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Minimizing Abbe Errors

When you are The Precision Automation Experts, accuracy in all areas of your machines matters. A lot. There are many components in an automated machine, all of which can affect accuracy. One particularly pesky inaccuracy is Abbe error.

What is Abbe error? Named after Ernst Abbe and also called sine error, it describes the magnification of angular error over distance. In machine design, some components are particularly sensitive to angular errors. Abbe errors may not be visible to the human eye, but will affect linear measurements. These errors can be insidious, but there are ways they can be minimized with careful design practices.

For example, in the illustration at right, pitch and roll motions would induce errors as the camera moved along the slide. While these errors would likely be manageable at the relatively small distance Dp, the same errors would be amplified by the physical height Dc to the optical focal point above the moving table on the slide. Such errors are inherent to a moving-camera design.

A similar situation would be created if the camera were installed on a moving robot arm instead of attached to the precision slide as shown.  A robot repeatability of 10-micron accuracy is not unusual, but in most cases is only specified at the center of the robots’ wrist mounting. The addition of a camera and mounting hardware would move the work point outward from the wrist, amplifying wrist rotation errors as well as any other Abbe errors created by the moving robot.

How can these scenarios be minimized? Consider the following machine design in the illustration below where the camera is rigidly mounted to a granite block or similar stationary mass. The part under inspection is carried on a platform mounted on the precision slide, such that the area to be inspected is close to the slide. Because the surface of the part under inspection is relatively thin, Abbe errors generated by the moving slide will now be defined by the minimal distance Dp alone.

The illustration describes an optimal situation and would result in greatly reduced Abbe errors over a system where a moving camera was focused on a stationary part. As can be seen from the illustration, critical parameters for Abbe errors are the magnitude of the pitch and roll reduced by the stage motion multiplied by the vertical distance between the pitch center (axis of feedback) and the point of interest on the part being scanned. The setup shown would be preferred for measuring a thin part such as a circuit board, and is generally the best solution whenever Dp<Dc.

If part/features under examination were tall, however, and the camera focal distance is short, note that the optimal solution could require reversing camera-part installation. It’s also important to note that an Abbe error table may be available for a precision stage, but that such information would not be available for a robot under consideration.

As always, the final solution must be based upon client requirements.