How to Use Fiber Optic Sensors for Accurate Absolute Measurements - INVITED

. The scientific community has been exploring new concepts as a result of the usage of optical fibers as absolute measurement sensors. While cross-sensitivity is a common issue with optical fiber sensors, this issue has been mitigated by simultaneous measurement techniques. But when it comes to absolute measurements, these methods have some limitations. The white light interferometer, which offers a superb solution for a range of applications, especially for absolute temperature measurement, is one of the most often used methods for absolute measurements.


Introduction
Fiber optics has revolutionized the field of sensing technology, but its susceptibility to temperature variations can hinder the accuracy of physical parameter measurements.To overcome this limitation, various techniques have been developed to obtain physical parameters with absolute values.One approach involves using two sensors with different characteristics to simultaneously measure two parameters, namely strain and temperature [1].Another technique, such as white light interferometry, provides readings in applied voltage, enabling absolute measurement.This brief review aims to explore and compare the different techniques used to obtain physical parameters with absolute values, highlighting their strengths and limitations [2].

Simultaneous measurement
The first concept is widely recognized, and to provide a clear illustration, two sensors with distinct characteristics can be utilized for the concurrent measurement of both strain and temperature.Equation 1 can be expressed in matrix form as follows: To determine the physical parameters, it is necessary to invert the matrix included in the equation.The matrix containing the sensitivity coefficients is the inverse matrix.In this way, one has: Where D is the determinant of the matrix defined by the equation.This result makes clear the baseline requirement for this process to work properly, i.e, D ≠ 0.
One possible solution is to use a sensor that is isolated from the deformation, ie, we have a sensor that measures deformation and temperature and another sensor that measures only temperature.Both sensors measure the same temperature.So the equation simplifies giving a term equal to zero (kε1= 0) and kT1 = kT2 = kT.So we will have two possible solutions to determine the temperature and the strain: As depicted in Equations 3, the strain value is obtained by calculating the difference between the two wavelengths.This approach allows for the strain value to depend exclusively on the strain sensitivity of the individual sensor, rather than the temperature sensitivity.To obtain absolute measurements of these parameters, it is necessary to have a fixed wavelength for each parameter.
In the presented example, the strain has an absolute value due to the fact that wavelength 1 is independent of the strain.The second sensor, on the other hand, provides an absolute response and derives its temperature component using the wavelength of sensor 1.

White Light Interferometry
One demodulation technique applied to quasi-static parameter measurements is White Light Interferometry (WLI), which uses a broadband source.WLI can perform , 09008 (2023) absolute measurement of the optical path difference (OPD) through multi-wavelength interferometry (MWLI) or spectral domain.However, due to its measurement complexity, it is not suitable for high-frequency measurements.Quadrature Point Intensity Demodulation (QPID) is the most common demodulation technique for high-frequency dynamic measurements.However, this method has limitations such as a dynamic range that cannot exceed λ/4 and difficulties with array multiplexing.An intermediate method is Quadrature Phase Demodulation, which is usually implemented through dual-wavelength quadrature phase demodulation and phase generation carrier demodulation methods.This method allows for higher dynamic ranges than QPID, making it suitable for certain high-frequency measurements, but it is still not as complex as WLI.This technique requires two interferometers, one as optical path finder and another as a sensor.When the optical path is the same the maximum intensity is obtained and corresponds to an absolute value of the size of the cavity.The size of the cavity depends directly on the temperature.When this signal is read on the oscilloscope it presents a known format and is denominated the sinc and can be written in the following Equation 4: Where IPD is the optical intensity that arrives at the photodetector, k = 2π/λ, λ is the wavelength, Λ is the optical path and the indices 1 and 2 allow allows the two cavities to be differentiated.Figure 1 presents an example of sinc for a cavity of 1 mm using a Mach-Zehnder interferometer configuration with an OPD of 2 mm.

Conclusions
Over the past decade, considerable research efforts have focused on various fiber-optic sensing mechanisms.However, it has become increasingly difficult to come up with entirely new and exciting sensing ideas, as many concepts remain purely theoretical and lack practical implementation in real-world settings.Fortunately, an emerging trend shows promise, as more research groups are adopting an application-oriented approach that prioritizes packaging, interconnecting, and, most importantly, ensuring reliability and multiplexing of fiber-optic sensors and systems.For these systems to be commercially successful and competitive with traditional sensing systems, three crucial aspects must be simultaneously addressed in the near future: developing accurate, reliable, and cost-effective sensor systems; ensuring safe packaging and interfacing of sensors with their working environment; and implementing optical multiplexing, signal processing, and remote sensing for the installed sensor arrays.

Fig. 1 .
Fig.1.Sinc signal for a cavity of 1 mm with an OPD of 2 mm.