Polarimetric characterization of transparent objects
Existing Mueller Matrix polarization techniques that rely only on polarization properties are insufficient for accurate characterization of transparent objects. Embodiments of the present disclosure provide a method and system for Mueller Matrix polarimetric characterization of transparent object using optical properties along with the polarization properties to accurately characterize the transparent object. The polarization properties of are derived from a decomposed Mueller matrix element. Additionally, the method derives the optical properties by further subjecting the decomposed Mueller matrix element to Fresnel's law-based analysis and a reverse Monte Carlo analysis to extract optical properties such as a material refractive index and a material attenuation index. Optical properties vary with changes in the material property caused due to several factors such as manufacturing defect, aberration, inclusion of an impurity such as bubble or dust etc. Thus, considering the optical properties along with the polarization properties enables enhanced, accurate characterization of the transparent object.
1. A processor implemented method for Mueller Matrix polarimetric characterization of transparent objects, the method comprising:
receiving, by one or more hardware processors, a plurality transformed polarization states for a transparent object to be characterized, wherein the plurality transformed polarization states are recorded by a polarization camera when a polarized light of a plurality of known polarization states is incident onto the transparent object;
estimating, by or more hardware processors, a plurality of Mueller Matrix image elements by observing a change in the plurality of transformed polarization states while the polarized light propagates through the transparent object to form a Mueller Matrix;
computing, by the one or more hardware processors, a plurality of polarization properties of the transparent object by decomposing the Mueller Matrix as product of three elementary matrices comprising, a depolarizer (M Δ ), a retarder (M R ), and a diattenuator (M D ), wherein the plurality of polarization properties comprising a diattenuation (δ), a retardance (r), a depolarization (Δ), and an optical birefringence (ΔN);
computing, by the one or more hardware processors, a plurality of optical properties, of the transparent object from the decomposed Mueller Matrix, wherein the plurality of the optical properties comprise a material refractive index (n) and a material attenuation index (μ α ), wherein
the material refractive index (n) is determined from a first element of the Mueller Matrix M(1,1) using Fresnel's law-based analysis, which represents a total intensity of the polarized light, wherein the material refractive index (n) is calculated from the total intensity M (1,1) element of the Mueller Matrix with refractive index of an external medium and air=1, the M (1,1) is the first element of the Mueller Matrix, which represents total intensity of the polarization light using the Fresnel's law-based analysis is given by:
M
1
1
=
(
n
-
1
)
2
(
n
+
1
)
2
wherein the material refractive index is calculated as:
⇒
n
=
-
2
M
1
1
±
3
M
1
1
2
+
2
M
1
1
-
1
2
where n is the material refractive index; and
the material attenuation index (μ α ) is determined by processing the total intensity M (1,1) of the Mueller matrix by using a reverse Monte Carlo technique, wherein the material attenuation index reflecting presence of defect and refers to attenuation of light due to travelling through the transparent object is calculated from reflectance that is the total intensity M 11 of the Mueller matrix;
characterizing the transparent object, via an Artificial Intelligence (AI) model executed by the one or more hardware processors, during inferencing stage, wherein the characterizing of the transparent object is based on the computed plurality of polarization properties and the computed plurality of optical properties, and wherein to the AI model is pretrained with gold standard polarization properties and gold standard optical properties of transparent objects, wherein the inferences of the AI model on characterization of the transparent object is displayed to an end user to decide upon presence of defects of a material,
wherein the characterization refers to identifying deviations of the transparent object from inferences, which the deviations include manufacturing defect, aberration, inclusion of an impurity as bubble or dust in the transparent objects.
2. The method of claim 1 , wherein the material attenuation index (μ α ) is determined from the first element of the Mueller Matrix M(1,1) using the reverse Monte Carlo technique and comprises steps of a) forward Monte Carlo model derivation, b) reference experimental signal collection and c) the material attenuation index measurement and optimization.
