Introduction

Demands on the precision and resolutions of metrological equipment and techniques have become more stringent in pace with technological advances. Metrological setups and systems have thus become more sensitive to external influences, such as temperature variations and vibrations.

Thermal effects may usually be minimized by thermostatting, use of temperature-compensated hardware and supporting structures, shortening the duration of mea-surement, and other relatively straightforward means. Special equipment is available for minimizing effects due to vibrations, but the full benefits provided by such equipment will be obtained only if all of the following requirements are met:

- All components of metrological setups or systems must be sufficiently rigidly aligned with respect to one another. This requirement may be met by mounting all such components on a single, extremely stiff, base. Optical table tops are used for this purpose.

 - The entire complex, consisting of the experimental setup itself plus its supporting base, must be mounted on vibration-isolators. Special supports equipped with various types of vibration-isolation systems are used for this purpose.

Optical Table Tops

Optical table tops must be designed to provide high structural stiffness if relative motions of components mounted on them due to external vibrations are to be minimized. In addition, any vibrations reaching table tops, in spite of the vibration-isolation systems incorporated into their supports, must be rapidly damped out; i.e., optical table tops must have highly effective internal damping mechanisms.

Optical table tops may thus be classified in terms of their structural rigidities and their internal damping characteristics. Their structural rigidities should be assessed in terms of both their static stiffness and their dynamic rigidities, i.e., their resistance to deformations due to dynamic applied loads.

 - Their static stiffnesses are equivalent to their Young's moduli, and are thus the ratio of their bending deflections to the magnitudes of the temporally constant (static), concentrated, applied loads causing these deflections.

- Their dynamic rigidities, on the other hand, express their Young's moduli as functions of the frequencies of temporally varying, i.e., dynamic, applied loads, such as vibrations, inducing bending deflections of their structures.

The frequency responses of table tops may be graphically represented in the form of so-called "compliance" curves, defined as the reciprocals of their dynamic rigidities, versus the frequencies of periodically varying applied loads, covering the full ranges of frequencies likely to be of interest.

An analysis of the compliance curves of optical table tops indicates that they may be roughly regarded as ideal rigid bodies up to frequencies of about 80 Hz. At higher frequencies, however, optical table tops exhibit resonances, evident by occurrence of peaks in their compliance curves. Compliance curves are a useful aid in assessing the dynamic rigidities of optical table tops at various excitation frequencies. They may also be used to compare the frequency responses of unloaded table tops of equal weight and equal dimensions.

Since the amplitudes of vibrational resonances of rectangular table tops are greatest at their corners, corner-compliance curves, or plots of their compliances at their corners versus the frequencies of dynamic applied loads, represent quantitative indicators of table-top performance. The widths of resonance peaks occurring in their corner-compliance curves are indicative of the effectiveness of their internal damping mechanisms.

In concluding our brief discussion of these topics, we should emphasize that the factors mentioned above refer to the performance of unloaded table tops, i.e., to table tops with no components mounted on them. These factors alone are thus inadequate to fully describe their performance under conditions of actual use. Since the static loads, and probably the dynamic loads as well, exerted on optical table tops by experimental setups will vary from case to case, purely qualitative design factors, particularly specifications relating to their honeycomb core mass density, should also be taken into account in selecting optical table tops. The material(s) used in fabricating their honeycomb cores, core thickness, plus specifications relating to their top and bottom plates and their sidewalls, constitute further major selection criteria. Any design features or mechanisms that have been incorporated in order to improve their internal damping characteristics should also be taken into account.

Details of the special design features of LINOS Photonics optical table tops are covered in the subsection entitled "Design Features".

Vibration-Isolation Systems

The choice of supports and vibration-isolation systems will have a significant affect on the performance of optical-table systems.

The purpose of vibration-isolation systems is isolating, to the maximum extent feasible, table tops from vibra-tions emanating from, or transmitted by, the floors or other surfaces on which their supports stand. The frequencies of these vibrations usually range from about 2 Hz up to 50 Hz, depending upon the characteristics and location of the floors, or other supporting surfaces, involved, as well as upon ambient conditions.

Practice indicates that spring-mass mechanisms are the best choices for such applications, but they must be tuned such that their natural resonant frequencies fall well below the frequencies of lowest-order building resonances if they are to provide high degrees of vibrational isolation.

The vibrational-transfer characteristics, or transmissibili-ties, of undamped spring-mass mechanisms are roughly as indicated in the graphs shown below, where ω₀ is their natural resonant frequency.

In addition to providing isolation from building vibra-tions, vibration-isolation systems should strongly isolate experimental setups from incidental vibrations due to, e.g., persons walking about, etc., and should strongly dampen these occurences; i.e., they should rapidly damp vibrations at all frequencies likely to be encoun-tered in actual use. This may be implemented by incor-porating various types of damping mechanisms, such as eddy-current damping or frictional/viscous damping using solid, liquid, or gaseous materials into vibration-isolation systems. Damping reduces the amplitudes of their natural resonance peaks, but the forces exerted on them by damping mechanisms increases their trans-missibilities at high frequencies, as can be seen from the graph shown below.

Thus, designing vibration-isolation systems entails arriving at a compromise that will provide the lowest resonant frequencies achievable, combined with the low-est resonance peaks consistent with strong damping of vibrations over the entire range of frequencies likely to be encountered in actual use.

Specially designed vibration-isolation systems are essential if all of these requirements are to be met.