Estimation of the Sensitivity of a Multi-Parameter Fiber Grating Sensor
Апстракт
In this paper, we use a powerful mathematical concept based on Fisher information (FI) to estimate the cross-sensitivity of multi-parameter sensors. FI has been used in various branches of natural and social sciences [1], in both classical and quantum systems [2]. Lately, it has been used for estimation of interferometer sensitivity in quantum optics [3], as well as in classical optical interferometers [4]. Here, we expand its application to fibre grating sensors that are sensitive to several environmental (temperature, humidity) and mechanical (strain, pressure, curvature) parameters simultaneously [5]. FI is a local probability measure of obtaining an unknown parameter θ from the data measured at the sensor output, X. In the theory of measurement, FI directly enters the relation which determines the lower bound of the measurement uncertainty known as Cramer-Rao bound (CRB = 1/ FI (θ ) ). The sensor sensitivity is optimized by maximization of the corresponding FI. In the case of a mul...ti-parameter sensor, FI assumes a matrix form defined via the probability distribution function f(X| θ) of the measured variable X conditioned by θ, where both X and θ are vector quantities. ( ) ( ) i n j n f X FI E i j i j ; 1,2,... ; 1,2,..., 2 ln , = = ∂ ∂ ∂ = − θ θ θ θ . Here, we develop a comprehensive model of the spectral response of fibre gratings to changes in multiple parameters and apply Fisher's formalism to optimize their sensitivity in the realistic parameter space. We start from a 1-parameter model of a long-period grating sensor of curvature and corroborate our approach by comparison with the conventional sensitivity models and the experimental data. We then expand the model to describe a 2-parameter long-period grating sensor of curvature and temperature. Based on this analysis, we recommend the multi-parameter interrogation scheme (estimator) and optimize grating parameters to render the highest sensitivity.
Извор:
PHOTONICA2015 : 5th International School and Conference on Photonics and COST actions: MP1204, BM1205 and MP1205 : book of abstracts; August 24-28, 2015; Belgrade, 2015, 173-173Издавач:
- Belgrade : Vinča Institute of Nuclear Sciences
Напомена:
- V International School and Conference on Photonics and COST actions: MP1204, BM1205 and MP1205 and the Second international workshop "Control of light and matter waves propagation and localization in photonic lattices" : PHOTONICA2015 : book of abstracts; August 24-28, 2015; Belgrade
Колекције
Институција/група
VinčaTY - CONF AU - Raičević, Nevena AU - Ivanović, Marija D. AU - Beličev, Petra AU - Maluckov, Aleksandra AU - Petrović, Jovana PY - 2015 UR - https://vinar.vin.bg.ac.rs/handle/123456789/12012 AB - In this paper, we use a powerful mathematical concept based on Fisher information (FI) to estimate the cross-sensitivity of multi-parameter sensors. FI has been used in various branches of natural and social sciences [1], in both classical and quantum systems [2]. Lately, it has been used for estimation of interferometer sensitivity in quantum optics [3], as well as in classical optical interferometers [4]. Here, we expand its application to fibre grating sensors that are sensitive to several environmental (temperature, humidity) and mechanical (strain, pressure, curvature) parameters simultaneously [5]. FI is a local probability measure of obtaining an unknown parameter θ from the data measured at the sensor output, X. In the theory of measurement, FI directly enters the relation which determines the lower bound of the measurement uncertainty known as Cramer-Rao bound (CRB = 1/ FI (θ ) ). The sensor sensitivity is optimized by maximization of the corresponding FI. In the case of a multi-parameter sensor, FI assumes a matrix form defined via the probability distribution function f(X| θ) of the measured variable X conditioned by θ, where both X and θ are vector quantities. ( ) ( ) i n j n f X FI E i j i j ; 1,2,... ; 1,2,..., 2 ln , = = ∂ ∂ ∂ = − θ θ θ θ . Here, we develop a comprehensive model of the spectral response of fibre gratings to changes in multiple parameters and apply Fisher's formalism to optimize their sensitivity in the realistic parameter space. We start from a 1-parameter model of a long-period grating sensor of curvature and corroborate our approach by comparison