Utilizing highly scattered light for intelligence through aerosols
A method for modeling light transport through a scattering medium prior to being incident on a detector and a corresponding system is disclosed. The method determines the effects of scattering and absorption caused by particles as a function of the density, size, and refractive index of the particles, as well as the wavelength of the light source. Based on the determined scattering and absorption coefficients, the signal incident on the detector may be calculated. The calculation may also be inverted such that based upon the detected signal, an object may be detected, and its location in the scattering medium may be estimated.
1. A method for determining a presence of an object in a moderately scattering aerosol with moving scatterers and a transport optical depth τ t between approximately 0.2 and 2, the method comprising steps of:
determining a macroscopic scattering coefficient μ s of the moderately scattering aerosol;
determining a macroscopic absorption coefficient μ a of the moderately scattering aerosol;
determining a macroscopic averaged anisotropy g of the moderately scattering aerosol;
providing a light source that emits a known power spectral density;
providing a detector;
taking an image of the light source with the detector;
determining an expected background signal when the object is absent using a moderately scattering light transport model;
subtracting the expected background signal from the image to thereby create a difference image; and determining the presence of the object based upon the difference image;
wherein the moderately scattering light transport model is:
I
(
r
,
Ω
)
=
μ
s
4
π
∫
0
∞
dR
exp
[
-
(
μ
s
+
μ
a
)
R
]
[
ϕ
(
r
-
R
Ω
)
+
3
g
J
(
r
-
R
Ω
)
·
Ω
]
,
with I being a radiance, r being a position, Ω being a direction, R being a line of sight distance, ϕ being a fluence rate, and J being a flux density.
2. The method of claim 1 ,
wherein the macroscopic scattering coefficient is a function of a particle density in the moderately scattering aerosol, a particle diameter distribution, and scattering cross-sections of particles that are a function of particle diameter;
wherein the macroscopic absorption coefficient is a function of the particle density in the moderately scattering aerosol, the particle diameter distribution, and absorption cross-sections of particles that are a function of the particle diameter; and
wherein the macroscopic averaged anisotropy is a function of a particle density in the moderately scattering aerosol, a particle diameter distribution, scattering cross-sections of particles that are a function of particle diameter, and anisotropies of particles that are a function of particle diameter.
3. The method of claim 1 , wherein each of the macroscopic scattering coefficient, the macroscopic absorption coefficient, and the macroscopic averaged anisotropy is determined using the moderately scattering light transport model.
4. The method of claim 1 , wherein the step of determining the presence of the object determines the object is present when a decision statistic is greater than a detection threshold, the step of determining the presence of the object being based upon a likelihood ratio test.
5. The method of claim 4 ,
wherein the decision statistic is a function of a ratio of a probability density in a presence of the object to a probability density in an absence of the object; and
wherein the detection threshold is a function of a standard deviation of the decision statistic and an inverse complimentary error function of a specified false alarm rate.
6. The method of claim 4 further comprising a step of determining a location of the object when the object is determined to be present, the step of determining a location of the object being based upon a maximum likelihood estimation.
7. The method of claim 6 , further comprising a step of determining at least one of a size of the object, a shape of the object, or a reflectivity of the object, the step of determining at least one of a size of the object, a shape of the object, or a reflectivity of the object being based upon the maximum likelihood estimation.
8. The method of claim 1 , wherein the step of determining the presence of the object employs a deep learning model.
9. The method of claim 8 further comprising a step of determining a location of the object when the object is determined to be present, the step of determining a location of the object employing a deep learning model.
10. A system for determining a presence of an object in a moderately scattering aerosol with moving scatterers and a transport optical depth τ t between approximately 0.2 and 2, the system comprising:
a detector adapted to take an image of a light source that emits light with a known power spectral density and to output the image;
a processor adapted to execute instructions; and
a memory adapted to store instructions that, when executed by the processor, cause the processor to perform steps of:
determining a macroscopic scattering coefficient μ s of the moderately scattering aerosol;
determining a macroscopic absorption coefficient μ a of the moderately scattering aerosol;
determining a macroscopic averaged anisotropy g of the moderately scattering aerosol;
receiving the image from the detector;
determining an expected background signal when the object is absent using a moderately scattering light transport model;
subtracting the expected background signal from the image to thereby create a difference image; and determining the presence of the object based upon the difference image;
wherein the moderately scattering light transport model is:
I
(
r
,
Ω
)
=
μ
s
4
π
∫
0
∞
dR
exp
[
-
(
μ
s
+
μ
a
)
R
]
[
ϕ
(
r
-
R
Ω
)
+
3
gJ
(
r
-
R
Ω
)
·
Ω
]
,
with I being a radiance, r being a position, Ω being a direction, R being a line of sight distance, ϕ being a fluence rate, and J being a flux density.
