[OPTICAL REVIEW Vol. 5, No. 4 (1998) 207-211]

Spectral Based Estimation of Optical Path Difference of Interference Colors

Satoru TOYOOKA,1 Nobuaki HAYASAKA,1,3 Munehide KATAGUCHI,1,4 and Fumio KOBAYASHI2

1Graduate School of Science and Engineering, Saitama University, 255, Shimo-okubo, Urawa, Saitama, 338-8570 Japan, 2Fuji Photo Optical Co., Ltd., 1-324, Uetake, Omiya, 330-0036 Japan

(Received February 2, 1998; Accepted April 22, 1998)

A spectral intensity distribution of interference colors which is a function of optical path difference (OPD) is represented as a pattern vector on a subspace. A new algorithm to design a color scale on the subspace to estimate OPD values is proposed. In experiments, interference colors generated by a differential interference microscope (DIM) were examined. A subspace spanned by four orthogonal bases was constructed to make a color scale to determine OPD values in the range between 0 nm and 1000 nm. Estimated OPD values almost coincided with these expected. In an experiment on two-dimensional interference colors obtained by a spherical surface of a ballbearing observed by DIM, the resultant OPD distribution coincided well with that expected within a standard deviation of 12.8 nm.

Key words : interference color, optical path difference, color scale, subspace method, parameter estimation, orthogonal expansion of pattern vectors