Phase extraction in speckle interferometry by a circle fitting procedure in the complex plane

Area of Science:

• Optical Metrology
• Signal Processing
• Interferometry

Background:

• Speckle interferometry (SI) signals are characterized by amplitude and frequency modulation with fluctuating backgrounds.
• Accurate background intensity elimination is crucial for subsequent phase computation in SI.
• Existing methods like empirical mode decomposition (EMD) can struggle with background removal in challenging sampling conditions.

Purpose of the Study:

• To develop a robust and novel method for background intensity elimination in speckle interferometry signals.
• To accurately determine instantaneous frequency and modulation depth from complex temporal signals.
• To compare the performance of the new method against empirical mode decomposition (EMD).

Main Methods:

• Constructing a complex signal from the raw speckle interferometry data.
• Fitting a circle to the sampled values of the complex signal in the complex plane.
• Locally adapting the length of the point set used for the circle fit to the signal characteristics.

Main Results:

• The novel circle fitting method successfully yields background intensity and modulation depth.
• The method accurately determines the instantaneous frequency of the signal.
• The approach demonstrates superior robustness compared to EMD, particularly for critically sampled or oversampled signals.

Conclusions:

• The proposed circle fitting technique offers a significant advancement for background removal in speckle interferometry.
• This method provides reliable computation of key signal parameters, enhancing the accuracy of SI measurements.
• The technique is particularly advantageous in scenarios where EMD-based background elimination is prone to errors.