Measured, Not Assumed

1. Three numbers that decide whether a table is quiet

An optical table has one job: to hold every component of an experiment at a fixed distance from every other component. It does not need to be heavy, and it does not need to be beautiful. It needs to be stiff, it needs to dissipate whatever energy does get into it, and its working surface needs to be flat enough that the mounts sitting on it are where the drawing says they are. Three measurable quantities describe those three properties, and together they tell you almost everything about how a tabletop will behave under a laser.

The first is the natural frequency, the frequency of the tabletop's first bending mode. Every plate rings at some frequency when it is struck; the stiffer and lighter it is, the higher that frequency. A high first mode matters twice over. Floor vibration and the machinery in a laboratory concentrate their energy below about 100 Hz, so a tabletop whose first mode sits at 200 Hz or more simply has nothing to resonate with. And a pneumatic or active isolator underneath the table works by being soft at 1 to 3 Hz; if the tabletop's own modes are far above that, the two systems never interact and the isolator does its work on a rigid body.

The second is the compliance, the displacement the surface produces per unit of force, expressed in nanometres per newton. Compliance is the inverse of dynamic stiffness and it is largest at the natural frequency, where a small periodic force, a shutter, a chopper, a pump line, can build up a deflection many times larger than the static one. The peak compliance therefore combines the stiffness of the structure with how well it is damped, and it is the number that predicts how far a mirror mount will move when something on the table starts to buzz. Lower is better, and the difference between a good tabletop and an indifferent one is not a few percent but a factor of ten or more.

The third is flatness, the deviation of the working surface from a true plane. It has nothing to do with vibration and everything to do with alignment: a surface that bows by a tenth of a millimetre across its length tilts every mount by an angle that a long beam path turns into a visible offset. Flatness is set by the skin material, the bonding process and the final machining, and it can only be known by measuring the finished surface.

2. Why a datasheet number is not a measurement

Almost every optical table on the market is a honeycomb sandwich: two steel skins bonded to a steel honeycomb core, closed at the edges by damped side walls. The design is well understood, and the natural frequency and compliance of an idealised sandwich plate can be estimated from its dimensions, skin thickness and core density before anything is built. That estimate is where most published specifications come from. It is a statement of design intent, not a property of the table that arrives in your laboratory.

The reason the two can differ is that the performance of a sandwich plate lives in its bonds. The core stiffens the skins only where the adhesive joins them, so a starved bond line, a core crushed out of square during pressing, a void along a side wall or a skin that was not flat when it was bonded each lowers the stiffness and shifts the first mode, and none of them are visible from outside. The flatness of the finished surface depends on the same steps. The only way to know what a particular tabletop does is to strike it, record how it responds and measure its surface, after it is built.

Across the industry, that final step is more often skipped than taken. Many suppliers quote a typical value taken from a calculation or from a single prototype tested when the product line was launched, some quote the specification of the table they resell under their own name, and some do not measure at all. The number on the datasheet is then a promise about a table that nobody has tested.

DAEIL SYSTEMS takes the other approach. The tabletops and breadboards in this note were designed, built and measured in our own factory: the honeycomb core, the bonding under a hydraulic press, the damped side walls, the sealed mounting holes and the finished surface. Because the product is made here, it can be measured here, and the measured results are what this note reports.

3. How DAEIL SYSTEMS measures a tabletop

Compliance and natural frequency are measured together in one impact test on the finished tabletop, resting on its supports. An instrumented impact hammer (Kistler 9728A20000) delivers a calibrated force impulse to the surface, and a piezoelectric accelerometer (Endevco 751-10 Isotron) records the response. Dividing the response spectrum by the force spectrum gives the frequency response function of the structure, from which two numbers are read: the frequency of the first peak is the natural frequency, and the height of that peak, converted to displacement per unit force, is the compliance. The spectrum is resolved to 0.625 Hz, and the frequencies in this note are rounded to the nearest hertz.

