# Micro Vibration Measurement with Microscopic Speckle Interferometry Based on Orthogonal Phase
## 1 Introduction  
With the increasing requirements for the functionality and miniaturization of electromechanical devices, the application of microelectromechanical systems (MEMS) and nanostructured devices has become more and more important. Vibration of nanometer and micrometer range is one of the most common dynamic characteristics both in the manufacturing process and practical applications of MEMS. By determining its vibration frequency and amplitude through measurement techniques, the non-destructive evaluation and error compensation can be carried out. Common vibration measurement methods, such as accelerometers, laser displacement meters and digital image correlation (DIC) methods are not suitable for vibration measurement of micro devices. Optical interferometry has the advantages of non-contact, high accuracy, and direct measurement of micro-vibration, so they have been widely used. Common optical interferometry includes homodyne interferometry [1, 2, 3, 4, 5, 6], heterodyne interferometry [7, 8, 9, 10, 11, 12], Sagnac interferometry [13] and stroboscopic white light interferometry [14, 15, 16, 17]. [PERSON], [PERSON] et al. [3] demonstrated a homodyne scanning Michelson interferometer, which can directly measure the surface acoustic wave in the range of 0.5 MHz to 1 GHz. The sensitivity is about \(10^{-5}\) nm\(/\sqrt{\text{Hz}}\), and the scanning speed is 49,200 points/h. [PERSON], [PERSON] et al. [4] used Mach-Zehnder interferometer to measure the vibration of high frequency thin film resonators. The measurement frequency range is 30 kHz to 12 GHz, and the amplitude is less than 10 pm. It also requires scanning to realize the measurement of the whole surface, and it takes 10 h to complete the entire measurement process. [PERSON], [PERSON] et al. [7] introduced a modulated heterodyne signal by using two acousto-optic modulators (AOM) in the measurement optical path to measure the vibration of the micro mechanical ultrasonic transducer. The frequency range is from 5 kHz to 35 MHz. The Bessel function method is used for theoretical calculation, so the maximum amplitude that can be measured is far less than the wavelength of the light source. The authors of [8] presented a scanning heterodyne laser interferometer. Under the premise of ensuring high accuracy, the maximum measurement is 300 pm. [PERSON], [PERSON] et al. [15]reported a stroboscopic white light interferometer used to measure the surface acoustic wave generated by a ring-shaped transducer with a working frequency of 74 MHz. The maximum vibration amplitude was 3 nm. We have summarized the frequency and amplitude of the above methods into a table, as shown in Table 1.  
At present, optical interferometry has obtained many achievements in the field of high-frequency vibration measurement. However, they generally achieve full-field measurement in a scanning manner, which causes the measurement process to take a long time and cannot achieve real-time measurement. The electronic speckle pattern interferometry (ESPI) can also be used in the field of non-contact vibration measurement, and can achieve full-field measurement. By analyzing the interferograms, we can obtain the vibration information of the measured object. Researchers have designed the corresponding optical measurement configuration and phase processing algorithm. [PERSON], [PERSON] et al. [18] reported a simple, compact ESPI incorporating holographic optical system for the study of out-of-plane vibration. The time-average subtraction method was used to generate the fringe pattern, and the amplitude and phase image were obtained through path difference modulation. [PERSON] et al. [19] proposed a method incorporating amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) with radial basis function (RBF) to investigate vibration characteristics of sandwich panels. This method can improve the quality of fringe pattern, but it did not increase the measurement sensitivity.