1 April 2002

Online Exclusive: Spot-On Position Feedback

If your motion feedback system requires high accuracy and/or resolution, you may want to consider an interferometer.

What comes to mind at the mention of "interferometer"? Do you ask, "What is it?" or say, "That's what we use to verify our machines' positioning accuracy; it's too expensive and delicate to be used for real-time feedback"?

Traditionally, laser interferometers have been used for real-time position feedback on only the most demanding motion control applications. Most people's exposure to these instruments is probably from observing a measurement specialist verify a machine's accuracy. Luckily, this limited role may be ready to expand, thanks to both the counterinflationary trend exhibited by most electronic products and the expiration of a patent held by Hewlett-Packard. Both Zygo and Renishaw now offer systems intended for motion control feedback. These systems provide A-quad-B feedback for easy integration into most motion controllers and support multiple axes on a single computer board.

It's now possible to purchase three axes of interferometer feedback for about $10,000. If you're used to paying less than $500 for rotary encoders and their performance is adequate, a laser interferometer may not be for you. However, if you need accuracy or resolution equal to or better than glass scales, or if you have long axis travels (greater than 3 meters), you may want to read on.

Laser interferometers are displacement feedback instruments capable of subnanometer resolution and submicrometer accuracy over significant distances. Accuracy of 1 part per million (ppm)-1 micrometer (µm) over 1 meter (m)-is achievable for most applications. To achieve accuracy greater than this requires operating the laser beam in either a vacuum or some inert gas. Most systems, however, operate in open air yet achieve near-ppm accuracy. Compare this with a glass scale, which will expand and contract with changes in temperature (approximately 10 ppm per °C for glass).

Because an interferometer is an optical instrument, robustness might be a concern. However, properly designed, it can be used just about anywhere you might consider using a glass scale. It does, however, require an area free of contaminants to prevent damage to the optics (e.g., it can be operated in machine tools, provided it's protected from coolant flow).

A typical system (Figure 1) consists of a laser, measuring optics, photodetector receivers with or without fiber optics, and electronics to process the signals into a measurement. By varying the optical arrangement, you can also measure displacement, straightness of motion, and angular motion. You can measure multiple axes using a single laser head by splitting the beam multiple times, as shown in Figure 1. You can use interferometers for motion feedback over large distances (20 m isn't uncommon). And the beauty is, there's no cost difference to increase from 1 to 20 m because the laser beam travels until it's reflected by a mirror.

If you think an interferometer might be right for your motion control application, it's good to know a little bit about its operation and limitations.

Basic Operation

Commercial laser interferometers come in two varieties: homodyne and heterodyne. Both types use the wavelength of laser light as their measurement standard. Typically, the laser has an internal control system to stabilize its wavelength within a very small range. (For calibration purposes, the laser is usually compared with a more accurate iodine laser that's traceable to the National Institute of Standards and Technology in order to verify its wavelength stability over time.)

One difference between homodyne and heterodyne systems is the way in which they derive a measurement from the phase change between two light waves. Homodyne systems count constructive and destructive interferences of the light caused by the moving mirror. Heterodyne systems, however, measure phase change directly by monitoring the beat signals generated by using light at two distinct frequencies.

A homodyne system's laser produces light at a single frequency (at least within an acceptable range). You derive a displacement measurement by separating this laser beam into two beams that traverse different paths. One path is fixed in length, and the other is along the subject measurement path (Figure 2). A prism called a beam splitter (BS) splits the laser's light. You can think of a beam splitter as a partially reflecting mirror. One leg of the separated beam (usually called the reference leg) is reflected to a fixed mirror, and the other (usually called the measurement leg) is transmitted to a moving mirror. Such an array is often called a Michelson interferometer after Albert Michelson, a physicist who first documented this optical arrangement in 1887. If it's more convenient, the mirror receiving the reflected beam can be moving and the other mirror fixed (this is handy if the motion must be at a right angle to the laser head).

