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TABLETOP DESIGNS

4.1 Design Objectives

There are two basic goals that guide the design of the optical tables made by Thorlabs: the natural resonances of the table should be as high as possible and the table should be well damped. The advantage to designing a table with resonances as high in frequency as possible is that the amplitude of the vibrations is proportional to 1/cf at the peak of a resonance. As discussed in section 3.3, increasing the frequency of a resonance requires an increase in the stiffness and/or a reduction in the mass of the optical table. To minimize the duration and amplitude of the vibrations that do occur on the table, additional damping mechanisms can be built into the table.

4.2 Tabletop Vibrations

For a typical rectangular tabletop, the lowest frequency vibrations (in order from lowest to highest frequency) are the long, torsional, and short bending modes. In Fig. 11 these bending modes are illustrated along with the first overtone of the long bending mode.

Figure 11. Vibrational modes of an optical table

Each of these independent modes has a characteristic resonant frequency, which gives rise to a corresponding peak in the compliance curve.

Therefore, to avoid any resonant effects from induced floor or tabletop vibrations, the resonant frequencies of the table need to occur at frequencies above the frequency of the vibrations created by sources in the vicinity of the table.

Figure 12. Compliance curve of an optical table with the resonance due to the first bending mode of the table labeled.

In addition to the first long, torsional, and short bending modes, there is a series of overtones (i.e., higher frequency resonances), which are responsible for the series of peaks in the compliance curve that occur at higher frequencies than the first bending frequency (see Fig. 12).

Figure 13. Schematic showing the nodes and antinodes of the 1st bending and torsional modes.

Different vibrational modes have their maximum amplitude displacement points (antinodes) and minimum amplitude displacement points (nodes) at different places on the table. Clearly, with the possibility of simultaneous excitation of several vibrational modes, the resultant compliance of an optical table is a complex function that will vary considerably over the table surface.

4.3 Tabletop Materials

The three basic requirements for an optical tabletop are:

• good static rigidity (i.e., stiffness)
• low mass so that no low frequency (<100 Hz) resonances are present. Note: Low frequency resonances have large amplitudes ,and most laboratory background vibrational noise occurs at low frequencies.
• a well damped structure.

For many years, scientists performed delicate optical experiments on home-built tables, which were usually quite massive. These optical tables were constructed from granite, concrete, wood, steel, and many elaborate composite structures in attempts to improve performance while keeping weight at a realistic level. Each of these materials has advantages and disadvantages. The disadvantages of granite and concrete are that the slabs tend to absorb water vapor, which causes them to deform. Steel has two distinct drawbacks: a high density and a tendency to resonate at several vibrational frequencies, with very little natural damping. The performance of wood is surprisingly good; however, it has a tendency to warp with time and/or exposure to moisture.

In the end, the best material for use in the construction of an optical table is a composite (i.e., some matrix of materials that combines the stiffness characteristic of pure metal, the damping associated with rubber, and the low density of wood). Most modern optical tables are made using solid steel or aluminum plates separated by an interior honeycomb structure, which is usually made from steel. The plates provide a stiff, flat working surface while the interior honeycomb structure greatly increases the dynamic rigidity of the optical table without significantly increasing the mass of the optical table. The honeycomb structure naturally damps table vibrations; however optical tables used in experiments sensitive to vibrations usually include additional interior damping mechanisms that specifically dampen the lowest frequency resonances of the optical table.

4.3.1 Stiffness of Hollow versus Solid Structures

Consider a solid bar of a homogeneous material such as steel. If this bar is bent, then one edge is stretched and the other is compressed while the core of the bar is relatively unaffected by this deformation. Consequently, the restoring force is primarily due to the edges of the bar. As a result, a hollow bar would be almost as resistant as a solid bar to this type of deformation. Therefore, the strength of a structure is dependent not only on the material of the structural elements but also on their shape and position; this idea can be further demonstrated by considering how an I-Beam responds to the same bending force that was applied to the solid bar discussed above. Under load, the top flange is under tension and the bottom flange is under compression, but at the "neutral axis (n.a.)" the stress is zero. The flanges carry the bending stresses and the web resists the shear forces. The further apart the flanges are, the lower the deflection for a given load; i.e., the higher the stiffness. Therefore, when designing an optical table, it is important to consider the shape of the structure.

Figure 14. Tubes and I-beams have a large stiffness-to-mass ratio

4.4 Optical Table Design

A hollow steel table would be very rigid for its mass because the sides, top, and bottom plates would act as an extended I-beam. However, this structure would tend to ring due to the absence of damping, and it would also sag in the middle under heavy load conditions. For these reasons optical tables are not hollow; instead, they are filled with a material that increases the damping of the optical table and its stiffness in the vertical direction. An interior honeycomb structure adds these properties to the optical table without making the optical table overly massive. Steel, aluminum, phenolic, graphite, Kevlar, and even wood pulp have all been used as honeycomb materials.

