**5. Discussion**

The results reported in Section 4 demonstrate that the small footprint of the sensor and absence of mechanical coupling between the measured signal and the sensing element are key ingredients for a minimally distorted PW signal. Although spectral interferometric demodulation provides the lowest noises, FPI sensor performance in terms of repeatability is slightly worse than the FBG one, presumably due to greater footprint and non constant mechanical coupling between the pulse wave and the sensor. Nevertheless, an additional experiment performed when the subject made palm movements, showed that the OCT sensor has superior performance in terms of motion artifacts reduction as compared to the rest tested sensors. The main cause for that is the more direct sensing mechanism of the *ϕ*-OCT approach—in contrast to FPI, FBG and SMS, it does not rely on mechanical deformation of the sensing element caused by the pulse wave. Instead, the *ϕ*-OCT approach directly monitors the displacement of biological tissues, which are induced by the pulse wave propagation. This is the main reason for high SNR and measurement repeatability, achieved by the *ϕ*-OCT approach.

Along with the sensors' measurement performance, their ability to be implemented in a portable format, be interrogated by cost-effective hardware and be integrated into modern gadgets is vital for their evolution from laboratory prototypes to commercial products, demanded by healthcare and sport industries. In this regard, there are two important limitations on the interrogation hardware: the use of a spatially incoherent light source, such as LED, which are much more cost-effective than SLED or ASE sources; and low spectral resolution of the optical spectrometer used to acquire sensors' spectra. Another important property is an ability to simultaneously interrogate several multiplexed sensing elements.

Regarding the desirable ability to work with spatially incoherent light, it, in turn, leads to the requirement of only multimode fibers being used in the whole fiber system since it is fundamentally impossible to efficiently couple spatially incoherent light into singlemode optical fiber [76]. This immediately leads to the problem of modal noise [61] that can give rise to parasitic interference signals, which will affect sensor resolution. However, smartphone-based interrogation of FPI [77,78] and FBG [61] sensors has already been successfully demonstrated. All-multimode sensors equivalent to SMS are definitely possible, with intermode interference used for sensing taking place in a largely multimode fiber, sandwiched between two MMFs with smaller number of propagating modes. OCT in all-multimode systems has already been experimentally demonstrated [79], paving the way for its use with portable devices.

Spectral resolution of an optical spectrometer used for sensor interrogation must be in accordance with the width of the sensor's spectrum features, such as reflection peak of FBG or interference fringes of interference sensors. FPI sensors offer the greatest flexibility in this regard, with periods of spectral interference signals ranging from tens of nanometers in case of short-cavity FPIs, allowing to use spectrometers with sufficiently low spectral resolutions of around several nanometers. Typically, the width of the FBG reflection spectrum is about 100–200 pm, therefore, requiring the use of spectrometers with relatively high spectral resolution for correct spectra measurement. However, gratings inscribed in multimode fibers exhibit complex multipeak spectra and therefore are typically chirped in order to obtain a single spectral feature, resulting in a several nm-width reflection peak [61], requiring spectral resolution of spectrometer about 1 nm. This, however, leads to a decrease of achievable measurement resolution and therefore, will result in further decrease of SNR, which, as shown above, even with FBG inscribed in SMF is not quite high. Sensors based on intermodal interference typically have rather complex spectra with fine spectral features, sometimes used for signal demodulation [24]. However, as shown in Sections 3 and 4, the signal of an SMS sensor was obtained from

the interference component, corresponding to the lower-order modes interference. This interference signal component has a large oscillation period and therefore can be acquired using a spectrometer with low spectral resolution (on the order of 10–20 nm). Finally, since the *ϕ*-OCT approach proposed for PW measurement relies on demodulation of phase of a lightwave, reflected from the bound between epidermis and dermis, and is realized using a common-path scheme, it is crucial that the interference signal with OPD equal to doubled optical length of epidermis is acquired without distortions. As follows from the known values of epidermis thickness and refractive index as well as from the obtained data, OPD of such interferometer is about 400 μm. This corresponds to a period of OCT spectrum oscillations about 5 nm, requiring spectral resolution of spectrometer not less than 1–2 nm, which is realizable even with smartphone-based spectrometers [61,80].

