The simultaneous measurement of temperature, pressure, and acoustic impedance is important requirement and technical challenge for many application fields such as equipment monitoring and material research [1]. For example, in oil drilling and natural gas extraction, it is necessary to simultaneously measure temperature, pressure and acoustic impedance of the oil/gas to ensure the safety of the exploration process [2]. In material science research, it is important to research the characteristics and performance of materials at different temperatures, pressures and acoustic impedances [[3], [4], [5], [6]]. Unfortunately, there are currently no reports of measurement of temperature, pressure and acoustic impedance simultaneously. How to realize simultaneous sensing of the three parameters with small size, high mechanical strength and electromagnetic interference resistance is a major challenge in the field of fiber optic sensing research.

In fiber optic sensing based on FBS, acoustic vibration involved in FBS in a fiber is related with a transverse acoustic field [7], and temperature or pressure can change the velocity of transverse acoustic waves involved in FBS, which further causes changes in the resonance frequencies of the acoustic waves [8]. As a result, a linear relationship between temperature or pressure and the resonance frequencies of acoustic waves can be used to provide temperature/pressure sensing [9,10]. In addition, due to the fact that transverse acoustic waves can be transmitted to the outside of the fiber cladding acoustic waves can be reflected at the interface between the fiber cladding and external media. Therefore, to achieve external medium acoustic resistance sensing, the linewidth or frequency shift of the FBS spectra is measured [11,12], which makes FBS unique in measuring external acoustic impedance and other parameters compared to other scattering effects. Measurement methods for single or dual parameter sensing have been presented based on the linear relationship between the frequency shift or linewidth of the optical fibers' FBS spectra and parameters (temperature, pressure and acoustic impedance). So far, it has been used for strain, temperature, pressure and acoustic impedance sensing via radial acoustic modes [[13], [14], [15], [16], [17]]. Recently, we have achieved simultaneous measurement of temperature and acoustic impedance [18], temperature and pressure [4], as well as temperature, refractive index, and axial strain [19], by utilizing the FBS induced by radial acoustic modes in fibers. However, there is currently no FBS-based method for simultaneous measurement of three parameters of temperature, pressure and acoustic impedance. To achieve three parameter measurement, it is necessary to have linear relationships between these three parameters and the FBS spectrum frequency shifts or linewidths of the fiber within a certain range.

In the three parameters simultaneous sensing, generally it is very difficult to achieve high measurement accuracy for all three measured parameters simultaneously. Fortunately, in many applications, sometimes only one or two measured parameters are required to have high measurement accuracy, while the measurement accuracy of other measured parameters may not need to be high. Therefore, a good measurement strategy is, according to application requirements, to customize the accuracy of the measured parameters according to the different requirements. To meet this measurement strategy, the measurement method should provide multiple combinations of different measurement accuracies for the three parameters. Fortunately, because certain optical fibers contain dozens or more auditory modes, the FBS-based three parameter measuring approach can give a variety of measurement accuracies for the three parameters to be assessed. Because optical fibers have several scattering peaks, their center frequency shift is linear within a particular range, creating ideal circumstances for tailored accuracy sensing. Customers can select from a variety of combinations and adjust sensor accuracies to their specifications.

On this basis, we propose a novel customized accuracy sensing method which can measurement of temperature, pressure and acoustic impedance simultaneously based on FBS. In this paper, we provide a measurement principle based on the linear correlations between three parameters (temperature, pressure and acoustic impedance) and the frequency shifts of various modes of FBS in optical fibers. The suggested approach not only enables simultaneous temperature, pressure and acoustic impedance monitoring, but it also introduces a new method of fiber optic sensing with tailored multi-parameter sensing accuracy.