4.4.1 Honeycomb Theory

If the interior support structure consisted of planes of parallel steel sheets bonded to the top and bottom solid steel plates, this would effectively make the table into a series of I-beams oriented along the long direction of the steel sheets as shown in Fig. 15. This geometry would dramatically increase the stiffness of the table along this direction due to the shape of the I-beam as discussed above. In order to create this I-beam-type structure along two axes, the plane sheets could be interlocked. At this point, the table would be most susceptible to bending along a plane at 45° with respect to either of the planes of parallel sheets, which means that the table’s resistance to torsional bending has not be significantly improved.

Figure 15. Planes of stiffness

Therefore, to resist the long, short, and torsional bending modes, the sheets in the structure must be oriented at intermediate angles. The disadvantage to the strategy of continuing to add parallel planes of sheets at intermediate angles is that each set of sheets increases the mass of the table; if the idea of adding new sets of parallel planes is projected forward, the resulting optical table would just be a solid steel object with a high mass and very little natural damping mechanisms. The most practical solution to the need for a light structure that provides stiffness along several planes is to create an interior with a hexagonal or sinusoidal cellular structure. A hexagonal structure is easy to fabricate by crimping the sheets and reduces the maximum angle from a plane supported by the structure to 30° without significantly increasing the weight of the table.

4.4.2 Thorlabs Metal Honeycombs

All of the standard tables made by Thorlabs consist of a sandwich structure (see Fig. 16) comprised of thick, steel top and bottom plates with a metal honeycomb core. Thorlabs’ honeycomb is fabricated from strips of precision-crimped steel, which are then bonded together with a high-tensile-strength epoxy adhesive.

FIgure 16. Construction of a honeycomb panel

4.4.3 Bonding Materials

The structural integrity of the composite optical table is extremely important to the performance of the optical table. As a result, Thorlabs uses a hot pressing method and a modified structural epoxy adhesive to bond the honeycomb to the steel plates; then, the adhesive is cured under vacuum for 18 hours. This results in a bond between the various pieces of the composite structure that has a high tensile strength as well as extremely high shear and peel strengths.

4.5 Damping Techniques

In theory, a resonating structure without damping has an infinitely high compliance peak at its natural frequency. Damping systems suppress these peaks by usually converting the energy of vibration into heat, which causes the amplitude of the disturbance to decay rapidly to zero.

As previously stated, the equipment mounted on the tabletop can be a major source of vibration (e.g., an out-of-balance laser beam chopper blade). Once a table is mounted on its pneumatic isolators (see Fig. 17), any vibrations induced on the top are not transmitted through the supports and dissipated in the ground. Therefore, these vibrations must be damped by the table's own internal damping.

Figure 17. Damping and vibration isolation

The damping of an optical table arises from several sources. The materials themselves have some natural damping, particularly in the case of the metal honeycomb. Producing a table with state-of-the-art performance, suitable for the most demanding applications, requires additional damping. At Thorlabs, the additional damping mechanism involves positioning dampers at strategic points in the core of the table. These dampers are specially shaped pieces of inhomogeneous material that act as though they contain a spectrum of masses, separated by a continuous spectrum of distances in an elastomeric polymer. The effect is dramatic, greatly reducing the height of the low frequency resonance compliance peaks, sometimes by more than an order of magnitude.

4.6 Surface Flatness

Tabletop flatness is critically important during many experimental setups. If the optical table surface is not flat, the height of a component will vary as it is moved to different positions on the optical table, and the possibility exists for components with flat bases to wobble when placed on the optical table. Thorlabs’ optical tables are extremely flat due to the high-precision magnetic stainless steel plates used to make the mounting surface. Each plate is specially handled to maintain its superior flatness throughout the manufacturing process.

4.7 Athermal Design

The optical tables made by Thorlabs have matching magnetic stainless steel plates on the top and bottom surfaces of the table. This design minimizes thermally induced stress and bowing of the optical table.

4.8 Evaluating Performance

As previously discussed, the performance of an optical table is quantified by its compliance. The compliance of Thorlabs’ tables is measured using a dynamic signal analyzer.

Figure 18. Evaluating the performance of an optical table

An impulse hammer is used to apply a measured force to the top surface of the table, and transducers attached to the surface detect the resultant vibrations. The signals from the transducers are interpreted by the analyzer and used to produce a frequency response spectrum (i.e., a compliance curve). During the development phase of an optical table, compliance curves are recorded at many points on the tabletop; however, the compliance is always greatest at the corners. The compliance curves and data published by Thorlabs are from the sensors located on the corner of the table and therefore represent the worst case data.

4.9 Summary
• The optical table should be a stiff, low mass structure.
• The compliance characteristics of an optical table should be as near as possible to that of an ideal rigid body.
• The table resonances should be shifted to as high a frequency as possible in order to minimize the number of common vibrational sources that produce vibrations at a resonant frequency.
• The table should have internal damping mechanisms that minimize the table’s compliance at resonant frequencies and damp all vibrations in the shortest possible time. The characteristic damping time is referred to as Impulse Decay and is usually reported with units of milliseconds.
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