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Methods And Systems For Monitoring Lubricant Oil Condition Using Photoacoustic Modelling

Abstract: ABSTRACT METHODS AND SYSTEMS FOR MONITORING LUBRICANT OIL CONDITION USING PHOTOACOUSTIC MODELLING The disclosure relates generally to methods and systems for monitoring lubricant oil condition using a photoacoustic modelling. Conventional techniques in the art for checking the condition of the lubricant oil is laboratory based and thus time consuming, error prone and not efficient. The present disclosure discloses a photoacoustic simulation model which is developed utilizing a photonic model such as a Monte Carlo method-based optical simulation integrated with a finite element model such as a k-wave toolbox-based acoustic measurement. The photoacoustic simulation model of the present disclosure is used to obtain a photoacoustic signal of the lubricant oil sample and a set of statistical features are determined from the obtained photoacoustic signal. The determined set of statistical features are then used as a training data to develop a machine learning (ML) model which is used to classify a type of contamination of the test lubricating oil. [To be published with FIG. 3]

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Patent Information

Application #
Filing Date
12 August 2022
Publication Number
07/2024
Publication Type
INA
Invention Field
ELECTRONICS
Status
Email
Parent Application

Applicants

Tata Consultancy Services Limited
Nirmal Building, 9th floor, Nariman point, Mumbai 400021, Maharashtra, India

Inventors

1. CHATTERJEE, Subhasri
Tata Consultancy Services Limited, Block -1B, Eco Space, Plot No. IIF/12 (Old No. AA-II/BLK 3. I.T) Street 59 M. WIDE (R.O.W.) Road, New Town, Rajarhat, P.S. Rajarhat, Dist - N. 24 Parganas, Kolkata 700160, West Bengal, India
2. GOREY, Abhijit
Tata Consultancy Services Limited, Block -1B, Eco Space, Plot No. IIF/12 (Old No. AA-II/BLK 3. I.T) Street 59 M. WIDE (R.O.W.) Road, New Town, Rajarhat, P.S. Rajarhat, Dist - N. 24 Parganas, Kolkata 700160, West Bengal, India
3. SINHARAY, Arijit
Tata Consultancy Services Limited, Block -1B, Eco Space, Plot No. IIF/12 (Old No. AA-II/BLK 3. I.T) Street 59 M. WIDE (R.O.W.) Road, New Town, Rajarhat, P.S. Rajarhat, Dist - N. 24 Parganas, Kolkata 700160, West Bengal, India
4. BHAUMIK, Chirabrata
Tata Consultancy Services Limited, Block -1B, Eco Space, Plot No. IIF/12 (Old No. AA-II/BLK 3. I.T) Street 59 M. WIDE (R.O.W.) Road, New Town, Rajarhat, P.S. Rajarhat, Dist - N. 24 Parganas, Kolkata 700160, West Bengal, India
5. CHAKRAVARTY, Tapas
Tata Consultancy Services Limited, Block -1B, Eco Space, Plot No. IIF/12 (Old No. AA-II/BLK 3. I.T) Street 59 M. WIDE (R.O.W.) Road, New Town, Rajarhat, P.S. Rajarhat, Dist - N. 24 Parganas, Kolkata 700160, West Bengal, India
6. GAIN, Supriya
Tata Consultancy Services Limited, Block -1B, Eco Space, Plot No. IIF/12 (Old No. AA-II/BLK 3. I.T) Street 59 M. WIDE (R.O.W.) Road, New Town, Rajarhat, P.S. Rajarhat, Dist - N. 24 Parganas, Kolkata 700160, West Bengal, India
7. PAL, Arpan
Tata Consultancy Services Limited, Block -1B, Eco Space, Plot No. IIF/12 (Old No. AA-II/BLK 3. I.T) Street 59 M. WIDE (R.O.W.) Road, New Town, Rajarhat, P.S. Rajarhat, Dist - N. 24 Parganas, Kolkata 700160, West Bengal, India

