Abstract

The odd moments of the autocorrelation function are zero, and the moments of the cross-correlation function for an unknown spectrum with a library entry have been used here to select the best fits. The use of the first moment or average wavenumber in six separate spectral ranges requires only 12 values per library entry, and 24 values are required per library entry if twelve separate ranges are used. The odd moment methods were found to yield results for searches with both library and experimental spectra that were comparable to correlation coefficients in selection of the proper chemical class for the unknown spectra and in making of the proper identification.

Improved measurement accuracy in optical scatterometry using correction-based library search

Xiuguo Chen, Shiyuan Liu, Chuanwei Zhang, and Hao Jiang
Appl. Opt. 52(27) 6726-6734 (2013)

Analysis of spectra using correlation functions

Reinhard Beer and Robert H. Norton
Appl. Opt. 27(7) 1255-1261 (1988)

Absolute testing of flats by using even and odd functions

Chiayu Ai and James C. Wyant
Appl. Opt. 32(25) 4698-4705 (1993)

Small random library method combined with local searching in optical critical dimension measurements

Wenxiu Zhao, Xiaocheng Wang, and Qianglong Zhong
Appl. Opt. 63(3) 861-864 (2024)

Second-order moments of Schell-model beams with various correlation functions in atmospheric turbulence

Guo Zheng, Jue Wang, Lin Wang, Muchun Zhou, Yu Xin, and Minmin Song
Opt. Lett. 42(22) 4647-4650 (2017)