Metrological errors in optical encoders
TL;DR: In this article, the error produced by optical encoders when the electrical signals vary from their nominal values is analyzed and simple expressions for the error estimation are obtained, which can be used to improve the design of the optical encoder.
Abstract: Optical encoders are commonly used for high accuracy position measurement, both linear and angular. In order to determine the position, the optical encoder generates two electrical signals that are combined using the arctangent algorithm. There are a number of situations, optical, mechanical and electronic, that affect these signals and produce an error in the position measurement. In this work, we analyze the error produced in optical encoders when the electrical signals vary from their nominal values. By using a linear expansion, simple expressions for the error estimation are obtained which can be used to improve the design of the optical encoders. In addition, an experimental verification of the theoretical results is performed.
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TL;DR: The influence of quadratures phase shift on the measured displacement error was experimentally investigated using a two-detector polarizing homodyne laser interferometer with a quadrature detection system and common nonlinearities were determined and effectively corrected by a robust data-processing algorithm.
Abstract: The influence of quadrature phase shift on the measured displacement error was experimentally investigated using a two-detector polarizing homodyne laser interferometer with a quadrature detection system. Common nonlinearities, including the phase-shift error, were determined and effectively corrected by a robust data-processing algorithm. The measured phase-shift error perfectly agrees with the theoretically determined phase-shift error region. This error is systematic, periodic and severely asymmetrical around the nominal displacement value. The main results presented in this paper can also be used to assess and correct the detector errors of other interferometric and non-interferometric displacement-measuring devices based on phase-quadrature detection.
76 citations
TL;DR: In this article, the authors presented a method of a six-degree-of-freedom (DOF) posture measurement in a linear stage by employing a single unit of an optical encoder.
Abstract: This paper presents the method of a six-degree-of-freedom (DOF) posture measurement in a linear stage by employing a single unit of an optical encoder. The proposed optical encoder was constructed to simultaneously measure the posture along the traveling axis; angular errors, pitch, yaw and roll; and translational errors, ?X, ?Y and ?Z. It consists of a diffractive optical element, a corner cube, four separate two-dimensional position-sensitive detectors, four photodiodes and auxiliary optics components. The circularly polarizing interferometric technique was integrated to measure the displacement of the stage along the traveling axis in a robust manner and the resolution was estimated to be less than 0.4 nm. Two types of stages were employed for the measurement implementation, the piezoelectric transducer-driven and the ballscrew-driven, and they were feedback-controlled for the traveling axis, respectively. With a single travel of the stage, it provided a six-DOF motion error with a high resolution, less than 0.03 arcsec, 20 nm and 0.4 nm for angular errors, ?Y and ?Z, and ?X, respectively, at the same time. As a result, it was seen that motion errors of the stage have relevance to the driving mechanism and the whole construction of the stage.
52 citations
TL;DR: In this paper, a linearization method with improved robustness for determining the displacement from sine and cosine signals generated by optical encoders is presented, which is based on a ratiometric technique and a dedicated compensation method.
Abstract: A linearization method with improved robustness for determining the displacement from sine and cosine signals generated by optical encoders is presented. The proposed scheme is based on a ratiometric technique and a dedicated compensation method. The scheme converts the sinusoidal signals into a nearly perfectly linear output signal, from which the displacement is determined precisely using a simple linear equation. Under the condition of ideal input signals, the theoretical analysis shows that the converter enables a determination of the displacement with a non-linearity error below 0.0029 µm for a linear optical encoder with a period of 20 µm. The performance of the converter with non-ideal input signals is also evaluated by establishing the relationship between the positioning errors and the parameter deviations of the input signals. Due to the robustness of the converter against the signal amplitude imbalance, a signal processing circuit is developed to convert the signal phase-shift error into the signal amplitude imbalance error. A displacement measurement experiment was carried out by applying the converter to a linear optical encoder with a period of 20 µm. A positioning accuracy of 0.2 µm over a travel length of 80 mm was achieved under laboratory conditions. The feasibility of the proposed converter has been confirmed from the experimental results.
43 citations
TL;DR: An electronic interpolator based on the ratiometric linearization conversion method is presented that converts the sinusoidal encoder signals into a nearly perfectly linear output signal through mathematical manipulation that only involves basic operations of addition, subtraction, multiplication, and division.
Abstract: Electronic interpolation is the key technology for further improving the measurement resolution of optical encoders In this paper, an electronic interpolator based on the ratiometric linearization conversion method is presented The proposed method converts the sinusoidal encoder signals into a nearly perfectly linear output signal through mathematical manipulation that only involves basic operations of addition, subtraction, multiplication, and division Thus, the displacement can be precisely determined using a simple linear equation Furthermore, quadrature interpolation pulses are also generated from the linear output signal by using the amplitude subdivision method Since the linearization procedure is based on the ratiometric operation, interpolation accuracy is independent of amplitude fluctuation of the encoder signals Theoretical analysis shows that the nonlinear error of the proposed interpolator is below ±00034 rad over a signal period of 2 π rad, which corresponds to an interpolation error of ±00108 μ m for a linear optical encoder with a pitch of 20 μ m In the experiment, the proposed strategy is successfully implemented within a field programmable gate array, and applied to a 20 μ m-pitch optical encoder Experiments are performed to demonstrate the effectiveness of the proposed method
38 citations
Cites background from "Metrological errors in optical enco..."
