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Continuous -time Fourier Transform01:11

Continuous -time Fourier Transform

The Fourier series is instrumental in representing periodic functions, offering a powerful method to decompose such functions into a sum of sinusoids. This technique, however, necessitates modification when applied to nonperiodic functions. Consider a pulse-train waveform consisting of a series of rectangular pulses. When these pulses have a finite period, they can be accurately represented by a Fourier series. Yet, as the period approaches infinity, resulting in a single, isolated pulse, the...
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Properties of Fourier Transform II01:24

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Coordinate-transform technique for closed-fringe analysis by the fourier-transform method.

Z Ge, F Kobayashi, S Matsuda

    Applied Optics
    |March 22, 2008
    PubMed
    Summary
    This summary is machine-generated.

    A new coordinate-transform technique allows Fourier-transform analysis of closed-fringe interferograms. This method converts closed fringes to open ones, enabling phase distribution determination for optical metrology applications.

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    Area of Science:

    • Optical metrology
    • Interferometry
    • Wave optics

    Background:

    • Analyzing interferograms with closed-fringe patterns presents challenges for conventional Fourier-transform methods.
    • Existing techniques may struggle with complex fringe formations.

    Purpose of the Study:

    • To propose a novel coordinate-transform technique for analyzing interferograms with closed-fringe patterns.
    • To adapt the Fourier-transform method for accurate phase retrieval in such cases.

    Main Methods:

    • Coordinate transformation from Cartesian to polar systems to convert closed fringes to open fringes.
    • Application of the conventional Fourier-transform method for phase distribution analysis.
    • Inverse coordinate transformation to retrieve the phase of the original closed-fringe pattern.

    Main Results:

    • Successfully demonstrated the conversion of closed-fringe patterns to open-fringe patterns.
    • Validated the phase retrieval accuracy through computer simulations.
    • Experimental verification confirmed the technique's effectiveness for spherical wave and plane wave interference.

    Conclusions:

    • The proposed coordinate-transform technique effectively enables Fourier-transform analysis of closed-fringe interferograms.
    • This method provides a robust solution for phase distribution determination in optical interferometry.