with the conventional sensitivity models and the experimental data. We then expand the model to describe a 2-parameter long-period grating sensor of curvature and temperature. Based on this analysis, we recommend the multi-parameter interrogation scheme (estimator) and optimize grating parameters to render the highest sensitivity. PB - Belgrade : Vinča Institute of Nuclear Sciences C3 - PHOTONICA2015 : 5th International School and Conference on Photonics and COST actions: MP1204, BM1205 and MP1205 : book of abstracts; August 24-28, 2015; Belgrade T1 - Estimation of the Sensitivity of a Multi-Parameter Fiber Grating Sensor SP - 173 EP - 173 UR - https://hdl.handle.net/21.15107/rcub_vinar_12012 ER -
@conference{ author = "Raičević, Nevena and Ivanović, Marija D. and Beličev, Petra and Maluckov, Aleksandra and Petrović, Jovana", year = "2015", abstract = "In this paper, we use a powerful mathematical concept based on Fisher information (FI) to estimate the cross-sensitivity of multi-parameter sensors. FI has been used in various branches of natural and social sciences [1], in both classical and quantum systems [2]. Lately, it has been used for estimation of interferometer sensitivity in quantum optics [3], as well as in classical optical interferometers [4]. Here, we expand its application to fibre grating sensors that are sensitive to several environmental (temperature, humidity) and mechanical (strain, pressure, curvature) parameters simultaneously [5]. FI is a local probability measure of obtaining an unknown parameter θ from the data measured at the sensor output, X. In the theory of measurement, FI directly enters the relation which determines the lower bound of the measurement uncertainty known as Cramer-Rao bound (CRB = 1/ FI (θ ) ). The sensor sensitivity is optimized by maximization of the corresponding FI. In the case of a multi-parameter sensor, FI assumes a matrix form defined via the probability distribution function f(X| θ) of the measured variable X conditioned by θ, where both X and θ are vector quantities. ( ) ( ) i n j n f X FI E i j i j ; 1,2,... ; 1,2,..., 2 ln , = = ∂ ∂ ∂ = − θ θ θ θ . Here, we develop a comprehensive model of the spectral response of fibre gratings to changes in multiple parameters and apply Fisher's formalism to optimize their sensitivity in the realistic parameter space. We start from a 1-parameter model of a long-period grating sensor of curvature and corroborate our approach by comparison with the conventional sensitivity models and the experimental data. We then expand the model to describe a 2-parameter long-period grating sensor of curvature and temperature. Based on this analysis, we recommend the multi-parameter interrogation scheme (estimator) and optimize grating parameters to render the highest sensitivity.", publisher = "Belgrade : Vinča Institute of Nuclear Sciences", journal = "PHOTONICA2015 : 5th International School and Conference on Photonics and COST actions: MP1204, BM1205 and MP1205 : book of abstracts; August 24-28, 2015; Belgrade", title = "Estimation of the Sensitivity of a Multi-Parameter Fiber Grating Sensor", pages = "173-173", url = "https://hdl.handle.net/21.15107/rcub_vinar_12012" }
Raičević, N., Ivanović, M. D., Beličev, P., Maluckov, A.,& Petrović, J.. (2015). Estimation of the Sensitivity of a Multi-Parameter Fiber Grating Sensor. in PHOTONICA2015 : 5th International School and Conference on Photonics and COST actions: MP1204, BM1205 and MP1205 : book of abstracts; August 24-28, 2015; Belgrade Belgrade : Vinča Institute of Nuclear Sciences., 173-173. https://hdl.handle.net/21.15107/rcub_vinar_12012
Raičević N, Ivanović MD, Beličev P, Maluckov A, Petrović J. Estimation of the Sensitivity of a Multi-Parameter Fiber Grating Sensor. in PHOTONICA2015 : 5th International School and Conference on Photonics and COST actions: MP1204, BM1205 and MP1205 : book of abstracts; August 24-28, 2015; Belgrade. 2015;:173-173. https://hdl.handle.net/21.15107/rcub_vinar_12012 .
Raičević, Nevena, Ivanović, Marija D., Beličev, Petra, Maluckov, Aleksandra, Petrović, Jovana, "Estimation of the Sensitivity of a Multi-Parameter Fiber Grating Sensor" in PHOTONICA2015 : 5th International School and Conference on Photonics and COST actions: MP1204, BM1205 and MP1205 : book of abstracts; August 24-28, 2015; Belgrade (2015):173-173, https://hdl.handle.net/21.15107/rcub_vinar_12012 .