222 IEEE TRANSACTIONS ON INSTRUMENTATION ANDMEASUREMENT, VOL. 54, NO. 1, FEBRUARY 2005 Narrow-Band Frequency Analysis for Laser-Based Glass Thickness Measurement Bing He, François Cabestaing, Member, IEEE, Jack-Gérard Postaire, and Ruodan Zhang Abstract—This paper presents a narrow-band frequency anal- ysis approach for a new laser interferometric heterodyne system, which is used for noncontact glass bottle wall thickness measure- ment. The measurement signal consists of a number of spectral components, the strongest of which is a reliable representation of the above-mentioned thickness. A fast method for searching and locating this frequency is vital for real-time implementations. As the standard fast Fourier transform (FFT) proved to be ineffec- tive for the given problem, we use a combination of a zero-padding discrete Fourier transform (DFT) with a coarse-to-fine technique to locate this frequency at a smaller processing cost. Considering also the Chirp- transform, a comparison of the different methods under investigation demonstrates the effectiveness of the proposed approach for online thickness estimation. Index Terms—Discrete Fourier transform (DFT), fast Fourier transform (FFT), glass thickness measurement, laser interferom- etry, narrow-band frequency analysis. I. INTRODUCTION I N GLASS bottle manufacturing, the wall thickness is one of the crucial parameters to be checked for quality control. Since bottles often have a narrow neck, it is difficult to introduce a mechanical sensor inside them and to access the inner surface in a nondestructive way. The quality control of glass bottles is traditionally performed offline by sampling, and the character- istics of the sample are generalized to the batch from which it is drawn [1]. However, to avoid introducing any bad bottle into the market, manufacturers should inspect 100% of them. Therefore, a noncontact, real-time glass wall thickness measuring system is required to gauge the thickness of each bottle on the produc- tion line. Advances in optoelectronics have a considerable impact on noncontact geometric measurement applications. Lasers usually play an important role as an information carrier in such opto- electronic systems because of their physical properties like fre- quency stability, coherence, etc. [2]–[4]. A new measurement technique, based on a glass thickness sensing device, has been developed and patented by Saint-Gobain Cinématique et Con- trôles (SGCC) [5]. This sensor takes advantage of the properties of a frequency-tunable laser diode and of the optical reflection characteristics of transparent materials. The measuring principle and the system structure are described in Section II. Manuscript received September 20, 2001; revised February 20, 2004. B. He and R. Zhang are with EurAsie Synergie, 92400 Courbevoie, France (e-mail: hebing@rocketmail.com). F. Cabestaing and J.-G. Postaire are with the Laboratoire d’Automatique, Génie Informatique & Signal, University of Lille, 59000 Lille, France (e-mail: fcab@ieee.org). Digital Object Identifier 10.1109/TIM.2004.838911 From a signal processing point of view, the signal delivered by the sensor contains a number of components which carry the significant information about the measured thickness. Under some ideal conditions, the frequency component with the largest amplitude in the signal’s frequency spectrum can be considered as a reliable representation of this thickness. So, a fast method for searching the spectrum and locating this frequency is the key problem for real-time implementation. In Section III, the emphasis is placed on a comparison between different compu- tation techniques in the frequency domain in terms of online computational efficiency. After revealing the inefficiency of the standard fast Fourier transform (FFT) for the given problem, we pro- pose a coarse-to-fine scheme for frequency analysis. Since the bottle rotates in front of the sensor, we combine this narrow-band frequency analysis scheme with a predictive model of the thickness variations around the bottle. The main advantage of this strategy is its computational efficiency for online implementation. This approach has been compared in terms of complexity and precision with other procedures, like the Chirp- transform, which is a realization of the -transform along a spiral contour on the plane. Under specific conditions, the Chirp- transform can be determined along the unit circle in order to reveal details within any subband of interest in the frequency spectrum. The results, presented in Section IV, show that this signal processing scheme can be implemented as an algorithm that supports real-time constraints imposed by manufacturing rates. II. SYSTEM STRUCTURE AND ESTIMATION BASIS The optoelectronic part of the measuring system is composed of a laser generator with a precisely controlled wavelength that can be varied within a narrow bandwidth, a beam-splitter, and a photodetector [5]. The output of the photodetector is filtered and digitized for further numerical processing. The system con- figuration is shown in Fig. 1. The frequency of the monochromatic laser source is con- trolled during a tuning period [see Fig. 2(a)], its wavelength is tuned to follow the theoretical formula (1) where is the time, a constant, and the initial wavelength at the beginning of the tuning period . When a laser beam is projected orthogonally onto a glass wall, one reflection arises on the outer surface and one on the inner surface (see Fig. 1). The difference between the lengths of the two optical paths is , where denotes the 0018-9456/$20.00 © 2005 IEEE