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Negative-Stiffness Vibration Isolation Gains Popularity
Jun 2009

By Dr. David L. Platus, Minus K Technology Inc. and Jim McMahon, Zebra Communications.

Negative-stiffness mechanism vibration isolation enables laser/optical instruments such as SPMs, microhardness testers and optical profilers to operate in severe vibration environments that would not be practical with other passive and electronic isolation systems.

Laser and optical systems, whether used in academic labs or industry, are very susceptible to vibrations from the environment, so these instruments frequently need vibration isolation. When measuring a very few angstroms or nanometers of displacement, an absolutely stable surface has to be maintained upon which to rest the instrument. Any vibration coupled into the mechanical structure of the instrument will cause vertical noise and, fundamentally, an inability to measure these kinds of high resolution features.


Figure 1. A schematic of an NSM vibration isolator. A vertical stiffness adjustment screw is used to regulate the compression force on the negative-stiffness flexures. A vertical load adjustment screw raises or lowers the base of the support spring in response to varying weight loads to keep the flexures in their straight, unbent operating position.

Traditionally, large air tables have been the isolators used for laser/optical equipment. The ubiquitous passive-system air tables, adequate up until a few years ago, are now being seriously challenged by the need for more refined imaging requirements. Bench-top air systems, however, provide limited isolation vertically and very little isolation horizontally. Yet, scanning probe microscopes (SPMs), for example, have vibration isolation requirements that are unparalleled in the laser/optical world. The vertical axis is the most sensitive for most SPMs; they can also be quite sensitive to vibrations in the horizontal axes. In order to achieve the lowest possible noise floor, on the order of an Angstrom, vibration isolation must be used. Negative-stiffness mechanism (NSM) isolators have the flexibility of custom tailoring resonant frequencies vertically and horizontally, providing increased isolation performance for SPMs over air tables.

Laser-based interferometers also are extremely sensitive devices, capable of resolving nanometer-scale motions and features. They often have very long mechanical paths, which makes them even more sensitive to vibrations. The sophisticated modern ellipsometry techniques that allow this high performance rely on low noise to be able to detect fringe movement. Properly isolating an interferometer will allow it to provide the highest possible resolution. 

Optical interferometers and other optical systems such as optical profilers are often quite complex, and have long optical paths that can lead to angular magnification of vibrations. Air tables can make the problems worse, since they have a resonant frequency that often matches that of floor vibrations – typically 2 to 3 Hz. And their isolation efficiency is quite limited below about 8 Hz. NSM isolators provide isolation in these environments when air tables simply cannot.

Improved transmissibility

What negative-stiffness isolators provide is quite unique to the field of laser/optical systems. In particular, the transmissibility – that is, the vibrations that transmit through the isolator relative to the input vibrations. Transmissibility with negative-stiffness is substantially improved over air systems, and even over active isolation systems.

Figure 2. The transmissibility of a passive negative-stiffness vibration isolator – the vibration that transmits through the isolator as measured as a function of input vibrations - can be 10X to100X better than high-performance air tables depending on the vibration frequency.

Also known as electronic force cancellation, active isolation uses electronics to sense the motion, and then adds forces electronically to effectively cancel out or prevent it. The efficiency of active isolation systems is adequate for applications with the latest lasers and optics, as they can start isolating as low as 0.7 Hz. But because they run on electricity, they can be negatively influenced by problems of electronic dysfunction and power modulation, which can interrupt scanning. Active systems also have a limited dynamic range – which is easy to exceed – causing the isolator to go into positive feedback and generating noise underneath the equipment. Although active systems have fundamentally no resonance, their transmissibility does not roll off as fast as NSM isolators.

Negative-stiffness isolators employ a unique and completely mechanical concept in low-frequency vibration isolation. Vertical-motion isolation is provided by a stiff spring that supports a weight load, combined with an NSM. The net vertical stiffness is made very low without affecting the static load-supporting capability of the spring. Beam-columns connected in series with the vertical-motion isolator provide horizontal-motion isolation. The horizontal stiffness of the beam-columns is reduced by the "beam-column" effect. (A beam-column behaves as a spring combined with an NSM.) The result is a compact passive isolator capable of very low vertical and horizontal natural frequencies and very high internal structural frequencies. The isolators (adjusted to 1/2 Hz) achieve 93 percent isolation efficiency at 2 Hz; 99 percent at 5 Hz; and 99.7 percent at 10 Hz. See Figures 1 and 2.

Horizontal and vertical motion isolators

Negative-stiffness mechanism isolators typically use three isolators stacked in series: a tilt-motion isolator on top of a horizontal-motion isolator on top of a vertical-motion isolator. MinusK3.jpg

Figure 3. An NSM vertical motion isolator.

A vertical-motion isolator uses a conventional spring connected to an NSM consisting of two bars hinged at the center, supported at their outer ends on pivots, and loaded in compression by forces P. (See Figure 3. The hinged bars are for illustration only. Flexures are used in the isolators to avoid stiction and friction.) The spring is compressed by weight W to the operating position of the isolator. The stiffness of the isolator is K=KS-KN where KS is the spring stiffness and KN is the magnitude of a negative stiffness, which is a function of the length of the bars and the load P. The isolator stiffness can be made to approach zero while the spring supports the weight W.

A horizontal-motion isolation system is illustrated by two beam-column isolators. Each isolator behaves like two fixed-free beam-columns loaded axially by a weight load W. Without the weight load, the beam-columns have horizontal stiffness KS. With the weight load, the lateral bending stiffness is reduced by the "beam-column" effect. This behavior is equivalent to a horizontal spring combined with an NSM so that the horizontal stiffness is K=KS-KN, and KN is the magnitude of the beam-column effect. Horizontal stiffness can be made to approach zero by loading the beam-columns to approach their critical buckling load. See Figure 4.


Figure 4. An NSM horizontal motion isolator.

As industry and universities continue to broaden their laser/optical research and applications necessitating more sensitive equipment and expanded lab facilities, vibration-handicapped environments will become more prevalent, and a better vibration isolation solution will be required than what has been available.

Negative-stiffness mechanism vibration isolation systems have become a growing choice for laser and optical applications. Not only is it a highly workable vibration solution, but its cost is significantly less – up to one-third the price compared to active and traditional passive systems – making it an economical solution to cost-conscious administrators.

Meet the authors

Dr. David L. Platus is president and founder of Minus K Technology Inc. in Inglewood, Calif.; email: Minus K develops, manufactures and markets state-of-the-art vibration isolation products based on the company's patented negative-stiffness-mechanism technology.
For more information, visit: or

Jim McMahon is the president of Zebra Communications in Simi Valley, Calif., and writes on industrial instrumentation and controls; e-mail:

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The measurement of the change in ellipticity of an optically polarized light beam after reflection from a surface in a particular manner.
The technology of generating and harnessing light and other forms of radiant energy whose quantum unit is the photon. The science includes light emission, transmission, deflection, amplification and detection by optical components and instruments, lasers and other light sources, fiber optics, electro-optical instrumentation, related hardware and electronics, and sophisticated systems. The range of applications of photonics extends from energy generation to detection to communications and...
scanning probe microscope
See atomic force microscope; magnetic force microscope; near-field scanning optical microscope; scanning tunneling microscope.
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