INSTITUTE OF PHYSICS PUBLISHING MEASUREMENT SCIENCE AND TECHNOLOGY Meas. Sci. Technol. 17 (2006) 2299–2305 doi:10.1088/0957-0233/17/8/035 Optical surface flatness recognized by discrete wavelet transform and grey level co-occurrence matrix Chuen-Lin Tien and You-Ru Lyu Department of Electrical Engineering, Feng Chia University, Taichung, Taiwan, Republic of China E-mail: cltien@fcu.edu.tw Received 24 April 2006, in final form 6 June 2006 Published 17 July 2006 Online at stacks.iop.org/MST/17/2299 Abstract Optical surface flatness evaluated by the discrete wavelet transform and grey level co-occurrence matrix (GLCM) is presented. A PC-based measurement system can be used to detect the interference fringe of an optical reflective surface captured from a Twyman–Green interferometer. Wavelet analysis and GLCM process associated with the entropy criterion appears to be a good method for recognizing automatically the flatness of the optical surfaces. Three-dimensional plots of the GLCM and surface deformation contour for various captured interference patterns of glass substrates have been compared and discussed. The parameter of entropy has been calculated from the GLCM and then can be used as an indicator for optical surface characteristics. Keywords: surface flatness, discrete wavelet transform, grey level co-occurrence matrix, entropy, interferometer 1. Introduction Optical surfaces have been produced for generations by a grinding and polishing process. Various surfacing methods produce very different defects. Fast inspection and test procedures are required to control quality standards and to avoid manufacturing defects. Surface flatness is a critical parameter of silicon wafers for making integrated circuits, and measurement of wafer flatness is an essential process for both wafer manufacturers and device manufacturers. In optical coating applications, the surface flatness of the glass substrates is also a very important property, since the adhesion of a thin film to the substrate depends critically on conditions at the substrate surface. To control the quality of optical coatings, it is necessary for all the substrates in the manufacturing process to be examined; however, only sample testing is currently available because of the slowness of the examination process. Surface flatness measurement in automatic, non- contacting, user-friendly ways is becoming necessary during the quality control process. There has been much interest in the automotive industry in developing non-contact techniques for the measurement of optical surfaces. A major problem in testing high-quality optical surfaces has been lack of a fast measuring technique for mapping their deviations from flatness. Several methods have been proposed to extend such measurements to map the deformation from flatness of the test surface [1–4]. There are several methods for determining the flatness of a test surface by means of non-contact measuring techniques. Fringe displacement method [5] in a Fizeau interferometer is one of the techniques used for determining the surface flatness. Interference fringes are produced by a reference flat whose flatness is known. The test plate is put on the reference plate and the displacement in the position of the interference fringe is measured. However, this is a very time-consuming process if it is based on visual methods. To properly evaluate the surface flatness of glass substrates, improved measuring instruments with high accuracy and high measurement speed must be developed. In this paper, we proposed an automated inspection method based on the discrete wavelet transform (DWT) and grey level co-occurrence matrix (GLCM) for recognizing surface defects and deformations. The wavelet transform acts like a band-pass filter which simultaneously reduces the low- frequency components of the object and the high-frequency 0957-0233/06/082299+07$30.00 © 2006 IOP Publishing Ltd Printed in the UK 2299