# Inside Metrology

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## That’s Highly Nonlinear!

### And perfectly normal

Many measurements assume that a measuring device performs in the same way throughout its measuring range. In other words, a 1 mm distance measured near the center of a machine will measure 1 mm at its periphery. But will it? This column discusses some of the factors that can cause nonlinear performance of various measuring devices (and what can be done about them).

Is linear the right word?
What I mean by the linear performance of a measuring device is that a given measurement should repeat no matter where it’s performed within the measuring range of the device. For example, a 0.125” pin should measure the same no matter where it’s positioned within the volume of a coordinate measuring machine (CMM), or within the beam of a laser micrometer. A distance of 0.125” should repeat if that change in distance occurs at one extreme of the device’s range or travel as well as within the middle of its range or travel. A measurement of 0.125” within the field of view of an optics-based system should measure the same if in the center of the image or at the edge. By “linear” I mean uniform performance throughout the entire range of the measuring device.

It depends on the scale
Like most things involving measurement, the effect and importance of nonlinearity of a measuring device depends on the necessary resolution and repeatability requirement of that measurement. Take a yardstick. Unless it was poorly made, you can be quite confident that a one-quarter-inch measurement made anywhere along the length of that yardstick will give the same result. One factor to consider about a yardstick—it works in any orientation without variation in measured results. You never think about calibrating it to some external standard. Those kinds of considerations do come up when the required resolution of the measurement increases, however.

The environment, again
As has been discussed before, the effects of environmental factors increase as the range and resolution of a measurement decrease. In other words, a wooden yardstick will work whether you use in it a shop, in the desert, or in a snowstorm. This is because its resolution of measurement is coarser than any possible change in length of the yardstick due to these variations in temperature. (Of course, if you get a wooden yardstick wet, it may expand and become inaccurate even for its relatively coarse measurements.) On the other hand, certifying the length of a gauge block requires control of the environment in which the block is measured, and of the block itself.

Macro- and microenvironments
The gauge block example brings up the point that environmental factors occur at several levels. The obvious environment we think of is that of the room in which the measurement is performed—the macroenvironment. Calibration labs have temperature controls that even take into account the heat generated by every person in the lab. This is why most labs limit the number of people allowed at a time. A metrology lab may have some less-stringent level of environmental control, while a shop floor might vary in temperature by several degrees.

The microenvironment is the one in and on the measuring machine itself. In general, the measuring machine will be directly affected by the macroenvironment. However, measuring machines can be designed to isolate the part and measurement area from the macroenvironment, or the entire measuring system can be placed inside a temperature-controlled enclosure. And there’s more.

Is environmental control enough?
Even if you assume a perfectly controlled macroenvironment, there can be environmental variations within the measurement area of certain devices. Think of heat sources. Motors generate heat. If a motor is located near the measurement area and isn’t thermally isolated from that area, it may cause localized heating. Heat causes parts to expand. If a metal part were placed on this machine, the area closest to the motor could be warmer than the rest of the part. The result would be a nonlinearity in the characteristics of that part, including its length. If that part had an evenly spaced pattern along its length, the spacing between those marks would be greater toward the heated end compared to the marks on the unheated end.

Other sources of heat include incandescent lamps used as light sources and indicators, and the human hand. The heat from a lamp is obvious if you touch a recently lit bulb. Heat from your hand is another matter. Remember those gauge blocks? The precision to which they are measured when their length is verified can be influenced by thermal expansion from simply picking up the block with bare hands. The overall length of a heated block would increase, even though there’s only localized heating where the block was handled. Then the block would shrink as it cooled. Although the part would eventually normalize to its environment, readings of its length during the cooling phase would vary. This is why tweezers are used for handling gauge blocks in a calibration lab.

Other environmental influences
Some environmental influences affect certain measuring devices, yet have no effect on others. For example, optics-based systems that use the interference of light can be influenced by the composition of the air or by air stratification. The composition of the air affects its index of refraction, and thus the way light behaves as it passes through. Like other nonlinear effects, variations in the composition, and thus the index of refraction, can cause measurements to vary even though the part under test is actually stable. Air stratification also results in a change in index of refraction from variations in air density (less dense, warm air rises; denser, cold air settles). Systems that are influenced by air stratification are normally in rooms that use fans to keep the air mixed so it can’t stratify.

Linearity and optics
We have discussed optical aberrations in earlier columns. You may have seen barrel or pincushion distortion where a grid pattern appears wider or narrower at the “waist” than along either edge. With such a lens, distances measured near the center of the field of view will measure differently than those same distances near the edges of the field of view.

Calibration
Many nonlinearities can be minimized through calibration. If a nonlinearity is repeatable—not continually varying—it may be calibrated out.

Consider a video measuring system that measures magnified images anywhere within a large XY area. Distances between known positions can be used to correct for repeatable nonlinearities in the system. One way this is done is with a grid pattern of points on a stable substrate where the spacing is known (and externally certified). The system measures that pattern, and any offsets in the readings from the known spacing can be entered as a calibration file to adjust future readings.

Of course, systems that measure in 3-D space may have one nonlinearity in X, another in Y, another in Z, and others in each of the XY, XZ, YZ, and XYZ diagonals. Or the machine may be designed well enough that measurements of “normal” resolutions aren’t influenced by minor nonlinearities in system performance. In other words, the part may be more of a variable than the measuring device.

Remember, it’s relative
All this discussion of linearity only matters if the resolution of measurement is so fine as to be influenced by changes in the environment, by nonlinearity of system performance, or by variations in the part itself such as localized heating from handling. It’s good to know these influences exist, because good metrology practice seeks to minimize as many variables as possible. At the end of the day you want to know that you measured the part, not some complex interaction of the part with the measuring device and its environment.

As always, yes, measurement matters.

### Fred Mason

Frederick Mason has more than 20 years of experience in metrology in engineering and in domestic and international marketing roles. He has a broad range of experience, including holography, laser and white-light interferometry, microscopy, and video and multisensor metrology. He’s the vice president, marketing communications, for Quality Vision International, parent company of Optical Gaging Products, RAM Optical Instrumentation, VIEW Micro-Metrology, and Quality Vision Services.

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