Specification

Description:FORM 2

THE PATENTS ACT, 1970
(39 of 1970)
&
THE PATENT RULES, 2003

COMPLETE SPECIFICATION
(See Section 10 and Rule 13)

Title of invention:

METHODS AND SYSTEMS FOR MONITORING LUBRICANT OIL CONDITION USING PHOTOACOUSTIC MODELLING

Applicant

Tata Consultancy Services Limited
A company Incorporated in India under the Companies Act, 1956
Having address:
Nirmal Building, 9th floor,
Nariman point, Mumbai 400021,
Maharashtra, India

Preamble to the description:
The following specification particularly describes the invention and the manner in which it is to be performed.
TECHNICAL FIELD
The disclosure herein generally relates to the field of lubricant oil condition analysis, and more specifically to methods and systems for monitoring lubricant oil condition using a photoacoustic modelling.

BACKGROUND
Analysis of lubricating oil is an effective approach in investigating the condition of a machine and providing an early warning of any failure in the performance and progression of the machine. Several sensing mechanisms are explored to depict different thermal, physical, and inherent properties of the lubricating oil for machine health monitoring. However, the standard industrial procedure for the oil inspection is time consuming and laborious.
Out of the different properties of the lubricating oil, one of the key thermophysical properties is a viscosity that changes with different parameters such as water ingress, soot particle contamination etc., occurring due to different faults of the machine. Conventional techniques in the art to measure the viscosity are usually laborious (i.e., taking the sample for chemical analysis, etc.), time-consuming and involve complex post-processing of data. A convenient approach to investigate the causality of machine faults and determine the viscosity of lubrication oil would need a multiparametric sophisticated robust measurement system. However, it is technically challenging to execute experiments in the lab with an industry-standard oil having variable contaminants. Hence the conventional solutions in the art for checking the condition of the lubricant oil is time consuming, error prone and not efficient.

