Investigation into the limitations of straightness interferometers using a multisensor-based error separation method

Abstract

The uncertainty of a straightness interferometer is independent of the component used to introduce the divergence angle between the two probing beams, and is limited by three main error sources, which are linked to each other: their resolution, the influence of refractive index gradients and the topography of the straightness reflector. To identify the configuration with minimal uncertainties under laboratory conditions, a fully fibre-coupled heterodyne interferometer was successively equipped with three different wedge prisms, resulting in three different divergence angles (4°, 8° and 20°). To separate the error sources an independent reference with a smaller reproducibility is needed. Therefore, the straightness measurement capability of the Nanometer Comparator, based on a multisensor error separation method, was improved to provide measurements with a reproducibility of 0.2 nm. The comparison results revealed that the influence of the refractive index gradients of air did not increase with interspaces between the probing beams of more than 11.3 mm. Therefore, over a movement range of 220 mm, the lowest uncertainty was achieved with the largest divergence angle. The dominant uncertainty contribution arose from the mirror topography, which was additionally determined with a Fizeau interferometer. The measured topography agreed within ±1.3 nm with the systematic deviations revealed in the straightness comparison, resulting in an uncertainty contribution of 2.6 nm for the straightness interferometer.

A New Method for On-line Measurement of the Straightness Error of Machine Tools Using an Acceleration Sensor

“…The prediction coefficients, , can be obtained by solving the regular equation of the AR model. The regular equation of the AR model has been shown in equation ( 7): (7) Corresponding to the forward prediction, the backward prediction is the prediction of earlier data from known data, which can be expressed as: (8) Fig. 5.…”

“…Then represents the whole length of the measurement. As the measurement is performed at various speeds v, x can be replaced by: (10) mm/s， corresponds to the measurement time, s. Then by substituting formula (10) into formula (8), the corresponding function of the straightness with respect to time can be obtained:…”

“…The acceleration signal generated by the machine tools' straightness error in the Y direction of the X-axis was measured. The data fusion algorithm was used to extract the high, medium and low speed test signals and extract the space [0.0025, 0.01], [0.01, 0.1], [0.1, 2] bands, respectively; according to the test speed, the corresponding time and frequency were calculated as [0.8, 3.2], [1.6, 16], [8,160], respectively. The algorithm that has been proposed in this paper was used to fuse and remove the error of the integral trend term, and finally the corresponding straightness error curve was calculated.…”

“…The shortcomings of the ball bar are its small range and poor accuracy of the results obtained from the separation model. Therefore, there is an urgent need to develop an on-line measurement system for the linear axis, as well as shorten the downtime, improve production quality, and enhance the efficiency of the measurement of the geometric accuracy of the linear axis [4][5][6][7][8] .…”

Calibration of Displacement Laser Interferometer Systems for Industrial Metrology

“…The mean value of the straightness deviations is the absolute straightness of the guidance and the difference between the measurements is divided by two is the effective straightness deviation of the optics. This method is mentioned by Evans in an overview of reversal methods [45] and was recently applied in a detailed analysis of these optics [46].…”