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.

Quadrature phase-shift error analysis using a homodyne laser interferometer

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.

https://iopscience.iop.org/article/10.1088/0957-0233/19/11/115104/pdf

Metrological errors in optical encoders

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.

https://iopscience.iop.org/article/10.1088/0957-0233/22/10/105901/pdf

Design and construction of a single unit multi-function optical encoder for a six-degree-of-freedom motion error measurement in an ultraprecision linear stage

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.

https://iopscience.iop.org/article/10.1088/0957-0233/25/12/125003/pdf

Design of a precise and robust linearized converter for optical encoders using a ratiometric technique

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

Ratiometric-Linearization-Based High-Precision Electronic Interpolator for Sinusoidal Optical Encoders

A simple collimation technique based on measuring the period of one self-image produced by a diffraction grating is proposed. Transversal displacement of the grating is not required, and then automatic single-frame processing can be performed. The self-image is acquired with a CMOS camera, and the period is computed using the variogram function. Analytical and experimental results are obtained, which show the simplicity and accuracy of the proposed technique.

/pdf/self-imaging-technique-for-beam-collimation-4q2nx28vke.pdf

Self-imaging technique for beam collimation

We present a collimation technique based on a double grating system to locate with high accuracy an emitter in the focal plane of a lens. Talbot self-images are projected onto the second grating producing moire interferences. By means of two photodetectors positioned just behind the second grating, it is possible to determine the optimal position of the light source for collimation by measuring the phase shift between the signals over the two photodetectors. We obtain mathematical expressions of the signal in terms of defocus. This allows us to perform an automated technique for collimation. In addition, a simple and accurate visual criterion for collimating a light source using a lens is proposed. Experimental results that corroborate the proposed technique are also presented.

https://eprints.ucm.es/26188/1/Bernabeu%2CE18libre.pdf

Collimation method using a double grating system.

We propose an accurate technique for obtaining highly collimated beams, which also allows testing the collimation degree of a beam. It is based on comparing the period of two different self-images produced by a single diffraction grating. In this way, variations in the period of the diffraction grating do not affect to the measuring procedure. Self-images are acquired by two CMOS cameras and their periods are determined by fitting the variogram function of the self-images to a cosine function with polynomial envelopes. This way, loss of accuracy caused by imperfections of the measured self-images is avoided. As usual, collimation is obtained by displacing the collimation element with respect to the source along the optical axis. When the period of both self-images coincides, collimation is achieved. With this method neither a strict control of the period of the diffraction grating nor a transverse displacement, required in other techniques, are necessary. As an example, a LED considering paraxial approximation and point source illumination is collimated resulting a resolution in the divergence of the beam of σ φ = ± μrad.

/pdf/dual-self-image-technique-for-beam-collimation-1i4zz278zx.pdf

Dual self-image technique for beam collimation

In this Letter, we analyze the near-field diffraction pattern produced by chirped gratings. An intuitive analytical interpretation of the generated diffraction orders is proposed. Several interesting properties of the near-field diffraction pattern can be determined, such as the period of the fringes and its visibility. Diffraction orders present different widths and also, some of them present focusing properties. The width, location, and depth of focus of the converging diffraction orders are also determined. The analytical expressions are compared to numerical simulation and experimental results, showing a high agreement.

/pdf/near-field-diffraction-of-chirped-gratings-4d0twq2ojp.pdf

Tomas Morlanes

Papers

Metrological errors in optical encoders

Self-imaging technique for beam collimation

Collimation method using a double grating system.

Dual self-image technique for beam collimation

Near-field diffraction of chirped gratings