SUMMARY
Embodiments of the present disclosure present technological improvements as solutions to one or more of the above-mentioned technical problems recognized by the inventors in conventional systems.
In an aspect, a processor-implemented method for monitoring lubricant oil condition using a photoacoustic modelling is provided. The method including the steps of: receiving a plurality of lubricant oil samples, and a classification label for each of the plurality of lubricant oil samples; simulating each lubricant oil sample, to obtain a plurality of simulated photoacoustic signals from the plurality of lubricant oil samples, using a photoacoustic simulation model; determining one or more statistical features, for each lubricant oil sample, from the corresponding simulated photoacoustic signal, using a signal processing technique; training a machine learning (ML) model with (i) the one or more statistical features for each lubricant oil sample of the plurality of lubricant oil samples and (ii) the classification label for each of the plurality of lubricant oil samples, to obtain a trained ML model; receiving a test lubricant oil sample for which the lubricant oil condition to be monitored; determining a test photoacoustic signal from the test lubricant oil sample, using an experimental model; determining the one or more statistical features of the test lubricant oil sample, from the test photoacoustic signal, using the signal processing technique; and passing the one or more statistical features of the test lubricant oil sample, to the trained ML model, to obtain the classification label for the lubricant oil sample, wherein the classification label provides the lubricant oil condition of the test lubricant oil sample.
In another aspect, a system for monitoring a lubricant oil condition using a photoacoustic simulation model is provided. The system includes: 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 of lubricant oil samples, and a classification label for each of the plurality of lubricant oil samples; simulate each lubricant oil sample, to obtain a plurality of simulated photoacoustic signals from the plurality of lubricant oil samples, using a photoacoustic simulation model; determine one or more statistical features, for each lubricant oil sample, from the corresponding simulated photoacoustic signal, using a signal processing technique; train a machine learning (ML) model with (i) the one or more statistical features for each lubricant oil sample of the plurality of lubricant oil samples and (ii) the classification label for each of the plurality of lubricant oil samples, to obtain a trained ML model; receive a test lubricant oil sample for which the lubricant oil condition to be monitored; determine a test photoacoustic signal from the test lubricant oil sample, using an experimental model; determine the one or more statistical features of the test lubricant oil sample, from the test photoacoustic signal, using the signal processing technique; and pass the one or more statistical features of the test lubricant oil sample, to the trained ML model, to obtain the classification label for the lubricant oil sample, wherein the classification label provides the lubricant oil condition of the test lubricant oil sample.
In yet another aspect, there is provided a computer program product comprising a non-transitory computer readable medium having a computer readable program embodied therein, wherein the computer readable program, when executed on a computing device, causes the computing device to: receive a plurality of lubricant oil samples, and a classification label for each of the plurality of lubricant oil samples; simulate each lubricant oil sample, to obtain a plurality of simulated photoacoustic signals from the plurality of lubricant oil samples, using a photoacoustic simulation model; determine one or more statistical features, for each lubricant oil sample, from the corresponding simulated photoacoustic signal, using a signal processing technique; train a machine learning (ML) model with (i) the one or more statistical features for each lubricant oil sample of the plurality of lubricant oil samples and (ii) the classification label for each of the plurality of lubricant oil samples, to obtain a trained ML model; receive a test lubricant oil sample for which the lubricant oil condition to be monitored; determine a test photoacoustic signal from the test lubricant oil sample, using an experimental model; determine the one or more statistical features of the test lubricant oil sample, from the test photoacoustic signal, using the signal processing technique; and pass the one or more statistical features of the test lubricant oil sample, to the trained ML model, to obtain the classification label for the lubricant oil sample, wherein the classification label provides the lubricant oil condition of the test lubricant oil sample.
In an embodiment, determining the test photoacoustic signal from the test lubricant oil sample, using the experimental model, comprising: obtaining a modulated signal for the test lubricant oil sample, using an arbitrary waveform generator; obtaining an intensity modulated laser signal for the test lubricant oil sample, by passing the modulated signal to a continuous wave laser source; obtaining an ultrasound signal for the test lubricant oil sample, by irradiating the intensity modulated laser signal on the test lubricant oil sample using an ultrasound sensor; and obtaining the test photoacoustic signal for the test lubricant oil sample, by correlating the modulated signal and the ultrasound signal.
In an embodiment, simulating each lubricant oil sample to obtain corresponding simulated photoacoustic signal, using the photoacoustic simulation model, comprising: determining one or more optical parameters, a contaminant concentration, a temperature, and one or more acoustic parameters, for the corresponding lubricant oil sample; determining a fluence for the corresponding lubricant oil sample, based on the one or more optical parameters and the contaminant concentration, using a photonic model; generating an initial acoustic pressure signal for the lubricant oil sample, using a finite element technique based on the one or more acoustic parameters, the contaminant concentration, the temperature, and the fluence; propagating the initial acoustic pressure signal to obtain a propagated acoustic pressure signal for the corresponding lubricant oil sample, using the finite element technique; and obtaining the simulated photoacoustic signal for the corresponding lubricant oil sample, by correlating the initial acoustic pressure signal and the propagated acoustic pressure signal.
In an embodiment, the one or more statistical features for each lubricant oil sample, are determined from a time-frequency signal of the corresponding simulated photoacoustic signal.
In an embodiment, the one or more statistical features of the test lubricant oil sample, are determined from a time-frequency signal of the test photoacoustic signal.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention, as claimed.

