Two roads or twin pillars? One of the pleasures of metrology is the lively and I believe healthy dialogue that takes place between mechanics and optics. But the division which I wish to discuss.is a different one, which shows itself in both these subjects.

In the field of mechanical design, for example, there are two apparently opposed principles, both of which help us to achieve precision of construction or performance.

The first of these is the kinematic principle, according to which, for any mechanism, just enough 6on- trol is applied to f ix or vary each of the degrees of freedom that are involved. Kinematic design ensures excellent repeatability, but the accuracy of a slideway for example may be spoilt by local flaws in its guiding members, and its load-bearing capacity may be limited.

The second is the principle of over-constraint, according to which the mechanism required is arranged to be the average of a multitude of individual mechanisms, each of which produces nominally the same result. Depending on the mechanism, the means used to accomplish the averaging can be an elastically deformable structure, an oil film, or the viscous memory of a pitch polishing lap. In some cases, too, the process can be iterative and self-generating; in the lapping of a spherical surface, for example, the errors of form being averaged are themselves progressively reduced unti l near-perfect cooperation is obtained.

Readers of this journal will know already that for many actual problems in precision engineering the best solution is found by judiciously combining both the above principles. If a kinematic slideway is large, for example, each rolling steel ball wi l l be replaced by a set of precision rollers or by opposed pairs of hydrostatic bearing-pads. In fabrication of an X-ray telescope, the aspheric profiles are generated at least init ial ly by single-point machining methods, but the bearing which is used to preserve revolution symmetry is based on the averaging principle.

In most of these situations, however, there is a third principle which may also be invoked - namely to reinforce good mechanical design with an optical measuring system, and use servo control.

Optical measuring systems take many forms, and during the last two decades their scope has been increased enormously by the invention of the laser and by the introduction of holographic and speckle techniques. For control of machine tools, however, many of the new techniques are largely irrelevant, since all that is required is to monitor the linear displacement of a carriage or the rotation of a bearing. In designing equipment to perform such tasks there are once again two approaches that can be followed.

In measuring a linear displacement, for example, one can use a sharply deterministictwo-beam laser interfero- meter, or one can use a moire fringe measuring system in which averaging is inherent.

For the laser interferometer both resolution and repeatability will be excellent, and for measurement over say 1.5m with a properly installed system an accuracy of 1 part in 107 is readily obtained: in the standards laboratory it may be 1 part in 108. For the do-it-yourself man, who may be content merely with getting a good fringe-counter signal, resolution and repeatability may still be excellent, but a systematic error of 1 part in 106 may creep in, caused for example by bad alignment or by a pressure correction wrongly applied.

With a moire fringe reading- head, resolution and repeatability are again excellent, and a best accuracy of 2 parts in 107 may well be sufficient for most machine tools. Each grating averages out the residual errors of the other, and the measurement is almost unaffected by source variations or by atmospheric changes. For gratings longer than 1.5m the errors can be calibrated with a laser interferometer and rechecked occasionally.

So far as linearity of movement is concerned, over short distances - say 100 mm - a mechanically averaging slide can produce exquisite smoothness. Over distances from 1 m to 20m both laser and white light methods of alignment have their pros and cons. Beyond this distance the superior brightness of the laser gives it a great practical advantage, but in most cases the limits on accuracy are set by the atmosphere.

Finally, in monitoring the rotation of a shaft or spindle the best accuracy is obtained by using an averaging system, based for example on radial gratings or on averaging by mechanical or electromagnetic methods. But the laser gyro is beginning to have comparable short-term performance, and can be used even when there is no fixed axis of rotation!

In the optical field, I suppose, the two types of system that I have been discussing correspond to the coherent and the incoherent. They represent two extremes of approach, each with its own advantages. Like the pillars of Hercules, they stand opposed, and the prudent • navigator knows when to hug one shore and when the other.

Dr J.M. Burch, National Physical Laboratory, UK

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