Root canal therapy is the most fundamental and effective approach for treating endodontics and periapicalitis. The length of the root canal must be accurately measured to clean the pathogenic substances in it. This study aims to present a multifrequency impedance method based on a neural network for root canal length measurement. A circuit system was designed which generates a current of frequencies from 100 Hz to 20 kHz in order to augment the data of impedance ratios with different combinations of frequencies. Several impedance ratios and other quantified characteristics, such as the type of tooth and file, were selected as features to train a neural network model that could predict the distance between the file and apical foramen. The model uses leave-one-out cross-validation, adopts the Adam optimizer and regularization, and has two hidden layers with nine and five nodes, respectively. The neural network-based multifrequency impedance method exhibits nearly 95% accuracy, compared with the dual-frequency impedance ratio method (which demonstrated no more than 85% accuracy in some situations). This method may eliminate the influence of human and environmental factors on measurement of the root canal length, thereby increasing measurement robustness.

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Beam splitters have a wide range of applications as a key component in optical systems. Adopting beam splitters with geometric defects in an optical system, e.g., an interferometric measurement system, may cause additional optical path difference and degrade the measurement accuracy. The quality inspection of beam splitters is essential to meet the accuracy requirements for modern optical systems. Most of the current quality inspection methods rely on inefficient and inaccurate manual observation. Therefore, for commonly used cube beam splitters (CBSs), we propose a digital method to quantify the geometric quality based on the white light interferometric principle. A Fourier domain analysis is used to calculate the CBS misalignment error and perpendicularity error. This method is verified by inspecting six different CBS samples. The experimental results show that all samples have varying degrees of misalignment and perpendicularity errors. The maximum perpendicularity error is 0.93°, and three of the six samples have misalignment errors larger than 50 µm. Nanometer level precision of the misalignment measurement can be achieved.

As one of the core components of ultra-precision machining and inspection equipment, the 2D stage plays a major role in sophisticated technology. Self-calibration is considered an excellent method to separate stage system errors because of its low cost and high efficiency. In this paper, the self-calibration model is represented using an overdetermined equations system. A weight matrix was used to solve the system through least squares with unequal accuracy. The error propagation ratios increase with a decrease in the number of positions or increase in the number of points, however, all the ratios are less than one. Self-calibration based on weighted least squares can suppress the noise, which was proved through simulation. Experiments were conducted to confirm that self-calibration separated the stage system errors successfully. The effectiveness and repeatability of the method were confirmed by the fact that the standard deviation among the plates returning to the initial position was of tens of nanometers. Two methods of self-calibration, namely self-calibration based on least squares and optimization self-calibration, were verified against each other. The differences between the stage system errors separated in the two methods were only a few nanometers.