BRIEF DESCRIPTION OF THE DRAWINGS
The accompanying drawings, which are incorporated in and constitute a part of this disclosure, illustrate exemplary embodiments and, together with the description, serve to explain the disclosed principles:
FIG. 1 is an exemplary block diagram of a system for monitoring lubricant oil condition using a photoacoustic modeling, in accordance with some embodiments of the present disclosure.
FIGS. 2A and 2B illustrates exemplary flow diagrams of a processor-implemented method for monitoring lubricant oil condition using a photoacoustic modelling, in accordance with some embodiments of the present disclosure.
FIG. 3 is an exemplary block diagram of a photoacoustic simulation model, in accordance with some embodiments of the present disclosure.
FIG. 4 is an exemplary block diagram of an experimental model, in accordance with some embodiments of the present disclosure.
FIG. 5A and 5B are graphs showing photoacoustic signals of a lubricant oil sample obtained by the photoacoustic simulation model and the experimental model, in accordance with some embodiments of the present disclosure.

DETAILED DESCRIPTION OF EMBODIMENTS
Exemplary embodiments are described with reference to the accompanying drawings. In the figures, the left-most digit(s) of a reference number identifies the figure in which the reference number first appears. Wherever convenient, the same reference numbers are used throughout the drawings to refer to the same or like parts. While examples and features of disclosed principles are described herein, modifications, adaptations, and other implementations are possible without departing from the scope of the disclosed embodiments.
The present disclosure solves the technical problems in the art for monitoring lubricant oil condition using a multiparametric and hybrid sensing methods is a photoacoustic sensing which is applied to investigate the viscosity of the lubrication oil and depict the fault of the machine. The photoacoustic sensing is one of the emerging technologies for non-invasive sensing of fluid properties with high sensitivity. The potential of the photoacoustic sensing to probe lubrication oil has not greatly explored by the researchers, probably due to the inconvenience to execute experiments in the lab with an industry-standard oil having variable contaminants. To understand the working principle of the technology and design a multiparametric measurement system for oil quality determination based on photoacoustic sensing, and to overcome the experimental limitations, a model-based investigation is imperative.
Hence the methods and systems of the present invention discloses a photoacoustic simulation model which is a robust in silico model of photoacoustic-oil interaction. In an embodiment, the photoacoustic simulation model of the present disclosure is developed utilizing a photonic model such as a Monte Carlo method-based optical simulation integrated with a finite element model such as a k-wave toolbox-based acoustic measurement. The photoacoustic simulation model of the present disclosure is used to obtain a photoacoustic signal of the lubricant oil sample and a set of statistical features are determined from the obtained photoacoustic signal. The determined set of statistical features are then used as a training data to develop a machine learning (ML) model. Then, the photoacoustic signal of the test lubricant oil sample whose condition to be monitored, is obtained using an experimental model, which is passed to the developed ML model to classify a type of contamination of the test lubricating oil sample.
Referring now to the drawings, and more particularly to FIG. 1 through FIG. 5B, where similar reference characters denote corresponding features consistently throughout the figures, there are shown preferred embodiments and these embodiments are described in the context of the following exemplary systems and/or methods.
FIG. 1 is an exemplary block diagram of a system 100 for monitoring lubricant oil condition using a photoacoustic modelling, in accordance with some embodiments of the present disclosure. In an embodiment, the system 100 includes or is otherwise in communication with one or more hardware processors 104, communication interface device(s) or input/output (I/O) interface(s) 106, and one or more data storage devices or memory 102 operatively coupled to the one or more hardware processors 104. The one or more hardware processors 104, the memory 102, and the I/O interface(s) 106 may be coupled to a system bus 108 or a similar mechanism.
The I/O interface(s) 106 may include a variety of software and hardware interfaces, for example, a web interface, a graphical user interface, and the like. The I/O interface(s) 106 may include a variety of software and hardware interfaces, for example, interfaces for peripheral device(s), such as a keyboard, a mouse, an external memory, a plurality of sensor devices, a printer and the like. Further, the I/O interface(s) 106 may enable the system 100 to communicate with other devices, such as web servers and external databases.
The I/O interface(s) 106 can facilitate multiple communications within a wide variety of networks and protocol types, including wired networks, for example, local area network (LAN), cable, etc., and wireless networks, such as Wireless LAN (WLAN), cellular, or satellite. For the purpose, the I/O interface(s) 106 may include one or more ports for connecting a number of computing systems with one another or to another server computer. Further, the I/O interface(s) 106 may include one or more ports for connecting a number of devices to one another or to another server.
