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Li, J. Liu, and L. Chang and C. Ojansivu and J. Yang, Z. Lei, S. Liao, and S. ICB, pages 1—6, June Pinto et al. Chung, J. Lee, H. Kim, S. Song, and W. Anjos and S. Joint Conference on Biometrics, , pp. Wold, S. Kotz and N. Haralick, K. Shanmugam, and I. Eskicioglu and P. Bharadwaj, T. Dhamecha, M. Vatsa, and R. CVPR Workshops, pages —, Chaudhry, A. Ravichandran, G. Hager, and R. Chingovska, A. Anjos, and S.
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Advances in Light Microscopy for Neuroscience
Zhang, J. Yan, S. Liu, Z. Lei, D. Yi, and S. ICB, , pp. ICCV, pages —, Kose and J. ICIEV, , pp. Galbally, S.
The theory of the moiré phenomenon / by Isaac Amidror - Details - Trove
Marcel, and J. Image Process. Patel, H. Springer, IEEE Conf. Chingovska, J. Yi, S. Li, O. Glaser, N. Damer, A. Kuijper, A. Nouak, J. Komulainen, T. Anjos, S. Gupta, S. Khandelwal, S. Bansal, A. Rai, T. Krishna, D.
Goyal, M. Waris, H. Zhang, I. Ahmad, S. However, for the analysis of non-regular and random grating structures with which is necessary to deal with during investigations of the influence of the transducer errors on generated measurement signals the methods based on Fourier analysis has limited performance. They enable the direct visual and mathematical analysis of images of grating superposition. The location of ones and zeroes in the matrix is in one-to-one correspondence with the geometrical view of the graduation lines.
Numerical models of vertical a and oblique grating lines b represented by binary arrays and their main characteristics. The position errors in the horizontal width and vertical height directions can be obtained as:. Each graduation is characterized by their light flux transmittance. It is assumed that the opaque lines are completely lightproof and the bright lines are ideally transparent for the light flux.
Then the transmittance function of a grating can be calculated as:. In the simulation model the interaction of two interfering gratings is presented as the logical sum of the two BM representing a combined result as:. It is important to note that Eq. The BM representation of the grating is obtained directly from the graphical images of the grating micro-geometry represented on the computer monitor as enlarged many times.
Thus graduation errors and deviations of the positions of graduation lines caused by external factors e. The interaction of both gratings is modeled by superimposing two graduation structures one upon another in the same image. In case the images are black-white, the interference pattern of both gratings  is simulated using the graphical processing capabilities of the computer monitor.
Geometrical errors inherited in the manufacturing process of the scale as well as ones acquired during the assembly are the main factors which are influencing the accuracy of the encoder. Therefore, a simulation model for the analysis of the influence of the encoder disc eccentricity and vibrations of disc center has been developed. The scheme of the geometric quantities which enables to determine the grating line position error is presented in Fig.
Calculation scheme for actual position of a grating line and resulting line position error. Ideally geometry of the transducer the center of the disc should always coincide with the rotation axis 0, 0 and a certain grating line depicted by a thicker dark line in Fig. However, any misalignment of gratings and geometrical inaccuracies will cause measurement errors that can be defined by:.
This means that during the rotation of the disc erroneous number of grating lines passing through the window may be counted and therefore the disc rotation angle evaluation may be incorrect;. Such geometrical inaccuracies may be generalized and regarded as time dependent position of the center of a circular grating:.
It is obvious that the eccentricity errors will change in time due to the rotation of the disc and due to elastic vibrations. The Fourier spectrum caused by such errors is obtained by simulating the grating interaction during the full rotation cycle of the disc. The grating line orientation error that is obtained as:.
It is assumed that the window is very narrow compared with the grating circle radius and orientation of several adjacent grating lines is approximately the same.
General algorithm developed for the analysis of performance of optical encoders, shown in Fig. The influence of these deviations on the optical signal of the interfering gratings is determined by employing the developed modelling software which simulates the interaction of two optical grating as described in previous section. The input data is geometry of both gratings as well as geometrical deviations governed by e. Different outputs can be used for in-depth analysis of sensitivity of the encoder to possible design and assembly faults.
Furthermore, information gained from simulated optical signals and Lissajous figures can be used for theoretical error estimation as it is described in .
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For the simulation of the grating interactions a computer program in MATLAB has been developed, the action of which is based on the image analysis of the grating interaction displayed on the monitor screen. The Lissajous curves characterizing the grating interaction are obtained by representing two light flux signals obtained in two different measurement windows in O x and O y coordinate axes correspondingly. In our research the sine and cosine signals are obtained by simulating interaction of graduations twice. Here the cases of obturative Fig.
Distortions of Lissajous figures are increasing along with increasing angle between the lines of both gratings. In this simulation measurement readings during the grating period are employed. For the experimental analysis of the measurement signals generated by an optical angular encoder an experimental test system was employed. The main objective is to determine design or assembly faults, an appropriate configuration that resembles that of actual performance and to compare the obtained experimental results with the results of numerical simulation.
Traditional test methods can be widely improved making use of signal analysis tools; although the Lissajous figure is a convenient graphical method, it is not well suited to make numerical analysis of the data.
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The aim is therefore to obtain an improved method that eases the evaluation of the encoder global performance and the particular signal deterioration. Test setup consists of the appropriate drive system which is capable to drive up the encoder up to speeds 13 rpm and the encoder system attached to the drive as shown in Fig. The encoder signals connected to the signal recorder. A trigger signal line is established between the drive control and the signal recorder. The process starts when the drive begins to move.