Abbe Error/Offset
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Abbe Error/Offset Richard Leach* Department of Mechanical, Materials and Manufacturing Engineering, Nottingham, UK
Synonyms Abbe error; Abbe offset
Definition The Abbe principle was first described by Ernst Abbe (1890) of Zeiss and states: If errors of parallax are to be avoided, the measuring system must be placed co-axially (in line with) the line in which displacement (giving length) is to be measured on the work-piece.
Abbe error occurs when the measuring point of interest is separated laterally from the actual measuring scale location (reference line or axis of measurement) and when angular error motions exist in the positioning system. Abbe error causes the measured displacement to appear longer or shorter than the true displacement, depending on the direction of angular motion. The spatial separation between the measured point and reference line is known as the Abbe offset. Application of the Abbe principle can be illustrated by comparing the design of a caliper and a micrometer (see Fig. 1). In the case of the caliper, the measurement position in the jaws is displaced from the axis of the scale. Therefore, any angular error of the motion of the moving jaw will amplify the error of the scale, which results in an amplified error in the length measurement. In the case of the micrometer, the measurement and scale axes are in line, and there is no error amplification effect.
Theory and Application Figure 2 shows the effect of Abbe error on an interferometric measurement of length. To ensure zero Abbe error, the reflector axis of movement should be collinear with the axis of measurement. To account for the Abbe error in an uncertainty analysis relies on knowing the magnitude of the Abbe offset and the magnitude of the angular errors in motion of the positioning system (e.g., straightness). The Abbe error is given by: e ¼ d tan y where d is the Abbe offset and y is the angular error motion of the positioning system. Thus, a tilt angle change of 1 arcsec (approximately 5 mrad) leads to a distance deviation of 5 nm/mm of Abbe offset. The Abbe principle is, perhaps, the most important principle in precision instrument design and is also one that is commonly misunderstood. Bryan (1979) described it as “the first principle of *Email: [email protected] Page 1 of 4
CIRP Encyclopedia of Production Engineering DOI 10.1007/978-3-642-35950-7_16793-1 # CIRP 2014
Fig. 1 Examples of a caliper (above) and a micrometer (below)
Fig. 2 Effects of Abbe error on an optical displacement measurement (From Leach 2014)
machine design and dimensional metrology,” and it has also been called “the principle of alignment” and “the Abbe comparator principle” (Evans 1989). Despite the importance of the Abbe principle, its interpretation in terms of single-axis displacement measurement means that many authors have approached the subject with a wider machine design perspective. Bryan restated the Abbe principle as: The displacement measuring system should be in line with the functional point whose displacement is to be measured.