The one or more hardware processors 104 may be implemented as one or more microprocessors, microcomputers, microcontrollers, digital signal processors, central processing units, state machines, logic circuitries, and/or any devices that manipulate signals based on operational instructions. Among other capabilities, the one or more hardware processors 104 are configured to fetch and execute computer-readable instructions stored in the memory 102. In the context of the present disclosure, the expressions ‘processors’ and ‘hardware processors’ may be used interchangeably. In an embodiment, the system 100 can be implemented in a variety of computing systems, such as laptop computers, portable computers, notebooks, hand-held devices, workstations, mainframe computers, servers, a network cloud and the like.
The memory 102 may include any computer-readable medium known in the art including, for example, volatile memory, such as static random access memory (SRAM) and dynamic random access memory (DRAM), and/or non-volatile memory, such as read only memory (ROM), erasable programmable ROM, flash memories, hard disks, optical disks, and magnetic tapes. In an embodiment, the memory 102 includes a plurality of modules 102a and a repository 102b for storing data processed, received, and generated by one or more of the plurality of modules 102a. The plurality of modules 102a may include routines, programs, objects, components, data structures, and so on, which perform particular tasks or implement particular abstract data types.
The plurality of modules 102a may include programs or computer-readable instructions or coded instructions that supplement applications or functions performed by the system 100. The plurality of modules 102a may also be used as, signal processor(s), state machine(s), logic circuitries, and/or any other device or component that manipulates signals based on operational instructions. Further, the plurality of modules 102a can be used by hardware, by computer-readable instructions executed by the one or more hardware processors 104, or by a combination thereof. In an embodiment, the plurality of modules 102a can include various sub-modules (not shown in FIG. 1). Further, the memory 102 may include information pertaining to input(s)/output(s) of each step performed by the processor(s) 104 of the system 100 and methods of the present disclosure.
The repository 102b may include a database or a data engine. Further, the repository 102b amongst other things, may serve as a database or includes a plurality of databases for storing the data that is processed, received, or generated as a result of the execution of the plurality of modules 102a. Although the repository 102b is shown internal to the system 100, it will be noted that, in alternate embodiments, the repository 102b can also be implemented external to the system 100, where the repository 102b may be stored within an external database (not shown in FIG. 1) communicatively coupled to the system 100. The data contained within such external database may be periodically updated. For example, data may be added into the external database and/or existing data may be modified and/or non-useful data may be deleted from the external database. In one example, the data may be stored in an external system, such as a Lightweight Directory Access Protocol (LDAP) directory and a Relational Database Management System (RDBMS). In another embodiment, the data stored in the repository 102b may be distributed between the system 100 and the external database.
Referring to FIGS. 2A and 2B, components and functionalities of the system 100 are described in accordance with an example embodiment of the present disclosure. For example, FIGS. 2A and 2B illustrates exemplary flow diagrams of a processor-implemented method 200 for monitoring lubricant oil condition using a photoacoustic modelling, in accordance with some embodiments of the present disclosure. Although steps of the method 200 including process steps, method steps, techniques or the like may be described in a sequential order, such processes, methods and techniques may be configured to work in alternate orders. In other words, any sequence or order of steps that may be described does not necessarily indicate a requirement that the steps be performed in that order. The steps of processes described herein may be performed in any practical order. Further, some steps may be performed simultaneously, or some steps may be performed alone or independently.
At step 202 of the method 200, the one or more hardware processors 104 of the system 100 are configured to receive a plurality of lubricant oil samples, and a classification label associated with each lubricant oil sample of the plurality of lubricant oil samples. In an embodiment, the plurality of lubricant oil samples is received in the form of measurement signals which may be obtained when the lubricant oil samples are passes through a measurement sensor.
The plurality of lubricant oil samples includes contaminated lubricant oil samples and non-contaminated lubricant oil samples. The contaminated lubricant oil samples are associated with the used lubricant oils may be obtained from machineries where the lubricant oils were used. In an embodiment, the machineries include but are not limited to industrial machineries, non-industrial machineries, and vehicles.
The classification label associated with each lubricant oil sample, defines the contamination type of the corresponding lubricant oil sample. The contamination type includes a ‘contaminated’ and a ‘non-contaminated’ label. Further, the ‘contaminated’ label further sub-labels, for example, whether contaminated with water ingress, whether contaminated with soot particle, whether contaminated with water ingress and soot particle, and so on. Hence an exemplary classification label list includes: ‘non-contaminated’, ‘contaminated with water ingress’, ‘contaminated with soot particle’, ‘contaminated with water ingress and soot particle’, ‘contaminated with others’.
