# Non-Contact and Real-Time Measurement of Kolsky Bar with Temporal Speckle Interferometry
## 1 Introduction  
In the fields of aviation, aerospace, packaging, transportation, and other areas of military and civil engineering, the materials used will encounter stress events such as explosions, rapid collision, and other impact load. It is of great practical significance to study the dynamic mechanical properties of materials under high strain rate conditions for engineering design and application. The Kolsky bar (also known as Split Hopkinson Pressure Bar) apparatus is the most popular and convenient system for characterizing the high strain-rate behaviors of materials [1]. The typical Kolsky bar is using two strain gages that past on the incident bar and transmitter bar to measure the dynamic mechanical properties of a material under high strain rate conditions. This method requires good adhesion between the bar and the strain gauge. Apart from this, the measurement accuracy that the conventional Kolsky bar provides is limited. The support of real-time and high-accuracy dynamic mechanical properties of materials under high strain rate conditions is required with the rapid development of industry, especially for the machinery defense industries. For example, it is useful to employ bars with diameters of only a few millimeters for testing at higher strain-rates. However, traditional strain-gauge measurements of the longitudinal waves within the bars become impractical at these sizes, because the strain gauge and the bar cannot be reliably connected when the diameter of the bar is less than 3 mm [2]. [PERSON] and [PERSON] proposed the application of a fiber-based velocity interferometry measurement method to directly measure the actual velocities of the bars. The two fiber lasersare irradiated onto the bars at a small angle, and then the Doppler-shifted light carrying the optical information is collected [3]. The dynamic stress-strain curves of the material are obtained from the measured velocity information by short-time Fourier transform and phase-based analysis. However, because the Kolsky bar is characterized by rapidly changing velocities, their system contains a 3 \(\times\) 3 single-mode fiber coupler to create three interferometric singles which are 120\({}^{\circ}\) out of phase relative to each other [4; 5]. For a single velocity trace, it is necessary to manually choose the transition points between high and low velocity. [PERSON] and [PERSON] proposed a method to permit wave separation of a Kolsky bar. The particle velocity at each strain gauge position is measured with PDV. This method can measure the strain of the scattered wave train present on each bar, which can extend the test time of the experiment so that more types of loads can be loaded into the specimen [6]. However, the data obtained by measuring the particle velocity with PDV will contain a significant bending wave component due to the errors introduced by the leading of wire motion. In order to account for bending, it is necessary to multiple the PDV measurements at each gauge position. [PERSON] and [PERSON] proposed TDI (transverse displacement interferometer) and NDI (normal displacement interferometer) for application to Kolsky bars. TDI is used to measure the displacement of the mid-point of the incident bar and provide measurements of the incident and reflected pulses. Similarly, NDI is used to measure the displacement of the free-end of the transmitter bar and provide a measurement of the transmitted pulse [7]. However, it is necessary to install a diffraction grating in the middle of the incident bar when measuring the incident pulse and the reflected pulse by TDI. The machining precision of the diffraction grating and the quality of the paste with the incident bar will have significant influence on the measurement accuracy of the whole experiment. [PERSON] and [PERSON] used a fiber micro-displacement interferometer system for any reflector to directly measure the actual velocities of the bars.