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Related Concept Videos

Time and frequency -Domain Interpretation of Phase-lead Control01:24

Time and frequency -Domain Interpretation of Phase-lead Control

Phase-lead controllers are commonly used in various control systems to enhance response speed and stability. Adjusting the brightness on a television screen offers a practical example of phase-lead control. When contrast is enhanced, a phase-lead controller is employed. Mathematically, phase-lead control is identified when the first parameter is smaller than the second.
The design of phase-lead control involves the strategic placement of poles and zeros to balance steady-state error and system...
Time and frequency -Domain Interpretation of Phase-lag Control01:21

Time and frequency -Domain Interpretation of Phase-lag Control

Phase-lag controllers are widely used in control systems to improve stability and reduce steady-state errors. A dimmer switch controlling the brightness of a light bulb serves as a practical example of phase-lag control, gradually adjusting the bulb's brightness. Mathematically, phase-lag control or low-pass filtering is represented when the factor 'a' is less than 1.
Phase-lag controllers do not place a pole at zero, but instead influence the steady-state error by amplifying any finite,...
IR Frequency Region: Fingerprint Region01:03

IR Frequency Region: Fingerprint Region

IR spectra are divided into two main regions: the diagnostic region and the fingerprint region. The diagnostic region of the spectrum lies above 1500 cm−1. The absorptions resulting from single-bond vibrations of the N–H, C–H, and O–H stretch at higher wavenumbers and appear on the left side of the spectrum. The stretching absorptions of the C≡C and C≡N occur between 2100–2300 cm−1. In contrast, those arising from stretching absorptions of the C=O, C=N, and C=C occur between 1600–1850 cm−1.
The...
IR Spectrum Peak Splitting: Symmetric vs Asymmetric Vibrations01:08

IR Spectrum Peak Splitting: Symmetric vs Asymmetric Vibrations

Identical bonds within a polyatomic group can stretch symmetrically (in-phase) or asymmetrically (out-of-phase). Similar to hydrogen bonding, these vibrations also influence the shape of the IR peak. Generally, asymmetric stretching frequencies are higher than symmetric stretching frequencies. For example, primary amines exhibit two distinct IR peaks between 3300–3500 cm−1 corresponding to the symmetric and asymmetric N-H stretching, while secondary amines exhibit a single stretching vibration...
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
IR Frequency Region: X–H Stretching01:24

IR Frequency Region: X–H Stretching

In IR spectroscopy, signals produced by the X−H bonds (such as C−H, O−H, or N−H) can be observed in the frequency range of  2700–4000 cm–1. The C−H stretching vibration forms sharp bands in the region 2850–3000 cm–1. The presence of the O−H stretching vibration leads to the forming of an absorption band in the frequency range 3650–3200 cm−1. At the same time, N−H stretching can be confirmed by absorption bands in the 3500–3100 cm−1 range. Even though both O−H and N−H bonds vibrate at a similar...

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The Frequency Domain Thermoreflectance Technique for Thermal Property Measurements
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Robust Three-Frequency Number-Theoretical Temporal Phase Unwrapping for Phase-Differencing Profilometry.

Zhimi Wei, Yiping Cao

    IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
    |July 9, 2026
    PubMed
    Summary

    This study introduces a novel three-frequency number-theoretical temporal phase unwrapping (TFNT-TPU) method for phase-differencing profilometry (PDP). The method enhances three-dimensional (3D) imaging flexibility and robustness in fringe projection profilometry.

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    Area of Science:

    • Optics and Photonics
    • Computer Vision
    • Metrology

    Background:

    • Fringe projection profilometry (FPP) traditionally faces challenges in achieving high flexibility and robustness for three-dimensional (3D) imaging.
    • Existing methods often struggle with error propagation and limited adaptability to complex object geometries.

    Purpose of the Study:

    • To propose and validate a novel three-frequency number-theoretical temporal phase unwrapping (TFNT-TPU) method for phase-differencing profilometry (PDP).
    • To enhance the flexibility and robustness of 3D imaging in FPP systems.

    Main Methods:

    • Development of a TFNT-TPU algorithm leveraging isophase closure features and a loose constraint relationship among three different frequency gratings.
    • Optimization of TFNT-TPU parameters to suppress random errors.
    • Implementation of a self-correction strategy to mitigate arctangent operation-induced computing errors.

    Main Results:

    • Demonstrated high flexibility in 3D imaging through the utilization of isophase closure and multi-frequency grating relationships.
    • Achieved enhanced robustness against random and computational errors via optimized parameter design and self-correction.
    • Experimental validation confirmed the effectiveness of the proposed TFNT-TPU method.

    Conclusions:

    • The proposed TFNT-TPU method significantly improves the flexibility and robustness of 3D imaging in FPP.
    • This advancement offers a more reliable solution for complex 3D reconstruction tasks.
    • The method provides a robust framework for high-quality 3D profilometry.