The Abbe’s principle of alignment is named after the German Professor Earnst Abbe. In 1890, he proposed a set of rules for taking linear measurements.


His principle consists of the following 3 points :


1. For best results, a linear reading should be taken either inline or sideways of the object.


2. In case the above is not possible, the measurement can be taken at a distance parallel to the line being measured. In this case, the distance separating the object and the scale is known as the Abbe Offset. The Abbe Offset introduces no more than a second order error and is negligible.


3. If the parallelism between the object and the measuring instrument is not respected, a first order error will be introduced. The error will be a function of the angle the scale makes with the object and the distance separating the two. This error is known as Abbe Error which is a subset of Cosine Errors.


The error introduced can be calculated using:

\( {\epsilon} = d({\sin}{\theta}) \)

Where, d is the distance between scale and line.


It is important to note that the error amplifies with both the distance and the angle.


Practical Implications

By design, Vernier calipers does not conform to the Abbe’s rule of alignment. It is therefore possible to introduce Abbe errors when taking measurements with one.

On the other hand, Micrometers follow the principle. This means that no error of this type can be introduced when using it.