Discrete fringe phase unwrapping algorithm based on Kalman motion estimation for high-speed I/Q-interferometry.

Area of Science:

• Optical Metrology
• Signal Processing
• Instrumentation

Background:

• I/Q-interferometers are crucial for high-speed measurements but are limited by Nyquist frequency constraints with under-sampled quadrature signals.
• Accurate phase demodulation is essential for precise displacement and vibration measurements.

Purpose of the Study:

• To propose a discrete fringe phase unwrapping algorithm (DFPUA) for accurate phase demodulation of under-sampled I/Q-interferometer signals.
• To overcome the limitations imposed by the Nyquist frequency in high-speed measurement scenarios.
• To enable high-speed and long-time measurements, including ultra-low frequency vibration calibration.

Main Methods:

• Development of a discrete fringe phase unwrapping algorithm (DFPUA) incorporating Kalman motion estimation.
• Estimation of current displacement based on previous motion states.
• Confirmation of the integer phase number by comparing estimated and actual phase decimals.
• Illustration of two DFPUA types: velocity estimation and velocity-acceleration estimation.

Main Results:

• The proposed DFPUA accurately demodulates phases from deeply under-sampled quadrature signals.
• Simulation experiments demonstrate a significant reduction in sampling rate requirements for low-frequency vibration measurement.
• A substantial decrease in data volume was observed for low-frequency vibration measurements.

Conclusions:

• The DFPUA effectively breaks through Nyquist frequency limitations for high-speed measurements.
• Peak acceleration/jerk, rather than peak velocity, becomes the determining factor for the required sampling rate.
• DFPUA offers a practical approach for high-speed, long-time measurements, particularly for ultra-low frequency vibration calibration.