Bias errors in subpixel displacement estimation for optical correlation-based measurement techniques

Abstract

The systematic error introduced when using 1-D peak detection algorithms to decompose elliptically shaped correlation peaks is investigated. First, an analytical description of this error is derived, and it is shown that this error can lead to a systematic influence of more than one pixel. Additionally, a general linear 2-D Gaussian algorithm based on least squares estimation is presented to allow correlation peak detection of elliptically shaped peaks without any significant bias error. Finally, the performance of the presented algorithms for subpixel displacement estimation, as well as algorithms provided by commercial software packages, is tested with artificial image pairs of random dot patterns.