Surface flatness of optical thin films evaluated by gray level co-occurrence matrix and entropy Chuen-Lin Tien * , You-Ru Lyu, Shiao-Shan Jyu Institute of Electrical Engineering, Feng Chia University, Taiwan, ROC Received 4 November 2007; received in revised form 17 January 2008; accepted 18 January 2008 Available online 26 January 2008 Abstract The surface characteristics of titanium oxide films evaluated by gray level co-occurrence matrices (GLCMs) and entropy are demonstrated experimentally. A PC-based measurement system was set up to detect the interference fringe of optical coating surface as captured by a Fizeau interferometer. Titanium oxide films were prepared by an electron-beam gun evaporation method. The proposed measuring system was used to evaluate the surface flatness of titanium oxide films coated on glass substrates. The variation of entropy in titanium oxide films before and after film deposition was found to be related to the root-mean-square (rms) surface roughness. Surface characteristics of thin films were fast measured by our proposed method and the test results were verified by atomic force microscopy (AFM) and scanning electrical microscopy (SEM). # 2008 Elsevier B.V. All rights reserved. PACS : 68.55.a; 42.79.Wc ;77.55.+f Keywords: Thin film; Surface flatness; Gray level co-occurrence matrix; Entropy 1. Introduction Optical thin films are widely used for various scientific and industrial purposes. In optics, surface flatness is a critical parameter of optical coating for making high quality optical devices. There has been much interest in the automotive industry in developing non-contact techniques for the measurement of reflective surfaces. Some techniques employed for optical surface measurement were reported in the literature [1–4]. There are several methods for determining the flatness of a surface. In the traditional method, a laser interferometer is used to produce intensity interference fringes and flatness is determined by measuring the shifts of a fringe. Interference fringes are produced by a reference flat of which the flatness is known. The test plate is put on the reference plate and the displacement in the position of the interference fringe is measured. The rotational averaging method [5] is one of the interferometric testing techniques used for determining surface flatness. Absolute measurements of deviations from flatness can be made by averaging the results of comparisons of three surfaces, taking two at a time, with both of the surfaces rotated in a series of steps. The spectral interferometric method [6] for determining surface flatness is based on spectral interferometry by observing spectral interference fringes in the frequency domain in a Fizeau interferometer. However, it is a very time-consuming process if it is based on point-by-point measurements. Tien and Lyu [7] previously reported a new approach to recognize optical surface flatness and deformations based on the discrete wavelet transform and gray level co-occurrence matrix. In order to obtain stable interference fringes, we have modified the measuring system. The surface characteristics of different coating specimens were measured by a Fizeau interferometer before and after film deposition. The interference fringe was acquired by a CCD camera and then transmitted to a frame grabber plugged in a personal computer. The system software capability was improved and integrated to capture inference image of the coating surface to be characterized. This software was developed by our group to analyze the captured images based on the gray level co-occurrence matrix (GLCM) and to perform entropy calculations. This approach for recognizing deformations www.elsevier.com/locate/apsusc Available online at www.sciencedirect.com Applied Surface Science 254 (2008) 4762–4767 * Corresponding author. Tel.: +886 4 24517250x3809; fax: +886 4 24516842. E-mail address: cltien@fcu.edu.tw (C.-L. Tien). 0169-4332/$ – see front matter # 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2008.01.088