Uncertainty In Length Measurement Research Articles

Salecker–Wigner–Karolyhazy Gedankenexperiment in light of the self-gravity

In Gedankenexperiment mentioned in the title, the imprecision in space-time measurement is related to the spreading of clock's wave-function with the passage of time required for the measurement. Special relativity puts a bound on the measurement time, it cannot be reduced arbitrarily as the signal used for the measurement cannot propagate with speed greater than that of light. In view of this reasoning, one is led to conclude that the clock should be heavy enough to slow down its wave-function from spreading with time. However, the general relativity puts an upper bound on clock's mass, since its size must remain greater then the Schwarzschild radius associated to it. This way one reaches a limit in length measurement. However, as is discussed below, an additional insight into the question comes by taking into account self-gravitational effects. As a result, the uncertainty in length measurement is reduced to the Planck length.

Analysis of the uncertainty in length measurement during the calibration of gauge block on the example of S4 from document EA-4/02 M:2013

Analysis of the uncertainty in length measurement during the calibration of gauge block on the example of S4 from document EA-4/02 M:2013

Uncertainty evaluation associated with versatile automated gauging influenced by process variations through design of experiments approach

Recent advances in versatile automated gauging have enabled accurate geometric tolerance assessment on the shop floor. This paper is concerned with the uncertainty evaluation associated with comparative coordinate measurement using the design of experiments (DOE) approach. It employs the Renishaw Equator which is a software-driven comparative gauge based on the traditional comparison of production parts to a reference master part. The fixturing requirement of each production part to the master part is approximately ±1mm for a comparison process with an uncertainty of ±2μm. Therefore, a number of experimental designs are applied with the main focus on the influence of part misalignment from rotation between master and measure coordinate frames on the comparator measurement uncertainty. Other factors considered include measurement mode mainly in scanning and touch-trigger probing (TTP) and alignment procedure used to establish the coordinate reference frame (CRF) with respect to the number of contact points used for each geometric feature measured. The measurement uncertainty analysis of the comparator technique used by the Equator gauge commences with a simple measurement task using a gauge block to evaluate the three-dimensional (3D) uncertainty of length comparative coordinate measurement influenced by an offset by tilt in one direction (two-dimensional angular misalignment). Then, a specific manufactured measurement object is employed so that the comparator measurement uncertainty can be assessed for numerous measurement tasks within a satisfactory range of the working volume of the versatile gauge. Furthermore, in the second case study, different types of part misalignment including both 2D and 3D angular misalignments are applied. The time required for managing the re-mastering process is also examined. A task specific uncertainty evaluation is completed using DOE. Also, investigating the effects of process variations that might be experienced by such a device in workshop environments. It is shown that the comparator measurement uncertainties obtained by all the experiments agree with system features under specified conditions. It is also demonstrated that when the specified conditions are exceeded, the comparator measurement uncertainty is associated with the measurement task, the measurement strategy used, the feature size, and the magnitude and direction of offset angles in relation to the reference axes of the machine. In particular, departures from the specified part fixturing requirement of Equator have a more significant effect on the uncertainty of length measurement in comparator mode and a less significant effect on the diameter measurement uncertainty for the specific Equator and test conditions.

21310 万能投影機による長さ測定の不確かさ評価(OS13 計測・試験における不確かさ評価と応用(2),オーガナイズドセッション)

21310 万能投影機による長さ測定の不確かさ評価(OS13 計測・試験における不確かさ評価と応用(2),オーガナイズドセッション)

A weight average method to improve the uncertainty of length measurement in a two-color interferometer

Some phase errors in a two-color interferometer result in a large uncertainty in length measurement due to the large A coefficient. We analyzed three kinds of phase errors, correlation, semi-correlation and non-correlation errors, and presented a weight average method to deal with different errors by using different weight factors. The uncertainties in length measurement can be reduced without effects on the resolution of length measurement. The experimental results show that the length can be obtained with a standard deviation of approximately 0.1 μ m by measuring the phase of the interference fringe using a heterodyne interferometry and processing the measured data using a weight average method.

A high-temperature dilatometer using optical heterodyne interferometry

A high-precision interferometric dilatometer developed for use at high temperatures is described. The dilatometer consists of a double-path laser interferometer with optical heterodyne interferometry and a radiant heating furnace, which provides high accuracy length measurement and rapid heating and cooling for the specimen. The uncertainty in length measurement by the newly developed dilatometer is estimated to be within 2 nm in the range between room temperature and 1100 K.