Towards a Uniform Metrological Assessment of Grating-Based Optical Fiber Sensors: From Refractometers to Biosensors
A metrological assessment of grating-based optical fiber sensors is proposed with the aim of providing an objective evaluation of the performance of this sensor category. Attention was focused on the most common parameters, used to describe the performance of both optical refractometers and biosensors, which encompassed sensitivity, with a distinction between volume or bulk sensitivity and surface sensitivity, resolution, response time, limit of detection, specificity (or selectivity),
... ty (or regenerability) and some other parameters of generic interest, such as measurement uncertainty, accuracy, precision, stability, drift, repeatability and reproducibility. Clearly, the concepts discussed here can also be applied to any resonance-based sensor, thus providing the basis for an easier and direct performance comparison of a great number of sensors published in the literature up to now. In addition, common mistakes present in the literature made for the evaluation of sensor performance are highlighted, and lastly a uniform performance assessment is discussed and provided. Finally, some design strategies will be proposed to develop a grating-based optical fiber sensing scheme with improved performance. Biosensors 2017, 7, 23 2 of 29 compared with different technology-based platforms. On the other hand, OFG sensors have the major disadvantage of being sensitive to different measurands at the same time, such as temperature, refractive index (RI) of the medium surrounding the fiber, axial deformation (i.e., strain), pressure and humidity. This aspect entails the application of different strategies in order to make the device sensitive to the parameter of interest. In this work, the surrounding RI (SRI) will be the main parameter considered with an insight into the cross-sensitivity issue. Another drawback may derive from their fragility, thus requiring ad-hoc developed packaging or protections, especially for industrial applications. However, given the increasing attention of the scientific community to OFG sensors, the need for a worldwide acceptable standardization of the sensing performance of an OFG sensor could be of general interest for both the research and industrial communities. The authors do not have the pretension of providing the "one and only" way of assessing the performance of an optical sensor. Instead, the aim of the present work is to offer a contribution based on both our knowledge and experience and on the literature published up to now, so as to provide a reference to facilitate any comparisons, not only within the same class of OFG sensors, but also among different kinds of sensors based on spectral resonance. The most significant parameters for a sensor are defined and described, along with the importance of denoting some crucial parameters with their correct names in order to be able to use the same parameters for describing the sensor performance. In addition, the most common and repeated mistakes in the literature, which arise from the great variety in the formulation and interpretation of the said parameters, are highlighted and discussed in detail. One of the first clear and targeted attempts to provide "some basic definitions of sensor properties" to the scientific community in a standardized manner was made by D'Amico and Di Natale in 2001 . In it, sensor response curve, sensitivity, noise, drift, resolution and selectivity are analyzed as the most frequently used parameters associated with sensor performance. The authors fittingly said of these features, "These words, if well-interpreted, represent a powerful vehicle of information and may symbolize part of a common knowledge useful for a sound dissemination of results relative to the sensor research." After this, other papers were published that provided guidelines specifically designed for chemical and biochemical resonant sensors     . In 2008, White and Fan  focused on the explanation of the limit of detection (LOD) and the influence of the quality factor (Q-factor) for resonant RI sensors. Our major criticism of this paper is related to the term "LOD", since in our opinion this could be misleading if related to refractometric sensors, in which it is more appropriate to talk about resolution, while its use fits perfectly for biosensors or, overall, for any sensor in which an interaction or binding with a target take place. In the same year, Janiga et al.  emphasized the important difference, for a chemical sensor or a biosensor, between the minimum detectable concentration (MDC) used by the International Organization for Standardization (ISO) and the LOD used by the International Union of Pure and Applied Chemistry (IUPAC). Both can be used, and represent compelling features, in assessing sensor performance. The key is simple: when considering the definitions, they both clearly state what the sensor is able to measure. In 2009, Hu et al.  proposed some "design guidelines for optical resonator biochemical sensors". They appropriately pointed out the relevance of having a widely accepted figure of merit (FOM) with which to compare different technology platforms and, in this context, they focused on the Q-factor and RI LOD that strongly depend on the