At step 204 of the method 200, the one or more hardware processors 104 of the system 100 are configured to simulate each lubricant oil sample of the plurality of lubricant oil samples received at step 202 of the method 200, to obtain corresponding simulated photoacoustic signal. A photoacoustic simulation model is used for simulating each lubricant oil sample to obtain the corresponding simulated photoacoustic signal. After the simulation, the plurality of simulated photoacoustic signals is obtained from the plurality of lubricant oil samples.
The photoacoustic simulation model makes use of both optical parameters and the acoustic parameters of the corresponding lubricant oil sample for the simulation to obtain the corresponding simulated photoacoustic signal. FIG. 3 is an exemplary block diagram of the photoacoustic simulation model 300, in accordance with some embodiments of the present disclosure. As shown in FIG. 3, the photoacoustic simulation model 300 includes a photonic model 302, a first finite element model 304, a second finite element model 306, and a first signal correlation unit 308. The first finite element model 304 and the second finite element model 306 are identical to each other. The simulation of each lubricant oil sample to obtain the corresponding simulated photoacoustic signal, using the photoacoustic simulation model 300 is explained in the below steps:
At the first step, one or more optical parameters, a contaminant concentration, a temperature, and one or more acoustic parameters, of the corresponding lubricant oil sample are determined. In an embodiment, the one or more optical parameters of the lubricant oil sample are the optical parameters selected from a list consisting of: an optical absorption coefficient µ_a, a scattering coefficient µ_s and a scattering anisotropy g. The one or more optical parameters of the lubricant oil sample are determined based on a predefined optical wavelength. In an embodiment, the predefined optical wavelength is 450 nm. Further, a sinusoidal beam of incident from a source with a diameter of 1 mm is considered for determining the one or more optical parameters.
The contaminant concentration of the lubricant oil sample is determined in the form of an effective absorption coefficient (?µ_a?_(o_eff )). For example, if the lubricant oil sample is contaminated with the water, then among the water and the oil, the water greatly affects the absorption of light. Hence the effective absorption coefficient (?µ_a?_(o_eff )) is determined based on an absorption coefficients of water ?µ_a?_W and the absorption coefficients of oil ?µ_a?_o at the wavelength 450 nm, using an equation 1:
?µ_a?_(o_eff )=V_w.µ_(a_w )+(1-V_w).?µ_a?_o……(1)
where V_w is a volume fraction of the water contamination within the oil.
Further, at the operating wavelength of 450 nm, the absorption coefficient of the oil ?µ_a?_o is experimentally acquired using spectroscopic measurements in the laboratory, i.e., ?µ_a?_o=3.23 mm^(-1). The absorption coefficient of water ?µ_a?_W at this wavelength is adapted from literature, i.e., ?µ_a?_w=4×10^(-3) mm^(-1) . The scattering coefficient and the anisotropy factor of the lubricant oil at the operating wavelength are adapted from literature as ?µ_s?_o=132.29mm^(-1) and g_o=0.86, respectively. Based on the experimental analysis, the soot particle concentration is varied from 0-8%, and that for water is varied from 0-2%, both with an interval of 0.1%.
The temperature for the corresponding lubricant oil sample is obtained through a temperature measurement sensor.
The one or more acoustic parameters includes a speed of sound, a density of the contaminated oil and a Grüneisen parameter. The speed of sound is considered to be approximately 1500 m/s at a temperature of 30^0C. The density of the oil effectively changes with the soot particle. The effective density d_(o_eff ) is considered as in equation 2:
d_(o_eff )=d_s+d_o……(2)
where d_s is the concentration of the soot particle, and d_o is the density of pure oil d_o=0.85g/cm^3.
Another acoustic parameter used is the Grüneisen parameter t which is a temperature dependent quantity depicting the lattice structure of the oil sample. For lubricant oil, this parameter is considered 0.85 at 30^0C temperature as found in literature.
At the second step, a fluence for the corresponding lubricant oil sample, is determined based on the one or more optical parameters and the contaminant concentration of the corresponding lubricant oil sample received at the first step, using the photonic model 302. The photonic model 302 is any simulation model which is able to determine the fluence using the optical parameters and the contaminant concentration.
In an embodiment, the photonic model 302 is a Monte Carlo simulation model which is a stochastic process to trace photon paths through a medium by random sampling of the probability distribution of the optical interaction properties such as scattering and absorption. The migration of photons from a laser source was simulated through the medium in random step sizes (s) calculated based on the probability distribution of the scattering through the medium as a function of the scattering coefficient µ_s as shown in the equation 3:
s= -ln?/µ_s ……(3)
where ? is a computer generated pseudo-random number lying between 0 to 1, and the probability distribution of scattering (p_s) was calculated by the equation 4:
p_s=?_0^X¦?µ_s e^(-µ_s x) dx ?……(4)
The scattering angle was calculated based on the Henyey Greenstein phase function, generating the probability p(?) of the photon being scattered in a direction as a function of the anisotropy factor g, as shown in equation 5:
p(?)=1/4p (1-g^2)/(1+g^2-2g Cos?)^(3/2) ……(5)
The scattering angle ? was calculated from the probability distribution function as a function of a random number ? (0

