Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

New Algorithm for the Measurement of Pitch in Metrology Instruments



Nien F. Zhang, Michael T. Postek, Robert D. Larrabee, L Carroll, William J. Keery


Traditionally, the measurement of pitch in metrology instruments is thought to be a benign self-compensating function. However, as the measurement uncertainty of metrology instruments is pushed to the nanometer level, evaluation of the performance of the pitch measurement algorithms becomes increasingly important. Such an evaluation was done during the development of the documentation required by NJST for the issuance of the new scanning electron microscope magnification calibration standard SRM 2090. In the course of this evaluation, a new algorithm for the measurement of pitch was developed. This algorithm, although currently applied to the data from the scanning electron microscope, also can be utilized for other types of metrology instrumentation. Traditionally, for a pitch measurement, a line is fitted to each edge of the data independently. Then the distance between some arbitrary threshold value on each of those lines is determined. The new algorithm eliminates the concern for the selection of a threshold. Two data sets are defined - one for each of the two edges used for the pitch measurement. Then regression lines are fitted to both sets of data simultaneously with the constraint that parallelism is maintained between these lines. In this way, the data sets are always evaluated in pairs. The evaluation of uncertainty for this measurement process has also been made. Comparisons with simulated data show that the mean square and variance of the pitch distance from the new algorithm is smaller than that from the traditional one. The development of the algorithm, as well as the analysis of NIST laser interferometer measurements, are presented and illustrated with data obtained from SRM 2090 prototypes.
Proceedings Title
Proceedings of SPIE, Metrology, Inspection, and Process Control for Microlithography X, Susan K. Jones, Editor
Conference Dates
March 11, 1996
Conference Location
Santa Clara, CA, USA
Conference Title
Standards and Calibration Methods for Critical Dimension Metrology


edge detection, metrology, pitch measurement, regression, scanning electron microscope, threshold level, uncertainty


Zhang, N. , Postek, M. , Larrabee, R. , Carroll, L. and Keery, W. (1996), New Algorithm for the Measurement of Pitch in Metrology Instruments, Proceedings of SPIE, Metrology, Inspection, and Process Control for Microlithography X, Susan K. Jones, Editor, Santa Clara, CA, USA (Accessed June 24, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created April 30, 1996, Updated October 12, 2021