Numerical and experimental study of the characteristic functions of polygon scanners

Abstract

ABSTRACT A MathCad analysis of the mathematical functions and parame ters of polygonal scanning heads is achieved. The results of a previous, rigorous analytical study we have performed are used. A scanning system for dimensional measurements has been considered. However, most of the results obtained are valid for any application of polygon mirror (PM) scanners. The characteristic functions and parameters of the PM scanner in the dimensional measurements setup, i.e. i.e. scanning function and velocity, characteristic angles and duty cycle are discussed. The analysis is performed with regard to the constructive parameters of the polygonal scanning system. An experimental stall is designed and constructed, and some of the experimental results concerning the scanning function, relevant for the analysis performed are presented. Keywords: scanner, polygon, measuring system, optical design, optical metrology. 1. INTRODUCTION The scanning techniques have a large range of applications [1], from those with average performances, e.g. barcode scanning, industrial measurements systems [2] or printers to high end applications in full development, i.e. biomedical optics, for confocal microscopy [3] and/or optical coherence tomography (OCT) [4-6]. Several scanning devices developed during several decades, since the early 1970s meet the needs of a certain application [1, 7, 8]. The main types of scanners are with rotating mirrors, i.e. monogon (plane mirror) [9-11], polygonal [12-20] or pyramidal, with oscillating mirrors (resonant or galvanometer-based [21-25]), holographic, electro-optical or acusto-optical [1]. These uni-dimensional (1D) scanning heads are coupled in various combinations, in order to achieve 2D [26, 27], 3D and even 4D scanning, the former considering time as the fourth dimension, in order to have real time characterization of phenomena, e.g. in medical imaging. In several of our previous studies we have approached tw o domains: (i) rotating mirrors scanners: for both monogon and polygon scanners, a rigorous mathematical analysis [8, 10] and an optimal designing calculus [18] have been achieved, in a different way than in the state-of-the-art [7, 9, 11-17]; (ii) galvanometer-based scanners, for both uni-dimensional (1D) [25] and 2D systems [27], suitable for a large range of applications, with an advantage on the polygon scanners in most domains, except those where a fast scan ra te is compoulsory, e. g. swept source OCT. In this paper we shall approach, as in previous studies, the domain of dimensional industrial, usually on-line measurements, with the remark that most of the results obtained are also valid for other applications where polygon mirror (PM) scanners are involved. Besides the theoretical studies, experimental ones were achieved in order to demonstrate the validity of the theoretical findings and to move on to applications. This paper is focused on both aspects, of the numerical studies of the characteris tic functions of the PM scanners, previously deduced and analized theoretically [10], and on experiments for some of the main aspects of the mathematical study. A first experimental stall that has been developed and used will be presented, as well as the bl ueprints for the second one we are currently developing. 2.