Each unit is tested at four points on the surface, and both numbers are recorded at each point. Repeating the test at four locations does two things: it confirms that the first mode is a property of the whole tabletop rather than of one corner, and it exposes a local defect, a poorly bonded region for instance, as a point whose compliance does not match the others. The values reported for a unit are the means of the four points.

Every unit is identified by its test number, so a measurement can be traced back to a specific tabletop of a specific size on a specific date. The data behind this note covers 154 production units tested between June 2024 and October 2025, from a 500 × 400 × 25 mm breadboard to a 3,600 × 1,500 × 400 mm tabletop, in every standard thickness from 25 to 400 mm along with a handful of imperial and custom sizes.

4. What 154 measured units show

The value of measuring production units, beyond verifying each one, is that the data as a whole shows whether the product behaves as its design says it should. It does, and the patterns are the ones sandwich-plate theory predicts.

4.1 Thickness sets compliance

The single strongest lever on compliance is thickness. Fig. 02 plots the measured sizes by nominal thickness; each dot is one size, the median of the tabletops or breadboards measured in that size, and the bar is the median of every unit in the class. The medians fall from about 2,000 nm/N at 25 mm to 810 nm/N at 50 mm, 420 nm/N at 100 mm, 290 nm/N at 200 mm and 56 nm/N at 300 mm; the three 400 mm units, all large tabletops, measured between 30 and 102 nm/N. The scatter within each class is mostly size: a class contains everything from a 600 mm breadboard to a 3.6 m tabletop, and the larger units sit at the top of each column.

4.2 Size sets natural frequency

Natural frequency depends on both size and thickness, but in Fig. 03 the size dependence is the clearer of the two. Within any one thickness the first mode falls smoothly as the surface area grows, following a power law with an exponent between −0.6 and −0.8 and a correlation of −0.94 or better in every class with enough sizes to fit. A 1,200 × 900 × 200 mm tabletop rings at 394 Hz; a 3,000 × 1,200 × 200 mm tabletop, with more than three times the area, rings at 126 Hz. Thickness moves the whole curve upward: at the same footprint a 300 mm tabletop sits above a 200 mm one, which sits above a 100 mm breadboard.

4.3 One law for the whole range

The two effects can be put on a single axis. For a sandwich plate the bending stiffness scales with the square of the thickness and the deflection under a point load scales with the area, so compliance should scale with the square of the slenderness, the ratio of the surface's characteristic length √(W × D) to the thickness T. Fig. 04 plots every measured size against that ratio. Over a range of compliance from under 20 to over 3,600 nm/N and of slenderness from 3.3 to 35, the fit has an exponent of 1.9, within a few percent of the theoretical 2, with a correlation coefficient of 0.87 across the 88 sizes (153 units).

This is the result that matters most from a manufacturing point of view. A tabletop whose bonds were starved or whose core was crushed would fall off this line on the compliant side. The measured sizes cluster around the theoretical law across the entire range, which is direct evidence that the bonded structure behaves as one plate, every time.

4.4 The same footprint, three thicknesses

Fig. 05 isolates the thickness effect at one footprint. At 1,800 × 1,200 mm, a 100 mm breadboard measures 797 nm/N, a 200 mm tabletop 262 nm/N and a 300 mm tabletop 38 nm/N: a 21-fold reduction in compliance for a threefold increase in thickness. The natural frequency rises from 142 Hz at 100 mm to 215 Hz at 200 mm, and settles at 200 Hz at 300 mm, where the added core mass offsets the added stiffness. That is why thicker is not simply higher-frequency, and why the compliance, not the frequency, is the number to compare when choosing a thickness.

4.5 Four points, one answer

The four-point protocol also says something about the tabletops themselves. Of the 154 units, 126 returned exactly the same natural frequency at all four measurement points, and 144 agreed within 1.5 Hz. The compliance varies more from point to point, as it should, because the amplitude of a mode depends on where on the plate it is measured; the median ratio between the highest and lowest of the four readings is 1.3. A tabletop that rings at one frequency wherever it is struck, with compliance that varies only by geometry, is a single, uniformly bonded structure.