A portion of the reflection from both the measurement and reference mirrors will exit the BS together. Because light is an electromagnetic energy, and its propagation can be described as a wave, its energy can constructively and destructively interfere, as shown in Figure 3. Such interference takes place between the measurement and reference beams as the measurement mirror continuously moves through a distance /2 ( = wavelength). (The distance is /2 instead of because the measurement beam has to travel both to and from the mirror, doubling the distance.) A photodetector placed in this path will detect alternating light and dark pulses (fringes) every /2 movement of the measurement mirror. This would permit a measurement resolution of /2, or 316 nanometers (nm) for a HeNe laser.

This is good, but such a system can't distinguish the direction of travel. This is akin to the problem arising when using an optical encoder without quadrature detection. Fortunately, there's a similar solution. A portion of the combined beams can be phase shifted by /4, using an optic called a quarter-wave plate. Using two photodetectors, one for the nonshifted beam and one for the /4-shifted measurement beam, there will be two interference beams 1/4 cycle out of phase, giving four state changes per cycle. This extends the measurement resolution to /8 (79 nm for a HeNe laser) and permits detection of direction.

One of the drawbacks to homodyne interferometry is the measurement's potential sensitivity to amplitude change. Disturbances can cause a change in signal amplitude at the detector that looks similar to the fringe changes caused by displacement of the measurement mirror. This results in erroneous measurements. Heterodyne systems inherently overcome this problem.

Heterodyne systems, like homodyne ones, derive measurements by detecting phase changes between light beams traversing two separate pathways. However, unlike their homodyne cousins, they monitor phase change directly rather than by fringe counting. This makes heterodyne systems insensitive to the amplitude-induced errors that may be encountered in homodyne configurations. Direct phase monitoring means displacement resolution is limited only by the phase-measuring technique. Currently, systems are available with /2,048 (0.31 nm for a HeNe laser) resolution.

Direct measurement of phase isn't possible in a homodyne system because the light's frequency is too high to resolve the sinusoidal signal using a photodetector. A heterodyne system overcomes this problem by using two beams at slightly different frequencies. Combining the two beams produces a beat frequency that's the difference between the two individual frequencies. This frequency difference is chosen to lie within a range detectable by photodetectors.

Heterodyne systems use lasers producing light beams at two distinct frequencies. Typically, 50% of the energy emanating from the laser is polarized vertically, while 50% is polarized horizontally and at a frequency different from the vertical polarization. Figure 4 shows a typical optical arrangement for displacement measurement. Note that it's similar to the Michelson arrangement shown for the homodyne system (Figure 2). In fact, many homodyne systems utilize this arrangement as well by using orthogonal polarizations for the reference and measurement beams. A polarization beam splitter (PBS) replaces the BS, and retroreflectors replace the mirrors. The PBS always reflects the vertical polarization and passes the horizontal polarization. A retroreflector is geometrically equivalent to the corner of a cube and has the property of keeping the return beam parallel to the incoming beam.

This property makes such an interferometer arrangement insensitive to any angular movement of the retroreflectors. The measurement and reference legs are combined at the photodetector and produce a measurement beat signal. This signal's phase change is equal to the individual phase change between the reference and measurement beams, and it changes directly with any change in phase between them. Consequently, heterodyne detection permits direct phase measurement with the photodetector. The measurement beat signal's phase is measured against the phase from a reference beat signal produced from the two beams before they enter the optics. The accumulated phase measurement is then converted into a displacement.

Errors to Consider

When using an interferometer for motion feedback, it's best to know what parameters affect accuracy so you can achieve the desired performance. Error contributors might include atmospheric effects, cosine alignment, and polarization mixing. For most applications (part per million, accuracy), attention to cosine alignment, atmospheric effects, and dead path should be sufficient. Other errors are usually negligible at this level of accuracy.

