Polygons are basic angle standards for angle measurement, particularly used for calibration of rotary angular indexing, and for measuring equipment such as dividing heads and tables. A main application in daily life is in bar-code readers. Calibration of such angle standards is required for traceability and at the highest accuracy it is a responsibility of national metrology institutes. In order to investigate uncertainty parameters on polygon calibration and to establish the capabilities of national metrology institutes, intercomparision measurements in the name of EUROMET project 371 "angle calibration on precision polygons" between 12 European countries have been carried out. Two precise polygons with 7 and 24 faces have been calibrated by the participants. Difficulties arose for precise calibration of seven-sided polygon for those institutes, which do not have a high-resolution angle comparator or two autocollimators. UME, the National Metrology Institute of Turkey, has applied an alternative technique for precise calibration of seven-sided polygon without using high-resolution angle comparators (i.e., indexing tables or angle dividers) or two autocollimators. The technique is based on the circle closure principle. The pitch and cumulative angles of the polygon are extracted from the angle measurement between some polygon faces (such as one and four (1/4), analogous 2/5, 3/6, 4/7, 5/1, 6/2 and 7/3) the angle of which can be generated close enough by the indexing table. This means that the polygon can be regarded as unfolded in seven 3-pitch angle intervals of 3×360°/7≈154°17′, making up 1080° in total. The method gives the differences between these seven intervals; with the closure condition (the sum must be zero) this gives all absolute angles. A full uncertainty evaluation is given that is based on the model function which relates the measured values to the polygon angles. For the calibration actually carried out, this yielded an uncertainty of 0.24″. Within this uncertainty the measured polygon angles corresponded very well with the reference values of the intercomparison. The method is of use for laboratories which do not have a high-resolution angle comparator (i.e., an indexing table or angle divider) or two autocollimators for the calibration of such angle standards.
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