## 1 Introduction  
Displacement is an important structural mechanical parameter that is used for identifying damage. The optical interferometer type of displacement sensor has the advantage of high sensitivity, small size, and immunity to electromagnetic interference. The interferometer type displacement sensor usually has multiple peaks and deeps. When demodulating the wavelength shift of a sensor with a uniform free spectra range (FSR), it is very difficult to mark one of the (notch) wavelengths as the sensing wavelength [1; 2; 3], because when the sensing wavelength shift is more than one FSR, it is hard to trace the chosen sensing wavelength. However, when the FSR changes monotonically, the tracing of the chosen sensing wavelength becomes very easy [4; 5; 6]. Moreover, we can conduct a cross-correlation process to the chirped spectra to achieve a single peak. Marking one peak in the spectra is easier compared with the marking of multiple peaks, especially in the high-speed time domain-sensing demodulation system [7; 8]. The spectral chirped optical fiber sensor can be also used in microwave photonics [9]. For example, in the field of microwave photonics radar systems, the chirped microwave signals can be generated with optical spectral-shaping techniques and frequency-to-time mapping techniques.  
The conventional structures to achieve the chirped shape of optical spectra are combining double arm Mach-Zehnder interferometers [7] or Sagnac fiber loop interferometers [8] with the chirped fiber Bragg gratings (CFBGs). However, the long fiber in the interferometer structure is very sensitive to environmental disturbance and also difficult to integrate due to its large size. Optical fiber Fabry-Perot (F-P) interferometers have been extensively investigated due to their high sensitivity, low cost, and compact size, but the FSR of an F-P interferometer is usually uniformed. The optical fiber taper is a key component that has a number of applications in the fiber optic area, such as optical fiber couplers, filters, and sensors. The optical fiber taper has the advantages of the ease of fabrication, stability from environmental changes, and compactness. Such applications mentioned above have attracted huge research attention in the past few years [10; 11; 12; 13]. Moreover, the optical fiber taper can also achieve CFBG due to the broadband characteristics of microfiber Bragg grating (mFBG) [14; 15; 16; 17]. Usually the microfiber F-P interferometer is achieved by inscribing two FBGs at the two taper regions of the microfiber. However, the monotonically decreasing FSR is hard to achieve, because the wavelength ranges of the spectra of the two FBGs are usually mismatched [4; 5; 6].  
In this paper, we propose and experimentally demonstrate a spectral chirped Fabry-Perot (F-P) interferometer displacement sensor based on a tapered microfiber. We continuously inscribed a long uniform FBG onto the microfiber by scanning the focus spot of a 193-nm ArF excimer laser with a phase mask (1072 nm). The available bandwidth of the chirped F-P interferometer is over 20 nm. We marked the notch wavelength of the reflective spectra under different tensions to show the good tunability of the F-P interferometer chirp rate. The cross-correlation analyzing for the reflective spectra is also given to enhance the sensing demodulation efficiency. The displacement sensing curves created by marking the first notch wavelength shifting and by a cross-correlation analyzing method are both given in the experimental results. The proposed chirped F-P interferometer has potential applications in the fields of high-speed stress measurement and microwave signal generation.