Documents

Application Documents

# Name Date
1 202221046212-STATEMENT OF UNDERTAKING (FORM 3) [12-08-2022(online)].pdf 2022-08-12
2 202221046212-REQUEST FOR EXAMINATION (FORM-18) [12-08-2022(online)].pdf 2022-08-12
3 202221046212-FORM 18 [12-08-2022(online)].pdf 2022-08-12
4 202221046212-FORM 1 [12-08-2022(online)].pdf 2022-08-12
5 202221046212-FIGURE OF ABSTRACT [12-08-2022(online)].pdf 2022-08-12
6 202221046212-DRAWINGS [12-08-2022(online)].pdf 2022-08-12
7 202221046212-DECLARATION OF INVENTORSHIP (FORM 5) [12-08-2022(online)].pdf 2022-08-12
8 202221046212-COMPLETE SPECIFICATION [12-08-2022(online)].pdf 2022-08-12
9 202221046212-Proof of Right [08-09-2022(online)].pdf 2022-09-08
10 202221046212-FORM-26 [20-09-2022(online)].pdf 2022-09-20
11 Abstract1.jpg 2022-11-24
12 202221046212-Power of Attorney [25-08-2023(online)].pdf 2023-08-25
13 202221046212-Form 1 (Submitted on date of filing) [25-08-2023(online)].pdf 2023-08-25
14 202221046212-Covering Letter [25-08-2023(online)].pdf 2023-08-25
15 202221046212 CORRESPONDANCE (WIPO DAS) 06-09-2023.pdf 2023-09-06
16 202221046212-FORM 3 [15-01-2024(online)].pdf 2024-01-15
17 202221046212-FER.pdf 2025-11-18

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1 202221046212_SearchStrategyNew_E_202221046212E_31-07-2025.pdf