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Related Experiment Video

Updated: Jan 25, 2026

High-resolution, High-speed, Three-dimensional Video Imaging with Digital Fringe Projection Techniques
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Two-frame fringe pattern phase demodulation using Gram-Schmidt orthonormalization with least squares method.

Hangying Zhang, Hong Zhao, Zixin Zhao

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    |May 5, 2019
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    Summary
    This summary is machine-generated.

    This study introduces a combined Gram-Schmidt (GS) and least squares iterative (LSI) method for improved fringe phase demodulation. The new algorithm enhances accuracy by refining GS results, overcoming limitations of the original GS method.

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    Area of Science:

    • Optical Metrology
    • Image Processing
    • Signal Processing

    Background:

    • Gram-Schmidt (GS) orthogonal normalization is a common method for two-frame fringe phase demodulation.
    • The precision of the standard GS method is limited by background noise and approximation errors.

    Purpose of the Study:

    • To enhance the accuracy of fringe phase demodulation.
    • To address the limitations of the traditional Gram-Schmidt method.

    Main Methods:

    • A novel algorithm combining Gram-Schmidt (GS) orthogonal normalization and a least squares iterative (LSI) phase shift algorithm (GS&LSI) was developed.
    • The GS method is initially used for phase acquisition, followed by LSI for refinement.
    • The LSI process refines the phase map, improving demodulation results.

    Main Results:

    • The combined GS&LSI method significantly improves the accuracy of phase demodulation compared to the standard GS method.
    • Simulation and experimental results validate the effectiveness of the proposed algorithm.
    • The refinement step using LSI effectively mitigates errors from background terms and noise.

    Conclusions:

    • The proposed GS&LSI algorithm offers a more accurate and robust solution for fringe phase demodulation.
    • This method has the potential to improve various applications relying on precise phase measurement.
    • The combination overcomes inherent limitations of the GS method, leading to superior phase maps.