast value is computed using a third equation defined as follows:
K
c
2
-
K
co
2
=
-
4
β
T
∫
0
T
c
v
τ
2
(
1
-
τ
T
)
g
1
0
(
r
,
τ
)
G
(
r
,
0
)
[
∫
G
(
r
′
,
r
d
,
τ
)
G
1
0
(
r
′
,
r
s
,
τ
)
Δ
V
2
ⅆ
r
′
]
ⅆ
τ
wherein
K c is the speckle contrast corrected for shot noise and intensity gradient;
r s and r d are spatial coordinates of the plurality of source positions and the plurality of detectors, respectively;
K co is the baseline speckle contrast value; and
g 1 0 and G 1 0 correspond to a baseline situation; and
c v =⅓(μ s′ k 0 ) 2 ; and
wherein the third equation is discretized in a source-detector geometry to obtain a linear system of equations having a solution provides a flow contrast ΔV 2 .