Cosine alignment error results when the laser and motion paths aren't parallel. This error is proportional to the cosine of the misalignment , as shown in Figure 5 — hence its name. Note that it always results in a measurement smaller than the displacement. This error is minimized by adjusting beam alignment to eliminate visible translation of the return measurement beam when observed on an opaque surface. A misaligned measurement beam will strike the retroreflector in different locations as it's displaced, causing a translation of the observed reflection. If you can visually detect such a translation to the order of 0.5 millimeter, and your travel range is 1 m, you can expect approximately 3 µm of error. For longer travel ranges, you can get a better alignment using this technique (i.e., 10 m of travel reduces the error to just 0.3 µm).

Atmospheric effects are present when the laser beam travels through air. Electromagnetic radiation has its wavelength affected by the medium in which it travels. Wavelength varies according to the relationship = _o/n, where _o is the wavelength in a vacuum, and n is a material property called the index of refraction (IOR). In air, pressure, temperature, humidity, and the ratio of gases present, all affect the IOR. In 1966, a gentleman by the name of Edlen published a relationship for the IOR of air relative to pressure, temperature, and humidity. His formula has since been revised to include variations of trace gases such as CO₂.

where

T	temperature (°K)
P	pressure (Pa)
X	CO₂ concentration
H	% relative humidity

A change in temperature of 1.0°C, or a change in pressure of 370 pascals (Pa), will cause a 1-ppm error (e.g., 1 µm per m). Temperature and pressure have the greatest effect on IOR and can easily be monitored to update the wavelength. Humidity can be measured with a psychrometer, and CO₂ concentration is approximately 370 ppm. With a precision electronic barometer and thermistor, pressure and temperature can be reasonably measured in situ to an accuracy of about ±25 Pa and ±0.1°C, respectively. Humidity can be measured easily to about ±5% with an electronic psychrometer. Using Edlen's formula and the atmospheric monitoring, you can mitigate the atmospheric-induced error to about 0.25 ppm (0.25 µm per m of travel). These calculations assume homogeneity of the air along the measurement path. In practice, temperature and pressure gradients might be present, degrading the accuracy further.

Dead path error is caused by a change in optical paths between the reference and reference path and the measurement path at the point of zeroing. An interferometer is a displacement measuring instrument; it measures only a change in movement. It must be zeroed to begin monitoring displacement. At the point of zeroing, if the distance to the reference retroreflector is different from that to the measurement retroreflector, you can encounter an error if the laser's wavelength changes (Figure 6). Atmospheric effects, as mentioned previously, can cause such a change in wavelength. Ideally, if you can zero the interferometer when the measurement and reference paths are the same, you can virtually eliminate this error. If not, use wavelength correction using Edlen's formula to mitigate the error. If you assume pressure and temperature monitoring to the accuracy levels mentioned before, the result is a 0.25-ppm error (0.25 µm per m of deadpath). Note that this error is a function of the dead path length and not actual travel.

By carefully considering the error contributors in your design, you should be able to reach your accuracy goals. Parts per million accuracy is possible with an interferometer, if you give care to the alignment and atmospheric effects.

If your motion control system requires high accuracy and/or resolution in its feedback system, you may want to consider an interferometer. If you use linear motors with axis travels greater than 2 meters, then you have few choices, and an interferometer should be among them. Knowing its limitations and understanding its error sources, you should be able to integrate an interferometer into your motion system to provide accuracy second to none. MC

Make Contact!

C. D. Mize, Ph.D., P.E., is vice president of Perry Automation Consulting, Inc. Dr. Mize received his B.S. in mechanical engineering from Auburn University in 1987 and his M.S. from the University of Florida in 1993, where his research involved designing laser interferometer- based measurement equipment to evaluate the motion control systems on machine tools. His doctoral degree focused on real-time compensation in the control system of a machine tool to mitigate thermally induced errors. Contact him at P.O. Box 22381, St. Petersburg, FL 33742; tel: (727) 526-3700; fax: (727) 526-4999; www.perryautomation.com.

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