Sensor calibration turns old technique into new trick

Sensor and source calibration has always been a challenge for scientists and engineers. The obvious way to perform this task is to use comparison and check your sensor or your source against a known, calibrated, better one. But this method reaches a limit, because, at some stage in the sequence, no better sensor or source for comparison exists, and you reach the end of the "better-standard" line. Further, the unavoidable errors inherent in the comparison chain and process itself always diminish your results.

The other approach is absolute calibration, in which you make your assessment by using fundamental physical quantities that are not directly related to your parameter of interest. For example, an atomic clock provides you with a way to check a microwave-frequency meter or timebase; the clock's timekeeping itself is based in atomic-level oscillations. In general, absolute calibration is more complex and costly than comparison calibration but yields results that you could not otherwise obtain.

The cost and complexity difference of the two approaches can be an order of magnitude or more for many physical quantities, but it's easier to provide absolute calibration for some parameters and sensors than for others. For example, length is relatively easy to check, because wavelengths of a type of light source define it. Similarly, because of the availability of moderately priced atomic clocks, timing accuracy is now among the easier parameters to verify.

But some physical quantities, such as temperature and acceleration, are difficult to provide with an absolute calibration technique. The calibration challenge becomes greater as you try to measure at the maximum or minimum extremes of these quantities. Many optical and motion-displacement calibrations use variations of interferometry, which US physicist Albert A Michelson and US chemist Edward W Morley used in their legendary eponymous experiment to disprove the existence of the luminiferous ether (see sidebar "I don't see any ether; do you?"). For accelerometer calibration at frequencies higher than 1 kHz, where the displacement is on the order of one wavelength of light, the technique of laser interferometry and fringe counting no longer worked well.

By adding some optical enhancements and digital-signal processing of data, along with a new mechanical structure for a shaker assembly, you can provide absolute calibration of accelerometers at frequencies as high as 50 kHz at a cost that is comparable with that of comparison calibration. Endevco Corp (www.endevco.com), a leading producer of accelerometers and calibration systems, developed such an automated system, which is in full accordance with relevant International Organization for Standardization standards (Reference 1).

In the basic interferometer setup for this calibration, the end of one of the arms is a movable mirror, rather than the fixed mirror that the Michelson-Morley experiment used. Using a movable mirror is a standard interferometer variation. With a helium-neonlaser having a wavelength of 0.63282 microns as a source, when you attach the mirror near the accelerometer under test, the mirror moves one-half of a wavelength, and the optical path changes by twice that value, or 0.31641 microns. You can count enough distinct interference fringes per period of vibration at low frequencies to achieve a meaningful and accurate result. But as the vibration period gets shorter and with realistic, moderate-sized displacements, the movement is too small to create even a single countable fringe; it may be only a single-digit percentage of a fringe and thus be hard to assess.

You base the final measurement on an estimate of what fraction of a single fringe the motion represents, rather than counting a large number of fringes. To make the observation even more difficult, the change in intensity of the fringe depends on where the deviation is in the sinusoidal cycle of the fringe. It has little or no variation at the top or bottom for small shifts; it has the greatest variation on the up and down slopes (Figure 1). The system would have better data if you could ensure that the fringe observation had occurred on a slope for all tests, but you can't do so with the conventional setup.

Endevco's team enhanced the interferometer itself and then applied sophisticated analysis algorithms to the output of the photodetector that observes the fringes. By employing a polarized laser source, two photodetectors, and an optical retarder, they built a single interferometer with one optical path length that is always one-quarter of a wavelength longer than the other, yet with the same physical path (Figure 2). This device, a quadrature interferometer, provides two waves that always have a 90° phase difference.

To build the quadrature system, Endevco oriented the polarized laser source at 45° degrees with respect to the beam splitters. The beam thus has equal horizontal- and vertical-constituent, or x and y, components. A polarizing beam-splitter separates the two components to create two interferometers in the same physical space. But a critical optical difference between the beams: The beams pass through an optical retarder that slows light that is polarized along the retarder's axis more than it slows light that is polarized perpendicular to its axis, thus adding one-fourth of a wavelength to the optical path of one of the beams. (You also have to add some other compensating tricks, because the beams travel back through the same retarder, yielding further delay, phase shift, and complications.)

As a result of this setup, one of the two photodetectors always sees a fringe pattern at or near the maximum slope region, so the observed data is consistent in its variation. Then, by using the outputs of both photodetectors to generate two sets of correlated data and correcting for differences in fringe intensity and other mechanical and optical errors, the system can extract the information about the displacement, even if it is much smaller than the wavelength of the laser output.

But marginal data doesn't become meaningful just by wishing it were so. The algorithms in the Endevco system look at the acquired data and invoke various techniques to extract data and enhance the validity of the data. If you plot the data from each photodetector in an x-y graph, you get a Lissajous pattern (Figure 3, see sidebar "Historical note").

The Endevco algorithm has several functions. In simplest terms, it must correct for the noncircular shape of the Lissajous pattern, which the misalignment of the beams and photodetectors and circuit offset and gain errors cause. Using a least-squares technique, it transforms the ellipselike data into circlelike data points. The algorithm then reconstructs the displacement history by summing differences between corresponding pairs of the data set. Finally, the algorithm uses a convolution technique to ascertain the peak sinusoidal displacement and phase at the vibration frequency. This action, in turn, leads to a calculation of the peak acceleration and accelerometer sensitivity. The two detector channels must have simultaneous triggering, so the acquired data has a defined phase relationship.

Testing an accelerometer also involves a sophisticated mechanical structure. To maintain traverse alignment of the motion armature holding the moving mirror and accelerometer under test, despite a 1-cm stroke, the design uses a self-centering air bearing. In addition, the beryllium armature is low-mass and stiff. The laser and interferometer must be largely isolated from motion of the shaker and the operating environment, which mandates a compliant mounting connected to a massive system using strain-isolated extension springs between the laser table and the shaker table. Using this system, you can calibrate accelerometers with uncertainties of about 0.5% from 20 to 2500 Hz, 1% from 5 Hz to 10 kHz, and 3% from 10 to 20 kHz.

Author Information

You can reach Executive Editor Bill Schweber at 1-617-558-4484, fax 1-617-558-4470, e-mail bschweber@edn.com.