Title
Algebraic solutions for the Fourier transform interrogator
Author
Peternella, F.G.
Harmsma, P.J.
Horsten, R.C.
Zuidwijk, T.
Urbach, H.P.
Adam, A.J.L.
Publication year
2021
Abstract
A new method for fast, high resolution interrogation of an array of photonic sensors is proposed. The technique is based on the integrated Fourier transform (FT) interrogator previously introduced by the authors. Compared to other interferometric interrogators, the FT-interrogator is very compact and has an unprecedented tolerance to variations in the nominal values of the sensors’ resonance wavelength. In this paper, the output voltages of the interrogator are written as a polynomial function of complex variables whose modulus is unitary and whose argument encodes the resonance wavelength modulation of the photonic sensors. Two different methods are proposed to solve the system of polynomial equations. In both cases, the Gröbner basis of the polynomial ideal is computed using lexicographical monomial ordering, resulting in a system of polynomials whose complex variable contributions can be decoupled. Using an NVidia graphics processing card, the processing time for 1 026 000 systems of algebraic equations takes around 9 ms, which is more than two orders of magnitude faster than the interrogation method previously introduced by the authors. Such a performance allows for real time interrogation of high-speed sensors. Multiple solutions satisfy the algebraic system of equations, but, in general, only one of the solutions gives the actual resonance wavelength modulation of the sensors. Other solutions have been used for optimization, leading to a reduction in the cross-talk among the sensors. The dynamic strain resolution is 1.66 nε/√Hz.
Subject
Modulation
Resonance
Algebraic solution
High-speed sensors
Multiple solutions
Orders of magnitude
Polynomial functions
Resonance wavelengths
System of polynomial equations
Systems of algebraic equations
High Tech Systems & Materials
Industrial Innovation
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DOI
https://doi.org/10.1364/oe.426544
TNO identifier
958261
Publisher
The Optical Society of America OSA
ISSN
1094-4087
Source
Optics Express, 29 (29), 25632-25662
Document type
article