In terms of multiplexing capacity, FBG sensors with the use of the wavelength-division multiplexing approach have an obvious advantage. For example, with the spectrometer used in our work with 85 nm spectral span, FBG spectral spacing of 1.5 nm, it is possible to simultaneously interrogate up to 56 multiplexed sensors. FPI sensors also offer multiplexing abilities, typically realized through spatial frequency-division multiplexing (SFDM), sometimes also referred to as OPD-domain multiplexing. Multiplexing tens of FPI sensors is technically possible, but will either require the use of a light source with a relatively high intensity or will result in reduced resolution [81]. Multiplexed OCT systems have already been demonstrated [82,83] with a principle that is similar to SFDM. Limiting factor for multiplexing of OCT probes will be imaging depth and spectral resolution of the spectrometer. In our case of imaging depth up to about 400 μm and spectral resolution of about 200 nm (with corresponding effective coherence length 6 mm and maximal imaging depth of a single probe system of 3 mm) it leads to potentially up to about 6–7 multiplexed probes. To the best of our knowledge, multiplexing of SMS sensors has not been reported yet, although in principle, it can be performed with the SFDM approach as well.

Other practical aspects of such sensing systems include repeatability of sensing characteristics, as well as reproducibility of characteristics of sensing elements and their fabrication cost. Repeatability mainly depends on mechanical coupling between the pulse wave and the sensing element, therefore, the OCT approach has a clear advantage, even despite its small area and seemingly higher requirement to sensor alignment. However, since there is no adhesive used to fix the OCT probe on skin, it is easy to manually adjust it while observing the demodulated signal in order to achieve the highest amplitude. An SMS sensor could also have some advantage in point thanks to its greater length and therefore, greater chance of coincidence of its section with the area of maximal sensitivity. However, this could not be observed in the current study due to the sensor nonlinearity.

In terms of reproducibility, fabrication of FPI sensor of the configuration used in our work is the simplest one in terms of required equipment, requiring a fiber stripper, a fiber cleaver, capillary cleaver (it can also be cleaved manually), glue and equipment for inserting cleaved fibers into capillary (the latter can be performed manually by a trained person). In terms of sensor characteristics reproducibility, the most crucial point is the flatness and cleavage angles of fiber end faces [84,85], which can be monitored right after the cleavage using a conventional optical microscope. For FBG sensor reproducibility of its characteristics solely depends on the grating inscription setup and recoating process and typically is quite high. Reproducibility of the proposed *ϕ*-OCT PW monitoring technique depends primarily on the difference between epidermis and dermis refractive index values, which is consistent within several independent studies [86–88]. The properties of the sensing element mainly influence the amplitude of the demodulated PW signal. Nevertheless, their reproducibility is quite high in case of high quality fiber cleaver and splicer used to produce the sensing element. Reproducibility of SMS sensor characteristics might be the most problematic at the moment due to the above-mentioned sensor nonlinearity. However, its fabrication is not much more complicated than for FPI and OCT sensors, requiring four fiber cleavages and two splices. From the current point, it is hard to predict the cost of sensing elements, however, we believe that for all of them it would be on the same order

of magnitude, since higher cost of grating inscription hardware required to produce FBG sensor is compensated by greater amount of required manual production operations (fiber cleaving, splicing) for FPI, OCT and SMS sensors. Anyway, sensing elements cost still might be several times lower than the cost of even the simplest interrogation hardware.

The above-mentioned parameters of the compared sensing configurations are listed in Table 3. To summarize, we believe that the *ϕ*-OCT approach of pulse wave monitoring may be of the greatest interest for the use in applications where the highest measurement accuracy is needed: medical research and cardiovascular clinics. At the same time, FPI sensors might be most well-suited for use in personal and portable devices since, as follows from the obtained results and the analysis above, they offer a compromise between signal quality and repeatability on the one hand and can be multiplexed, interrogated by simple and cost-effective hardware and demonstrate very weak temperature cross-sensitivity on the other hand. According to the reported results, the main drawbacks of the FBG sensor are relatively low SNR and susceptibility to motion artefacts. However, both of these problems can be solved by the use of FBGs inscribed in polymer fibers, which are also compatible with low-cost interrogation hardware, making them a tight concurrent of FPI sensors, which, according to our study, turn out to be preferable. The use of SMS sensors for pulse wave monitoring and other biomedical tasks may also be prominent if more advanced signal processing algorithms based on detailed analysis of mode propagation in the MMF section are developed.

**Table 3.** Comparison of technical properties of the investigated sensors. *<sup>σ</sup>*SPEC—spectral resolution, *N*MULT—number of multiplexed sensors.

