Radial period extraction method employing frequency measurement for quantitative collimation testing

• Precise and stable quantitative collimation testing is realized employing frequency measurement.
• A frequency measurement technique is proposed to extract the characteristic parameter of the moiré fringe.
• A restrict condition for setting the parameters of the wavelet is introduced.

A radial period extraction method employing frequency measurement is proposed for quantitative collimation testing using spiral gratings. The radial period of the difference-frequency fringe is treated as a measure of the collimation condition. A frequency measurement technique based on wavelet transform and a statistical approach is presented to extract the radial period directly from the amplitude-transmittance spiral fringe. A basic constraint to set the parameters of the wavelet is introduced. Strict mathematical demonstration is given. The method outperforms methods employing phase measurement in terms of precision, stability and noise immune ability.