影像测量仪/光学三坐标/影像三次元/2.5D精度详解

2012/9/19 8:00:54

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Funneling Accuracy
The smaller the travel, the more accurate the measurement
In last month’s column, I talked about the format of accuracy In last month’s column, I talked about the format of accuracy specifications for video measuring machines. The following is a typical format for a single axis accuracy specification:
Ex = ±[k + (multiplier * L)/1000] μm
And this is an example of an actual specification (linear accuracy in the X-axis):
(X) E1 = ±(1.5 + 6L/1000) μm
As you can see from the equations, there’s only one variable, L, which is the length of stage travel (how far the part or the optics have to move) in millimeters.
Standing still Use basic algebra to solve the above equation where L = 0 (in other words, no stage travel). Because 6 x 0 = 0, and 0/1000 is undefined, that E1 specification when there’s no stage motion equals ±1.5 μm. This is a systemic value that is independent of any motion of the X-axis.
If this were the specification for an actual measuring device, it means that for measurements made within the field of view where there is no motion of the part, the uncertainty of the measured result is plus or minus 1.5 μm, or a range of 3.0 μm. In other words, if the measuring device were constrained to measurements only within the optical field of view, the measurements would be accurate to ± 1.5 μm.
Plot the points If you plot the + 1.5 and – 1.5 μm points on a graph where the abscissa (x-axis) is at zero, and positive points are above the axis and negative points are below, these points would be symmetric for the point where L = 0. To add more points, along the x-axis of the graph, evenly space out marks for 50, 100, 150, and 200 mm.
Now let’s move Because L is the variable for distance of stage travel in the referenced axis, let’s see what happens when L = 50 mm. In other words, if the X-axis stage were to move 50 mm, what would be the measurement uncertainty over that distance?
Back to the equation, 6 x 50 = 300; 300 divided by 1,000 = 0.3; 1.5 + 0.3 = 1.8. This means that a length measurement in the X-axis over a distance of 50 mm would be accurate to ± 1.8 μm.
The plot thickens Now let’s plot these two points on the graph mentioned earlier, where the horizontal axis equals 50, plot the points +1.8 and –1.8.
You can see where this is going Repeat the process for stage travel L of 100, 150, and 200 mm and you will get ± 2.1, ± 2.4, and ± 2.7 μm respectively. If you connect the plotted points on either side of the horizontal axis, you will see that they resemble a funnel shape. This is the “accuracy funnel.”
Figure 1. The accuracy funnel for ±(1.5 + 6L/1000) μm
Using the accuracy funnel It’s easy to plot the accuracy funnel for any video measuring machine that specifies accuracy or measurement uncertainty in the format of these equations. The funnel means that the uncertainty or accuracy of any measurement made in that particular axis will be within the two calculated values that solve the equation for that particular distance. Yes, this analysis assumes that measurement error is linear over distance; high-accuracy video measuring machines are calibrated to provide linear, or nearly linear, performance in the measured axes. However, even if the performance isn’t truly linear, assuming repeatable errors, plotting enough points throughout the overall stage travel will still generate a funnel shape within which measured data points should fall.
As a practical example, if a measurement were made over 100 mm, that measurement would be accurate to ± 2.1 μm. That means the actual length is anywhere between 99.9979 and 100.0021 mm. For that same specification, a measurement of 200 mm is anywhere between 199.9973 and 200.0027 mm, and so on.
Inaccurate accuracy? All of this may appear elementary, but there’s a potential fly in the ointment. What good is the accuracy funnel if the accuracy equation that defines it is incorrect? Any accuracy specification will produce a funnel, even if the constant and multiplier are arbitrary. Stated another way, the actual performance of a video measuring machine may or may not match a stated or published accuracy specification. This means that attractive accuracy specifications and actual system performance may be two different things. It’s easy to fall into the trap of simply comparing accuracy specifications among different products and selecting the one with the lowest values, assuming that the stated specifications are accurate. However, is the accuracy specification accurate?
Performance in the funnel Derivation and validation of the accuracy/uncertainty specification require measurement of certified length artifacts. An example is a National Institute of Standards and Technology-traceable scale or grid. NIST-traceability means, in this case, that the artifact has been certified by a third party to have specific dimensions between marks along its surface under particular environmental conditions.
To use a calibration artifact, start by plotting the differences in the measured and known length values over specific distances. By plotting a large enough sample size, a point distribution will result, typically scattered somewhat symmetrically around the zero-crossing vertical axis value (where the measurement matches the artifact value exactly).
When performing this process to derive an uncertainty specification it will be necessary to identify the points within which all, 99 percent, 95 percent, or 68 percent of the plotted points fall (depending upon the confidence interval of the specification). The lines connecting those points form the funnel and derive the accuracy specification.
Figure 2. Points within the accuracy funnel
Validating the performance of a measuring device relative to its published specification is done the same way. First plot the lines that fit the accuracy equation, then plot the measured point deviations at different travel (length) intervals. Most, if not all, points should fall between the lines if the system is performing to specification.
Yes, environment matters Of course, the environment influences the performance of any measuring machine. A machine capable of highly accurate measurements can perform poorly if there’s too much vibration, variation in temperature, or there are cleanliness issues. Trying to validate accuracy specifications under poor conditions is impossible. Instead of measuring machine performance, you end up measuring environmental influences. If testing is done in an adequate environment, don’t forget other influences on the outcome. For example, bringing the certification artifact from a room of a different temperature, or simply handling the artifact, can affect its length. Thermal expansion of the artifact can invalidate its published values because you’re trying to measure a moving target.
What’s it all mean? Measurement uncertainty—the accuracy of measurements—is important. Published performance specifications help users match measurement machine performance to part dimensions and tolerances. Knowing how to interpret those specifications, especially those that vary with measured distance, can help avoid incorrect product or process decisions. And most important is knowing that anyone can come up with a specification. It’s the actual measurement performance that matters

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