Abstract
All the techniques that measure displacements, whether in the range of visible optics or any other form of field methods require the presence of a carrier signal. The carrier signal is a wave form that is modulated (modified) by an input, deformation of the medium. The carrier is tagged to the medium under analysis and deforms with the medium. The wave form must be known both in the unmodulated and the modulated conditions. There are two basic mathematical models that can be utilized to decode the information contained in the carrier, phase modulation or frequency modulation, both are closely connected. Basic problems that are connected to the detection and recovery of displacement information that are common to all optical techniques will be analyzed. This paper is concentrated in the general theory common to all the methods independently of the type of signal utilized. The aspects discussed are those that have practical impact in the process of data gathering and data processing.
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A.V. Oppenheim, J.S. Lin, The importance of phase in signals. Proc. IEEE 69(5), 529–541 (1981)
C.A. Sciammarella, Basic optical law in the interpretation of the moiré patterns applied to the analysis of strains-Part 1. Exp. Mech. 5(5), 154–160 (1965)
C.A. Sciammarella, A numerical technique of data retrieval from moiré or photoelastic patterns. In: Seminar in depth pattern recognition studies. Proc. SPIE. 16, 91–101 (1969)
C.A. Sciammarella, F.M. Sciammarella, Experimental Mechanics of Solids (Wiley, Chichester, 2012)
J.R. Carson, Notes on the theory of modulation. Proc. Inst. Radio Eng. (IRE) 10(1), 57–64 (1922)
C.A. Sciammarella, F.M. Sciammarella, Heisenberg principle applied to the analysis of speckle interferometry fringes. Opt. Lasers Eng. 40, 573–588 (2003)
J.P. Havlicek, D.S. Harding, A.C. Bovik, Multidimensional quasi-eigenfunction approximations and multicomponent AM-FM models. IEEE Trans. Image Process. 9(2), 227–242 (2000)
A. Papoulis, Systems and Transforms with Applications to Optics (McGraw-Hill, New York, 1968)
E. Bedrosian, A product theorem for Hilbert transforms. Memorandum RM-3439-PM. The Rand Corporation, Santa Monica (1962)
E. Bedrosian, Hilbert transform of bandpass functions. Proc. IEEE 51, 868–869 (1963)
A.H. Nuttall, E. Bedrosian, On the quadrature approximation to the Hilbert transform of modulated signals. Proc. IEEE 54(10), 1458–1459 (1966)
C. Pachaud, T. Gerber, N. Martin, Consequences of non-respect of the Bedrosian theorem when demodulating. In: Proceedings of The Tenth International Conference on Conditions Monitoring and Failure Prevention Techniques, Krakow, 2013
Y. Xu, D. Yan, The Bedrosian identity for the Hilbert transform of products of functions. Proc. Am. Math. Soc. 134(9), 2719–2728 (2006)
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Sciammarella, C., Lamberti, L. (2016). Basic Foundations of Signal Analysis Models Applied to Retrieval of Displacements and Their Derivatives Encoded in Fringe Patterns. In: Sciammarella, C., Considine, J., Gloeckner, P. (eds) Experimental and Applied Mechanics, Volume 4. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-22449-7_3
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DOI: https://doi.org/10.1007/978-3-319-22449-7_3
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-22448-0
Online ISBN: 978-3-319-22449-7
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