Straightness Deviations Research Articles

An intercomparison on roundness and form measurement

Intercomparison measurements have been carried out by twelve manufactures of form measurement equipment, industrial users and national metrology institutes to determine the present-day agreement in form measurement at an accuracy level of approximately 0.1 μm and to formulate ways to improve agreement. This work has been supported by the Commission of the European Communities under its programme for Applied Metrology and Chemical Analysis (BCR). All participants measured two cylindrical artefacts to determine the deviations from roundness, straightness, parallelism and cylindricity. The artefacts were chosen to have some roundness and straightness deviations comparable to the guide errors of the instruments used (up to 0.5 μm) as well as other characteristic form deviation features (up to 15 μm), allowing the amplification and transmission properties of the instruments to be investigated. Satisfactory agreement of the participants' results has been observed with respect to roundness and straightness, whereas large variations have been found in parallelism and cylindricity, where the position and form deviations of several measuring lines are taken into account to evaluate quantities. It is recommended that future efforts to achieve a higher degree of accord of form measurement should concentrate on the different techniques used for transducer calibration and the different characteristics of the software filter applied.

Some results of flatness measurement

The flatness evaluation method which has been described in the previous paper in this issue makes use of the straightness measuring results obtained on lines of a rectangular grid pattern drawn on the surface = . In fact, any straightness measuring method may be applied, but experience of this institute has been in two particular methods: the straight edge method and the height-difference measuring method. Both methods are principally different. The first one gives straightness deviations at each grid point, so the measured values are independent of each other, while in the second method the deviation at a grid point is measured in comparison with the previous point.

Optimum Coupling for Random Guides with Frequency-Dependent Coupling

We obtain exactly the covariance of the signal-signal and signal-spurious mode transfer functions of the coupled line equations with two forward-traveling modes, white random coupling with statistically independent successive values (e.g., white Gaussian or Poisson coupling), and a coupling coefficient that varies with the frequency of the signals on the line. No perturbation or other approximations are made in this work. Time-domain statistics for the corresponding impulse responses are obtained for moderate fractional bandwidths. These results are extensions of a similar treatment for frequency-independent coupling coefficients, given in a companion paper. If the coupling were independent of frequency, the signal distortion would ultimately decrease as the coupling increased, approaching zero as the coupling approached infinity. The frequency dependence of the coupling coefficient prevents the distortion from approaching zero; the optimum coupling, which achieves minimum signal distortion, is independent of guide length. Millimeter waveguides and optical fibers with random straightness deviations have coupling coefficients inversely proportional to the frequency. The above results yield the optimum random straightness deviation for such a guide. More forward modes can be treated in a straightforward way by more complicated calculations.

Measured TE01Attenuation in Helix Waveguide with Controlled Straightness Deviations

A helix circular waveguide 380 feet long has been deformed into three different curves. The added mode conversion loss for a TE <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">01</inf> signal mode has been measured and calculated theoretically, with good agreement. For a curve with 30-inch deflection over a distance of 100 feet, peak-to-valley (200-ft period), the measured added loss at 55.5 kmc was 0.23 db/mile, the calculated 0.20 db/mile.

Transmission deviations in waveguide due to mode conversion: theory and experiment

Coupling to spurious modes at imperfections in a long circular waveguide may cause the TE01 loss to increase and to fluctuate randomly with frequency. The statistical properties of the TE01 loss/frequency curve can be expressed in terms of the statistical properties of the random geometric imperfections of the guide and therefore in terms of its mechanical tolerances. Such imperfections as poor joints and elliptical waveguide have negligible effect under reasonable tolerances. However, random deviations of the guide axis from a straight line may have very serious effects under certain conditions. The use of mode filters or of helix waveguide to increase the spurious-mode loss reduces the TE01 loss fluctuations but leaves the average TE01 loss due to mode conversion relatively unaffected.Experimental measurements of loss/frequency curves, of spurious-mode content and of mechanical tolerances which have been made on existing waveguides support these conclusions. Random straightness deviations introduced during manufacture of the waveguide are the primary cause of the observed transmission behaviour.