5. Representative measured units

The tables below list measured values for standard sizes. Each value is the mean of the four measurement points on a production unit; where more than one unit of a size was measured, the median of those units is given and the number of units is shown.

Breadboards

Optical tabletops

The performance figures on our product pages are taken from these tables. The headline pair for tabletops, 38 nm/N and 200 Hz, is the 1,800 × 1,200 × 300 mm row, the median of seven production units; the pair for breadboards, 406 nm/N and 250 Hz, is the 1,200 × 900 × 100 mm row, the median of six. They are four-point means measured on the size stated, and they describe that size: a smaller or thicker plate measures stiffer, a larger or thinner one more compliant, as §4 shows. A specification quoted without its size is not comparable to anything; ours are quoted with the size they were measured on and the number of units behind them.

6. Flatness, the third number

Flatness is measured on every unit, on the finished working surface, after the mounting grid has been machined and the holes sealed. The surface is divided into eight zones, the flatness of each zone is measured, and the flatness of the unit is the mean of the eight readings. The specification, ±0.03 mm, applies to that mean, and it applies to every standard size: every catalogue thickness from 25 to 400 mm, on any footprint up to 3,600 × 1,500 mm. Plates built outside that envelope are finished to the tolerance agreed on their drawing and are not part of the figures below.

Fig. 06 shows the flatness record of the last eighteen months of standard-size production: 600 tabletops and breadboards measured between March 2025 and August 2026. The median unit measures 15 µm, half the specification; 96 per cent of units are at or under 20 µm; the highest unit in the record measures 25 µm; and every one of the 600 is within the 30 µm specification.

One thing in the record is worth pointing out: flatness does not depend on size or thickness. The median is 14 to 15 µm in every thickness class from 25 to 400 mm, and it is 14 µm for units larger than 3 m² and 15 µm for units smaller than 0.5 m². Stiffness is set by the geometry of the sandwich; flatness is set by the process, bonding and final machining, and the same process gives a 3.6 m tabletop the same surface as a 600 mm breadboard.

Flatness and stiffness are set in the same operations, bonding and final machining, so a table whose surface measures flat is also a table whose skins were flat when they were bonded, and the flatness record is one more check on the structure underneath.

7. How to read a supplier's specification

If you are comparing optical tables, four questions separate a measured number from a quoted one.

Ask what size the number was measured on. Compliance and natural frequency change by a factor of ten across a product range, so a single value with no dimensions attached describes nothing. Ask whether the compliance is the peak of the frequency response or a static value; the peak is the one that predicts motion under a periodic disturbance, and it is the larger of the two by a wide margin. Ask whether the value was measured on production units or estimated from the design, and whether the supplier can show the frequency response of a unit like yours. And ask how flatness was measured: over how many points, against what reference plane, and on the finished surface or the raw skin.

A manufacturer that measures will have the answers, and usually the plots, at hand.

8. Where the DAEIL SYSTEMS lineup fits

DAEIL SYSTEMS optical tabletops are built in Research, Scientific and Non-magnetic grades at 200, 300 and 400 mm thickness, from 1,000 to 3,600 mm wide and 600 to 1,500 mm deep, on pneumatic or rigid supports. Optical breadboards use the same honeycomb construction at 25, 50 and 100 mm thickness, from 500 to 1,500 mm wide and 400 to 1,200 mm deep, in magnetic and non-magnetic versions. Both carry an M6 × 1.0 (or 1/4-20) mounting grid on a 25 mm pitch with individually sealed holes, and both are measured as described in this note.

If your application needs a particular compliance or natural frequency, tell us the size and the disturbance you are designing against, and we will recommend a thickness from the measured record rather than from a calculation.