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TL;DR: A five-degrees-of-freedom (5-DOF) laser linear encoder is developed to simultaneously measure the position, straightness, pitch, roll, and yaw errors along one moving axis.
Abstract: Linear laser encoders have been widely used for precision positioning control of a linear stage. We develop a five-degrees-of-freedom (5-DOF) laser linear encoder to simultaneously measure the position, straightness, pitch, roll, and yaw errors along one moving axis. This study integrates the circular polarized interferometric technique with the three-dimensional diffracted ray-tracing method to develop a novel laser encoder with 5-DOF. The phases encoded within the +1 and -1 order diffraction lights reflected from the diffraction grating are decoded by the circular polarized interferometric technique to measure the linear displacement when the diffraction grating moves. The three-dimensional diffracted ray tracing of the +1- and -1-order diffraction lights induced by the motion errors of the moved grating were analyzed to calculate the other motion errors based on the detection of light spots on two quadrant photodiode detectors. The period of the grating is 0.83 microm and the experimental results show that the measurement accuracy was better than +/-0.3 microm/+/-41 microm for straightness, +/-1 arc sec/+/-215 arc sec for angular error components, and +/-160 nm/2 mm for linear displacement.
32 citations
References
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01 Jan 1997TL;DR: A brief history of spectral analysis of gratings can be found in this article, where a review of electromagnetic theories of grating efficiencies is presented, along with an acousto-optic gratings review.
Abstract: A brief history of spectral analysis fundamental properties of gratings the types of diffraction gratings efficiency behaviour of plane reflection gratings transmission gratings icily gratings concave gratings surfacewaves and grating anomalies waveguide, fibber, an acousto-optic gratings review of electromagnetic theories of grating efficiencies testing of grating performance instrumental systems grating damage and control mechanical ruling of gratings holographic recording of gratings alternative methods of grating manufacture replication of gratings.
516 citations
TL;DR: In this paper, the authors discuss the theoretical and applicational aspects of the self-imaging phenomenon, that is, the property of the Fresnel diffraction field of some objects illuminated by a spatially coherent light beam.
Abstract: Publisher Summary This chapter describes the self-imaging phenomenon and its applications. The self-imaging phenomenon requires a highly spatially coherent illumination. It disappears when the lateral dimensions of the light source are increased. When the source is made spatially periodic and is placed at the proper distance in front of the periodic structure, a fringe pattern is formed in the space behind the structure. The chapter discusses the theoretical and applicational aspects of the self-imaging phenomenon—that is, the property of the Fresnel diffraction field of some objects illuminated by a spatially coherent light beam. The applications of self-imaging are summarized in four main groups—namely, (1) image processing and synthesis, (2) technology of optical elements, (3) optical testing, and (4) optical metrology. The chapter describes the double diffraction systems using spatially incoherent illumination. The first periodic structure plays the role of a periodic source composed of a multiple of mutually incoherent slits. Depending on whether the periods of two periodic structures are equal, the Lau or the generalized Lau effect is discussed. Various applications of incoherent double-grating systems are described in the fields of optical testing, image processing, and optical metrology. After examining some cases of coherent and incoherent illumination, the general issue of spatial periodicities of optical fields and its relevance to the replication of partially coherent fields in space is discussed.
457 citations
TL;DR: A simple method for determining the quadrature errors from experimental data obtained in the interferometer and correcting for them is described and a numerical example demonstrating the significant improvement in the precision of interferometers data is given.
Abstract: The precision and accuracy of interferometers using quadrature fringe detection are often limited not by the interferometer itself but by the detector system. There are three typical errors: unequal gain in the two channels; quadrature phase shift error; and zero offsets. This paper describes a simple method for determining the quadrature errors from experimental data obtained in the interferometer and correcting for them. A numerical example demonstrating the significant improvement in the precision of interferometer data is given.
425 citations
01 Oct 1990-Precision Engineering-journal of The International Societies for Precision Engineering and Nanotechnology
TL;DR: A calibration technique that uses two signals derived from the optical outputs of an interferometer to achieve nanometric uncertainties in path length determinations and describes a simple experimental technique for verifying the accuracy of fringe subdivision is described.
Abstract: Reliable bidirectional optical fringe counting is normally obtained by using two signals derived from the optical outputs of an interferometer varying sinusoidally with path difference and in phase-quadrature. This paper describes a calibration technique that uses these signals to achieve nanometric uncertainties in path length determinations. It discusses some of the limitations to achieving this uncertainty and describes a simple experimental technique for verifying the accuracy of fringe subdivision.
129 citations