This book provides mathematical analyses of scanning devices in optical and laser systems to yield results with higher accuracy than those obtained by geometrical imaging an object with a movable mirror or prism. Topics include the laws of reflection and refraction and the mathematical preliminaries of analytical raytracing; mirror-scanning devices with one axis of rotation (conic-section scanning) and with two axes of rotation (gimbaled mirror and galvanometric scanners in cascade for 2D scanning); and Risley-prism-based beam-steering systems. Readers should have a foundation in vector operation and calculus, and a reasonable knowledge of elementary optics and lasers.
Starting with ray tracing through a single-mirror beam steering system, an analytical approach is developed to predict the scan pattern on a flat screen. The results for a single-mirror system are then extended to a two-mirror/two-axis beam scanning system, which paves the way to a performance comparison of single-mirror and two-mirror/two-axis laser projection systems. Some fundamental aspects of mirror-based laser projectors of different configurations are investigated, such as maximization of image size on screens of different format, the effect of pixel rotation and size changes on image resolution, and the relationship of angular motion of the mirror in a single-mirror system and the two mirrors in a two-mirror/two-axis system.
Regression models are developed for lifetime prediction of diode lasers with increasing or decreasing
operating current in the gradual degradation stage of their lifetime. Programmable expressions for laser lifetime
extrapolation are presented. Analytical results are explicated by case examples based on measured data from
reliability tests of commercially available 10mW and 650nm wavelength InGaAlP lasers conducted under
accelerated ageing conditions.
A model for low power (optical output power ≤10mW) InGaAlP lasers operating in the 650nm wavelength band is introduced. This model enables the user to predict lifetime of a diode laser under different operating conditions. Statistically meaningful data can be obtained from the model which gives quantitative values for the considerably increased laser lifetime when operating under less stress conditions.
A class of annular light beams with flat-topped Gaussian profile (i.e., Gaussian doughnut mode) is introduced. Field distribution of this kind of beams can be obtained by subtracting from a flat-topped Gaussian function [Proc. of SPIE, 5525, 128-137 (2004)] with another flat-topped Gaussian function of different width. The proposed expression can be easily expanded into a series containing the lowest order Gaussian modes of different waist parameters. This situation significantly improves the numerical calculation efficiency in the investigation of propagation properties of annular beams and also provides the possibility to investigate the aperture effect that a beam may be experienced when the beam passes progressively from smooth Gaussian aperture toward the hardedge limit. Results are illustrated by examples and compared with the prediction of Lommel theory of diffraction of plane waves at an annular aperture.
A method is proposed which makes it possible for beam shaping by superposition of fundamental mode Gaussian beams with different waist parameters. This study includes two topics: 1) Superposition of co-axial fundamental mode Gaussian beams to form flat-topped light beams, and 2) Superposition of tilted fundamental mode Gaussian beams to form Bessel-Gaussian beams.
Beam waist shift in optimum focusing of Gaussian beams is investigated under different conditions. We show that the minimum spot size on a target is only distinct from the beam waist when the target distance is fixed and either the lens focal length, the input beam waist, or the wavelength is varied.
An accurate approximation is presented of the focal shift in the diffraction field of a Gaussian laser beam that is focused by a thin lens that fills a circular aperture of any prescribed radius. The limiting cases of beam truncation by the aperture are discussed and formulas for nontruncated Gaussian beams and for uniform beams are obtained. The proposed formulas provide a convenient means for circumventing the transcendental equations in the focal-shift problem.
Invariant pattern recognition is achieved by providing the binary codes of moment invariants to the input end of Hopfield network. Combination of moment invariants with neural computing allows us to recognize image patterns which have been subjected to various distortions such as noise translation rotation and scale variation. 1.
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