By Manuel Servin

The most goal of this e-book is to provide the elemental theoretical rules and functional functions for the classical interferometric innovations and the main complex tools within the box of recent fringe trend research utilized to optical metrology. an enormous novelty of this paintings is the presentation of a unified theoretical framework in response to the Fourier description of part transferring interferometry utilizing the Frequency move functionality (FTF) in addition to the speculation of Stochastic approach for the simple research and synthesis of part moving algorithms with wanted homes reminiscent of spectral reaction, detuning and signal-to-noise robustness, harmonic rejection, and so forth.

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Extra info for Fringe Pattern Analysis for Optical Metrology: Theory, Algorithms, and Applications

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H(t) = ????{????(t)}. 13 (a) Continuous-time and (b) discrete-time linear systems. 15 16 1 Digital Linear Systems impulse response. For instance, assuming the input I(t) as a sampled function } { ∞ } { ∞ ∑ ∑ ????(t − n) = ???? I(n)????(t − n) . 41) f (t) = ???? I(t) n=−∞ n=−∞ Since the system is linear, we have f (t) = ∞ ∑ I(n)???? {????(t − n)} . 42) n=−∞ Applying the time-invariant condition, we have h(t − n) = ????{????(t − n)}. 43) Finally, substituting Eq. 43) in Eq. 42), we obtain f (t) = ∞ ∑ I(n)h(t − n) = I(t) ∗ h(t).

On the other hand, if the second sum converges, there must exist some region where the sequence { f (n)r −n } is absolutely summable; this region will be given by the points in the complex plane outside a circle of some radius r2 . Therefore, the ROC for both summations will be given by some annular region defined by r2 < r < r1 . Following our chain 19 20 1 Digital Linear Systems of inequalities (Eqs. 60), we know that such annular region also guarantees the convergence of |F(z)|. Thus, in general, the ROC for a given Z-transform can be described in the form { } { } ROC = z ∶ |F(z)| < ∞ = z ∶ r2 < |z| < r1 .

However, nowadays one is able to acquire a two-dimensional set of data with millions of samples from a single frame, which usually allow us to neglect the influence of spatial aliasing and to apply some anti-aliasing filtering whenever required. 23 Fourier domain representation of anti-alias filtering to remove those components that do not fulfill the Nyquist criterion (as defined in Eq. 87). 5 Fourier Analysis of Digital LTI Systems fringe patter analysis, particularly in phase-shifting interferometry, we are usually restricted to work with a few temporal samples so temporal anti-aliasing filtering may not be feasible.

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Fringe Pattern Analysis for Optical Metrology: Theory, Algorithms, and Applications by Manuel Servin

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