Accuracy and time in surface measurement, Part 1: Mathematical foundations

R. Liang, T. C. Woo, C. C. Hsieh

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


Accuracy and time are known to be conflicting factors in measurement. This paper re-evaluates the two-dimensional sampling problem for measuring the surface roughness and establishes that an optimal sampling strategy can be obtained by utilizing the point sequences developed in Number Theory. By modeling a machined surfaces as a Wiener process, the root-mean-square (RMS) error of measurement is shown to be equivalent to the L2-discrepancy of the complement of the sampling points. It is further shown that this relationship holds for more general surfaces, thus firmly linking the minimum RMS error of the measurement to the celebrated lower bound on L2-discrepancy asserted by Roth (1954), a 1958 Fields medalist.

Original languageEnglish
Pages (from-to)141-149
Number of pages9
JournalJournal of Manufacturing Science and Engineering, Transactions of the ASME
Issue number1
Publication statusPublished - 1998 Feb 1

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Mechanical Engineering
  • Computer Science Applications
  • Industrial and Manufacturing Engineering


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