11. The system of claim 10 ,
wherein the macroscopic scattering coefficient is a function of a particle density in the moderately scattering aerosol, a particle diameter distribution, and scattering cross-sections of particles that are a function of particle diameter;
wherein the macroscopic absorption coefficient is a function of a particle density in the moderately scattering aerosol, a particle diameter distribution, and absorption cross-sections of particles that are a function of particle diameter;
wherein the macroscopic averaged anisotropy is a function of a particle density in the moderately scattering aerosol, a particle diameter distribution, scattering cross-sections of particles that are a function of particle diameter, and anisotropies of particles that are a function of particle diameter; and
wherein each of the macroscopic scattering coefficient, the macroscopic absorption coefficient, and the macroscopic averaged anisotropy is determined using the moderately scattering light transport model.
12. The system of claim 10 further comprising:
a transmissometer adapted to measure a particle density in the moderately scattering aerosol; and
a particle sizer adapted to measure a particle diameter distribution in the moderately scattering aerosol.
13. The system of claim 10 , wherein the step of determining the presence of the object determines the object is present when a decision statistic is greater than a detection threshold, the step of determining the presence of the object is present being based upon a likelihood ratio test.
14. The system of claim 13 ,
wherein the decision statistic is a function of a ratio of a probability density in a presence of the object to a probability density in an absence of the object; and
wherein the detection threshold is a function of a standard deviation of the decision statistic and an inverse complimentary error function of a specified false alarm rate.
15. The system of claim 13 , wherein the memory further stores instructions that, when executed by the processor, cause the processor to perform a step of when the object is determined to be present, determining a location of the object based upon a maximum likelihood estimation.
16. The system of claim 15 , wherein the memory further stores instructions that, when executed by the processor, cause the processor to perform a step of determining at least one of a size of the object, a shape of an object, or a reflectivity of the object, the step of determining at least one of a size of the object, a shape of the object, or a reflectivity of the object being based upon the maximum likelihood estimation.
17. The system of claim 10 , wherein the memory further stores instructions that, when executed by the processor, cause the processor to perform the step of determining the presence of the object employing a deep learning model.
18. The system of claim 17 , wherein the memory further stores instructions that, when executed by the processor, cause the processor to perform a step of determining a location of the object when the object is determined to be present, the step of determining a location of the object employing a deep learning model.
19. A non-transitory computer-readable storage media comprising instructions to determine a presence of an object in a moderately scattering aerosol with moving scatterers and a transport optical depth τ t between approximately 0.2 and 2, the instructions implement steps comprising:
determining a macroscopic scattering coefficient μ s of the moderately scattering aerosol using a moderately scattering light transport model, the macroscopic scattering coefficient μ s being a function of a particle density in the moderately scattering aerosol, a particle diameter distribution, and scattering cross-sections of particles that are a function of particle diameter;
determining a macroscopic absorption coefficient μ a of the moderately scattering aerosol using the moderately scattering light transport model, the macroscopic absorption coefficient La being a function of a particle density in the moderately scattering aerosol, a particle diameter distribution, and absorption cross-sections of particles that are a function of particle diameter;
determining a macroscopic averaged anisotropy g of the moderately scattering aerosol using the moderately scattering light transport model, the macroscopic averaged anisotropy g being a function of a particle density in the moderately scattering aerosol, a particle diameter distribution, scattering cross-sections of particles that are a function of particle diameter, and anisotropies of particles that are a function of particle diameter;
taking an image with a detector of a light source that emits light with a known power spectral density;
determining an expected background signal when the object is absent using the moderately scattering light transport model; and
subtracting the expected background signal from the image to thereby create a difference image; and determining the presence of the object based upon the difference image;
wherein the moderately scattering light transport model is:
I
(
r
,
Ω
)
=
μ
s
4
π
∫
0
∞
dR
exp
[
-
(
μ
s
+
μ
a
)
R
]
[
ϕ
(
r
-
R
Ω
)
+
3
gJ
(
r
-
R
Ω
)
·
Ω
]
,
with I being a radiance, r being a position, Ω being a direction, R being a line of sight distance, ϕ being a fluence rate, and J being a flux density.
20. The non-transitory computer-readable storage media of claim 19 ,
wherein the step of determining the presence of the object determines the object is present when a decision statistic is greater than a detection threshold, the step of determining the presence of the object being based upon a likelihood ratio test; and
wherein the steps further comprise a step of determining a location of the object when the object is determined to be present, the step of determining a location of the object being based upon a maximum likelihood estimation.