resonance peak full width at half maximum (FWHM). As in ref. , when someone wants to deal with the minimum RI change discernible from the noise that the sensor is able to measure, they should simply talk about sensor resolution in order to avoid an inexact usage of LOD. However, they also highlighted the influence of thermal fluctuations on sensor performance and the importance of their both having a good fitting procedure in order to reliably evaluate the resonance shift and to increase the number of measurements so as to reduce the noise contribution. All those features turn out to be crucial for improving sensor performance. More recently (2012), Loock and Wentzell  focused on the LOD evaluation for chemical and biochemical sensors, and reported the results obtained by comparing three different approaches for determining the detection limit: (i) an analysis of the standard deviations at low concentration; (ii) an evaluation of the instrumental resolution limit and (iii) Biosensors 2017, 7, 23 3 of 29 an examination of the calibration curve. They concluded that the most appropriate way to evaluate the LOD is not to involve the sensor sensitivity and resolution, which in any case are two other important parameters. Rather, it should be determined either from the standard deviations at a low concentration by repeated measurements near the suspected LOD, as also suggested by the American Chemical Society (ACS) , or be calculated using the calibration curve, provided that the calibration points can be considered repeatable and reproducible. The first attempt to give a metrological standardization focused only on OFG sensors was provided by Possetti et al. in 2012 . They discussed in detail a method for evaluating uncertainties of measurement, applying it to both the FBG as a temperature sensor and the LPG as an RI sensor. The main conclusion was that, in OFG sensors, the major source of uncertainty (see Section 3.1.1) is related to repeatability (see Section 3.1.4) and reproducibility (see Section 3.1.5). This is ascribed to the combined effect of OFG cross-sensitivity and of environmental conditions, thus requiring some compensation procedures as well as an increase in the number of measurements. The present work attempts to review critically and, at the same time, to combine all the assertions contained in all the papers published previously in the field, with the aim of providing a proper definition of the metrological parameters for the two main classes with regard to optical fiber sensors: the optical refractometers in which the measurement of SRI changes involves all the volume surrounding the sensor (in this case, we should talk about volume or bulk RI measurements) and the optical biosensors in which the measurement of SRI changes involves only the surface of the sensor on which the interaction with the target takes place (in this other case, one should talk about surface RI measurements). This distinction is particularly crucial in small volume analysis , as will be pointed out in Section 2. To be more precise, the work is divided as follows: Section 2 illustrates the fundamentals of OFGs focusing on both fiber Bragg gratings (FBGs) and long period gratings (LPGs); Section 3 defines the metrological parameters useful for assessing sensor performance, with some demonstrative examples of the most common mistakes and error present in the literature; Section 4 deals with the most challenging literature on OFG-based refractometers, whereas Section 5 details the same but as related to OFG-based biosensors with a detailed analysis of the cross-sensitivities' issue of OFG sensors in the last two sections; Section 6 highlights some common mistakes present in the literature for the evaluation of OFG-based sensors and makes an attempt to provide a uniform procedure for assessing sensor performance. Lastly, Section 7 provides an outlook on the future perspective of OFG-based sensors. Fundamentals of Optical Fiber Gratings An OFG is a diffraction structure characterized by a periodic modulation of the RI within the core of a single-mode fiber (SMF), which satisfies the phase matching condition between the fundamental mode and other modes, either the core mode or the cladding modes or radiation (or leaky) modes  . Thanks to this phase matching, the fiber grating makes possible a controlled and efficient power transfer between modes within the optical fiber leading to a modulation of the transmitted spectrum. Depending on the range of its grating period Λ, OFGs can be classified into short period gratings, better known as FBGs, and into LPGs. The grating period of an FBG is typically of the order of hundreds of nm, resulting in a device that satisfies the phase matching between the fundamental core mode and its respective counter-propagating mode. Therefore, when a broadband optical signal reaches the grating, a narrow spectral fraction is reflected and the remaining is transmitted. The resonance wavelength λ res at which the light is reflected satisfies the well-known Bragg condition : λ res = 2 n eff core Λ, where n eff core is effective RI of the core mode. The spectral width of the resonance peak is of the order of few hundreds of picometers, depending on the physical length of the grating. Figure 1 illustrates the principle of operation of an FBG.