{'fraction_non_alphanumeric': 0.015615962984384037, 'fraction_numerical': 0.001156737998843262, 'mean_word_length': 5.3837638376383765, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Phase correlation method for subpixel in-plane vibration measurements of MEMS by stroboscopic microscopy

Accurate estimation of displacement between successive images is a significant topic in the measurement of in-plane vibrations of microscopic objects such as micro-actuators. Actual subpixel motion estimation algorithms require the interpolation of interpixel values which undesirably increases the overall complexity and data flow and deteriorates estimation accuracy. Methods that do not use interpolation for achieving subpixel accuracy are scarcer in the literature. One approach for subpixel movement estimation without interpolation is based on phase correlation algorithm. This algorithm estimates the relative shift between two image blocks by means of a normalized cross-correlation function computed in the 2-D spatial Fourier domain. Indeed, the method is based on the Fourier shift theorem. The cross power spectrum of two images, containing subpixel shifts, is a polyphase decomposition of a Dirac delta function. By estimating the sum of polyphase components one can then determine subpixel shifts along each axis. Phase correlation is the state of the art for interpolation-free subpixel shift measurement between two frames, but this method is strictly limited to subpixel shifts. So, we have implemented this method using a standard optical microscope in order to observe subpixel translations with high spatial resolution measurements (down to 1 nm in the best cases). In this paper, we propose an application of this method to characterize the vibration mode shapes of a small silicon beam used in near-field acoustic microscopy. Harmonic movements of a few tens of nanometers are measured and presented.