## Fringe Pattern Analysis for Optical Metrology: Theory, Algorithms, and ApplicationsThe main objective of this book is to present the basic theoretical principles and practical applications for the classical interferometric techniques and the most advanced methods in the field of modern fringe pattern analysis applied to optical metrology. A major novelty of this work is the presentation of a unified theoretical framework based on the Fourier description of phase shifting interferometry using the Frequency Transfer Function (FTF) along with the theory of Stochastic Process for the straightforward analysis and synthesis of phase shifting algorithms with desired properties such as spectral response, detuning and signal-to-noise robustness, harmonic rejection, etc. |

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### Contents

Digital Linear Systems | 1 |

A 4 | 4 |

A 8 | 8 |

6 | 23 |

5 | 29 |

2 | 37 |

Synchronous Temporal Interferometry | 57 |

3 | 92 |

A 2 | 132 |

Spatial Methods with Carrier | 149 |

5 | 201 |

6 | 241 |

Appendix A List of Linear PhaseShifting Algorithms PSAs | 271 |

FourStep Linear PSAs | 277 |

Zero at ajo a0 12 | 298 |

315 | |

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### Common terms and phrases

amplitude analytic signal band-pass filter BIBO stable calculated Carr´e Carré algorithm demodulation detuning error distorting harmonics equation estimated phase example fails to reject formula four-step PSA Fourier transform frequency response Frequency transfer Frequency transfer function fringe direction fringe orientation fringe pattern analysis Gabor filter given harmonic-rejection capabilities illustrated in Figure impulse response input I𝜑 line integration linear PSAs lobes low-pass filter meta-frequency response modulating phase noise nonlinear obtained phase demodulation phase unwrapping phase-step estimation phase-step value pixelated carrier pixels power ratio gain quadrature conditions quadrature filter quadrature linear filter robustness against detuning S/N power ratio samples second-order self-tunable five-step PSA self-tunable PSA shown in Figure spatial carrier spatial frequency spectral zeros spectrum step stochastic process synchronous technique temporal carrier temporal phase-shifted interferogram three-step LS-PSA three-step PSA transfer function tunable PSA vortex transform wrapped phase Z-transform 𝛿 𝜂 𝜑 𝜑x