3. A system, its method of use and its corresponding NTCRM, for Mueller Matrix polarimetric characterization of transparent objects, the system comprising: a memory storing instructions; one or more Input/Output (I/O) interfaces; and one or more hardware processors coupled to the memory via the one or more I/O interfaces, wherein the one or more hardware processors are configured by the instructions to: receive a plurality transformed polarization states for a transparent object to be characterized, wherein the plurality transformed polarization states are recorded by a polarization camera when a polarized light of a plurality of known polarization states is incident onto the transparent object; estimate a plurality of Mueller Matrix image elements by observing a change in the plurality of transformed polarization states while the polarized light propagates through the transparent object to form a Mueller Matrix; compute, a plurality of polarization properties of the transparent object by decomposing the Mueller Matrix as product of three elementary matrices comprising, a depolarizer (M Δ ), a retarder (M R ), and a diattenuator (M D ), wherein the plurality of polarization properties comprising a diattenuation (δ), a retardance (r), a depolarization (Δ), and an optical birefringence (ΔN); compute a plurality of optical properties, of the transparent object from the decomposed Mueller Matrix, wherein the plurality of the optical properties comprise a material refractive index (n) and a material attenuation index (ρ α ), wherein the material refractive index (n) is determined from a first element of the Mueller Matrix M(1,1) using Fresnel's law-based analysis, which represents a total intensity of the polarized light, wherein the material refractive index (n) is calculated from the total intensity M (1,1) element of the Mueller Matrix with refractive index of an external medium and air=1, the M (1,1) is the first element of the Mueller Matrix, which represents total intensity of the polarization light using the Fresnel's law-based analysis is given by:
M
11
=
(
n
-
1
)
2
(
n
+
1
)
2
wherein the material refractive index is calculated as:
M
11
=
(
n
-
1
)
2
(
n
+
1
)
2
where n is the material refractive index; and the material attenuation index (μ α ) is determined by processing the total intensity M (1,1) of the Mueller matrix by using a reverse Monte Carlo technique, wherein the material attenuation index reflecting presence of defect and refers to attenuation of light due to travelling through the transparent object is calculated from reflectance that is the total intensity M, of the Mueller matrix; characterize the transparent object via an Artificial Intelligence (AI) model executed by the one or more hardware processors, during inferencing stage, wherein the characterizing of the transparent object is based on the computed plurality of polarization properties and the computed plurality of optical properties, and wherein to the AI model is pretrained with gold standard polarization properties and gold standard optical properties of transparent objects, wherein the inferences of the AI model on characterization of the transparent object is displayed to an end user to decide upon presence of defects of a material, wherein the characterization refers to identifying deviations of the transparent object from inferences, which the deviations include manufacturing defect, aberration, inclusion of an impurity as bubble or dust in the transparent objects.
4. The system of claim 3 , wherein the material attenuation index (μ α ) is determined from the first element of the Mueller Matrix M(1,1) using the reverse Monte Carlo technique and comprises steps of a) forward Monte Carlo model derivation, b) reference experimental signal collection and c) the material attenuation index measurement and optimization.
5. One or more non-transitory machine-readable information storage mediums comprising one or more instructions which when executed by one or more hardware processors cause:
receiving, by one or more hardware processors, a plurality transformed polarization states for a transparent object to be characterized, wherein the plurality transformed polarization states are recorded by a polarization camera when a polarized light of a plurality of known polarization states is incident onto the transparent object;
estimating, by or more hardware processors, a plurality of Mueller Matrix image elements by observing a change in the plurality of transformed polarization states while the polarized light propagates through the transparent object to form a Mueller Matrix;
computing, by the one or more hardware processors, a plurality of polarization properties of the transparent object by decomposing the Mueller Matrix as product of three elementary matrices comprising, a depolarizer (M Δ ), a retarder (M R ), and a diattenuator (M D ), wherein the plurality of polarization properties comprising a diattenuation (δ), a retardance (r), a depolarization (Δ), and an optical birefringence (ΔN);
computing, by the one or more hardware processors, a plurality of optical properties, of the transparent object from the decomposed Mueller Matrix, wherein the plurality of the optical properties comprise a material refractive index (n) and a material attenuation index (μ α ), wherein
the material refractive index (n) is determined from a first element of the Mueller Matrix M(1,1) using Fresnel's law-based analysis, which represents a total intensity of the polarized light, wherein the material refractive index (n) is calculated from the total intensity M (1,1) element of the Mueller Matrix with refractive index of an external medium and air=1, the M (1,1) is the first element of the Mueller Matrix, which represents total intensity of the polarization light using the Fresnel's law-based analysis is given by:
M
1
1
=
(
n
-
1
)
2
(
n
+
1
)
2
wherein the material refractive index is calculated as:
⇒
n
=
-
2
M
1
1
±
3
M
1
1
2
+
2
M
1
1
-
1
2
where n is the material refractive index; and
the material attenuation index (μ α ) is determined by processing the by using a reverse Monte Carlo technique, wherein the material attenuation index reflecting presence of defect and refers to attenuation of light due to travelling through the transparent object is calculated from reflectance that is the total intensity M 11 of the Mueller matrix;
characterizing the transparent object, via an Artificial Intelligence (AI) model executed by the one or more hardware processors, during inferencing stage, wherein the characterizing of the transparent object is based on the computed plurality of polarization properties and the computed plurality of optical properties, and wherein to the AI model is pretrained with gold standard polarization properties and gold standard optical properties of transparent objects, wherein the inferences of the AI model on characterization of the transparent object is displayed to an end user to decide upon presence of defects of a material,
wherein the characterization refers to identifying deviations of the transparent object from inferences, which the deviations include manufacturing defect, aberration, inclusion of an impurity as bubble or dust in the transparent objects.
6. The one or more non-transitory machine-readable information storage mediums of claim 5 , wherein the material attenuation index (μ α ) is determined from the first element of the Mueller Matrix M(1,1) using the reverse Monte Carlo technique and comprises steps of a) forward Monte Carlo model derivation, b) reference experimental signal collection and c) the material attenuation index measurement and optimization.